Tuning, Temperament and Pedagogy for the Vihuela in Juan Bermudo’S “Declaracion De Instrumentas Musicales” (1555)

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Tuning, temperament and pedagogy for the vihuela in Juan Bermudo’s “Declaracion de Instrumentas Musicales” (1555)

Annoni, xvlaria Theresa, Ph.D.

The Ohio State University, 1989

UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106

TUNING, TEMPERAMENT AND PEDAGOGY FOR THE VIHUELA IN JUAN BERMUDO'S DECLARACION DE INSTRUMENTOS MUSICALES (1555)

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University

Maria Therese Annoni, B.A., M.A.

*****

The Ohio State University 1989

Dissertation Committee: Approved by Dr. David M. Butler Dr. Burdette L. Green Adviser Dr. Thomas F. Heck School of Music Copyright by Maria Therese Annoni 1989 To My Parents, Florence Schober Annoni and Anthony Michael Annoni

11 ACKNOWLEDGMENTS

Second only to the satisfaction of completing my studies at Ohio State is the pleasure I take in recognizing the many contributions to my education and life in Columbus Ohio that have been made by so many people. In receiving my PhD, I am completing the education that both of my parents always wanted and deserved. Despite the distance from Minnesota, my family has been an ever-present source of support and love. I thank them and I dedicate this work to my parents. At Ohio State, Dr. Burdette Green has proved himself to be a skillful and able dissertation adviser. He has shared my fascination with Juan Burmudo, and has worked closely with me to uncover the contributions of this 16th-century genius. Dr. David Butler has played many roles during my academic career. In addition to serving as my academic adviser, he served on my Master's and General's committees, and now has provided much needed advice as a member of my dissertation committee. Words fail me as I try to express my gratitude to Dr. Thomas Heck and his family. Tom Heck has been a trusted advisor, a colleague and mentor, and a treasured friend for many years. It is no exaggeration to say that I could not have completed this disseration—at this time—without his help. When I was in need of shelter, the Hecks opened their home and hearts to me, and

111 became my Columbus family. Tom, Ann, John, and Lara: I love you, and thank you from the bottom of my heart. My work as a liturgical musician at the St. Thomas More Newman Center has been important to the preservation of my sanity during this process. I thank the wonderful worhip community and in particular Pete McClemon for their sense of humor and unflagging faith in me. Eric Celeste, friend and President of Appropriate Technology, provided much needed computer support, including the debugging of my graphics, and the laser printing of my final draft. His efforts are all the more appreciated in view of the fact that I needed him most just at the time he broke his hip; and he still came through! Dr. Kathleen Nuccio has provided round-the-clock mental, physical and emotional support. She provided warm meals and hugs, manuscript proofreading, and faith in both me and Juan Bermudo. She has improved the quality of both my life and this dissertation.

IV VITA

June 10,1954 Born - Duluth, Minnesota

1972-Present ...... Guitar Instructor - Private and Classroom

1976 ...... B.A., College of Saint Scholastica, Duluth, Minnesota

1976-1978 ...... Choral Director and Music Instructor, Duluth Cathedral High School, Duluth, Minnesota

1980-Presen t ...... Assistant to the Music Director, Saint Thomas More Newman Center, Campus Ministry, The Ohio State University, Columbus, Ohio

1981-1986 ...... Graduate Teaching Associate, Division of Music Theory, School of Music, The Ohio State University, Columbus, Ohio

1982 ...... M.A., The Ohio State University, Columbus, Ohio

FIELDS OF STUDY

Major Field: Music Theory

Minor Fields: Studies in Music History: Medieval, Renaissance, Classical, and N otation Studies in Foreign Languages: Spanish, Italian, French, Latin, German, Russian, and Ancient Greek TABLE OF CONTENTS

ACKNOWLEDGMENTS ...... iii

VITA ...... V LIST OF TABLES ...... ix LIST OF FIGURES ...... x CHAPTER PAGE I. INTRODUCTION AND LITERATURE RE\TEW ...... 1

Sources ...... 2 Secondary Literature ...... 3 Methodology and Organization ...... 12

n. JUAN BERMUDO: TEXT AND CONTEXT ...... 15

The Political Situation in Renaissance Spain ...... 15 Spain's Cultural History ...... 18 Juan Bermudo and the Friars Minor of the Observance .... 24 Bermudo's Early Publications ...... 27 Declaraciôn de Instrumentos Musicales ...... 33 Interrelatedness of Bermudo's Publications ...... 36 Conclusions ...... 43

m . THEDECLARACION : ITS PURPOSE, LAYOUT AND PEDAGOGICAL INTENT ...... 44

The Purpose of the Treatise: Some Retrospective Views ...... 44 The Purpose of the Treatise According to Bermudo and Figueroa ...... 46 The Layout of the Treatise ...... 49 Bermudo's Unpublished Books ...... 59 References to the Sixth Book ...... 60 References to the Seventh Book ...... 63 The Interconnection of the Books ...... 64

VI Bermudo's Pedagogical Method ...... 68 Bermudo's Instruction for the Musical Instruments ...... 68 Elementary Vihuela Instruction ...... 68 Intermediate Vihuela Instruction ...... 70 Advanced Vihuela Instruction ...... 72 Conclusions ...... 76

IV. BERMUDO'S VIHUELAS: DESCRIPTION AND DOCUMENTATION OF THE INSTRUMENTS AND THEIR TUNINGS ...... 77

Vihuela: the Term and its Usage ...... 77 Brief History of the Instruments ...... 80 The Six-Course Vihuela ...... 83 Additional Templates for the Six-Course Vihuela ...... 89 The Seven-Course Vihuela ...... 98 Additional Templates for the Seven-Course Vihuela ...... 104 The Four-Course Guitar ...... 105 Additional Templates for the Four-Course Guitar ...... I ll The Five-Course Guitar ...... 112 The Bandurria ...... 116 The Rabel ...... 120 Conclusions ...... 121

V . BERMUDO'S METHODS OF FRET PLACEMENT: PYTHAGOREAN TUNING AND EQUAL TEMPERAMENT ...... 124

Prerequisites for the Art of Fret Placement ...... 124 Pythagorean Tuning ...... 126 Pythagorean Fret Placement for the Elementary Student ...... 128 Pythagorean Fret Placement for Bermudo's Theoretical2Seven-Course Vihuela ...... 130 Pythagorean Fret Placement for the Individual Six- Course Templates ...... 141 Method of Fret Placement Using Temperament ...... 157 Towards Equal Temperament ...... 163 Conclusions ...... 167

vu VI. AN EVALUATION OF BERMUDO'S PYTHAGOREAN TUNING ON THE VIHUELA ...... 169

In tabulation ...... 170 The Use of Templates ...... 173 Selecting the Proper Template ...... 176 Faults on the Templates and How to Fix Them ...... 178 The Application of Bermudo's Theories to Music ...... 182 Complete Concordance With the Selected Template ...... 184 Minor Problems and Bermudo's Solutions ...... 190 Problematic Passages and Bermudo's Solutions ...... 193 Conclusions ...... 196

VII. SUMMARY AND CONCLUSIONS ...... 197

Juan Bermudo the Pedagogue ...... 197 Juan Bermudo the Theorist ...... 199 Juan Bermudo the Vihuelist .... 203

APPENDIX: TRANSLATION OF BERMUDO'S METHODS OF FRET PLACEMENT ...... 207

BIBLIOGRAPHY ...... 219

vin LIST OF TABLES

TABLE PAGE

1. Concordance of the Chapters from Bermudo's Three Publications...... 42

2. Summary of Bermudo's Instruments From the Three Levels of Study: Elementary, Intermediate and Advanced ...... 123

3. Summary of Fifths in Bermudo's System of Temperament ......

4. Summary of Whole Tones in Bermudo's System of Temperament ...... 166

5. Summary of Major Thirds in Bermudo's System of Temperament ...... 166

6. Summary of Semitones in Bermudo's System of Temperament ...... 167

7. List of Intabulations With Complete Concordance With the Selected Template ...... 189

8. List of Intabulations Contining Minor Problems With the Selected Template ...... 193

IX LIST OF FIGURES

FIGURES PAGE

1. Bermudo's List of Sources, (El Libro Primero, 1549, folio xii,v)...... 32 2. Chronology of the Three Editions ...... 36 3. The Expansion of Book H into Books HI and IV...... 57

4. The Layout of the Declaraciôn ...... 65

5. Summary of Elementary Vihuela Instruction, Book n,9Chapters 30-36 ...... 67

6. Summary of Intermediate Vihuela Instruction, BooklV, Chapters 54-74...... 72

7. Summary of Advanced Vihuela Instruction, Book IV, Chapters 75-86 ...... 75

8. Bermudo's Diag;ram of the Standard Six-Course Disposition, (Declaraciôn, folio xci, r)...... 85

9. Template for the Alternate Six-Course Disposition on Gamaut, Derived from Bermudo's Instructions...... 88

10. Six Additional Templates for the Standard Six-Course Disposition ...... 92-3

11. "Flat" Templates Based on Previously Established Principles ...... 95

12. "Sharp" Templates Based on Previously Established Principles ...... 96 13. Template for the Seven-Course-A Disposition Derived From Bermudo's Instructions...... 99

14. Derived Template for the Seven-Course-B Disposition ...... 101

15. Derived Template for the Seven-Course-C Disposition ...... :...... 102

16. Bermudo's Diagram of the Seven-Course-D Disposition, {Declaraciôn, folio ciiii, r)...... 103

17. Derived Template for the Four-Course-A Disposition ...... 109

18. Derived Template for the Four-Course-B Disposition ...... 110

19. Derived Template for the Five-Course-A Disposition ...... 113

20. Derived Template for the Five-Course-B Disposition ...... 114

21. Derived Template for the Five-Course-C and Five- Course-D Dispositions...... 115

22. Derived Template for the Bandurria-C Disposition ...... 117

23. Derived Template for the Bandurria-A Disposition ...... 118

24. Derived Template for the Bandurria-D and Bandurria-E Dispositions ...... 120

25. The Pythagorean Tuning of the Diatonic Scale ...... 127

26. The Pythagorean Tuning of the Diatonic and Chromatic Pitches Within the Octave ...... 127

27. The Pythagorean System Showing the Enharmonic Pitches (and Cents) ...... 128

28. Bermudo's Elementary Method of Fret Placement ...... 131

XI 29. Extent of the Pythagorean System Used in Bermudo's Elementary Method ...... 132

30. Placement of the Diatonic Frets on Bermudo's Theoretical Seven-Course Disposition ...... 135

31. Continuation of Bermudo's Method—Placement of the Chromatic Frets ...... 137

32. Continuation of Bermudo's Method—Placement of Frets 12,13 and 14 ...... 139

33. The Frets and Pitches on the Seventh Course (Gamaut) of Bermudo's Theoretical Disposition 140

34. Derived Template for Bermudo's Theoretical Seven- Course Disposition Showing All Chromatic Frets...... 141

35. Bermudo's Classification of the Templates According to Species of Diatessaron ...... 143

36. Bermudo's Method for Placing Diatonic and Chromatic Frets on the Gamaut Template ...... 147

37. Bermudo's Diagram of the Gamaut Template, (Declaracion,folio cvi, r)...... 147

38. Bermudo's Diagram of the C/flMf Template,(D£c/arfldd?i,folio cvi, r) ...... 148

39. Bermudo's Diagram of the Ffaut Template,(Dedflrflc/dn,folio cvi, r) ...... 149

40. Bermudo's Diagram of the Are and Dsolre Templates, (Declaraciôn, folio cvi, v)...... ,...... 151

41. Bermudo's Diagram of the Elami and bmi Templates, Declaraciôn, folio cvii, r)...... 152

42. Method for Placing the Alternate Chromatic Frets, Including the Adjustment of the Fourth Fret on the hmi Template ...... 154

Xll 43. The Placement and Value (in Cents) of the Frets on the Sixth Course of Each Template ...... 155

44. Summary of the Disposition of Mi~ and Fa-Frets on Bermudo's Templates ...... 156

45. Bermudo's Diagram of String Division in His Method of Fret Placement Using Temperament (Declaraciôn, folio cix, v)...... 162

46. Dispositions and Values (in Cents) of the Frets in Bermudo's System of Temperament ...... 164

47. Tablature and Transcription of Bermudo's Version of the Romance viejo, "Mira Nero de tarpea," (Declaraciôn, folio d, r) ...... 185-6

48. Tablature and Transcription of Josquin's "Sanctus" by Luis de Narvaez, (Los sej/s libros del Delphin deSMusica, folio xxxiv, r) ...... 186

49. Tablature and Transcription of Josquin's "Ossana" by Luis de Narvaez, (Los seys libros del Delphin de Müsica, folio xxxiv, v) ...... 191

50. Tablature and Transcription of Pisador's villancico (Libro de Müsica de Vihuela, folio ix, r)...... 192

51. Tablature and Transcription of Willaert's motet, "Augustine lux doctorum," by Enriquez Valderrabano, Silva de Sirenas, folio xvii, r)...... 195

X lll CHAPTER I INTRODUCTION AND LITERATURE REVIEW

Juan Bermudo (c.l510-c.l565) was a Spanish friar and a self-taught musical theorist. His place in the history of music is somewhat controversial. Some scholars consider his writings to be largely self- promotional and outside the mainstream of music-theoretical thought; others view them as merely archaic and old fashioned, while a few perceive his concepts as reflecting a certain ingenuity and purposefulness. The diversity of opinion regarding Bermudo reflects a state of scholarship which until now has been broad but superficial and rarely systematic. This dissertation attempts to remedy this situation. Bermudo's writing style has hindered research efforts; it is verbose and often cryptic. Moreover, misunderstandings about his approach to the publication of his treatisess have led to serious misinterpretations of his writings. One of my major theses is that Bermudo conveyed his ideas within a coherent pedagogical structure. Each section of his work builds on previous sections, and it is not uncommon for material to be repeated so as to reinforce prior learning. By the same token, rudiments are often omitted in intermediate and advanced chapters because they were introduced earlier. Scholars who have studied Bermudo have typically sampled his ideas piecemeal, at selected locations across or within his treatises. By doing so. 2 they have misconstrued introductory level material as reflecting his fully developed theories, or have mistaken his repetitious strategy for carelessness. The goal of this investigation is to examine the principles of tuning, fret placement and intabulation on the vihuela, presented in Bermudo's Declaraciôn de instrumentos musicales (1555), and to determine the practicality of his theories by applying them to representative pieces from the vihuela literature. To date, no one has undertaken a study of this kind.

Sources All three of Bermudo's publications are currently available in a number of the world's libraries in their original printed form, in facsimile, or in microfilm. None of them has ever been translated into English. His final publication, Declaraciôn de instrumentos musicales, is the most widely known, with copies available in Western Europe and in the United States (library of Congress, Newberry Library and the New York Hispanic Society).^ It has been published in a facsimile edition by Bârenreiter, with introductory material by Santiago Macario Kastner. Unfortunately, this particular reprint lacks all the prefatory material that is vital to a lucid understanding of the work's purpose and organizetion.z

1 Répertoire de Sources Musicales: Écrits Imprimés Concernant la Musique, BVI^ (Munich- Duisburg: G. Henle Verlag, 1971),140. Also see Alfred Cortot, Traités et autres ouvrages theoretiques des XV, XVI, XVII e XVIII siècles, edited by Frederick Goldbeck (n.p.; Société Internationale de Musicologie, 1936), 20, and Julia Gregory, Catalogue of Early Books on Music (Before 1800) (Washington, D.(i.: Government Printing Office, 1913),32. 2 Juan Bermudo, Declaracion de instrumentos musicales (1555) ed. Santiago Macario Kastner, Documenta Musicologica 11 (Kassel und Basel: Bârenreiter, 1957). It is difficult to determine whether the copy Kastner used for this edition actually contained these folios, or whether he chose to omit them. Bermudo's first publication,- El libro primero de la declaraciôn de instrumentos (1549), is found in fewer locations, including two in the United States—the Newberry Library and the New York Hispanic Society. El arte tripharia (1550) circulated the least; the only known copy is in the Biblioteca National in Madrid. According to Repertoire de Sources Musicales, this copy is a facsimile of the original.^

Secondary Literature There are only two major studies that examine Bermudo and his T /ritings in depth—one in English, and one in Spanish. The first, Robert M. Stevenson's ground-breaking 1960 study, Juan Bermudo, reveals much concerning the theorist's life and works.^ Following a brief biography, Stevenson discusses many aspects of Bermudo's three treatises, El libro primero de la declaracion de instrumentos (1549), El arte tripharia (1550) and Declaraciôn de instrumentos musicales (1555), eventually concentrating on the last. Stevenson compares the treatises and provides a concordance of their chapters which shows how Bermudo incorporated most of the material from the earlier publications into the Declaraciôn. Stevenson's investigations of the prefatory matter (printing copyright, ecclesiastical license, dedication, prologues to the reader, and letters from prominent musicians) from all three treatises enable him to place each in a chronological perspective and to supply many details about their purpose and contents. He presents a thorough investigation of the various

^The Library of Congress has a microfilm copy of this treatise in its holdings. According to the L. C. card, this microfilm is actually a copy of the "photolithic reproduction of the original" in Spain. ^Robert M. Stevenson, Juan Bermudo (The Hague: Martinus Nijhoff, 1960). 4 theoretical, historical and philosophical sources employed by Bermudo in El Libro Primero (1549) and the Declaracion (1555); these include books of the Bible, Christian doctors, classical doctors and Christian theorists. While summarizing the Declaraciôn, Stevenson mentions Bermudo's teaching approach, indicating the theorist's intention to present material for the elementary student in Book II, and intermediate and advanced material in Book IV. This reference is given only in passing. Stevenson focuses on presenting the publication history of all three treatises, and gives a brief

synopsis of the Declaraciôn. Stevenson's study also includes a limited discussion of the musical instruments (keyboard, vihuela and harp), in which he focuses mostly on the keyboard and its related topics. The second major study of Bermudo's life and works is found in Estudios de Historia de la Teoria Musical by Francisco José Leon Tello.5 In Part I of this book, Leon Tello presents the major theorists of the Medieval and Renaissance eras. He begins with Boethius as the foundation, and includes many other figures, several of whom are Spanish. Part II concentrates on the major Spanish theorists of the fifteenth and sixteenth centuries. Here, Leôn Tello highlights Bermudo's life, works, and some of his theories within the context of the principal theorists of this era. He discusses Bermudo under three main headings: general theory and philosophy, theory of plainchant, and theory of polyphony. Unfortunately, Leôn Tello says very little about the vihuela. Even the chapter entitled "The contribution of the vihuelists" neglects Bermudo's vihuela theories, concentrating on the composers rather

^Francisco José Leôn Tello, Estudios de Historia de la Teorta Musical (Madrid: Consejo Superior de Investigaciones Cienti'ficas, 1962). 5 than the theorists. Leôn Tello culminates his chronology with an in-depth study of Francisco Salinas' theories in Part HI. Otto Kinkeldey presents his observations of Bermudo's three treatises in his book, Orgel und Klavier in der Musik des 16. Jahrhunderts.^ He suggests that Bermudo's writing is intended primarily for the elementary student^—a view that is debatable, since Bermudo specifically states that certain portions of the treatise are designed for the advanced student. Bermudo's internal repetitions evidently caused Kinkeldey to construe Bermudo's instructional approach as blatantly prolix, instead of systematic and accurate. Apparently Kinkeldey was unaware of Bermudo's pedagogical design for the treatise. Since Kinkeldey's book obviously focuses on source materials for the organ and keyboard, little mention is made of the vihuela. Santiago Macario Kastner presents a similar description in the Nachwort to the facsimile edition of the Declaraciôn. He includes a minimum of biographical information and a limited discussion of the contents.* He states that Bermudo's treatise is a far-reaching compendium of musical practice of that time, and rejects any previous arguments that Bermudo's writings are merely instruments of self-aggrandizement, or the means of the recognition needed to acquire special favors from those in authority. Contrary to Kinkeldey's assessment, Kastner reckons that Bermudo consistently directs equal amounts of material to the elementary student and to the "studious musician"—a fact that adds to the confusion over the

^Otto Kinkeldey, Orgel und Klavier in der Musik des 16. Jahrhunderts (Wiesbaden: Breitkopf & Hartel, 1968), 8-55. 7lbid., 10. ^Santiago Macario Kastner, ed., "Nachwort," to Declaracion de Instrumentos musicales, by Juan Bermudo, Documenta Musicologica, 11 (Kassel und Basel: Bârenreiter, 1957). 6 purpose of this treatise, since Bermudo directs most of his attention to the studious musician. The purpose of the treatise is likewise obscured by Thurston Dart, in his review of the facsimile edition of the Declaraciôn. He designates it as a "useful but rather rambling compendium," implying that it is an encyclopedic work with little direction.^ Henri Collet, in Le Mysticisme Musical au XVIe Siècle, refers to Bermudo's work as a "diffuse treatise...often incomprehensible to the reader." Collet adds that Bermudo seems to falter and even contradict himself, implying that Bermudo is a confusing and confused author. Apparently Collet, too, was unaware of the instructional intention of this treatise. Later in his book, he made a similar reference to Bermudo's obscurity as he refuted Menéndez and Pelayo who claimed that Bermudo was not only the most methodical, but also the clearest of the writers in the vernacular.^0 Nan Cook Carpenter, in Music in the Medieval and Renaissance Universities, recognizes Bermudo's intention to teach others when she describes the Declaraciôn as a specialized type of instruction book.^^ She declares that its purpose is to concentrate on the various problems of instrumental music (tuning, tabulature, notation, fingerings, etc.), combining musica practice and musica speculative into one source. Carpenter

^Thurston Dart, Review of Documenta Musicologica,XI, Declaracion de instrumentos musicales (1555), by Juan Bermudo, ed. Santiago Macario Kastner, Music and Letters 39 (October, 1958): 392-93. ^^Henri Collet, Le Mysticisme Musical espagnol au XVle Siècle (Paris: Librairie Félix Alcan, 1913), 26 & 217. ^^Nan Cook Carpenter, Music in the Medieval and Renaissance Universities (Norman, Oklahoma: University of Oklahoma Press, 1958.), 220 & 327. 7 adds that this type of book was needed to promote the cultivation of music of refined quality among university students, James Tyler's book. The Early Guitar: A History and Handbook, an excellent account of the history and performance practice of the early guitar, includes details about the vihuela and related instruments.^^ But Tyler oversimplifies by describing only one of Bermudo's dispositions of strings for the 6-course vihuela. A, d, g, b, e^, a^ (or G, c, f, a, d^, gl—a transposition).^^ In the Declaraciôn , Bermudo presents not only this disposition, but another two—Italian (G, c, f, b^, d^ g^) and a proposed alternate (G, B, d, g, b, d^). Tyler oversimplifies again in the case of the 7-course vihuela disposition. He presents Bermudo's 7-course dispositions as: G, d, g, d^, gl, d^, g Zand G, d, g, b, f#l, bl, dZ. In fact Bermudo does propose these dispositions, but as alternatives to the standard disposition (G, c, f, a, d^, g^, cZ) and to his own theoretical disposition (G, c, f, g, c^, f^, gf), neither of which is mentioned by Tyler. Other discrepancies can be found in Tyler's discussions of the related instruments as well. Despite tlie fact that Sibyl Marcuse intends to provide easily accessible details of any instrument in her book, A Survey of Musical Instruments, most of her descriptions of Bermudo's string dispositions for the vihuela are incomplete. She states that Bermudo describes two dispositions for the 7- course vihuela, when he actually presents four. She lists the standard and theoretical dispositions, which were not mentioned by Tyler, and then omits the two proposed dispositions (alternates) that Tyler describes. She also

^Zjames Tyler, The Early Guitar: A History and Handbook, Vol. 4 of Early Music Series (London: Oxford University Press, 1980), 15-24. ^^Heimholz' system of octave designation is used here to differentiate the octaves. ^^Sibyl Marcuse, A Survey of Musical Instruments (New York: Harper & Row, 1975), 452. 8 mistakenly believes that Bermudo intended his purely theoretical disposition to be one that is commonly used. A similar discrepancy appears in Alfred Berner's article on the vihuela in Die Musik in Geschichte und Gegenwart, because he presents the standard disposition and the theoretical disposition for Bermudo's 7-course vihuela only, omitting the two alternate dispositions.^^ Diana Poulton addresses the two alternate dispositions and the theoretical disposition for the 7-course vihuela in her article on the same subject in The New Grove Dictionary of Musical Instruments.^^ However, she overlooks the standard disposition. Curt Sachs, on the other hand, mentions only one of Bermudo's 7-course dispositions in his book. The History of Musical Instruments—the theoretical disposition.^^ The inaccuracy of these scholars is due to the complex organization of the Declaraciôn, and as seen here, results in inconsistent reporting of Bermudo's documentation of the vihuela. Lately there have been some writings which attempt to deal with the

Declaraciôn in the context of tuning and temperament (fret placement). The most recent interpretations of Bermudo's methods of fret placement are found in Lutes, Viols and Temperaments, by Mark Lindley.^8 He discusses these methods in light of the various types of tuning and temperament: Pythagorean intonation, equal temperament and meantone temperament. Lindley states that Bermudo gives only two methods of fret placement using

^ ^Alfred Berner, "Vihuela," In Die Musik in Geschichte und Gegenwart, edited by Friedrich Blume (Kassel and Basel: Barenreiter, 1952), 13:1621-23. ^^Diana Poulton, "Vihuela," In The New Grove Dictionary of Musical Instruments, edited by Stanley Sadie (London: Macmillan Publishers, 1984), 3: 724-27. ^^Curt Sachs, The History of Musical Instruments (New York: W. W. Norton & Company, 1940), 345. Sachs give no other indications of Bermudo's numerous descriptions of the dispositions for the vihuela. ^®Mark Lindley, Lutes, Viols and Temperaments (Cambridge: Cambridge University Press, 1984). 9 the Pythagorean system, but, in fact Bermudo gives three methods. While interpreting Bermudo's fret placement in the Pythagorean system, Lindley attempts to present it as a form of meantone temperament. He also claims that Bermudo's fret placement method for the elementary student uses equal temperament, whereas Bermudo clearly indicates the use of the Pythagorean system. Bermudo's fourth and final method, often considered to be an approximation of equal temperament, is however properly designated as an irregular temperament by Lindley. J. Murray Barbour, inTuning and Temperament: A Historical Survey, is of this same opinion.^® Barbour does not examine Bermudo's methods in the Pythagorean system in depth, but rather focuses his attention on Bermudo's fourth method of fret placement. He describes it as an irregular system, involving a procedure of tempering fifths by one-sixth comma. Louis Jambou, in his bookLes Origines du Tiento, also discusses Bermudo's methods of fret placement.^o Here, he examines Spanish modal theory in light of noteworthy treatises of this period (e.g., Declaraciôn by Bermudo, and Arte de Taner Fantasia by Sancta Maria). By surveying the modes, ranges, ornamentation and cadences of tientos by Milan, Fuenllana and Mudarra, Jambou attempts to describe the manner in which Bermudo's ideas are applied to the vihuela and keyboard tientos. In his investigation, he presents all of Bermudo's methods of fret placement (Pythagorean and approximate equal temperament), and attempts to determine the coincidence

M. Barbour, Tuning and Temperament: A Historical Survey (East Lansing: Michigan State College Press, 1951). 20Louis Jambou,Les Origines du Tiento (Paris: Centre National de la Recherche Scientifique, 1982). 10 between a given template igamaut, Are, etc.) and the final of the mode.^^ He does not deal with the practicality of Bermudo's theories of Pythagorean tuning for the vihuela. He suggests that Luis Milan's music (E/ Maestro, 1536) called for an inequality of frets (semitones), but concludes that the "vihuelists" seemed to gravitate toward some form of equal temperament on the fretted instruments by about 1550.22 Other scholars have written about similar theoretical concepts, attempting to interpret Bermudo's writings as well as the music of the period. In his dissertation. The Vihuela de Mano and its Music (1536-1576),John Ward addresses Bermudo's fret placement methods, but in a rather unsystematic manner that leaves the reader confused as to Bermudo's intentions. Ward describes only two of Bermudo's four methods of fret placement—one for the Elementary musician and one to be implemented on his own theoretical prototype.23 Since Ward's study focuses primarily on the vihuela music, it is not necessary for him to investigate Bermudo's theories in depth. Bermudo's description of seven templates (diagrams depicting the names of the strings and frets at various scale degrees or pitch levels) for each disposition of strings on the vihuela has been the subject of much misunderstanding. Some scholars believe them to be references to seven different sizes of vihuelas, tuned at designated pitch levels. Others, aware of

2^ A "template" is a diagram, or grid, that shows the letter names of the frets and strings of the vihuela at different pitch levels. Bermudo's templates depict the names for all the strings up through the tenth fret. 22jambou, Les Origines du Tiento,130. Although Jambou indicates that Milan's publication, El Maestro (1536), seems to specify a certain type of inequality of frets (semitones), he explains no further. 23john Ward, The Vihuela de Mano and its Music (1536-1576) (Ann Arbor, Michigan: University Microfilms,1953), 29-37. 11 pitch variability and the limitations of the vihuela, restrict these possibilities to three different sizes. Chapter IV of this dissertation shows that Bermudo does not refer to the physical dimensions of the vihuela in the context of these templates. Instead, he simply recommends them as an aid to intabulation. The interpretation of this concept differs among many writers. Emilio Pujol, in his "Introduction" to Mudarra's Tres Libros de Müske. en Cifra para Vihuela, states that Bermudo illustrates schemes for seven different "vihuelas," and gives a chart that shows the disposition of the two sizes of semitone for each. Unfortunately, he does not apply these dispositions to the music, since he assumes equal temperament in the transcription.24 Similarly, Rodrigo de Zayas, in his article "The Vihuela: Swoose, Lute, or Guitar?" refers to Bermudo's "seven different instruments tuned according to the seven lowest notes or keys of the hexachordal system."25 Thomas Greene also provides the same interpretation in his article, "The Hexachord System as it Applies to the Spanish Vihuelists," but, at the same time recognizes and agrees with Zayas' attempts to modify this understanding.^^ Zayas' explorations conclude that Renaissance musicians probably worked with three different sizes of vihuelas which would accommodate Bermudo's requirement of seven templates. The three sizes would be necessary, due to the physical limitations of the vihuela and its strings. In contrast, Lindley refers to these "seven vihuelas," as schemes, and

24Emilio Pujol, ed., "Introduction" to Tres Libros de Mûsica en Cifra para Vihuela by Alonso Mudarra, In Monumentos de la Mûsica Espanola, 7 (Barcelona: Instituto Espanol de Mu sicologfa,!949). ^Rodrigo de Zayas, "The Vihuela: Swoose, Lute, or Guitar?" Guitar Review 38 (Summer, 1973): 2-5. 26Thomas E. Greene, "The Hexachord System as it Applies to the Spanish Vihuelists," Chelys, Monthly Journal of the New England Society of the Plucked String 1, no. 3 (1976): 23-27. 12 indicates no change in the size of the instrument itself for any of them—an interpretation which reflects Bermudo's theories more closely.

Methodology and Organization The methodology employed n this study involves: (a) a thorough text analysis, (b) the interpretation of Bermudo's theories, and (c) the testing of his theories by applying them to representative contemporary vihuela music. After reviewing relevant details of Bermudo's biography, this dissertation focuses on the several pertinent facets of the Declaraciôn'. its goal, its format, the interconnection of books and its underlying pedagogical structure. Bermudo's pedagogical structure is shovm to consist of three teaching levels: Elementary, Intermediate, and Advanced. Bermudo's principles ultimately are tested by using them to transcribe representative intabulated vihuela music. Chapter II considers the historical and cultural atmosphere in Spain during the Renaissance and investigates Bermudo's life in this light. It also examines the contents and chronology of Bermudo's treatises. These investigations result in a new revised concordance of all three of Bermudo's treatises. Chapter m probes the Declaraciôn in depth. The investigation examines the interconnection of the books within the treatise, and establishes the pedagogical substructure that is critical to the proper interpretation of Bermudo's theories. This pedagogical substructure (Elementary, Intermediate, and Advanced) is clearly demonstrated in the material dealing with the instruments, especially the vihuela. 13 Chapter IV concentrates on Bermudo's discussion of the vihuela and related instruments. The chapter presents basic terminology pertinent to the vihuela, pointing out the multiple uses of the term vihuela. Included in Bermudo's discussion of the instruments are the 6-course vihuela, the 7- course vihuela, the 4-course guitar, the 5-course guitar, the bandurria and the rabel. It includes a compilation and classification of all the dispositions of strings that Bermudo supplies for each instrument, and also investigates his references to the need for additional templates. Chapter V explains Bermudo's four methods for placing frets on the vihuela, founded on two basic schemes—Pythagorean tuning and an approximation of equal temperament. Bermudo gives two of the Pythagorean tuning methods for the standard 6-course disposition, and provides one Pythagorean method and the approximation of equal temperament for his theoretical 7-course disposition. Chapter VI examines the applicability of Bermudo's theories for Pythagorean fret placement to a sampling of vihuela tablature. Compositions are selected from those employing clefs, something which, arguably, is totally irrelevant to purely instrumental music (solo vihuela dances, etc.). But, as will be seen, the presence of specific "clefs" at the beginning of vihuela intabulations tends to link them to specific templates. The procedure developed to test the relevance of Bermudo's templates to then-current transcription practice is simply the reciprocity test. It involves re-transcribing selected intabulations into modern notation, using nothing but Bermudo's templates—a kind of reverse intabulation.^7 By allowing

27intabulation is the process of converting vocal notation into a practical notation that displays the actual fingerings needed to play the designated music on the vihuela—tablature. 14 only those chromatic pitches provided on the designated template, with no enharmonic substitutions, one will see to what extent Bermudo's templates form a logical link in both directions between sixteenth century vocal models and contemporary vihuela transcriptions of them. This procedure will also examine whether the Pythagorean systems proposed by Bermudo were workable on the vihuela from the viewpoint of the dissonances engendered. Throughout this dissertation, Helmholz' system of octave designation is used. In this system, the pitches in the octave below "middle c" are designated the "small octave" and given lower case letters (c, d, e, etc.). The great octave (below small octave) is given upper case letters (C, D, E, etc.). The octave above and including middle c is labelled: c^, d^, e^, etc.; the c above middle c and its octave begins with c^ and continues accordingly, as do the subsequent octaves.

The result of intabulation is a set of lines (representing the strings of the vihuela) and numbers placed on those lines (representing the frets). CHAPTER II JUAN BERMUDO: TEXT AND CONTEXT

Juan Bermudo (c.l510-c.l565), whose treatises provide our only knowledge of vihuela tunings during the mid-sixteenth century, is the central figure in this study. To interpret his theories properly, we must seek to understand his motives and to place his ideas in context. This chapter examines Bermudo's life in relation to the prominent political, cultural and social conditions in Renaissance Spain that influenced his scholarship and literary production. After summarizing the political and cultural situation, it explores Bermudo's relationship with his religious order, and concludes with a brief examination and concordance of

Bermudo's treatises.

The Political Situation in Renaissance Spain Fourteenth century Spain was a land of turmoil and upheaval, in which Moors, Christians and Jews sought to co-exist as three separate cultures. The recent reconquest campaigns of the Christians had driven the Moors to Granada, and suppressed the Jews politically and socially. ^ No

^Henry Kamen, Spain 1469-1714: A Society of Conflict (London and New York: Longman Inc., 1983), xiii. This book provides valuable information on the situation in Spain—social, 15 16 semblance of political unity emerged until the reign of Ferdinand and

Isabella (1480). Isabella's right to the throne was the source of controversy that led to a series of dvil wars from 1464-1480. The previous ruler, Henry IV, had raised the ire of the nobles by his choice of Isabella as his successor. One faction of lords supported Henry's choice of Isabella, his half-sister, while the other preferred the succession of Henry's infant daughter, Juana. The issue was complicated by the fact that Henry stipulated that to inherit the throne, Isabella must marry the elderly king of Portugal, Alfonso V. Isabella, in the meantime, was secretly betrothed to Ferdinand of Aragon by Alfonso of Carillo, Archbishop of Toledo, and she married him in 1469 in Valladolid. When Henry found this out, he renounced Isabella's succession, and declared Juana, his daughter, the rightful heir to the throne in 1470. The tension did not subside until Henry's death in 1474. During 1474, Alfonso V invaded Castile in retaliation, and promised to marry Juana, an action that prompted a faction of the nobility to recognize him as king, thereby continuing the atmosphere of anarchy in Castile. Isabella eventually overcame the dissension created by Henry, but only with the aid of her husband, Ferdinand, who was also caught up in dvil wars of his own in Aragon.2 she was crowned Queen of Castile in 1474. In 1478, Isabella gave birth to Juan, an heir to the throne of Castile. Shortly thereafter, all dvil wars over succession ended, and representatives political, economic, cultural, etc. Unless otherwise indicated, the following discussion is based on this book. Z-phe three maritime kingdoms of Naples, Aragon, and Sicily were ruled over by Alfonso the Magnanimous until his death in 1458. These three realms maintained a dose relationship despite divisions among family members. Later, Ferdinand arranged important marriages of key people to secure Naples, and to maintain Spanish sovereignty over the kingdom. 17 of Castile and Portugal agreed to renounce all claims to the throne.^ Similar conflicts over Ferdinand's succession in Aragon were also resolved peacefully. Consequently, Isabella and Ferdinand were able to establish royal authority in 1480. In September of that year, Isabella issued the first commissions for the commencement of the Inquisition. Then, the monarchs directed their attention to conquering the remaining Moorish strongholds on the peninsula, finally forcing the capitulation of Granada in 1492. That same year they granted Columbus his commission for explorations, and signed a decree expelling Jews from all of Spain. Isabella's death in 1504 again threatened the stability of the two crowns of Castile and Aragon. In her will, Isabella named her eldest surviving child, Juana, as heir, and stipulated that if Juana refused to reign, or was deemed incapable of doing so, Ferdinand should remain as acting Regent until Juana's son, Charles, came of age.^ After several disagreements with Juana and Philip, Ferdinand conceded his position as Regent and retired to Aragon. In 1510, after the death of Philip (Juana's husband) and the mental collapse of Juana, Ferdinand returned as governor of Castile, unifying the two kingdoms once again.^ Under Ferdinand's reign, Spain continued its policy of conquests in Navarre, North Africa and the New World, leading Spain to a position of political and economic prominence. Spain exploited the riches and resources of the Americas, and soon became a world power. In 1512,

^This was accomplished with the Treaty of Alcaçovas in September of 1479. Although Juana had retired to a convent in Portugal ini480, she still proclaimed her rights to the throne of Castile until her death in 1530. ^Juana was mentally unstable and living in the Netherlands with her husband, Philip. Ferdinand had Juana and Philip proclaimed rulers of Castile in 1505, but also confirmed his Regency, so that Castile would not fall into foreign hands. ^Cardinal Cisneros, the acting regent in Ferdinand's absence, requested Ferdinand's return. 18 Ferdinand was stricken with a lingering illness that eventually led to his death in 1516. During the period following Ferdinand's death. Cardinal Cisneros assumed the duties of regent until Charles, whose court was at Brussels, was able to succeed to the throne later that same year. In 1517, Charles arrived in Spain to claim his throne.^ In 1519, his grandfather. Emperor Maximilian, died; the German electors in Frankfurt unanimously chose him to be the Holy Roman Emperor—Charles V. Upon hearing this, he left Spain for Brussels to assume the responsibilities for a vast expanse of territories—European, Mediterranean, and American. Although Charles was mostly an absentee monarch, he found it necessary to pay increased attention to Spain because of the revolutions that broke out there shortly after his departure to Brussels. In 1522, he returned to Spain, and devoted seven years to settling the government there. During this period, he reformed the court, reorganized the civil administration, and presided over a continued cultural revival. Clearly, the Spanish political and economic atmosphere was tumultuous, until it was unified through the efforts of Ferdinand and Isabella, and strengthened by Charles V.

Spain's Cultural History Because of the political turmoil, cultural life in Spain also remained fragmented until the reign of Ferdinand and Isabella. After the mid-fifteenth century, Italy's reputation as the center of humanism prompted many

^Most Castilians recognized Charles as king, but looked upon him with muted suspicion. After all, he had been bom and raised in the Netherlands while his brother, Ferdinand, had been raised in Spain. The Spaniards preferred overwhelmingly to see Ferdinand assume the throne, since they viewed him a Spaniard. To eliminate the possibility of civil dispute over succession, Charles arranged for Ferdinand to "disappear" to Germany during this period. 19 Spanish scholars, such as Juan de Lucena and Antonio de Nebrija, to go to Italy to study Latin literature and contemporary philosophy. Moreover, Italians soon came to assume important positions in Spanish universities, and thus contributed to an important exchange of ideas among artists and scholars. By the late fifteenth century, several foreign cultures were influencing the arts in Spain: Italian, Burgundian and Flemish. Each reinforced a particular link between Spain and other parts of the empire. Because Spanish territories included courts in Naples and Sicily, the Italian influence was particularly prominent. Burgundian and Flemish influences were also strong because of the close commercial links between Spain and the Netherlands. Italian influences are evident in the paintings of Pedro Berruguete (d. 1506), while Burgundian influences are seen in the architecture of Hans Wass and the sculpture of Gil de Siloé. During this period, another cultural style was also prominent in Spain—the Mudéjars. They were, in fact, the Moorish peoples who survived the Christian Reconquest (c. 13th century) and the capitulation of Granada (1492). Ferdinand and Isabella encouraged all forms of cultural life and promoted a free exchange of knowledge among nations, which further reinforced the connections between Spain and the rest of the empire, especially Italy and the Netherlands. Charles V allowed this exchange to continue during his reign, and this policy resulted in an increase of activity in the Humanist and Erasmian movements. These movements presented 20 many opportunities for broader international horizons, an outlook that was highly regarded by many of Charles' courtiers.^ The Humanist and Erasmian movements began to weaken in the 1520's, largely because of the Inquisition. Due to the spread of Lutheranism, many Catholic theologians viewed Humanist and Erasmian thought as a threat to orthodoxy, and therefore, as subversive. When the Humanists gradually lost their most effective support in the royal courts in the 1530's, the movement dissipated, and most of the movement's major figures either died, or fled the country.® Subsequently, the Inquisition caused Spain to revert to conservatism and to a limited Mediterranean circle of influence. Ferdinand and Isabella actively supported cultural advancements, and this support gave great impetus to education in Spain. They insisted that members of councils and chancelleries be lettered with at least ten years of law, an attitude that instigated public acceptance of education, and encouraged small towns to open grammar schools. This excitement over education, led to the founding of new universities. In 1450, there were only four universities in Spain: Salamanca, Huesca, Valladolid, and Lérida. By the mid-sixteenth century, more than twenty new universities were established. The most outstanding one was at Alcalâ—the university that Bermudo attended.^ Within each university, a number of colleges were created—thirty-eight alone during Bermudo's lifetime. Learning at these

^The high tide of these movements swept through Spain when Charles V spent his longest sojourn in Spain from 1522-1529. The peak of humanism is best exemplified by the philosopher, Juan Luis Vives. °The decade closed with the deaths of Vives (1540), and Juan De Valdes who had earlier fled to Italy in 1530. ^Alcalâ was founded by the Franciscan Provincial Minister, Cardinal Cisneros, in 1508. 21 educational institutions was usually reserved for clerics and society^s elite.^o Education enjoyed this type of expansion well into the sixteenth century as the state continued to select its officials from college and university graduates, thus, creating a group of people that soon would become a part of the emerging Spanish bureaucracy. The interconnection of kingdoms within Spain and within the Holy Roman Empire played an important role in the exchange of musicians and musical ideas. Many foreign composers and theorists traveled to Spain to study and to serve in the courts—a circumstance which greatly influenced native composers. Several noted composers from the Netherlands visited Spain at some point between 1450 and 1550: Johannes Ockeghem (1469-70), Martin Agricola (1506), Pierre de la Rue (1501-2,1505), and Nicolas Gombert." The famous composer-theorists, Johannes Tinctoris and Franchino

Gaffurius, spent time in Naples, a Spanish t e r r i t o r y Spanish theorists, composers and musicians, in turn, went to Italy to study, teach, or serve in various courts and chapel choirs. Ramos de Pareja taught at Salamanca before departing for Bologna, where he gave public lectures and published his famous treatise, Musica Practica in 1 4 8 2 .^^

l^There were some institutions {colegios mayores) that were open to mature students of "poor origin." Of the six colegios mayores, four were at Salamanca (founded between 1401 and 1521); one at Valladolid (1484) and one at Alcala (1508). ^ ^Gustave Reese, Music in the Renaissance, rev. ed. (New York: W.W. Norton, and Company, 1959), 118 (Johannes Ockeghem), 208 (Martin Agricola), 267 (Pierre de la Rue), and 303 (Nicolas Gombert). 12ibid., 178. 13lbid., 586-87. Ramos later went to Rome and was still there in 1491. His Musica practica (1482) was a revolutionary treatise in his day, because he proposed various concepts that broke with conventional thought, and aroused much controversy. His theories also became a focal point of much controversy in Spain as well. Gonzalo Martinez de Bizcargui supported Ramos' ideas, while Juan de Espinosa attacked Ramos. Despite Ramos' importance in the history of Spanish music theory, Bermudo never mentions his name in any of his writings. 22 Evidence shows that other Spanish theorists, such as Francisco Tovar, Pedro Ciruelo, and Martin de Azpilcueta, either visited Spanish protectorates, or other European territories.^^ Others elected to remain in Spain—Domingo Marcos Durân, Alfonso de Spafton, Gonzalo Martinez de Bizcargui, Martin Tapia Numantino, and Juan Bermudo.^^ Two prominent Spanish composers went to Italy to serve in the Papal Choir in Rome: Christobal de Morales in the first half of the sixteenth century; Tomâs Luis de Victoria in the second half. On the other hand, Juan Vasquez and Francisco Guerrero never left the Iberian Peninsula. In Spain, most of the famous musicians either served at a royal court, or in the Church. Vihuelists (e.g., Miguel Fuenllana, Luis de Narvâez and Alonso Mudarra) and organists (e.g., Antonio de Cabezon) played and composed for the royal courts.^^ Courtly service gave these musicians the opportunity to experience foreign influences either by travelling abroad with the royal entourage, or by coming in contact with foreigners visiting the Spanish courts. During the sixteenth century, there were only seven composers who published music specifically for the vihuela, and two others who published collections of organ music that also included a few select pieces for vihuela and guitar. The first publication of music for vihuela, Luis Milan's Libro de mûsica de vihuela de mano intitulada El Maestro, appeared in Valencia in 1536. It

^^The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie, (London: Macmillan Publishers Ltd., 1980), 1: 760 (Azpilcueta), 4:411 (Ciruelo), and 19: 102 (Tovar). ^^Leôn Tello, Estudios de Historia de la Teorta Musical Other theorists who stayed in Spain include: Alfonso de la Torre, Sanchez de Arevalo, Guillermo de Podio, Pedro de Fuentiduena, Pedro Ferrer, Gomez Herrera, Fray Bartolomé Molina. ^^Reese, Music in the Renaissance, 587 (Morales), 599 (Victoria), 612 (Vasquez), and 594 (Guerrero). ^^T/ie New Grove, 13:39 (Narvdez), 12: 757 (Mudarra), and 3: 572 (Antonio de Cabezon). 23 was set with movable type (a Parisian invention of Attaingnant, 1527) using modified Italian tablature and fonts—another witness to the cultural cross- fertilization taking place in Spain at the time. Luis de Narvâez's Los seys libros del Delphfn de mûsica de cifras para taner vihuela, was published two years later, in Valladolid. Alonso Mudarra included works for the vihuela and the four-course guitar in Tres libros de musica en cifras para vihuela, published Seville in 1546. Enriquez de Valderrâbano's Libros de musica de vihuela, intitulado Silva de Sirenas appeared in Valladolid in 1547, and in 1552, Diego Pisador published Libro de mûsica de vihuela in Salamanca. Another collection containing compositions for four- and five-course guitar, as well as vihuela was Miguel de Fuenllana's Libro de mûsica para vihuela, intitulado Orphenica lyra, published in Seville in 1554. The last collection devoted to the vihuela, Esteban Daza's Libro de mûsica en cifras para vihuela, intitulado el Parnasso, appeared in Valladolid in 1576. Two other keyboard collections containing some compositions for string instruments were Luys Venegas de Henestrosa's Libro de cifra nueva para tecla, arpa y vihuela. ., published in Alcala in 1557, and Tomaso de Sancta Maria's Libro llamado arte de taner fantasia, published in Valladolid in 1565. Henestrosa's collection includes some compositions for the harp as well. Clearly, most of the vihuela music was published in the major cities and towns of Castile: Valladolid, Seville, Salamanca, and Alcalâ, with the majority published at Valladolid.^® Valencia, where Luis Milan published his collection, was a

^®Not only was Valladolid the most popular location in which to publish, it was also the administrative center for the joined kingdoms of Castile and Aragon. 24 coastal, commercial shipping center in Aragon, and thus remained rather isolated from Castile. In all, these collections comprise over 700 compositions for the vihuela (and guitar) in tablature. The genres included are: fantasias, villancicos, romances, sonetos, variations, masses, motets, villanescas, cancions madrigals, pavannes, and related forms, representing in large part the courtly vocal and instrumental style of this period.

Tuan Bermudo and the Friars Minor of the Observance

In C.1510, Juan Bermudo was born into a noble fanüly of Ecija, asm all Andalusian town situated approximately fifty miles northeast of Seville.^^ In 1525, at the age of fifteen, he entered the religious Order of the Observant Minorites (frayles menores de la obseruancia), in the Franciscan province of

Andalusia.2i As a young friar, Bermudo began his studies at Seville, and later studied mathematics at the prestigious Franciscan University of Alcalâ de Henares.22 There, he became interested in music and its relation to the mathematical sciences. Finding some animosity toward music on the part of the Observants, he foresook musical study at this time.23

^^Because these two kingdoms maintained a rather autonomous relationship, it comes as no surprise that Bermudo, who lived and worked in Castile, not once mentions Luis Milan in the Declaraciôn. 20Robert Stevenson, ]mn Bermudo, 1, and The New Grove, 2:611-12. Although no definite birth date is given, Stevenson approximates it by the date Bermudo entered the Observants— at age fifteen. Le6n Tello, Estudios de Historia de la Teoria Musical, 246, gives no birth date for Bermudo. Bermudo clearly designates his birthplace as Ecija in the colophon to El libro primera de la declaraciôn de instrumenios (1549), folio cxlv, v. 2lLe6n Tello, Estudios de Historia de la Teorta Musical, 246. 22The University of Alcalâ de Henares is located approximately twenty-five miles northeast of Madrid, and was founded in 1508 by the Franciscan Provincial Minister, Francisco Jimenez de Cisneros (1436-1517). ^The history of the Observants and their "reform" tradition, will not be detailed here. For a more complete treatment of this topic, see Zephyrin Englehardt, "Friars," The Catholic 25 Although Bermudo reports a negative attitude toward music in his community, nothing suggests that this attitude was condoned by St. Francis, the founder of Bermudo's religious order. St. Francis' writings indicated his love of music, especially that intended for God's praise. He praised God by writing poems and setting them to music, and instructed his followers to do the same. In a letter to a general chapter in 1224, St. Francis stressed that words and music do not have equal roles. To praise God in the best way, one must emphasize the words, and treat the music as a secondary vehicle for enhancing that praise. Music must not be used as a source of pleasure.24 The episode that evidently enabled Bermudo to reconcile his musical avocation with the strictures of his order was a serious and prolonged illness that removed him from the daily routine of his order. During his convalescence, he found the time to study music independently.^^ Bermudo devotes an entire chapter of the Declaraciôn to justifying his shift from the study of mathematics to music, which he considers just as important to the order as the daily routine. He explains that although his order contends that the best service to God is through strict observance of the rule and recitation of the Divine Office, there is no reason why he should not explore music

Encyclopedia, edited by Charles G. Herbermann et al., (New York: Rolxrt Appleton Co., 1909), 6: 281-302; and C. J. Lynch, "Franciscans," New Catholic Encyclopedia, (New York: McGraw- Hill Book Co., 1967), 6:36-46. 24st. Francis of Assisi, V/ritings and Early Biographies, 3rd rev. ed., edited by Marion A. Habig, (Chicago: Franciscan Herald Press, 1973), 107. "The clerics should say the Office devoutly, not concentrating on the melody of the chant, but being careful that their hearts are in harmony so that their words may be in harmony with their hearts and their hearts with God. Their aim should be to please God by purity of heart, not to soothe the ears of the congregation by their sweet singing. I myself promise to observe this strictly, as God gives me the grace, and I will hand it on to the friars..." 2SNeither Stevenson nor Leôn Tello give any dates for this unidentified illness. Bermudo states near the end of Book IV of the Declaraciôn (folio cix, r), that he had been studying music for eight years, which led to the completion of his final treatise in 1555. This evidence places his illness at about 1548—shortly before the appearance of his first publication. 26 theory as well, especially if the ultimate goal is to "praise God."^^ He continues to rationalize his commitment to music by referring to the

"unhealthy" condition of church music that needs "healing,"27 and by viewing his prolonged illness as a directive from God to study it. Bermudo states:^®

Because the music is "unhealthy," I feel that Our Lord God gave me a serious and lengthy illness so that I might "heal" it. This compelled me to digress from the duties and exercises which obedience demands of me...When I was unable to serve because I was physically weak from this illness, God granted me books on music. My conscience and the words from the servants of God [fellow friars], persuaded me to write...It was no small matter to do this, because there was the need to correct the errors in the chant, to compose new offices, and to understand the many parts of the Roman Ordinary for our family [order].

26juan Bermudo, Declaraciôn de instrumenios musicales (Ossuna, 1555), folio i, r. Ténia entendido (aunque falsamente) seruir mas a Dios en solos los exercicios, y officios de la orden: que si tractara de Musica. Como si ambas cosas no se pudieran hazer...Teniendo la Music por cosa accesoria: délia no hazia cuenta. [Although I learned falsely that it is better to serve God by means of the exercises and duties of the order than by dealing with music,...1 did not imagine music to be a superficial thing ] ^^Gustave Reese, Music in the Middle Ages (New York: W. W. Norton and Company, 1940), 109-112. Although Charlemagne had ordered the use of the Roman rites as the norm throughout his kingdom (9th century), Mozarabic continued to flourish in Spain. It was maintained at Toledo, despite Alfonso Vi's order making the Roman rite obligator}' in 1085. Cardinal Francisco Ximenes de Cisneros, a Franciscan, sought to revive the Mozaribic rite at the end of the fifteenth century, and had his own version printed in 15(X). Perhaps, Bermudo was striving to strengthen the use of Roman Chan» 2®Bermudo, Declaraciôn, folio i, r. Estando en mi la Musica enferma, para sanarla nuestro senor Dios: dame una graue y prolixa enfermedad, que me compelio a dexar los officios y exercicios en que la obediencia me tenia occupado... Viendo que en aquellos no podia seruir, porque me faltauan las fuerças, y que no auia de estar ocioso: dime auer libros de musica. De una parte la consciencia, y de otra palabras de sieruos de Dios: me persuadian a escreuir...No pequena parte fue para hazer esto: la necessidad de enmendar yerros en el canto, de componer officios nueuos, y de entender muchas partes del ordinario romano para nuestra familia. 27 Believing this work would benefit not only his fellow friars, but also the rest of the church, he eventually published three major treatises dealing with music and music theory. Little is known of Bermudo's life after 1555. It is evident that he had earned the approbation of his order, for on June 24,1560, he was elected to the post of difinitor for the Observants in Andalusia.29 Stevenson suggests that this honor would normally have led to further distinction and promotion in rank within the order, such as provincial minister. Because there are no more facts available about his life beyond this point, Stevenson conjectures that Bermudo probably died around 1565.^°

Bermudo's Early Publications Bermudo's diligent pursuit of music theory led to the publication of three major works between 1549 and 1555. They are: El libro primera de la declaraciôn de instrumentas (1549), El arte tripharia (1550), and El libro llamado declaraciôn de instrumentas musicales (1555).^^ Since his two earlier publications are similar, sharing certain dates and facts, it is appropriate to examine them together.

^^Leôn Tello, 247. Footnote 306. Leôn Tello refers to Fr. Angel Ortega's "Las casas de estudios de la Provincia de Andalucfa." In Archiva Ibero Americano, 4, no. 10 (July-August, 1915): 217. El dia 24 de junio de 1560 se celebrô Capftulo Provincial en el convento de San Francisco de Baeza, presidiendo el Rmo. P. Fr. Francisco Zamora, General de la Orden, y fue electo en Ministro Provincial el R. Padre Francisco Morales y para Definidores los PP. Fr. Pedro Azpetia, Fr. Pedro Villalon, Fr. Juan Bermudo y Fr. Juan Villavicencio. Duré este Provincialato cuatro afios, cuatro meses y cuatro dias. 30stevenson, Juan Bermudo, 2. Stevenson, The New Grove, 2: 611-612. These titles appear in Stevenson's bibliography for this article in this form, although they may vary in other bibliographic sources. 28

Bermudo wrote his first treatise, El Libro Primero (1549), in Ecija. He completed it in the octave of the Feast of All Saints (November 1st) in 1548.32 On August 1,1549, Fr. Gomez de Llanos, Provincial Minister of Andalusia, granted Bermudo a license to publish a series of books on music. This license was granted at the Monastery of the Mother of God at Ossuna, and was valid for both El Libro Primero (1549) and El Arte Tripharia (1550). This evidence suggests that Bermudo had written El Arte Tripharia shortly after El Libro Primero. For that reason he was able to acquire the license for both treatises at the same time.33 On September 17,1549, the printing of El Libro Primero was complete—almost an entire year after Bermudo finished writing it.34 Further examination of the treatise shows that Juan de Leon, the

32juan Bermudo,El libro primero de la declaraciôn de instrumentes (Ossuna: Juan de Leon, 1549), folio cxlv, v. Compuso se la presente obra llamada libro primero de la declaraciôn de instrumenios en la muy noble y muy leal citxlad de Ecija, de adonde el author es natural, ano de mil y quinientos y quarenta y ocho de la encamacion de nuestro redemptor Jesu Christo; el quai fue acaljado infra octaua de todos los Sanctos. [The present work entitled El libro primero de la declaraciôn de instrumenios was written in the very noble and loyal city of Edja, whence the author is a native, in the year of Our Redeemer Lord Jesus Christ, 1548. It was finished within the octave of the feast of All Saints.] Stevenson, Juan Bermudo, 14. Stevenson interprets these statements to mean that Bermudo wrote and finished the treatise within the span of a week— the first week of November, 1548. 33Bermudo, El Libro Primero, folio ii, r, and El Arte Tripharia, folio ii, r. Fray Gomez de Llanos de la orden de los frayles menores de obseruancia, Ministro Prouincial en la prouincia del Andaluzia: a vos el venerando padre fray loan Bermudo de la mesma orden predicador egregio y confessor benemerito: salud y paz en nuestro senor.. .For tanto os doy licencia con merito de obediencia para los imprimir, y sacar en publico estos... Dada en el conuento de madre de Dios de Ossuna primero de Agosto de 1549 Anos. [Friar Gomez de Llanos of the Friars of the Observant Minorites, and Provincial Minister in the province of Andalusia, to you, the venerated Father Friar Juan Bermudo of the same order, illustrious preacher and worthy confessor, health and peace in Our Lord. ..For so much I grant you permission with merit of obedience to print and distribute to the public these...Granted in the Monastery of the Mother of God in Ossuna, on August 1,1549.] 34Bermudo, El Libro Primero, folio cxlv, v. Fue impressa la presente obra en la villa de Ossuna por el honrrado [sic] varon Juan de Leon impressor... Acabo se a diez y siepte dias del mes de Setiembie, Afio del sefior de mil quinientos y quarenta y nueua, y fue la primera impression esta. [The present work was printed in the town of Ossuna by the honorable nobleman Juan de Leon, printer of the University of the most illustrious lord, don Juan Tellez Giron, Count of Uruefia... It was completed on the 17th day of the month of September, in the year of Our Lord, 1549, and this was the first printing ] 29 printer, used a single column layout of an octavo-size page, and employed a Gothic typeset. On November 18,1549, Bermudo obtained a six year copyright from the government in Cigales. This copyright covered both El Libro Primero and El Arte Tripharia. One should bear in mind that since Bermudo obtained the copyright for both treatises at the same time, he had probably written all, or part of El Arte Tripharia at this point. This copyright prohibited the publication and selling of El Libro Primero without Bermudo's permission, and at the same time fixed the price of the book at eighty-six maravedis.^^ The only difference between the copyright for El Libro Primero, and that for El Arte Tripharia is the fixed price. The fixed price for El Arte Tripharia was set at "two maravedis per sheet," or a total of eighty maravedis.^^ Although Bermudo does not disclose his completion date of El Arte Tripharia, the colophon clearly indicates that Juan de Leon of Ossuna finished printing it in May of 1550, on the Feast of Saint Bernardino.^^ The page layout for El Arte Tripharia is also

^^Bermudo, El Libro Primero, folio i, v. Manifiesto sea a todos los que el libro presente vieren, como su Magestad hizo merced a fray loan Bermudo, para imprimir en sus reynos y senorios el libro primero de la declaraciôn de instrumentos, y que ninguno lo pueda imprimir ni vender sin licencia de quien tuuiere el poder de el dicho fray Joan Bermudo por seys afios... La summa en que fue tassado el dicho libro es ochenta y seys marauedis. Dado en Cigales a diez y ocho dias de nouiembre afio de el sefior de mil y quinientos y quarenta y nueue. [Let it be manifest to all who may see the present book as His Majesty has done, thanks to Juan Bermudo, for printing in his kingdoms and lordships the first book of the declaration of instruments, and that no one may print it nor sell it without a license of authority from Friar Juan Bermudo for six years... The price of that book was fixed is eighty-six maravedis. It was granted in Cigales on November 18th, in the year of Our Lord, 1549.] Kamien, Spain 1469-1714, xi. The maravedi was the principal coin used for accounting in Castile, and usually was issued in units of two. ^Bermudo, El Arte Tripharia (Ossuna: Juan de Leôn, 1550), folio i, v. La summa en que fue tassado el dicho arte es a dos marauedis cada pliego. Since this treatise consists of forty folios, it will cost about eighty maravedis. ^^Ibid., folio xl, V. (Conclusion) Fue impresso enla villa de Ossuna en casa de Juan de Leon impresor. Siendo primeramente visto y examinado por el consejo real. Acabose dia del bienauenturado sanct Bernardino el mes de mayo afio de 1550. [It was printed in the town of Ossuna, in the house of Juan de Leon, printer. It was primarily seen and examined by the royal 30 the same as for El Libro Primero—single columns, octave page, and Gothic type. Since Bermudo received both license and copyright for this work prior to its actual publication, it is logical to assume that both treatises were published consecutively, soon after the completion of texts. The content and purpose of these two treatises differ greatly. Bermudo dedicates El Libro Primero to "the most merciful and very powerful Don Joan ni. King of Portugal."^® Stevenson conjectures that although Bermudo never claims to have known the king personally, he was hoping to gain some favor from Don Joan ni.39 El Libro Primero comprises: title page, copyright, license, letter from Bernardino de Figueroa, epistolary prologue (addressed to King Don Joan), general prologue, letter from Bernardino de Figueroa to Friar Gom.ex de Llanos, list of sources, text consisting of fifty chapters, and a colophon. In the general prologue, Bermudo discusses his purpose for writing El Libro Primero.^ He acquaints his reader with the important historical and philosophical facts about music and presents the primary goal of the treatise—to teach students enough about music to enable them to intabulate vocal music for instruments. He states:^!

adviser. It was completed on the day (feast] of the Blessed Saint Bernardino, the month of May in the year 1550.] ^Berm udo, El Libro Primera, folio i, r. (Title page) Comiença el libro de la declaraciôn de instrumentos, dirigidos al clementissimo y muy podercso don Joan tercero deste nombre, rey de Portugal. ^^Stevenson, Juan Bermudo, 10. Years earlier, the king had named Matheo de Aranda to the position of professor of music at the University of Coimbra. Bermudo may have studied with Aranda at the University of Alcala, and perhaps thought he might be next in line for such a prestigious appointment. ^Berm udo, El Ubro Primero, folio vii, v. General prologue of the entire work for the reader. '*^Ibid., folio xi, r. El fin ultimado que en mis libros pretendo: es que enteniendo los tanedores los intrumentos sepan cifrar, o poncr con facilidad canto de organo en ellos. Ibid., folio ii, v. In a letter to the King of Portugal, Bernardino de Figueroa makes statements to the same effect. Similar references are also found in the prologue to the Declaraciôn. 31

The ultimate goal that I claim in my books is that the player will know how to intabulate and place polyphony on the instruments easily when they are fully understood. Bermudo does not intend to teach techniques for any particular musical instrument inEl Libro Primero. He makes this point explicit in subsequent statements in the general prologue, where he delegates this task to the accomplished musician. He reasons that, since there are many able musicians available, he will concentrate on the theory of music so that one will be able to comprehend what one plays.^2 Throughout El Libro Primero Bermudo alludes to numerous scholarly sources—ancient and contemporary. He documents the breadth of his scholarship in an extensive list containing four categories: Pagan Musicians, Christian Musicians, Sacred Scripture, and Doctors. [See Figure 1.] The list in Figure 1, however, is not complete, for it does not cover all the sources indicated in the marginalia or employed in the printed text. Indeed, Bermudo incorporates many other references, including mythological sources, such as Orpheus and M e rcu ry .43

42ibid., folio xi, v. Pues no pretendo ensenar a taner, porque ay grandes tafiedores de todos los instrumentos, que esto mejor que yo puedan hazer. [Thus, I am not claiming to teach you how to play, because there are great players of all the instruments, who can do this better than 1 can.] 43These sources play an important role in the Declaraciôn (1555). There are additional sources scattered throughout the treatise, that do not appear in this list. Among these arelslamic writers, such as Al-Farabi and Ibn Sina. For additional sources, see Stevenson, Juan Bermudo, 27-28. 32

PAGAN MUSICIANS CHRISTIAN MUSICIANS SACRED SCRIPTURE DOCTORS Aristotle St. Gregory Genesis St. Basil Plato St. Bernard Exodus St. Augustine Diogenes Boethius Deuteronomy St. Ambrose Quintilian Glareanus David St. Jerome Cicero Berno of Reichenau Ecclesiastico St. John Chrysostom S en eca Guido d'Arezzo Ecclesiastes St. Thomas Aquinas Pope John XXII Wisdom St. Isidore Gaffurius Canticle of Canticles Origen Ornlthoparchus Isaiah Eusebius Faber Stapulensis Daniel Richard of St. Victor Margarita Tobias Hugo of St. Victor Ciruelo Amos Joachim of Floris Guillermo Despuig St. Matthew Peter Comestor Michael Castellanis St. Mark Denys the Carthusian Giorgio Valla St. Luke Placentino St. John Rubineto Apocalypse Joannes Goscaldos St. Paul Francisco Tovar St. Jam es Luz [sic] Bella Acts of the Apostles Bizcargui Decrees

Figure 1. Bermudo's List of Sources, {El Libro Primero, folio xii, v).

Bermudo's second publication, El Arte Tripharia, is dedicated to Dona Isabel Pacheco, the Abbess of the Convent of Saint Clare in Montilla.44 The format of El Arte Tripharia is similar to that of El Libro Primero ; it consists of title page, copyright, license, letter to the reverend Mother from Francisco Cervantes de Salazar, epistolary prologue from the author, prologue to the reader, text (comprising forty chapters), and a colophon. The focus of El Arte Tripharia is much different. In the epistolary prologue, Bermudo states that the Abbess Dofia Isabel Pacheco has specifically

'^^Bermudo, El Arte Tripharia, folio i, r. (Title page) Comiença el arte Tripharia dirigida a la yllustrey muy reuerenda sehora Dofia Ysaljel Pacheco, abadessa en el monesterio [sic] de sancta Clara de Montilla [Here begins El Arte Tripharia, addressed to the illustrious and very reverend mother, Dofia Isabel Pacheco, Abbess of the Monastery (Convent) of Saint Clare of Montilla.] 33 requested an instructional method that would teach musical principles to the novices, particularly, her niece. Dona Teresa, daughter of the Count of Osomo. This material is to be presented in such a way that Dona Teresa will quickly learn to play the organ and sing the Divine Office.^^ Obliging the abbess, Bermudo presents three musical methods (artezicas): singing plainchant, composing polyphony and "playing the organ." In his introductory material, he stresses his intention to abbreviate everything as much as possible, and claims that his coverage of the three crafts will be sufficient for any studious person—novice or professed religious—desiring to learn quickly the basic principles of music.^^ Therefore, he has omitted many of the historical and philosophical aspects of music theory, in favor of maintaining simplicity and practicality.

Declaracidn de înstrumentos Musicales Bermudo's final publication, El libro llamado declaracidn de instrumentas musicales, did not appear until 1555. According to the title page, Bermudo dedicated this treatise to Don Francisco de Zuniga, Count of Miranda, Lord of

^^Ibid., folio ill, v. Cognosci la voluntad, que, U. M. tenia a la senora dona Teresa, hija del seftor Conde Osomo. Como a sobrina desseays (pues ha de ser monja) que en breue tiempo supiesse cantar para el seruicio del officio diuino, y taner para su sancto exercido. [I recognized the desire that Reverend Mother had for Senora Doha Teresa, daughter of the Count of Osomo. She is your niece, and since she is becoming a nun, you want her to know, in a brief time, how to sing for the service of the Divine Office and to play for her holy exerdse.] ^Ibid., folio iii, v. Acorde de hazer tres artezicas breues, una de canto llano, otra de canto de organo, y la tercera de tafier organos. Todo quanto se pudieron abreuiar: se abreuiaron. Sufficientes son para dar en alguna manera noticia de la Musica: mayormente a religiosas, que son estudiosas, y no pretenden saber, sino el offido diuino. Creo, que en breue tiempo aprouechara la senora dofta Teresa por esta manera de pradica la Musica. [1 agree to present three artezicas briefly. One is plainchant; another is polyphony; and the third, is playing the organ. Everything that can be abbreviated, is abbreviated. These artezicas are suffident for providing, in some way, information about music, especially for the religious that are studious, and do not claim to know anything except the Divine Office. I think that, Doha Teresa will rapidly benefit from the practice of music through this manner.] 34

the Houses of Avellaneda and Bazan.'*^ This massive work comprises: title page, table of contents, royal copyright, a sonnet praising music, epistolary prologue, letter of recommendation from Bernardino of Figueroa, first prologue, second prologue, five books, letter of recommendation from the reknowned Christôbal de Morales, final statement to the student, errata, and a colophon. The royal copyright guaranteed Bermudo the same rights he enjoyed for the two earlier publications (1549 and 1550). For a period of six years, no one was allowed to print or sell this book in any of His Majesty's kingdoms or lordships without Bermudo's permission.^® Since no date is indicated, one may assume that it is was granted in 1555. Stevenson suggests that Bermudo chose to copyright the Declaracidn using the royal copyright granted

'^^Bermudo, Declaracion de los instrumentas musicales (Ossuna: Juan de Leon, 1555), folio +i, r. (Title page) Comiença el libro llamado declaracion de instrumentes musicales dirigido al illustrifiimo senor el sefior don Francisco de Çuniga, Conde de Miranda, senor de las casas de auellaneda y baçan.. .examinado y aprouado por los egregios musicos Bernardino de Figueroa, y Christoual de Morales. [Here begins the book called Declaracion de instrumentas musicales, dedicated to the most illustrious lord. Lord Don Frandsco of Zuniga, Count of Miranda, Lord of the Houses of Avellaneda y Baçan,.. examined and approved by the famous musidans, Bernardino de Figueroa and Christdbal de Morales.] As is the case with King Don Joan III of Portugal, there is no evidence that Bermudo knew the Count of Miranda personally. He probably was expecting some favor in return, perhaps, the underwriting of the printing costs. The prefatory folios to this treatise are not paginated. For this study they have been numbered in the following manner, beginning with the title page: +i,r, +i, v, +ii, r, etc, ^Ibid., folio +ii, v. Summa del priuilegio real concedido al padre Fray luan Bermudo Manifiesto sea a todos los que la presente vieren: como al padre fray luan Bermudo...fue concedido priuilegio real para ciertos libros de Musica por tiempo de seys ahos: en el qual tiempo ninguno los puede imprimir, ni vender en los reynos y senorios de su Magestad: sopena que los libros, que sin su licencia se imprimieren o vendieren, sean perdidos segun mas largamente es contenido en el priuilegio. [The highest of Royal privilege granted to father Friar Juan Bermudo.. .Let it be manifest to all those who would see the present work: since a royal privilege was granted to Friar Juan Bermudo for certain books on music for the time of six years, in which time no one may print or sell them in the kingdoms and lordships of His Majesty. Under penalty that the books, if they were printed or sold without his permission, will be confiscated, according to what is contained largely in the privilege.] This reference to "kingdoms and lordships" implies that these restrictions applied to all Spanish possessions, including the colonies. 35 earlier in 1549,'*® but one should bear in mind that the copyright for the Declaracidn appears to grant permission for an additional six years. If Stevenson's assumption were correct, then Bermudo, using the 1549 copyright for the Declaracidn, would have had only one more year of protection for his work.^ The assumption that Bermudo secured a second copyright, granting six more years, is the more logical one. Information about the publication of the Declaracidn, found on the colophon, indicates tliat Juan de Leon of Ossuna printed this massive tome. It was completed on July 13,1555—the eve of the Feast of St. Bonaventure.®^ The page layout and typeset for this final work differ from those of El Libro Primera and El Arte Tripharia. The earlier works were printed in Gothic type, in single columns, and on octavo-sized pages, while the Declaracidn was printed in italics, in double columns, and on quarto-sized folios. Clearly, a sufficient of time had lapsed between the publication of the two earlier works and the Declaracidn, to allow Juan de Leon to make these changes. Figure 2 summarizes the chronology of Bermudo's three treatises.

^®Stevenson, Juan Bermudo, 9. 5®The copyrights for El Libro Primera and El Arte Tripharia both indicate coverage for a designated series of books. One may assume that the Declaracion could be included in this series, and would retain the 1549 copyright as well. Bermudo, Declaracidn, folio cxlii, v. Fin de los cinco libros de la declaracion de los instrumentos musicales.. .y fueron impreCos en la villa de Ossuna por luan de Leon impreCor de libros de la insigne Universidad del Illustrissimo senor don luan Tellez Giron conde de Uruena. Y acabaronse de imprimir a treze dias del mes de Iulio siendo bispers de sanct Buenauentura Afto de MDLV. (The end of the five books of the Declaracidn...and they were printed in the town of Ossuna by Juan de Leon, printer of books of the eminent University of the most illustrious Lord Don Juan Tellez Giron, Count of Uruefia. And the printing of them was finished on July 13,1555, the eve of the Feast of Saint Bona venture.] 36 DATES EL LIBRO PRIMERO EL ARTE TRIPHARIA DECLARACION completion of text November, 1548 n. d. 1555 copyright November 8,1549 November 18,1549 1555 license August 1,1549 August 1,1549 none publication September 17, 1549 May, 1550 July 13, 1555 page layout single column single column double column page size octavo octavo quarto type Gothic Gothic Italic

Figure 2. Chronology of the Three Editions.

In the first prologue of the Declaracidn, Bermudo surveys the many topics and issues to be undertaken. The primary goal of this comprehensive work is virtually the same as for El Libro Primera, except that here, Bermudo intends to include many more practical details to meet his goal.^z

The ultimate goal that I claim in my books is that the players will know how to intabulate, and set polyphonic music on the instruments by understanding them. All the methods necessary to achieve this goal are found in my books. Because this dissertation focuses on the topics and issues in the Declaracidn, further descriptions of it are deferred until Chapters 3,4 , and 5.

Interrelatedness of Bermudo's Publications By comparing these three treatises one can discern various links among them. A comparison of their preliminaries (prologues, letters, licencias, etc.) shows an overlap of goals and of ideas. An examination of their individual chapters demonstrates that coverage of certain material

^^ibid., folio +vi, r. El fin ultimado que en mis libros pretendo: es, que entendiendo los taüedores los instrumentos: sepan cifrar, o poner canto de organo en ellos. Y todos los medios que para este fin son menester: los hallareys en mis libros. 37 overlaps extensively, in some places involving a direct transfer of ideas, sentences, and at times, complete chapters from one treatise to the next. While evidence suggests that Bermudo intended from the start to write a "set" of books, or fascicles on music, the facts are somewhat confusing. In the licenses of both El Lihro Primero and El Arte Tripharia, Fr. Gomez de Llanos refers to a total of three books to be published and distributed by Bermudo. It is obvious from the license that Fr. Gomez was aware of an additional book on music, but he gives no hint as to its specific contents.53 In the general prologue of El Libro Primero, Bermudo describes the contents of an additional book. According to statements here, this book was to contain brief introductions to four methods (artezicas): plainchant, polyphony, manichord, and vihuela. These four topics were to be published in individual books.^'*

In order to introduce the new things in music, I have [written] some brief methods on plainchant, polyphony, the manichord and the vihuela. All four of these go in a book by themselves. Regarding the other matters that I must address,...I left them for those specific books where they are necessary. There is no evidence that this particular book was published by itself. Clearly, these statements do not refer to El Arte Tripharia, since it is designed

^^Bermudo, El Libro Primero, folio ii, r. ...y que teneys compuestos tres libros de mucha utilidad para los que en este loable exercido se quisieren occupar. Por tanto os doy licencia con merito de obedienda para los imprimir, y sacar en publico estos,.. [...and that you have written three books of much utility for those who would want to occupy themselve with this laudable practice. For so much, I am giving you permission to print them and distribute them to the public with merit of obedience....] ^Ibid., folio xi, v. Para introduzir los nueuos en Musica tengo unas artezicas breues de canto llano, organo, monachordio, y de vihuela. De otras cosas auia necessidad de auisar...las dexe para los dichos libros, donde fueron menester. 38 specifically to deal with only the first three of these topics: plainchant, polyphony, and manichord. Perhaps, the writing of El Arte Tripharia led Bermudo to change his mind, and to become uncertain as to how many books he would actually write. In any case, it is likely that he is describing a book that eventually appeared within the structure of the Declaracidn —Book n.55 One should recall that Bermudo indicates the possibility of placing material left undiscussed in El Libro Primero and El Arte Tripharia into supplementary books. It is reasonable to assume that this material was ultimately intended for other books of the Declaracidn, particularly Books V, VI, and Vn, of which only the first was published. Despite earlier indications, in the license, that three books were written, Bermudo confuses the issue by referring to four books in the "prologue to the reader" of El Arte Tripharia. Here, he directs the singer to use "all four books," in order to understand music, but at the same time implies that these four books form a larger work. It is difficult to determine whether Bermudo intended to publish a series of books separately (or in one tome), or whether he intended to divide El Arte Tripharia into four books. He is also unclear as to which books are to be included in this particular group.^^

I have vn-iiten four books on music, and there is nothing in them that will be obscure to the singer who studies them. I am saying that to be able to understand my books, the singer does not have to be a master...All my books form one work. Thus, when you see that I

will Ije seen in Chapter III below. Book II of the Declaracion presents introductions to the four main topics: plainchant, polyphony, monachoriio [keyboard] and vihuela. ^Berm udo, El Arte Tripharia, folio v, v. Quatro libros tengo compuestos en Musica, y no ay cosa en ellos que sea obscura para el cantor acertado en estudiar. Digo, que para entender mis libros: no ha menester maestro el cantor.. .Todos mis quatro libros es una obra. Pues quando vicredos que en un capitulo presupongo alguna cosa: tened por entendido, que ay capitulo expresse de ella en aquel libro, o en otro. 39 presuppose something in one chapter, understand that there is a specific chapter on it in that book or in another. In the Declaracidn, Bermudo explains his change in plans for continuing a series of separate books on music. Instead of publishing and distributing his books separately, he decides to combine them all within one volume. He feels that it is far more useful to have all this material together as he states in the second prologue:^^

After printing El libro primero de la declaracidn de los instrumentos musicales and El Arte Tripharia, in which I promised certain books, 1 agreed to change my purpose and print all my works in one volume. 1 had great reasons for dividing it into books. Having assumed, as experience has shown us, that none of my books can be understood fully without the others, then the musician who wants to enjoy my books must have all six dealing with music. Those who wish to be wise in music, need all six books, and this is the reason why they should be found together in one volume. He proposes that the consolidation of the books into one volume also makes it possible to provide all the material on music at once, and suggests that publication of the books separately could lead to inconsistencies in distribution to the public. The student may be able to purchase one, but may not be able to find a copy of one of the others.^s Another explanation may be

S^Bermudo, Declaracion, folio vi, v. Despues de auer impresso el libro primero de la declaracion de los instumentoslsic] musicales, en el qual y en el arte tripharia prometia ciertos libros; acorde de mudar el proposito y emprimir todas mis obras en un volumen y cuerpo, aimque diuisas por libros: para lo qual tuue grandes razones. Presupuesto (como la experiencia nos dene ensefiado) que un libro de los mios no se puede radicalmente entender sin los otros: luego el cantante que de mis libros vuiere de gozar: todos los seys libros (que hablan de Musica) deue tener. Pues, si los tales que defiean ser sabios en la Musica ban menester todos seys libros: razon es de hallarlos junctos en un volumen. ^Ibid., folio vi, v. Se, que los que ban gustado del libro primero: buscan los otros, y aunque estuuiera cada uno por si impresso, no siempre van los unos libros donde los otros se ban vendido, y por tanto imprimiendose cada uno por si: algunas vezes carecerian los cantantes de la verdadera intelligencia de la musica, por no poder los auer todos junctos. [I know that those who liked El Libro Primero, seek the others, and although each one would have been printed individually, some of the books do not always follow where the others have l)een sold. If each 40 found in the fact that at the time he was considering the publication of these additional books, Spain was caught in the throes of a severe inflation caused by demands for products and supplies for the New World.^9 Bermudo evidently decided that his ends would best be served by the combination of several books into one—the Declaracidn. In it, he not only included those topics promised earlier, but also used the material already printed, some of which he corrected and extensively revised. As a result, this one volume would avoid excessive repetition.^®

With the hope that they [students] may take advantage of my work and vigils, and seeing the benefit that would result from it, I changed my initial intention and ordered the present book. In it, I printed not only those matters I had intended to print, but also those I had already printed, even though I have changed many things, correcting and adding others things...If each book were printed individually, the work would be very prolix, because there would be a need to repeat not only sentences, but entire chapters. This is avoided by printing it all in one volume. An even closer examination proves that Bermudo incorporated virtually all the material from El Libro Primero and El Arte Tripharia into the body of the Declaracidn. Table 1 demonstrates this assimilation. The asterisks in the table denote chapters that were extensively revised by Bermudo as they reappeared in the Declaracidn.

one were to l>e printed individually, there would be some times when musicians would lack the true knowledge of music by not being able to have all of them together.] S^Kamen, Spain 1469-1714, 99. ^B erm udo, Declaracidn, folio vi, v. Con desseo que se aprouechen de mis trabajos, y vigilias: mude el proposito primero (viendo el prouecho que dellos resultaria) y ordene el libro presente, en el qual imprime, no tan solamcnte lo que tenia por imprimir: sino tambien lo impreCo, aunque mudadas muchas cosas, y otras corregidas y afiadidas...Si cada libro imprimiera por si, fuera obra muy prolixa porque auia necefiidad de repetir, no solamentc sentencias: pero capitulos enteros: lo qual se euita imprimiendolo todo en un volumen y cuerpo. 41

As one can see, all but Chapters 1 and 50 from El Libro Primero are incorporated, in some way, into select books of the Declaracidn. Some are directly transferred with no changes, while others undergo extensive revisions along the way. A comparison of the Declaracidn and El Arte Tripharia shows that only one chapter (Chapter 38) of El Arte Tripharia was not

retained in the Declaracidn.^'^

(Table 1 follows)

^^Some chapters are revised so extensively that they are unrecognizable—now comprising two, three or four chapters in the Declaracidn. For another concordance, see Stevenson, Juan Bermudo, 4-5. However, Stevenson does not give a concordance for the following chapters: El Libro Primero (1549), chapters 1,30,32 and 50, and El Arte Tripharia, chapters 29 and 38. 42 Table 1. Concordance of the Chapters from Bermudo's Three Publications.

DECLARACION EL LIBRO PRIMERO EL ARTE TRIPHARIA BOOK I 1 1 2-18 3-19 19 & last sent. 20 49 BOOK II 1-12 1-12 13 14 14-15 2 at 9th sentence 16-29 15-28 BOOK III 1-2* 20-21 3-4" 22 6-8* 23-25 10-13* 26 5* 27 14* 28 16-18* % 19* 13 20-23 30 24* 31 25-26* 33 27* 34 28-30 35-37 31-32 38 33-35* 39 36-37 40-41 38-39 42 40-41 43-44 42-45 45 46-47 46 48-49 47-48 50 BOOK IV 7-12 32 21-22 29 25 30 37-39* 31-33 26* 34 35 35 40* 36 48 37 38 41* 39-40 4 3

Conclusions Spain was an active participant in the Renaissance, with her cultural ferment set in motion by Ferdinand and Isabella, and continued by Charles V. Not only did the arts advance, but so also did education. Statements in Bermudo's prologues reveal the circumstances surrounding his zeal for music, despite an apparently hostile attitude projected by the Observants. His providential illness enabled him to pursue the study of music on his own, ultimately leading him to publish three major treatises. A closer examination of those treatises discloses intricate relationships among them. El Libro Primero and El Arte Tripharia coincide in several respects, while it is also obvious that almost all the material from both was incorporated into the bulk of the Declaracidn. CHAPTER ni THE DECLARACION: ITS PURPOSE, LAYOUT AND PEDAGOGICAL INTENT

This chapter examines the Declaracidn carefully from three different perspectives: first, to discover the purpose it is intended to fulfill; second, to delineate its overall layout; and third to demonstrate its pedagogical approach adopted by Bermudo. An awareness of these particular perspectives will enable readers to formulate logical interpretations of pertinent sections of this treatise.

The Purpose of the Treatise: Some Retrospective Views The purpose of the Declaracidn has been misconstrued by many scholars. Some refer to it as an encyclopedia; some designate it as an instruction book, while still others consider it a purely theoretical treatise. None of these views is adequate in itself. In his book entitled Le mysticisme Espagnol au XVIe Siècle, Henri Collet acknowledges Bermudo's intellectual capabilities, and at the same time suggests that.

44 45 because of its encyclopedic nature, the Declaracidn tends to treat important questions lightly, and often it obscures them^ Thurston Dart, in his review of Kastner's facsimile edition of the Declaracidn, likewise recognizes the value of Bermudo's work by stating that the treatise is "quite important and tells us much of its period." At the same time. Dart also classifies it as an encyclopedia, describing it as a "useful, but rather rambling compendium."^ The Declaracidn is indeed a very comprehensive work dealing with musica practical composition, performance and musical instruments (keyboard instruments, vihuela and harp). In it, Bermudo specifically discusses how to sing, compose, play instruments, and intabulate for instruments. In essence, it is a comprehensive, theory-based instruction book. Bermudo thoroughly supplements his practical material with musica speculativa? The speculative content of this treatise involves the integration of ancient and medieval ideas with contemporary issues. References to ancient and medieval writers include Boethius, Pythagoras, Guido d'Arezzo, and Sts. Augustine, Gregory and Isidore. Bermudo also documents his work with contemporary writers, such as Glareanus, Gaffurius, Tinctoris and Ornithoparchus. Nan Cooke Carpenter, in Music in the Medieval and Renaissance Universities, recognizes that the Declaracidn combines both the practical and speculative aspects of music.^ She claims that it is an example of a new type of treatise that specialized in the problems of instrumental music.^ Carpenter also claims that these instructional treatises were written in the

^ Henri Collet, Le mysticisme Espagnol au XVIe Siècle, 217. 46 vernacular so that the authors could reach a larger audience than that represented by a strictly academic readership.

The Purpose of the Treatise According to Bermudo and Figueroa Bermudo explicitly limits the main goal of the Declaracidn in the prologue entitled 'Tor the reader." He intends to instruct the student in the art of intabulation and the playing of vocal polyphony on musical instruments, with no mention of technique (fingerings, ornamentation, etc.).^

The ultimate goal that I claim in my books, is that players will know how to intabulate, or set vocal polyphony on the instruments by understanding them. In my books, you will find all the necessary means for this goal. He asserts that he intends to create a useful, accessible tool comprised of related musical topics. His method will be to compile material from various practical and speculative sources, including his earlier publications, and to assemble it in a single tome. By doing this, he can present everything needed for instruction, and at the same time avoid unnecessary repetition of key explanations. Bermudo clarifies his intentions in these words:^

^Thurston Dart, Review, Music and Letters 39:392-3. ^Bermudo often uses the termsmusica theoretica and musica speculativa interchangeably. '*Nan Cook Carpenter,Music in the Medieval and Renaissance Universities, 221. ^Ibid., 326-7. The oldest source of this type was Sebastian Wirdun^s Musica getutscht. Similar treatises were written by Arnold Schlick (organ), and Oronce Fine (lute), and John Dowland (lute). 6ibid., folio +vi r. Para el lector...El fin ultimado que en mis libros pretendo: es, que entendiendo los tanedores los intrumentos: sepan cifrar, o poner canto de organo en ellos.. Y todos los medios que para este fin son menester: los hallareys en mis libros. Bermudo also discusses this goal at length on folios +v, r and +v, v. (Prefatory folios are numbered +i, r, +i, V, etc.) ^Ibid., folio +vi, v. Si cada libro imprimiera por si, fuera obra muy prolixa porque auia neeefiidad de repetir, no solamente sentencias: pero capitulos enteros: lo qual se euita imprimiendolo todo en un volumen y cuerpo. Todo quanto la materia se ha podido abreuiar: lo 47

If each book were printed by itself, each would be very prolix, because there would be a need to repeat not only sentences, but entire chapters. By printing them in a single volume, that problem is avoided. Whenever the material can be abbreviated, I have done it. In the same way that I am not being fastidious for the learned by using many words, I am also considering the need of beginners in music. Some say that I am prolix, and others say that I am obscure. I do not know how both claims can be compatible, especially taking this work into consideration. These statements indicate that Bermudo desires to make particular principles of music accessible to all musicians—learned, as well as beginners. His comprehensive intent is apparent here and in many other places in the Declaracidn. This predilection for comprehensive pedagogy will be discussed later in this chapter. Bernardino de Figueroa, a teacher and maestro de capilia at Granada, provides a similar witness to Bermudo's intentions in his "Letter of Recommendation" for the treatise. He acknowledges the role of the Declaracidn as one of instructing the student in the principles of singing and playing musical instruments, and also stresses the importance of incorporating musical theory into a work such as this. He begins by praising Bermudo for combining musica speculativa and musica practica into a single volume, and then gives two reasons why it is beneficial to do so. First, many learned musicians are so concerned with practical music that they tend to bypass the necessary theory. As a result, Figueroa fears that Spanish music suffers from errors, due to a lack of understanding of musical he hecho. De tal manera miro no dar fastidio a los doctos con las muchas palabras: que considère la neceGidad que üenen los principiantes en la musica. Algunos dizen, que soy prolixo, y otros obscure: y no se como amtws cosas se compadecen, mayormente tenicndo consideracion a la obra. 48 fundamentals. Bermudo's treatise provides the needed instruction in fundamentals. Figueroa states:®

One reason that men lack perfect knowledge they desire is that they do not understand the terms of science that the philosopher uses, and thus, they make errors by not knowing the truth. As a result, music in Spain is at the point of needing [musical] fundamentals. The most learned musicians deal only with practice, and do not correct the theory. When they see something written that they do not understand, they condemn it without waiting for a convincing reason as to why the things they create do not conform to musical principles. Figueroa's second reason reinforces the advantage of having an abundance of material at one's disposal in a single tome. The concepts necessary for good playing and singing would normally be found in several different books, but Bermudo reduces and consolidates this needed material. Figueroa adds:®

To understand the basics of music—both sung and played—one must combine many books and precepts, and then spend much time understanding it. The very reverend Father Fray Juan Bermudo of the Order of Saint Francis wanted to undertake the task of combining the material from many books, and reduce the obscurity of theory (along with many other new things that he has invented) to practice, so that topics which normally

®Ibid., folio +iv, r. (Epistola recomendatotia de la presente obra)...Una de las cosas que haze no saber los hombres perfectamente lo que dessean: es no entender los terminos de las sciencias: como lo dize el philosophe, y assi caen en errores, y no saben verdades: por lo qual la Musica en Espana ha venido a tanta necefiidad de fundamento, que los mas doctos solamente tractan de la practica, sin curar de la theorica, y quando veen algo escrito que no entienden: luego lo reprueuan, y no quieren esperar razon para conuencerse en cosas que hazen fuera de arte. ®Ibid., folio +iv, r. Y para auer de entender de rayz la musica, assi la que se can ta, como la que tahen; era menester junctar muchos libros, y muchos preceptores, y gastar mucho tiempo para entenderlo. Y el muy Reuerendo padre Fray luan Bermudo de la orden de sanct francisco ha querido tomar el trabajo en junctar todo lo de muchos libros, y reduzir a practica la obscuridad de la theorica, con otras cosas muchas nueuas que ha inuentado para que lo que en mucho tiempo y con difficultad se entendiera y supiera: se pueda entender y saber con solo este libro... 49 require a long time and effort to understand, can be understood and known with just this book... Clearly, Figueroa appreciates Bermudo's expertise and style of presentation.

The Layout of the Treatise The Declaracidn consists of a title page, eight folios of prologue (not numbered), five books, and a colophon containing final comments. Each book focuses on a particular aspect of music. Bermudo describes the contents of each book in two ways. In the prologue, a table of contents entitled: "Catalog of the books contained in the present volume and what is covered in each one," presents concise abstracts, and indicates the number of chapters within each book.^o Comparable but more detailed descriptions of the contents of each book appear at their respective beginnings. Book I, consisting of twenty chapters, is devoted to the praises of music. It is introduced by a general caption: "Here begins the first book of the Declaracidn de instrumentos musicales... and by a specific heading, "The Praises of Music" (Alabanças de Musica). The preface characterizes the purpose and contents in this way.^^

[Book I] presents, with skill and profundity, the praises of practical and theoretical music. [Here, music is presented]

^®Ibid., folio +i, v. Cathalogo de los libros contenidos en el presente volumen, y de que tracta cada uno dellos. ^^Ibid., folio i, r. Comiença el libro primero de la declaracion de los instrumentos musicales... Ail of the books begin in this manner, except Book IV which begins differently. Although the words appear in reverse order their meaning is precisely the same: El libro quarto de la declaracion de los instrumeri’tos musicales comiença...[The fourth book of the Deckracion de instrumentos musicales begins (here)...] ^^ibid., folio i. r. .. en el qual se tractan con muy grande artihcio, y profundidad las alabanças de la Musica practica, y theorica, con ciertas diuisiones, y determinaciones, y diffiniciones della, y otras cosas a esto anexas, y dependientes. The description given in the Table of Contents (folio +i, v), is similar, but less extensive. It provides the number of chapters contained in the book, which the preface does not supply. 50 with its true divisions, determinations and definitions, as well as with other matters related to it. As Chapter II of this dissertation indicates, Bermudo's religious order restricted the study and use of music. Only the singing and study of plainchant, used for the ultimate praises of God, were considered legitimate pursuits. Thus, the order frowned upon the study of general music theory. However, Bermudo feels it necessary to change this attitude, and to persuade his ecclesiastical community of the benefits of music by emphasizing the importance of all forms of music. In his "Argument for the first book" {Argumento del lihro primero), Bermudo offers reasons why all music should be valued.^3

In this first book, the author wishes to make the usefulness, delight and truth of music seen and understood, and to stress the obligation of understanding it that we, the ecclesiastics, have. May those who have grown fond of it, continue to grow even fonder, and may those not devoted to it, commit themselves to learning it. In the manner of an eisagogé, a work in the tradition of musica speculativa, this book probes the history and philosophy of music, and provides concise definitions of musical terms. Bermudo refers to many religious figures, in addition to lay personalities, evidently to make the study of music more fitting and proper in the eyes of his ecclesiastical brethren. The traditional theorists he invokes include Boethius, Pythagoras, Plato, Socrates, Quintilianus, and some Islamic authors as well. Among sacred authors, he mentions David, Saul, Samuel, Jesus Christ, Saints Matthew,

ï^lbid., folio i, r. El intento del author en este libro primero fue, que uista, y sabida la utilidad, deleyte, y honestidad de la musica, y la obligaciôn que los ecclesiasticos tenemos de saberla: a los afficionados a ella, afficionasse mas y a los indeuotos combidasse a la deprender. 51 Francis and Bernard, and some prominent church fathers, such as Augustine, Gregory, Jerome and Isidore. The second book proves to be "primer" for the beginning music student. It offers a series of elementary practical instructions for singing plainchant and polyphony, and for playing musical instruments. In the preface, Bermudo indicates the topics to be covered:

[Book II] introduces music for beginners; that is, the art of plainchant with the intonations of the psalms in all the modes, and other matters necessary for those beginners; also, the art of polyphony, and an understanding of the keyboard and all genres of vihuela. Although very practical, the presentation here is elementary, and too incomplete for those wishing to understand musical concepts in depth. Bermudo acknowledges the limitations of Book II and refers to expansions in later books:^^

In this second book, the author presents the first rudiments and elements of music for those who should know how to sing all kinds of song and play musical instruments. It focuses on primary principles, and is imperfect. By imitating nature, it begins with the imperfect, and ends with the perfect. Therefore, omissions by the author in this book, will be found most copiously covered in the third [book].

folio XX, V. ...en el qual se tracta introduciones en Musica para los principiantes en ella, conuiene a saber arte de canto llano con las entonaciones de los psalmos en todos los modos, y otras cosas necessarias a los dichos principiantes, arte de canto de organo, y para entender el monachordio, y todo genero de vihuela. The description of this Ixwk in the Table of Contents is very limited. The Spanish word, monacordio refers to a keyboard instrument (clavichord). See Sibyl Marcuse, Musical Instruments: A Comprehensive Dictionary, s.v., "monocordio," "manicorde," "manicordio," and "manicordion." ^^Ibid., folio XX, v . En este libro segundo pone el author los primeros rudimentos, y elementos de la Musica para los que han de saber cantar todo canto, y tafier instrumentos musicales. Tracta la materia en primeros principios, y aCi queda imperfecta: imitando a naturaleza, que comiença de lo imperfecto, y acaba en lo perfecto. Pues lo que en este libro faltare el author: en el tercere [sic] lo hallareys copiosifiimamente. 52 Book II deals with four main topics, dearly delineated by the following captions:

1)The art of plainchant 2)The art of polyphony^ ^ 3)The art of understanding the keyboard^® 4)The art of understanding all genres of vihuela^^ There are thirty-six chapters in Book n. Chapters 1-15 present the preliminary study of plainchant; Chapters 16-25 deal with principles of polyphony; Chapters 26-29 introduce the monachordio (keyboard instrument family); and the remaining chapters, 30-36, describe various vihuelas and rudiments for each. Book ni concentrates on the art of vocal music, both plainchant and polyphony. Bermudo describes the purpose and contents of the book in the preface.20

[Book III] discusses the methods of singing plainchant and polyphony, completely and accurately, with its great peculiarities, beauties and novelties never seen in music, and omits nothing on the genre of singing that has not already been said [in this tome]. When Bermudo states that this book "omits nothing...that has not already been said," he clearly indicates that this book is an elaboration of the discussion of rudiments in Book II. In a short paragraph dedicated to "the serious reader" (Para el piadoso lector), Bermudo indicates the difference

îÎbid., folio XX, v. Arte de canto llano. ^Îbid., folio xxiv,v. Arte de canto de organo. ^®Ibid., folio xxvi, v. Arte para entender el monachordio. îÎbid., folio xxvii, v. Arte de entender todo genero de vihuela. 20lbid., folio xxxi, r. .. en el qual se tracta el modo de satxr cantar profunda y ciertamente aCi canto llano, como de organo con grandes particularidades, primores, y nouedades nunca uistas en Musica, sin dexar cosa alguna en genero de cantar que no se diga. A similar description of Book III is found in the Table of Contents. 53 between the material of both books, while stressing the fact that Book III is directed at the experienced and knowledgeable singer. This paragraph is important because in it, Bermudo establishes a direct link between Book III and Chapters 1-25 of Book 11.^^

Although I may have presented the art of singing in the second book, and the title of this third book promises more of the same, there is a great difference in the material. In Book II, I introduced the primary elements and principles of music that are necessary for beginning to sing. In this book, I speak to those who want to be consummate in music. I will not repeat in this book what I said in Book II, unless it was incomplete. This third book will be almost a gloss of the second directed to the singer. There is nothing difficult or exquisite in the singing of polyphony or plainchant that will not become very clear and manifest for one who would understand this book. Book m is also divided, but into only two topics—those focusing on vocal music. Chapters 1-29 provide an extensive study of "The art of plainchant,"22 while Chapters 30-50 discuss "The art of polyphony."23 Knowing the relationship between Books II and III, leads one to expect the same connection between Books II and IV. Although Bermudo does not explicitly state that Book IV is intended as a continuation of parts of Book II, such an intent can be inferred from the preface to Book rV;24

2^Ibid., folio xxxi, r. Aunque en el libro segundo aya tractado el arte de cantar, y el titulo de este libro tercero promets lo mesmo: ay gran différencia de la materia de ambos. En aquel tracte los primeros elementos de la Musica, los principios para començar a cantar: y en este hablare para los que quisieren ser consumados en Musica. Lo que alii dixe: en este no repetire, sino fuere compelido. Sera este libro tercero quasi glosa del segundo en lo que tocare al cantar. No ay difficultad, o primor afii en canto de organo, como en canto llano que no sea muy claro y manifiesto, al que este libro entendiere. This short paragraph functions in the same manner as the Argumento del libro segundo. 22ibid., folio xxi, r. Arte de canto llano This section contains headings employing the same title . 23lbid., folio xlvii, v. Arte de canto de organo The headings are used in the same manner here. 24ibid., folio Ix, r. ... en el qual se tracta el modo de taner profundissima y ciertamente todo genero de instrumentos de tecla y cuerda con grandes particularidades, nouedades, y secretos 54

[Book IV] presents the method of playing all genres of keyboard and stringed instruments completely and accurately. It [the method] is described with craft and clarity, and displays the great peculiarities, novelties and secrets. This book begins with understanding and playing the organ [emphasis added]. The implication here is that the information in Book IV is also a detailed expansion of the fundamentals in Book II, Chapters 26-36. The instructions in this book center on the two types of musical instruments: keyboard and stringed instruments. Moreover, there is a similarity of wording in the prefaces to Books III and IV. A comparison demonstrates identical terminology in both. He employs the same adverbs: "completely and accurately," and similarly describes the contents with the phrase, "displays the great peculiarities, novelties and secrets." In Book m 's preface, this same phrase appears with one change—"beauties" instead of "secrets." Book IV is divided in the same manner as Book III. Of its ninety-three chapters, numbers 1-53 are dedicated to the keyboard, while 54-92 deal with the stringed instruments, subdivided into two types—fretted and non fretted. Chapters 54-86 focus on the vihuela; while Chapters 87-92 introduce and discuss the harp briefly. Chapter 93 concludes Book IV with an examination of "five common questions on music." The topics covered deal with the fundamentals of music theory and how they relate to musical instruments in general.25 puestos en artificio, y claridad, y primero de entender y taner el organo. Bermudo makes similar statements in the Table of Contents. 25ibid., folio cxiii, r. "De cinco preguntas communes en Musica. " Oddly, the heading on this folio returns to: "De taner el organo," The folio itself has been numbered twice, both times incorrectly. First as "folio cxxi," and then as "folio cxii." It should read "cxiii." 55 Book IV, as the preface indicates, begins with the study of the keyboard: "And [this book] begins with the understanding and playing of the organ [keyboard]." This material is also identified by the heading, "On playing the organ" (De taner el organo), printed on every folio. The section on the vihuela is clearly marked with the words, "The art of the vihuela begins [here]" (Comiença el arte de la vihuela)?-^ There is a lengthy introduction, "For the reader" (Para el le c to r ), and each folio in the section displays the heading, "On playing [the] vihuela" (De tafier vihuela). The harp is introduced in Book IV by the subtitle, "The art of understanding and playing the harp" (Arte de entender y tafier la harpa)?-^ The only other markings that separate this material from the rest are the headers: "On playing the harp" (De taner harpa). There is no prefatory material for this section. Chapter 93 seems to stand apart from the other material in this book. It is assigned the same folio heading as that used for the organ (On playing the organ), but this final chapter to Book IV focuses on "five common questions in music." They are:

1. The mixing of species of diatessaron and diapente in a mode 2. Consonance vs. dissonance 3. Art vs. the ear 4. The use of the ear to tune—for instrument builders 5. The rule of the diapason These questions deal with important theoretical and philosophical concepts as they pertain to musical instruments. They indicate that Bermudo was aware of the discrepancies betweenmwsfcfl practica and musica

26lbid., folio xc, r. 27lbid., folio xc, r. 28ibid., folio xcv, v. 56 speculativa. He recognizes that the changes often made in practice, eventually are allowed in theory, especially if they sound good. But, Bermudo formulates no general theoretical principle at this point. This final chapter is followed by an appended section of original compositions for keyboard (organ). In a short preface, "For the reader" (Para el lector), Bermudo explains that they are unique because he wrote them specifically for the keyboard; they are not transcriptions of vocal music. Consequently, he feels it necessary to tell the reader how to read the accidentals, and stipulates that the compositions be played as notated.^^

I am well aware that players are able to take advantage of an abundance of good music in Spain. Thus, there was no need for my own [compositions]. But, I have been pestered by friends to publish some music composed specifically for playing. Particularly, friends from the Indies [New World] have implored me to do it. It seemed a justifiable thing to do. I am saying that this music was composed for playing, and not for singing. Therefore, it must be played just as it is notated, because if it is transposed, it may not fit the keys, or it may not fit the hands. The marks [accidentals] for the black keys are given. Any note that would have such a mark is played on the black key, and those without are not, although they may have the same letter name. Obviously, Book IV comprises many topics dealing with instrumental music. The breakdown of this book appears in Figure 3.

29ibid., folio cxiii, r. Bien tengo entendido auer en Espaüa mucha y buena musica de la qual se pueden los taüedores aprouechar, y assi no auia necessidad de la mia: pero he sido importunado de amigos, que imprimiesse alguna hecha aposta para taner, mayormente que de indias me han rogado por ella; y parecio me cosa justa hazerlo. Digo esta musica ser hecha para tafier, y no para cantar, y que se ha de tafier por donde va puntada: porque amudar se una vez faltaran teclas, y otra vez manos. Las sefiales de teclas ncgras lleua puestas. El punto que tuuiere serial se poma en la tecla negra, y el otro no: aunque esten en un signo. 57

From the evidence above, it can be seen that the elementary material of Book n feeds directly into Books HI and IV. Detailed information on vocal music (plainchant and polyphony) appears in Book III, while instrumental music (keyboard, vihuela and harp) is covered in Book IV. Thus, the expansion from Book II may be expressed in the following fashion.

BOOK II VOCAL INSTRUMENTAL -plainchant -keyboard -polyphony -vihuela

r 1

BOOK 111 BOOK IV VOCAL INSTRUMENTAL -plainchant -keyboard -polyphony -vihuela -harp -5 common questions -original compositions

Figure 3. The Expansion of Book II into Books HI and IV.

Book V is concerned with the composition of vocal music (plainchant and polyphony), and should be considered an extension of Book III. Bermudo delineates its contents in the preface.^°

30lbid., folio cxxi, r. ...en el qual hallareys las propriedades y effectos de los modos, arte de componer canto llano, de hechar contrapunto, y componer canto de organo, y vereys practicados los primores quo los cantores han hecho, y puestas las causas dellos, y dedarado todo por sus exemplos con artificio profundifiimo, y gran certidumbre. In the Table of Contents, Bermudo describes the contents in the same manner, using almost the same phraseology (folio +i, v). 58 [In Book V], you will find the properties and effects of the modes, the art of composing plainchant, and the art of improvising and composing polyphony. You will see those beautiful things that composers have done, and the reasons for them. Everything will be declared in the most thorough and accurate way by using examples. In addition. Book V has the distinction of being prefaced by a lengthy commendation by Christobal de Morales, entitled "Letter from the illustrious musician. Morales" (Epistola del egregio musico Morales). Morales commends Bennudo's work and exhorts the reader to study and value the importance of good composition:^^ Read this book alertly and with care, and you will find in it all that you can desire on composition. Theory is embedded in practice, and practice runs conjunctly with theory. Until now we have not seen this [combination] in our Spain. Consequently, the practical musicians are unable to say truthfully that theory is contrary to practice. Padre Fray Juan Bermudo shows so excellently (not only in this book on composition, but in all his works) both sciences in consonance and proportion. Stevenson states in his book, Juan Bermudo, that the Declaracidn is the only printed Spanish theoretical work that contains a signed testimonial by such an eminent composer. ^2

31lbid., folio cxx, v. Leed con auiso y cuydado este libre: y hallareys en el todo lo que en composicion podeys defiear. Theorica engastada en practica, y la practica corriefie junctamente con la theorica: hasta ahora en nuestra Espaha no auemos visto. No pueden pues con verdad dezir los musicos practicos ser la theorica contraria a la practica: pues que tan excelentemente muestra el padre fray luan Bermudo (no tan solamente en este libro de composicion, sino en todas sus obras) venir ambas sciencias a consonancia y proporcion. Morales' letter is dated 155C. There is some question as to which publication Morales was actually commending, since he died in 1553. 32stevenson, ]uan Bermudo, 60-1. Stevenson also notes that this letter survives as Morales's only known bit of published prose. Morales was the only first-rate Renaissance composer to give his stamp of approval to such a theoretical treatise. Theorists, such as Glareanus, Zarlino, Artusi, Zacconi, and Morley all "waited in vain for written testimonials from any of the various contemporary composers whose works they professed to admire most enthusiastically." 59 Bermudo's Unpublished Books Although only five books were published in the Declaracidn, Bermudo promised at least two more. His many prefatory references imply that these additional books are contained within this volume. However, on the last folio (colophon), he informs his readers of his intention to forego publishing them until a later date. Here, Books VI and VU are mentioned together in a final letter to the reader, located on the last folio of the treatise, entitled, "The author to the judicious musican" (El author al cudicioso musico). Bermudo clarifies why the sixth and seventh books must be published apart from the other five. He apologizes for their absence and explains why Book VI is excluded from the present volume, although it is specifically referred to on the title page and in other prefatory material;33

Since I have promised it many times, it would be an appropriate matter to print the sixth book in this volume, and I would not have promised it, if I had not seen the need to cleanse Spanish music of some of the barbarisms...! will explain the two chief reasons, although there are many, why it [Book VI] will not be published. The first reason: to give time to the writers on music to look over their works, and especially to emend them. And if they do not do this, then they cannot justifiably complain that I did not warn them first. Therefore, let them consider this a brotherly admonition.

33Bermudo, Declaradôn, folio cxlii, r. Cosa justa fuera (pues que muchas vezes lo auia prometido) imprimir en este volumen el libro sexto, y si no lo vuiera prometido, mirando la necessidad que del auia para quitar en Espafia algunos barbarismes en musica,.. .Y aunque muchas causas ay para que ahora no saliesse: las dos potiGimas explicare. Es la primera, para dar tiempo a los escriptores en Musica de mirar sus obras de proposito, y las enmienden. Y si esto no hazen: no se quexaran de mi con razon, diziendo que primero no les amoneste. Tengan pues esto por amonestacion fratema. Es la segunda, la falta y carisda del papel, que subio tanto, que en otro tiempo costaua la tercera parte menos el impreâo: que ahora lo bianco. Flaziendo a Dios en auiendo abundancia de papel se imprimira: y libro es que por si puede ser impresso. Quanto mas que auiendo copia de limosna se imprimira el septimo libro con el sexto, y entretanto gozad de mis vigilias y trabajos puestos en estos cincos libros. Rogad a Dios (si con mi vida es seruido) me la de para concluyr y acabar los dos libros que por imprimir quedan. 60 The second [reason]: the scarcity of paper. The cost of paper has risen so much that previously, the printing of a third of the book cost less than the plain blank pages cost now. When there is an abundance of paper, thanks be to God, it will be printed. The [sixth] book will be able to be printed by itself. However, if there is an abundance of additional alms, the seventh book will be printed along with the sixth. Meanwhile, enjoy my vigilance and work already placed in these five books. Pray to God (if He is to be served with my life), that He may grant me enough life to conclude and finish the two books that remain to be printed.

References to the Sixth Book On the title page, Bermudo clearly indicates that a Table of Contents on the following folio will describe six books:^'^

[Here] begins the book called Declaracidn de instrumentos musicales...wTitten by the most reverend father. Fray Juan Bermudo of the Minorite Order. In it, you will find everything that you wish to know about music. The contents of the six books will be seen on the following page... [emphasis added] In the Table of Contents which follows, Bermudo delineates the contents of Book VI:35

In the sixth book, I compiled some errors of music by those who wrote on this subject in our maternal language. I confuted them sufficiently, and demonstrated the truth. I divided it into four tractates. After those, I

34ibid., folio +i, r. (Title page) Comiença el libro llamado declaradôn de instrumentos musicales,.. .compuesto por el muy reuerendo padre fray Juan Bermudo de la orden de los menores: en el qua] hallaran todo lo que en musica dessearen, y contiene seys libros: segun en la pagina siguiente se vera... 35lbid., folio +i, v. En el sexto libro copile algunos errores de Musica, de los que en esta facultad escriuieron en nuestro matemo lenguaje, y sufficientemente los confute, y ensefie la verdad y lo diuido por tractados, y contiene quatro: en fin de los quales hago otros dos, en el uno hablo de los generos de Musica, y en otro pongo el modo de tafier mis instrumentos, y ay cosas nueuas en todas seys tractados: espedalmente de affinadon de los instrumentos. 61 am creating another two [tractates]. In one, I speak of the genera of music, and in the other I place the method of playing my instruments. There are new things in all six tractates, especially on the tuning of the instruments. Notice the use of the past tense when describing the first four tractates of the sixth book. It implies that these were already finished. Likewise, the present tense in describing the remaining two tractates suggests that these were not yet finished, but only in progress.36 In any case, the fact that he was able to list the contents of Book VI, suggests that it was partially, or even entirely, written at the time of publication. However, no trace of Books VI and Vn has been found.^^ References elsewhere, in a number of places in the preliminary material, suggest that the sixth book is included in this volume. In the first reference, Bermudo advises the reader of the need to study "all six books" in order to understand music completely.^ In the second, he informs the reader of the possibility of finding more complicated concepts on the subject of vocal music in selected "tractates" of Book VI.^^ In the third, he discusses the apparent discrepancies between information in Book IV and Book VI.

^^The use of present tense here can be taken literally to represent action taking place in the present. But, it also can be used to imply a future action. ^^Stevenson, The New Grove, 2:611-12. Bermudo is reported to have died around 1565, and there is no evidence of any further writing on his part. ^Berm udo, Declaradôn, folio +vi, v. Luego el cantante que de mis libros vuiere de gozar: ted os los seys libros (que hablan de Musica) deue tener. FUes si los tales que defiean ser sabios en la Musica han menester todos seys libros. [Then the musician who wishes to enjoy my books, must possess all six books (that speak of music). Thus, if those musicians desire to be wise in music, they need all six books.l 3®rbid., folio +vii, r. Quando en mis libros leyeren alguna materia de canto llano, o de organo, y quisieren en ella ver mayores cosas; miren los quatro tractados primeros del hbro sexto... [When they would read some material on plainchant or of polyphony in my books, and they would want to see more things, let them look at the first four tractates of the sixth book...]. 62

He cautions the reader that the apparent discrepancies are baseless, and that there are no contradictions in his theories.^® Additional references to Book VI appear in the text of the treatise. Bermudo refers to Book VI while discussing the keyboard in Book H. He indicates the need to develop principles relevant to these instruments, especially the keyboard instruments he aspires to invent:'*^

Everything said above [about the monachordio] is to be understood on the instruments constructed up to now, but on those that I am making, it is another matter. Other rules are necessary, and these will be found in the sixth tractate of the sixth book. Another reference to the sixth book is found in Book HI, under the topic of plainchant, where Bermudo indicates his intention to refute some of the modal theories proposed by his fellow countryman, Alonson E s p a n o n ; 4 2

If the reader seeks more [details] in this case, he will find it in the sixth book—the first tractate, chapter 3, and the third tractate, chapter 4, as a refutation of Alonso Espanon. In Book rv, Bermudo again informs that reader that he is placing more discussion on the keyboard in the sixth book;43

^Ibid., folio +vii, r. Afii tracto de la vihuela, y organos y pongo muchos preceptos en el libro quarto: y en fin del dicho libro, y en el tratado ultimo del sexto libro escriuo en contrario. Consyderando el tiempo, y para quien scriuo, y arüficio de los instrumentos: no ay contradicion en mi doctrina...[Thus, I deal with the vihuela and organ, and present many precepts in the fourth book, and at the end of that book [fourth]. In the last tractate of the sixth book, I write to the contrary. Considering the time, for whom I am writing, and construction of the instruments, tiiere is no contradiction in my doctrine... ]. '^'ibid., folio xxvii, r. Todo lo sobredicho se entiende en los instrumentos hasta ahora hechos: porque en los que yo hago otra cosa es, y otras reglas son menester, y se hallaran en el tractado sexto del sexto libro. ^ Ib id ., folio XXXvi, v. Lo que mas el lector en este caso deCeare: lo hallara en el libro sexto en el tractado primero capitulo tercero y en el tractado tercero capitule quarto contra Alonso espanon. ^^Ibid., folio Ixxxix, v. Para que los tafiedores tengan monachordio en que se exerciten en este modo primero por Ffaut y en otros: en fin del tractado sexto pongo un monachordio nueuo. 63

So that players may have a manichord on which they can play the first mode on Ffaut and on others. I am adchng a new monachordio at the end of the sixth tractate. Although this passage does not explicitly state that this material is found in the sixth book, it is clear from his description in the Table of Contents that the last tractate of Book VI was to be devoted to the tuning of his own newly created instruments—namely keyboard instruments.

References to the Seventh Book Bermudo alludes to his seventh book in at least four places. In the "First Prologue for the Serious Reader"(Pro/ogo primero para el piadoso lector), he writes: "They will obtain the other great beauties and secrets in the discourse of the seven books of the Declaracidn." In a discussion on the harp in Book IV, he explicitly states that "the way the harp will be constructed remains for the seventh book."45 The language here implies that the book had not been written, but that he did have its contents in mind. Again, in Book IV, Chapter 93, Bermudo clearly refers to a seventh book in his discussion of the "five common questions on music." He states that "every instrument has an accurate division of the diapason. You find

Bermudo's intentions, here are unclear, since he gives no specific details Therefore, it is difficult to determine whether he is referring to an inventai keyboard, such as Vicentino's arcicembalo (1555), or to new systems of tuning for the keyboard—meantone temperament or just intonation. 44lbid., folio +5, v. ...y otros grandes primores, y secretos que en el discurso de siete libros d e la sobredicha declaracion alcançaran. 45ibid., folio cxii, r. El como se hara la harpa queda para el septimo libro. The use of the future tense here implies that Book VII will appear later, and Bermudo's selection of the word "para" (for) seems to indicate that this topic is reserved for that proposed book, but that it has not been written yet. Moreover, only Book VI is indicated on the title page, while references to Book VII appear only in the running text. 64 this proven in the seventh book."^^ Another reference to Book VII is found in the fifth book, in a discussion pertaining to "perfect consonances." Here, Bermudo gives the reader a further indication of what to expect in the proposed book:^^

[There] I assume that the major third that we play and sing does not consist of two sesquioctaves, nor of a sesquiquarta as organists claim. I will prove it in the seventh book.

The Interconnection of the Books The interconnection of the books in the Declaradôn can perhaps best be appreciated through a schematic presentation, as in Figure 4. As was shown earlier. Book II forms the basis for Books III and IV. Two of the topics from Book n, "plainchant" and "polyphony,"are expanded in Book m. Elaborations of the remaining two topics, keyboard and stringed instruments, result in a very lengthy Book IV. Since Book V delves into the actual composition of plainchant and polyphony, it is directly related to III.

^Ibid., folio cxlii, v. Todo instrumento tiene cuenta de diapafion. Esta halkreys prouada en el libo [sic] septimo. 47jbid., folio cxxx, y. Presupongo, que la tercera mayor que tafiemos y cantamos no son dos sequioctauas, ni una sesquiquarta, como los organistas pretenden: y en el libro septimo prouare. The topic of "consonances" is covered extensively in Book III. The tuning implications in this passage will be discussed in Chapter V, below. 65 BOOK I Praises of Music

BOOK II Musical Rudiments Vocal Instrumental -plainchant -keyboard -polyphony -vihuela

BOOK III BOOK IV Vocal Music Instrumental Music -plainchant -keyboard -polyphony -vihuela -harp -5 common questions -original compositions

BOOK V Composition -plainchant -polyphony

BOO K VI* Vocal Music Instrumental Music -tractate 1 -tractate 5 -tractate 2 -tractate 6 -tractate 3 -tractate 4

BOOK VII" "never published Instrumental Music

Figure 4. The Layout of the Declaracidn.

Judging from the information divulged in the aforementioned references to Books VI and VII, it is reasonable to assume that they would have been further elaborations of Books HI and IV. The first four tractates of 66 Book VI would develop material from Book UI, while the other two tractates would deal with concepts previously treated in Book IV. Book VU, which would have dealt with theories of tuning and temperament for the musical instruments (keyboard and harp), would also be related to Book IV.

Bermudo's Pedagogical Method In order to understand the layout of this treatise, Bermudo's pedagogical method must be examined. The recurrence in later books of themes and topics treated in earlier ones has led some to question the very existence of a rational organization in Bermudo's treatise. The judgment of several writers (dted earlier) that the Declaracidn is, in effect, a kind of "encyclopedia" or "rambling compendium" certainly does not support the notion that Bermudo had a pedagogical method in mind when he wrote the treatise. These assessments are incorrect, however, because a careful examination of the whole treatise enables one to discern the author's underlying pedagogical plan. In the "First Prologue for the Serious Reader," Bermudo praises good teaching, and discusses at length the need for teachers to provide students with as much knowledge as possible.'*®

Some teachers think erroneously, that when they convey the beauties [of music] to their students, they should omit knowledge. By doing this, they take away the benefits. Knowledge is of such a condition that the more it is transmitted, the more it enriches and pours forth like a

'*®Ibid., folio +4, v. Piensan algunas maestros (no sin falta de error) que communicar los primores a sus discipulos: ha de faltar a ellos la sdencia, y les han de quitar el partido. Las sciencias son de tal condicion, que quanto mas se communican: mas se augmentan y nrtana, a manera de fuente. Nunca secareys la Puente, pwr mucha agua que saqueys del lio, o del arroyo. Fuente es el entiendiirdento humano, y mana sdencia: no temas secarse, por communcar los arroyos, que del salen. 67 fountain. You will never dry up the fountain by whatever amount of water you extract from the river or stream. The human mind is a fountain and it pours forth knowledge. Do not fear that it will become dried up as the small rivulets branch off and communicate [further]. Bermudo is very conscious of his readership. He stipulates that the material is suitable for students at various levels of study. In the "Second Prologue for the Serious Reader," he demonstrates his sensitivity for beginners as well as advanced students. He states: "In the same way that I do not bore the erudite with wordiness, I also consider the needs of beginners in music." Consequently, certain concepts are described with only a beginner in mind. This material is sufficient for the elementary level, and may seem quite incomplete to an accomplished musician. But, Bermudo indicates that he intends to expand upon those concepts in later chapters so that the learned musician may also benefit. In the same prologue, he provides this key statement: "Some of the words that I use at the outset for beginners, I rebuke in the end for the perfect musicians."^® He also declares that some topics are not intended for everyone, but are reserved for certain readers:^^

I know very well that everything [in this volume] is not appropriate for everyone. I know that there are matters for only the curious ones and friends of the compass, and for that rare one who will understand them, I am writing, [emphasis added]

folio +6, v. De tal manera miro no dar fastidio a los doctos con las muchas palabras: que considero la neceHidad que tiencn los principiantes en la musica. ^Ibid., folio +7, r. Prologo segundo para el piadoso lector....De algunas palabras uso alos principios para los principiantes, que en fin las repiuevo para los perfectos musicos. ^^Ibid., folio +7, r. Bien se, que todo no es para todos, porque ay cosas para solos los curiosos, y amigos del compas, y estas para solo uno que las ha de entender: las escriuo. 68

Bermudo's Instruction for the Musical Instruments Bermudo's pedagogical intent is clearly reflected in the material on musical instruments in the Declaracidn, especially that of the vihuela. His discussion of both keyboard and stringed instruments is also exemplary in this respect. In this dissertation, we shall consider Bermudo's "layered" treatment of the vihuela in detail, since it is typical of his pedagogical approach to all the instruments—keyboard, harp and vihuela.

Elementary Vihuela Instruction The student first encounters material on stringed instruments in Book n. Chapters 30-36. This short section gives basic, practical information for the beginning student. Bermudo introduces the various stringed instruments that he considers vihuelas. These instruments are presented in a fixed order that recurs in later coverage of the vihuela: 6-course vihuela, 7-course vihuela, 4-course guitar, 5-course guitar, bandurria and rabel. (See Figure 5.) Bermudo's elementary treatment of the vihuela is divided into seven main topics: 1) the purpose of the section, paired with advice for beginners; 2) a description of each instrument, in which only common dispositions of strings are given; 3) the exposition of an elementary system of forming intervals, in which one fret equals a semitone, two frets equal a whole tone, three frets equal a minor third, etc.; 4) a tuning method for begiimers in which the student is expected to simply match octaves;®^ 5) an elementary

52Bermudo eliminates the 7-course vihuela and the 5-course guitar from this discussion, because his predilection for simplicity and details prompts him to consolidate wherever possible. For example, he simply explains the 7-course vihuela in terms of the 6-course vihuela by saying that "whatever one does for the 6-course instrument is likewise viable for the 7-course instrument." He similarly consolidates the discussion of the guitars. 69 discussion of movable frets and pitch variability; 6) an introductory discussion of good vihuelists and their music; and 7) a series of questions and answers examining various aspects of the vihuela. These questions focus on; the origins of the vihuela, the reason for the dispositions of the strings, the number of frets a vihuela should have, whether the bandurria and rabel have frets or not, the use of a capo, and the concept of variant tuning (scordatura).

1 Purpose Introduction to Fundamentals 2 Disposition of Strings: 6-course vihuela G-C-F-a-d-g / G-C-F-b-d-g 7-course vihuela G-C-F-adg-c 4-course guitar G-C-E-a / F-C-E-a 5-course guitar GCE-ad bandurria G-C-g / G-D-g rat)el G-D-a

3 Formation of intervals 1 fret = 1 semitone, 2 frets = whole tone, 3 frets= minor third, etc. 4 Tuning methods: by octaves, for beginners 6-course vihuela 4-course guitar bandurria and rabel

5 Movable frets and valid for all fretted instruments variable pitch 6 Good vihuelists & their they are models for good musician music ship 7 Questions on musical -origins of the vihuela instruments -reason for disposition of strings -number of frets used -frets vs. no frets on the bandurria and rabel -use of the "capo" -use and methods of variant tunings

Figure 5. Summary of Elementary Vihuela Instruction, Book II, Chapters 30- 36. 70 Figure 5 displays the the seven main topics, along with their subtopics in the left hand column. They appear in their order of presentation. The details described in the right hand column make it obvious that the topics covered in this section lack the thoroughness of coverage found in subsequent material.

Intermediate Vihuela Instruction The next section on the vihuela is located in Book IV, Chapters 54-74. As indicated earlier. Book IV is intended to be an expansion of Book II. The material is divided into four main topics, as shown in Figure 6. They are: 1) the purpose of the section as it is delineated in the prologue; 2) an extensive description of each instrument; 3) suggested methods for playing various fretted string instruments together; and 4) an exposition of the principles of intabulation. At a glance, one can see that much more information is divulged here than in the Elementary section. Indeed, Bermudo repeatedly alludes to these expansions in the Elementary section:53

He who needs more information, should examine the general prologue to the entire work [table of contents], and other advice which is found in various parts of these books, especially in the fourth book where I deal with this particular material. Although many more details are provided here, the order of the instruments is still the same: 6-course vihuela, 7-course vihuela, 4-course guitar, 5-course guitar, bandurria and rabel. As Figure 6 shows, each instrument is discussed along with several related topics. This discussion

^^ibid., folio xxviii . Tv El que tuuiere necefiidad de mayor mfonin.acion: vea el prologo general de toda la obra, y otros auisos que en diverses partes en estos libros hallara, specialmente en el libro quarto donde de proposito tracto la presente materia. 71 includes the following features: initial templates in tuning methods for experienced players requiring the use of fifths and unisons; description of range; principles of variant tuning(scordflfwrfl); placement of "clefs" for intabulation; and additional templates for other pitches of the gamut. In a separate discussion that follows, Bermudo explains how various fretted stringed instruments can perform together. This leads directly into a large discourse on intabulation, and the section culminates with two examples of intabulation for the vihuela.^s In fact, the goal of this entire section is preparation for intabulating. For reasons of expediency, the material outlined in Figure 6 will be referred to in the future as "Intermediate" vihuela instruction.

^T h e term templates here refers to the diagrams Bermudo supplies that show the letter names for each string and fret. They are explained in more detail in Chapters IV, V, and VI below. SSrbid., folio ci, r. and d , v. The first example is for the ( course vihuela in Are and the second is for Bermudo's own 7-course vihuela (on gamaut), with each course corresponding to Guidonian deduciones. 72 1 Purpose Preparation for intabulation 2 The instruments: 6-course vihuela G-C-F-a-d-g / G-b-D-g-b-d tuning methods by 5th and unison range clefs variant tuning additional templates

7-course vihuela G-C-F-a-d-g-c / G-D-g-d-g-d-g & G-D-g-b-f#-b-d tuning method by unison and octave (same topics as above)

4-course guitar G-C-E-a / F-C-E-a / G-C-D-g (ancient) tuning method by unison, etc. (same topics as above) requintada

5-course guitar G-Dgbd tuning method by unison and octave range

bandurria and rabrei G-D-a / G-C-g (ancient) G-C-F / a-d-g (new) tuning method by unison and octave (same topics as above) 3 Method playing various fretted instruments together 4 Intabulation explanation of figures various methods musical examples

Figure 6. Summary of Intermediate Vihuela Instruction, Book IV, Chapters 54-74.

Advanced Vihuela Instruction Bermudo's advanced treatment of the vihuela follows immediately after the Intermediate section, in Book IV, Chapters 75-86. This section centers on fret placement and performance practices. It is marked by a separate preface, different from the one marking the Intermediate level. 73 Entitled "For the curious musician" (Para el curioso tanedor), this preface indicates the goal of this section—fret placement, and its proper implementation, using a compass rather than the ear.^^

What remains for curious musicians is the craft of placing the frets on the vihuela by means of a compass. It is the most perfect, since the compass is truer than the ear...What I am presently claiming is that the compass may be used to place the frets, so that those who are not musicians can place them with facility and certainty. Then the vihuela will be more [nearly] perfect. Bermudo has emphasized the importance of this section to the more experienced student, by giving it its own preface, thereby distinguishing it

from the previous material.57 Although it is difficult to subdivide this section as neatly as the Intermediate material, it can be broken into five main topic areas as shown in Figure 7. They are: 1) a preface that delineates the purpose of the section; 2) three methods of Pythagorean fret placement demonstrated on the vihuela, but intended for all the stringed instruments; 3) a cursory discussion of instrument construction; 4) a short discourse on how to time two vihuelas together, and 5) a proposed system of fret placement that approximates equal temperament. Within these areas, Bermudo also discusses string division in terms of mathematical ratios; problems resulting from improper fret placement; and solutions to these problems. The highly detailed and complex nature of the material justifies our labeling it as "Advanced."

folio d. v. Resta para los musicos curiousos dar artifido de poner los trastes por compas en la vihuela: y quedara mas perfecta, por ser mas derto el compas, que el oydo.. .Lo que al presente pretendo, es dar compas con que se pongan los trastes: para que los que no son musicos con fadlidad, y certidumbre los pongan, y afii quedara la vihuela mas perfecta. S^This marked separation of instruction levels is not as clear in the keyboard or harp material. 74 As noted earlier, Bermudo follows a certain order of presentation of the instruments. A similar order is found here, however, with some exceptions. First, he incorporates his own theoretical instruments, a 7-course vihuela and a 5-course guitar. Second, he interjects discussions which focus on two loosely related topics: construction of the instruments, and a method of tuning two vihuelas to each other by using sympathetic vibration. Since these two topics are not as fully developed as the other material in the section, they are shown with asterisks in Figure 7. Third, he modifies the precise order of instruments in order to present a series of systematic methods of fret placement. In keeping with his pedagogical intent, Bermudo begins with the easiest method of fret placement and concludes with the most complex. In these four methods, he uses the 6-course vihuela for the first and third methods of fret placement (both Pythagorean), and the 7-course vihuela (Bermudo's theoretical disposition) for the second method (Pythagorean) and the fourth (approximate equal temperament). The first method, shown in Figure 7, is a rather primitive method of Pythagorean fret placement. It is done partially with the compass (calipers) and partially by ear, and is very simple to execute. The second and third methods require much more precision that only the compass can give. The fourth, appearing in Book IV, Chapter 86, focuses on a method that Bermudo considers to be a new and even more complex scheme for fret placement. Here, Bermudo departs from the Pythagorean system and sets up a tuning scheme that is more complicated to construct, but more versatile for 75 performance. This last method is the most advanced because it approximates equal temperament, and requires comma division.

1 Purpose Preparation for fret placement 2 The instruments: 6-course vihuela Pythagorean fret placement for beginners

7-course vihuela G-C-F-g-c-f-g (theoretical invention) Pythagorean fret placement tuning method by unison, etc. (same as Intermediate Section) movable frets faults and remedies

6-course vihuela Pythagorean fret placement for 7 vihuela templates movable frets and faults vihuela template with fixed notes

•Instrument construction few details (2 continued) 6-course guitar F-G-C-f-g / G-C-F-g-c little description (use principles from hypothetical 7-course)

4-course guitar Pythagorean fret placement double first fret (use principles from 6-course)

bandurria and rabel Pythagorean fret placement (use principles from 6-course)

•Tuning method tuning two vihuelas to each other use of sympathetic vibration (2 continued) approximate equal temperament 7-course vitiuela (Bermudo's theoretical invention)

Figure 7. Summary of Advanced Vihuela Instruction, Book IV, Chapters 75- 86 . 76 Conclusions A comparison of the three sections of vihuela discussion. Elementary, Intermediate and Advanced, reveals that some topics are covered more than once, but usually in different ways to accommodate the appropriate level of the intended reader. The information presented in the Elementary section is not nearly as elegant or detailed as that of the two subsequent sections. Bermudo's thorough and systematic approach becomes apparent when one recognizes his sequential technique, and pursues the topics linearly. A comparable "layering" of the sequential material on the keyboard instruments and the harp is also apparent when one examines specific sections of the Declaradôn. Obviously, the recognition of Bermudo's pedagogical intent and method are essential to a proper understanding of his treatise. He has considered all pedagogical needs, from elementary to advanced, in his treatise. Short and simple introductions for beginners soon lead to highly refined techniques for advanced musicians. If words or phrases are taken out of context, as they have been by some scholars, errors and problems in interpretation inevitably will arise. CHAPTER IV BERMUDO'S VIHUELAS: DESCRIPTION AND DOCUMENTATION OF THE INSTRUMENTS AND THEIR TUNINGS

Bermudo's description of the vihuela and its related instruments in the Declaracidn requires a thorough examination. This investigation begins with a brief discussion the term vihuela, followed by Bermudo's description of each instrument. The discussions focus on the string dispositions for each instrument, and on the templates specified by Bermudo for intabulation. Since Bermudo structures his presentation to fit his pedagogical intent, the details about each instrument must be compiled from the three levels of study—Elementary, Intermediate and Advanced—and interpreted in this context.

Vihuela: the Term and its Usage At the time of Bermudo, a vihuela was, in simplest terms, a generic string instrument with a neck and a resonator. It was the terminological equivalent, in Spanish, of the word viola in Italian.^ Both terms could and did signify a variety of instruments (e.g. lute, vihuela, guitar, bandurria, rabel). But in certain circumstances the term was restricted to guitar-shaped

Igibyl Marcuse, Musical Instruments: A Comprehensive Dictionary, 180. Other rela., 1 words are: Lat., fidicula ; Middle French, vielle, vièle, viole ; German, Fiedel ; Medieval Latin, fidella, vigella, vitula, vidula, vialla, viella. 77 78 instruments—those with a waist. To further distinguish them, qualifying words were added according to how they were played:^ vihuela de mano —a vihuela plucked with the fingers vihuela de arco —a vihuela played with a bow vihuela de penola, or de pendola—a. vihuela played with a plec

trum Usually, the vihuela de mano was simply referred to as the vihuela, since it was the most common of these instruments in sixteenth-century Spain and had a long tradition.^ A careful reading of the Declaradôn reveals that Bermudo uses the term vihuela in three different ways. The broadest meaning appears in the Table of Contents, where he describes the contents of Book IV, stating that among the various topics to be covered, one will find "the true under standing of all species of vihuela.'"* Another instance occurs in the preface to Book n, where Bermudo promises material "for understanding the mona chordio [keyboard] and all species of vihuela.''^ In both places, vihuela refers to a group of fretted string instruments that include the 6-course vihuela, 7- course vihuela, 4-course guitar, 5-course guitar, bandurria, and rabel.^

2james Tyler, Early Guitar: A History and Handbook, 17, and Diana Poulton, "Vihuela," The New Grove Dictionary of Musical Instruments, 3:724. ^Tyler, Early Guitar, 17-18, and Poulton, The New Grove Dictionary of Musical Instruments, 724. ‘*Bermudo, Declaradôn, folio +1, v. Cathologo de los libros. Contiene el libro quarto la verdadera intelligencia del organo, de todo genero de vihuela,... The prologue material to the Declaradôn lacks any pagination, and has been assigned numerals for each folio in the following manner: + l,r. +1, v .,+2, r., etc. Sjbid., folio XX, v. ...y para entender el monachordio, y todo genero de vihuela... ^At the beginning of Book IV, Bermudo omits the word zHhuela in the prefatory words : "the method of playing thoroughly and accurately all types of keyboard and stringed instruments." This was no accident. He cannot refer to the stringed instruments discussed in this book simply as "vihuelas" (fretted string instruments) because he inserts a short description of the harp (an unfretted instrument) in this book. He cannot label them as plucked string instruments either, because he includes the rabel, which is bowed. 79

When Bermudo uses the term vihuela to differentiate individual types of instruments, he identifies each one by certain criteria, namely the number and dispositions of the strings/ For example, Bermudo's 6-course vihuela is a specific instrument with six courses of strings, and a string disposition of G- c-f-a-d^-g^. It is uniquely distinguishable from the 7-course vihuela, any of the guitars, the bandurria and the rabel. In the first statement of Chapter 30 in Book II, Bermudo uses the term vihuela in both contexts—general and specific. Here, not only does he state that several instruments fit the category of vihuela, but he also refers to the vihuela as a specific instrument. He states/

Because there are many species of vihuelas, I will only present the common [standard] vihuela, guitar, bandurria and rabel—in this order [emphasis added]. This passage gives a clear indication of which stringed instruments are typi cally grouped under the general heading (.vihuela). Since Bermudo seems to concentrate on those instruments prevalent in Renaissance Spain, other species of vihuela, such as the lute (vihuela de Flandres) are mentioned only in passing. Bermudo also uses the term vihuela in a very special situation—one that is usually misinterpreted. In this case, he is referring to thevihuela templates proper which he so carefully describes in the Intermediate section of his treatise, i.e. those parts concerned with teaching intabulation skills to students who have already mastered the basics of the vihuela. Some writers

^Bermudo never refers to the actual physical dimensions of any of the instruments. ®Bermudo, Declaradôn, folio xxviii, r. Porque ay muchos generos de vihuela: solamente tractare de la que conmunmente es dicha vihuela, de guifsrra, y de bandurria, y rabel, por el orden aqui puestas. 80 have misconstrued this usage to mean individual vihuelas of different sizes beginning on the seven letters of the finals. However, the context makes it clear that the term refers to the use of the templates for intabulation.9

A Brief History of the Instruments According to Diana Poulton, in her article in The New Grove Dictionary of Musical Instruments, the vihuela was a plucked chordophone that flourished in Spain during the fifteenth and sixteenth centuries. The only surviving instrument is found in the Musée Jacquemart-André of the Institut de France. It had a slight waist (not as much as the modern guitar) and a very shallow body. The neck was long and narrow, with the head being flat and set back at a slight angle. It usually had six or seven courses of strings and movable frets as well. The common disposition of strings for the 6-course was: G-c-f-a-d^-g^ (same as the lute), and it was plucked with the fingers. Harvey Turnbull indicates that there is some difficulty in defining the features that distinguish the guitar from other members of the lute (and vihuela) family, since the name has been applied to a wide variety of string instruments.^^ Several theories have been proposed to account for the development of the guitar in Europe. Some believe it to be related to the

®Ibid., folio xcii, r. No tan solamente de la vihuela que dexo pintada tienen necessidad los tanedores: sino que a la forma de ella, mudados los signos, pinten otras seys. Començara cada una dellas en su letra final. [Not only do players need the vihuela (template) that I have diagrammed, but another six (templates) in the same manner with the letter names changed. Each one will begin on its letter of the finals.] ^(^Diana Poulton, "Vihuela," The New Grove Dictionary of Musical Instruments, 3: 724. Harvey Turnbull, "Guitar,"The New Grove Dictionary of Musical Instruments, 2:87. 81 Ancient Greek kithara. Others maintain the existence of guitars among the

long-necked lutes of early Mesopotamia and A natolia.^^ The guitar as we know it can be easily traced back to the Renaissance period, but its earlier history is founded in the documentation of the ancient long-necked lutes dispersed among the various cultures of Asia, Central Asia, and North Africa.^ ^ Depictions of the guitar show an instrument having a central rose, lute-type bridge and frets, and were built with either curved or flat backs. However, the main feature of the guitar is its shape— having a waist—which is the same as that of the vihuela.^'* The Renaissance guitar had four courses of strings (the fourth containing a borddn), eight to ten gut frets tied around the neck, an intricate rose, and a bridge set low in the table.^^ Although there were a variety of tunings for the four-course guitar, the basic disposition of strings was G-c-e-a. Bermudo describes this disposition, and presents two others: F-c-e-a and another which he labels as ancient: G-c-d-g. There was also a five-course guitar present by the end of the fifteenth century. Its disposition of strings was G-c-f-a-d. The earliest known printed music for this guitar is found in Fuenllana's Orphenica Lyrfl(1554).i^ Bermudo describes a five-course guitar (although he gives no indication of pitch names) in which one simply adds another course a perfect fourth above

12lbid., 87. ^^Ibid., 89, and Marcuse, A Survey of Musical Instruments, 448, and Musical Instruments, 218. Other morphologically related names from the Middle Ages are: ghiterra, ghiterna, or ghiterna (Latin). In England, it was called the gittem. These terms are derived from kithara (Greek) and qitara (Arabic). Modem cognates are: guitare (French), gitane (German), and chitana (Italian). ^ ^Turnbull,The New Grove Dictionary of Musical Instruments, 2: 89-90. ïSibid., 90. :6lbid., 92. 82 the first.^7 He proposes other alternate dispositions, and explains their purpose as well. Little is known of the medieval bandurriaA^ It was first mentioned (as mandurria) by the fourteenth-century writer, Juan Ruiz, in his Libro de buen amor.^^ Bermudo was the first author to give details. According to his account, the Renaissance instrument could be fretted or unfretted, and usually had three strings, disposed variously in fourths and fifths. In the Declaracidn, he mentioned that he had seen bandurrias with more than three strings. He suggested that one could add more strings to this instrument only if the neck was wide enough to accommodate it. He supported his suggestion by reporting a bandurria with five strings brought back to Spain from the New World.^® The bandurria is a plucked lute; its shape is that of a cittern having comparatively deep ribs flat back and a short fretted neck. It has a large open soundhole, a large peg-holder with the pegs projecting from the rear (as on a guitar). The strings are attached to a string-holder. and the instrument is played with a plectrum (pua in Spain).2i

^^Tlie first string, or course represents the highest in pitch on all the vihuelas and related instruments. ^^Marcuse, A Survey of Musical Instruments, 457-8. The term bandurria is derived from the Greek pandourion or pandoura. Other related names are mandera ,bandora, bandolon, bandurilla and mandurria. * ^®John M. Schechter, "Bandurria," The New Grove Dictionary of Musical Instruments, 1:148. 20Bermudo, Declaracion, folio xcviii, r. Pueden poner en la bandurria quatro cuerdas, y mas: si lo suffrierelaanchura del cuello...De indias han traydo bandurria con cincocuerdas...[They are able to place four strings, and more on the bandurria, if the width of the neck can support it...They have brought a bandurria with five strings from the Indies...] Schechter, The New Grove Dictionary of Musical Instruments, 1:148. 83 The rabel is the Spanish cognate for the bowed string instrument known as the rebecP- It evolved from a Moorish origin (possibly Persian)— the rahah, which was first mentioned by A1 Farabi (d. 950) and Ibn Khurdadhbih.23

The rabel was a small piriform instrument. Its short neck and wooden body were made from a single piece of wood. It had three strings (usually tuned in fifths), was played with a bow, and usually exhibited lateral tuning pegs, as did the rabab.^*

The Six-Course Vihuela In each of his pedagogical "levels," Bermudo illustrates three basic dispositions of strings for the 6-course vihuela.^s They are: G-c-f-a-d^-g^, G-c- f-bh-dl-gl, and G-B-d-g-b-dV He uses the 6-course vihuela to establish the theoretical and practical concepts for all fretted instruments. Thus, by providing the necessary fundamentals on this instrument, he can then refer the reader back to these principles when describing the other instruments.^^

22Mary Remnant, "Rebec," The New Grove Dictionary of Musical Instruments, 3:201. The term rabel is derived from the Arabic word rabab, and the Byzantine word, lura. Other cognates are: [rebeck, rebecke, rebekke] rebec, rebecq, rebecquet, rebef(French); rebeca, ribeca (Italian); Rebec (German); rabé, rabel, rebequin (Spanish). Also, see John M. Schechter, "Rabel," The New Grove Dictionary of Musical Instruments, 3:184. ^^Alastair Dick, "Rabab," The New Grove Dictionary of Musical Instruments, 3:177. Khurdadhbih claimed the rababto be similar to the Byzantine lura. ^^Marcuse, Musical Instruments, 437. 2^In this discussion, the vihuelas will appear in Bermudo's original order—an order that he maintains in all three levels of study: elementary, intermediate and advanced. This procedure will enable us to interpret his descriptions most effectively. '^Bermudo uses the proven theories and practices on the 6-course vihuela to demonstrate similar concepts on ttie keyboard and harp as well. For example, when he discusses the division of the whole tone on the keyboard, he uses the strings of the vihuela to illustrate his theories. 84 The reader encounters the first disposition of strings for the 6-course vihuela in the Elementary section (Book II, Chapters 30-36). Bermudo calls it the vihuela commun which, for purposes of clarity, will be translated as the "standard vihuela." Because this section is intended for the beginner, the description is very elementary, avoiding the use of pitch or letter names. He labels the courses of strings with numbers, and provides only the intervallic distances between the courses (from lowest in pitch to highest):

The standard vihuela has six courses of strings that are called sixth, fifth, fourth, third, second, and firsl. There is a diatessaron from the sixth string to the fifth... Throughout the vihuela, you will find this same distance between adjacent strings, except from the fourth to the third. That distance is a ditone, or a major third... Thus, there is a diatessaron from the fifth string to the fourth, the third to the second, and the second to the first, just as there is from the sixth to the fifth. Because Bermudo supplies only the intervallic relationship of the strings and no letter names, the first disposition of strings must be derived from this text by labelling the lowest string gamaut: G-c-f-a-d^-g^.^s Bermudo also acknowledges a second disposition of strings. Found in Italian tablature, it differs only in the tuning of the third string:^^

^^Bermudo, Declaraciôn, folio xxviii, r. La vihuela conmun tiene seys ordenes de cuerdas: las quales se llaman sexta, quinta, quarta, tercera, segunda, y prima...Desde la cuerda sexta hasta la quinta ay un diate6aron....Esta mesma distancia hallareys en toda la vihuela desde una cuerda inferior a la otra mas cercana superior: excepto desde la quarta cuerda a la tercera, que ay un ditono, que es tercera mayor...Pues desde la quinta cuerda a la quarta, desde la tercera a la segunda, y desde la segunda a la prima ay un diatefiaron: como lo ay desde la sexta a la quinta. Bermudo often uses the terms orden and cuerda interchangeably when referring to the courses of the vihuela. However, when he wishes to make a distinction, referring to a particular "string of a course," he uses each word precisely. ^Gamaut has been selected as the foundation for all string dispositions (unless Bermudo specifies otherwise), because Bermudo usually describes the instruments with gamaut for the lowest string, in the Intermediate and Advanced sections. 29ibid., folio xxviii V. ...perc en cifras de Ytalia auemos visto otro. Suben la tercera cuerda un semitono, quedandose todas las demas en el temple que estauan. Ay pues en este temple desde 85

We have seen another disposition of strings in Italian tablatures. They [the Italians] raise the third string by a semitone and leave the rest as they are [here]. Thus, in this disposition, there is a major third from the third string to the second. This distance from the third string to the second is the same as the distance from the fourth string to the third on the standard vihuela Thus, Bermudo's "Italian" disposition of strings is: G-c-f-bh-d^-gl.^o In his intermediate-level passages, Bermudo describes the standard 6- course disposition in more detail, placing his own engraving of the standard vihuela at the beginning of the section (Book IV, Chapter 54), as seen in Figure 8. He refers to it as the principal model for subsequent discussions.

^^fExemplo deja vihuela comun%^

r 1 Z r tf J ^ 4 r JB — 1 c — t 1 J ^ E 1 I ___ f 1 1 __ 1 U _ a L I j

Figure 8. Bermudo's Diagram of the Standard Six-Course Disposition (.Declaraciôn, folio xci, r).

la tercera a la segunda una tercera mayor. De forma, que la distancia que en la vihuela conmun ay desde la quarta a la tercera: ay on esta desde la tercera a la segunda. ^This is the intervallic relationship of strings on the modem guitar. Ibid., folio xci, r. 86 Here, instead of relying solely on intervallic relationships to describe the string disposition and fret names, as before, Bermudo now gives the spe cific letter names for each course and fret. Unfortunately, his presentation is verbose and tedious for the reader. His prolixity is apparent as he

commences his description of the engraving:^^

In this illustration [Figure 8], the open sixth string begins (as we imagine it) on gamaut. To the left, it has a Greek g, that is said to be gamaut. Whatever I say about the [space] left of this sixth string also applies to the other five...I am saying that the Greek g, located to the left of the sixth string represents gamaut on the open string. The c at the beginning of the fifth string represents Cfaut on that open string... Bermudo then proceeds to delineate the diatonic letter names on the vihuela up through the tenth fret, incorporating both "b natural" and "b flat" into his diagram.His protracted instructions exhaustively supply the letter names (and necessary theoretical principles) for each string and fret;34

By beginning the vihuela above on gamaut, there is a tone from this letter to Are; to form it, two frets are necessary. Since gamaut is the open sixth string. Are will

32ibid., folio xci, r. Comiença en esta demonstracion la cuerda sexta en vazio (segun nuestra ymaginacion) en gamaut: per lo qual dene al nascimiento una g griega, que se dize ser gamaut. Lo que digo del nascimiento desta cuerda sexta: se endeda [sic] de todas las otras...Dize pues la g que esta al prinicipio de la sexta: que la tal cuerda en vazio es gamaut. La c que esta al principio de la quinta dize ser Cfaut la tal cuerda en vazio...When Bermudo uses the word "imaginadon," here, he is referring to the variability of pitch, an accepted concept on the Renaissance vihuela. 33Bermudo employs the term b cuadraio for "b natural;" and b mollado or b pequem for "b flat." 34lbid., folio xci, r. Començando pues la sobredicha vihuela en gamaut: desde este signo al de Are ay un tono, y para formarlo, son menester dos trastes. Siendo pues gamaut en la sexta en vazio: Are sera en el segundo de la dicha sexta, aCi formaremos ut en gamaut, y re en Are. De re a mi es un tono: formando el re en el segundo traste, el mi se hallara en el quarto. Notad que en los signos donde ay h assi como en bmi, y en sus octauas: pongo dos. La pequefia que senala fa, la qual se pone un traste delante de la a: porque forma semitono. Pongo otra quadrada en esta figura b o por formar tono se pone adelante de la a dos trastes. Ordenadamente procédé esta cuerda en el quinto Cfaut, en el septimo Dsolre, en el nono Elami, en el decimo Ffaut. 87 be on the second fret of the sixth string. Thus, we will form ut on gamaut,and re on Are. There is a tone from re to mi and by forming re on the second fret, mi will be found on the fourth. Notice that, on the letters where there is a b, (for bmi and its octaves), I am placing two. The "small b" marks fa, and I place it one fret beyond the a because it forms a semitone. I also place the "squared b" in this figure. Because it forms a tone, I place it two frets beyond the a. This string continues in order: Cfaut on the fifth fret, Dsolre on the seventh, Elami on the ninth, and Ffaut on the tenth. Bermudo continues the process in this fashion until he has delineated all the diatonic frets on all six strings of the vihuela. His exactitude ensures a complete and accurate template of this disposition for the student. This precision demonstrates his systematic approach to teaching—a style that is evident in his subsequent discussions. By speaking only of the diatonic frets, Bermudo shows his concern for the intermediate student by not confusing the issue with the inclusion of the chromatic frets. In passing, he acknowledges the existence of chromatic frets, but chooses not to discuss them in this section.35 These particular frets are the subject of later discussions of fret placement. In the Intermediate section, Bermudo presents for the first time the third basic disposition for the 6-course vihuela. Given as an alternative to the first two, he refers to this disposition as one of his "proposed vihuelas." He presents this disposition in the same manner that he does the standard disposition above; first, he names the courses: G-B-d-g-b-dl; and second, he meticulously delineates the names of the frets. Figure 9 shows a template representing Bermudo's proposed alternate disposition. In it, the octave

^^Ibid., folio xci, v. Los trastes que demas de los ya dichos tiene la vihuela: no son baldios. [The rest of the frets that the vihuela has are not unused.] The frets in question here, represent the chromatic pitches, and will be explored further in Chapters V and VI. 88 designations are indicated according to Helmholz' system (C=Great C; c=small c; c^=middle c, c^=c above middle c, etc.).

frets 3 4 10

r A Bb B c d e f B c d e r q a d e f q a b*> b c‘ q a b" b J f: 2 b c* é e* fi q^ al 1 d' p: _qll b^' hi

Figure 9. Template for the Alternate Six-Course Disposition on Gamaut Derived from Bermudo's Instructions.

As before, he gives only the diatonic frets. Likewise, he proposes that this disposition of strings may be useful on other similar instruments that have six courses, such as a large guitar or even a discante?^ Bermudo notes that this disposition is interesting because it creates a major triad on the open strings. He recognizes that it is advantageous for intabulating music with a limited range.^^

^Ibid., folio xciii, v. Esta manera de vihuela es buena para una guitarra grande encordada con seys ordenes como vihuela, o para un discante. {This disposition of strings is good for a large guitar or discante, strung with six courses like the vihuela.] Bermudo is using the word grande to actually refer to the physical dimensions of the instrument. However, he more often employs the same term in reference to the "range" of available pitches on the fingerboard (up through the tenth fret). 3^Ibid., folio xciii, V. Poniendo obras que andan en pocos puntos en este temple: facilmentey presto se pueden cifrar. Y la mayor excelencia que tiene: es, que a penas dara golpe, que no de una,0 dos bozes en vazio, y aun golpe puede venir, que todas quatro bozes den en vazio, acertando a poner las claues donde se nan de poner.. .De adonde infiero tener esta vihuela los 89 In the Advanced section, only the standard 6-course disposition for the vihuela is examined and used for demonstration. Here, Bermudo attends to fret placement, establishes the previously omitted chromatic frets, and provides an engraving that includes these chromatic frets.^s This particular template will be introduced in Chapter V (below), because it illustrates one of Bermudo's methods of Pythagorean fret placement.

Additional Templates for the Six-Course Vihuela According to Bermudo, the templates can be "imagined" at any desired pitch, meaning that the letter names for the frets will be different depending on the names of the strings. For example, if the sixth course of the vihuela is labelled Are, instead of gamaut (as in the initial template), the strings and frets correspondingly will bear different letter names. The result of Bermudo's directions is a set of additional templates, renaming the strings and frets of the vihuela. In essence, the role of these templates appears to be that of "cheat sheets," which allow musicians to intabulate vocal composi tions easily. The musician selects the template according to the range of the composition; this eliminates the need to transpose. By using the proper template, the musician can intabulate the composition in such a way that the tablature will reflect all the characteristics inherent to the music (musica ficta, difference in the sizes of semitones, etc.). doze puntos: los quales quedan en tal disposicion, que hueridas [sic] todas las cuerdas en vazio: hazen consonancia. [By placing works that have a small range on this disposition, they can be intabulated easily and quickly. And the best thing that this disposition has, is that there may be beats on which four voices may ring on the open strings...From which 1 infer that this disposition consisting of a range of twelve notes, allows consonance.by striking all of the strings open.] Bermudo's statements here refer to the simultaneous sounding of consonances, rather than "strumming" (rasgueando). 2®Ibid., folio cviii, r. 90 Since the Elementary section avoids the use of specific pitch names, Bermudo apparently sees no need to offer additional templates. He implies that they exist, indicating that players may use, at times, a string disposition with "the open sixth string on gamaut, and, at other times, on Are."^^ Although he refers to other possible templates, he does not indicate exactly how many there are, or how to diagram them.^ He merely states that they will be explained later. Bermudo derives additional templates in the Intermediate section. His intention here is to prepare the student for the intabulation of vocal music, and therefore, these templates are important. Because vocal music at the time was written in many modes, demanding various accidentals, Bermudo describes the disposition of the 6-course vihuela with its strings "imagined" at other pitch levels. Here, he suggests another six templates, whose use is determined according to certain principles that he sets forth under the topic of "intabulation." In addition to gamaut, he proposes the

creation of templates on Are, bmi, Cfaut, Dsolre, Elami, and FfautA'^

^Îbid., folio xxix, v. Communmente los tanedores de vihuela que son diestros en el arte de cifrar, y de poner en este instrumento cifras: ymaginan començar la sexta cuerda en vazio en gamaut, y algunas vezes en Are. [Usually vihuela players that are dexterous in the art of intabulating, especially for this instrument, imagine the open sixth string beginning on gamaut, and sometimes on Are.] Îbid., folio xxix, v. Puede ser la sexta en vazio, no solamente gamaut, or Are.. .pero bmi, y Cfaut, y Dsolre, y qualquiera de los otros signos. [The open sixth (course) can be not only gamaut or Are. . but bmi, Cfaut, Dsolre, and whatever of the other different signs ] '^Îbid., folio xcii, r. No tan solamente de la vihuela que dexo pintada tienen necessidad los tahedores; sino que a la forma de ella, mudados los signos, pinten otras seys. Cbmençara cada una dellas en su letra final. Como la que yo pinte començo en gamaut: la segunda començara en Are, la tercera en bmi, la quarta en Cfaut, la quinta en Dsolre, la sexta en Elami, la septima en Ffaut, o en sus octauas. [Not only do players need the vihuela (template) that I have diagrammed, but they may also diagram another six in the same manner, changing the letter names. As I have drawn one on gamaut, the second will begin on Are, the third on bmi, the fourth on Cfaut, the fifth on Dsolre, the sixth on Elami, the seventh on Ffaut, or on their octaves] 91 Not only do players need the vihuela [template] that I have diagrammed, but they may diagram another six by changing the names of the strings. Each one will begin on its own letter of the finals. Just like the one I diagrammed beginning on gamaut, the second will begin on Are, the third on hmi, the fourth on Cfaut, the fifth on Dsolre, the sixth on Elami, the seventh on Ffaut, or any of their octaves. Bermudo also admits the possible use of octave transposition, if needed, indicating that players often choose a template "imagined" an octave lower:42

Many times you will find tablature in the octave below the vihuelas [templates] given above, especially those of Dsolre and Elami. He apparently feels the construction of these templates would involve un necessary repetition. Therefore, he does not discuss them any further, nor does he supply any details. In a lengthy discourse, Bermudo carefully describes each template, fixing all the diatonic pitches just as he does for the initial gamaut template. The templates in Figure 10 reflect those descriptions, and display the diatonic pitches for each template.

^Ibid., folio xciii, r. Muchas vezes hallareys cifras por la octaua abaxo de las sobredichas vihuelas: specialmente de la vihuela de Dsolre y Elami. The reason for the octave transposition would probably be to ease intabulation and fingerings, depending on the ambitus of the composition. 92

frets 1 2 2 4 6 6 7 8 S 1( A Bb B c d e f g f g a b ' o ' % 5 d h S 4 a b ^ b d1 e^ f ' 3 g Are 8 3 b c i d ' e l fi g' a i 2 e ' fi q ^ a^ b' d2 1 b " ' bi d2 e ' f 2 q

frets 3 4 8 9 10 B c d e f g a 6 a kf b c' d ' 5 e f 9 e ' f' A b ' b c' d ' q' bmi C#^ d ' e' f' q' ai b' a' b ^ bi d2 e 2 2 f#' g^ c‘ f2 a " 1 b ' ( f e" (f

frets 3 4 10 bb 6 C d e f g a 5 f q a bb b c' d' 1 4 ff h c' ri' ft ...o’ CO 3 d' e* fi q ' a' bi Cfaut f2 8 ? g ' a< bbl b i c2 d ' e2 1 c2 d ' f^ g^ a^ b ^ '

Figure 10. Six Additional Templates for the Standard 6-Course Disposition. 93 frets 3 4 8 9 10

6 d e f g a bb b c ' *) q a b‘ b c' d ' e^ fi s 4 di el f1 g’ a ’ 3 Dsolre 8 3 e^ fi çf al b' c" d" a ’ d^ f^ 9^ 2 2 (f f' q ' a b' c-

frets 3 4 8 10

e f a bb b c’ d 6 g a bb 5 ti ç’ d^ e’ f ’ q^ d ' fi a' b' c" 8 4 q ’ f#* a ' bb1 b' d2 e ' Elami 8 3 bi c2 e" f2 a2 2 d^ 1 e" f2 a" bb^ b" ç® d'

frets 3 4 6 7 8 9 10

f g a bb b c ' d ' 6 5 & b c’ d ’ e ’ f ’ 8 1 2 <0 b"^ 4 f ' o’ a h’ fi f1' Ffaut b^1 f2 8 3 q^ a’ b' d" d2 e2 f2 l!?2 2 c2 g" a" 1 f' q' 1 1^2 b2 C3 d^

Figure 10 (continued) 94

In addition to these seven templates for the standard 6-course disposi tion (Figures 8 & 10), Bermudo suggests two other possibilities located on the chromatic pitches or "black keys"—one built on a flat, and the other a sharp.'*^

The diligent player can diagram other vihuelas [templates] that begin on the black keys; and there will be two of them; one beginning on fa, and another, on mi. I describe this because you will find some intabulated works that do not correspond to any of the seven [templates] above. Therefore, I say he [the player] could diagram others that are in between. Bermudo does not state clearly the names of these chromatics (flats and sharps), but we can infer that he is referring to the standard chromatics of his time—flh. Eh, F#, C#, and G#. These are the only accidentals that he allows in his discussions on the vihuela, keyboard and h arp .44 Although Bermudo provides an elaborate description of the previous seven dispositions and their templates, he sees no need to do the same for these two. He reasons that understanding how to diagram the first seven will enable the reader to repeat the p r o c e ss.^ s

43ibid., folio xciii, r. Otras vihuelas puede pintar el curioso tanedor, que comiencen en teclas negras: y seran dos. Una que comience en fa, y otra en mi. Esto digo, porque algunas obras hallareys cifradas, que no corresponden alguna de las sobredichas siepte vihuelas: por lo qual dixe, que podia pintar otras que fueCen médias. The significance of mi -frets and fa -frets pertains to the inequality of the semitones. Simply said, mf-frets are associated with the sharps and represent a larger interval, and fa -frets are associated with the flats, the intervals being smaller. ^These accidentals are the standard chromatic tones admitted to the system in Bermudo's time. Other accidentals (D#, A^, etc. ) are admitted, but only because they happen to be found on the frets of the vihuela in a particular template. This phenomenon, according to Bermudo, gives the vihuela a distinct advantage over the keyboard and harp. 45ibid., folio xciii, r. For euitar prolixidad no pome estas dos vihuelas por extenso: segun puse la [sic] siepte. El que leyere y bien entendiere lo sobredicho de las vihuelas: sabra pintar estas dos. [To avoid prolixity, I am not presenting these two vihuelas extensively like 1 presented the other seven. He who reads and understands well what I said about the vihuelas above, will also know how to diagram these two ] 95 Using the previously established principles, it is not difficult to derive the following templates. The first two (Figure 11) illustrate the templates constructed on the "flats" (B^ and E^), and thus, will be referred to as the "flat templates."^ Those letter names in bold type represent the chromatic letters inadmissable to Bermudo's system.

frets 1 3 4 8 10

Bb B 0 d e f 6 9 bb e" f g a b o ' 5 1 CO a»’ a bb b c d ' e ' f' % 4 =3 d' e' fi g ' a ' bb' 8 3 2 fi 9' bb' b' 1 hb' b' e" f" cf

frets 3 4 8 9 10

6 eb e f g a b^ b o' 5 ab a bb b ç' d' q' f ' Î2 4 d' e' f' q' a' b' 3 1 8 3 f' q a' b^' b ' (f d ' o hb' b' C2 d^ e^ f^ g' e ' f ' a" bb2 1 Pb' çf

Figure 11. "Hat" Templates Based on Previously Established Principles.

4^CharIes Jacobs, "Introduction" to Orphénica Lyra (Seville, 1554) by Miguel Fuellana (Oxford: Clarendon Press, 1978), xxxiii. Footnote No. 2. Jacobs claims that Bermudo never discusses this possibility in the Declaraciôn. 96 The remaining templates (Figure 12) represent the three arrangements on F#, C# and G#, and are designated as "sharp templates."^^

frets 1 2 3 4 5 8 7 8 9 1

f# 9 a bb b c"' d' e' b c' d' e^ f 1 q ' a' % 5 f 1 a^ b' C2 § 4 9^ bb1 d ‘ g#^ c2 d2 e^ f^ 8 3 a' bi c#2 d2 e2 bb2 b2 2 f' 9^ ê f#2 a2 bb2 b2 C3 d3 e3 1 g"

frets 1 2 3 ^t Î5 5 7 8 9 1

6 c# d e f 9 a bb b f# q a bb b c' d' e^ b c' d' e' fi 9' a' bbi b' o d#^ e' f' b' c2 d2 e2 f2 2 g#^ c#2 f2 a2 b2 1 d" b^

frets 1 2 3 4 5 6 8 9 10

6 G# A Bb B c d f c# d e f q a b i: f# g a bb b di e' V 8 3 a# b c’ d' e' g^ e^ fi a^ b^ C2 2 d # ’ g' b ^ 1 q#^ b^’ b' d' ê

Figure 12. "Sharp" Templates Based on Previously Established Principles.

^^Bermudo consolidates these templates because of the identical location of mi-frets and fa- frets in the templates, despite the different letter names for each. 97 Bermudo presents an additional six templates for his third disposi tion—a proposed alternate disposition. He provides extensive details for these templates in the same manner as for the standard disposition.^^

The player who wishes to use this disposition of strings should diagram six of them in the manner they were described above. Because some musicians are more capable than others of understanding everything said, I wish to help those who cannot figure out how to diagram them. [Therefore], I am describing them as extensively as I did those for the common vihuelas [standard templates]. Although Bermudo stresses the need for additional templates for each disposition of strings, he nevers suggests this possibility for the 'Italian" disposition, i.e. vihuelas tuned as guitars. He also leaves the topic of the two chromatic templates (sharp and flat) open to speculation in this case. He gives complete directions for another six templates for the alternate disposition, but again refrains from describing the chromatic templates for this disposition. Since he often stipulates that the standard 6- course disposition functions as the model for all the other instruments, it is reasonable to assume that he would expect the player to apply the principles of creating the chromatic templates to the other dispositions as well. It is very likely that a total of twelve templates could be created for each instrument—seven on the diatonic letters (G, A, B, C, D, E, and F), and five on the chromatic letters (E^, B^, C#, F# and G#).

^Berm udo, Declaraciôn, folio xdv, r. Necessidad tiene el tanedor (que deste temple de vihuela quisiere usar) pintar seys a la manera de la sobredicha. Y porque entre los hombres ay mas abiles, y menores, y algunos puede auer que con todo lo dicho no atinen a piniarbs: con deSeo de ayudarles (pues principalmente para ellos scriuo) las pone por extenso: como lo hize en las vihuelas conmunes. 98 The Seven-Course Vihuela Details of the 7-course vihuela are interspersed in the three levels of instruction. Bermudo presents a total of four basic dispositions of strings for this instrument: G-c-f-a-d^-g^-c^, G-d-g-d^-g^-d^-gZ, G-d-g-b-f#^-b^-d^, and G-c-

f-g-cl-fl-gl. In the Elementary section, Bermudo introduces the standard disposi tion for the 7-course vihuela, referring to it as the standard 6-course disposition with an additional course a perfect fourth above the first course. This modification suited music of large ambitus, such as found in Guzman's intabulations. Bermudo writes:^^

In the intabulations of the famous musician Guzman, you will find a 7-course vihuela which was usually used for music that ranged over many notes. He placed another first course above the one already on the vihuela. It was a diatessaron above this first course. As in the case of the 6-course disposition, Bermudo does not provide the names of the strings or frets in this section, but only the intervals between the courses. Although his description is elementary, this 7-course disposition can be created easily from the standard 6-course disposition by placing another course a perfect fourth above the first course. The 7-course disposition, with gamaut on the sixth string,is: G-c-f-a-d^-g^-c^. For the sake of convenience, it will be referred to as the "7-course-A" disposition in subsequent discussions. In the Intermediate section, Bermudo again discusses this disposition of strings for the 7-course, but also includes two

folio xxviii, v. En cifras ds el notable musico Guzman hallareys una vihuela de siepte ordenes. Esta solia usar para musica, que andaua en muchos puntos. Ponia otra prima arriba de la que tiene la vihuela; la qual estaua un diateEaron sobre la dicha prima. Luis de Guzman (d. Naples, 1528) was a Spanish vihuelist, who was considered, especially by Bermudo, to be the greatest of his time. 99 others: G-d-g-d^-g^-d2-g2 and G-d-g-b-f#^-b^-d2. These will be labelled "7- course-B" and ^V-course-C" respectively. The description of the 7-course-A disposition in the Intermediate section is almost identical to the one in the Elementary section, including the reference to Guzman^o The reader can readily construct a template for the 7-course-A disposition from the principles previously established on the 6- course vihuela (sixth string named gamaut). See Figure 13.

frets 1 2 G 4 j 6 7 8 9 1 7 r A Bb B C d e f bb 6 c d e f q a a bk b c’ d’ €A oc f q 0) bb b fl g 4 ® 3 e' f’ a’ b’ 8 n g’ bb' a' bb’ b’ (?■ d ' f2 2 2 1 q2 cf ? bb"

Figure 13. Template for the 7-Course-A Disposition Derived From Bermudo's Instructions.

^Ibid., folio xcv, r. Una vihuela de siepte ordenes de cuerdas usan algunos tafiedores, y es, que sobre las seys cuerdas que tiene la vihuela commun, ponen una que forma un diatessaron sobre la prima En algunas obras cifradas de el claro Guzman hallareys esta manera de vihuela. A otros buenos tafiedores se la he visto usar. [Some players use a 7-course vihuela which is a common disposition on which they have placed another string a diatessaron above the first. You will find this type of vihuela in some works intabulated by the famous Guzman. I have seen other good players using it ] 100 Bermudo then proceeds to describe the 7-course-B disposition, in which he specifies the addition of the seventh course below the sixth course. He states that this disposition is best if it is used on a large tenor instrument, and begins describing it by supplying the intervals between the courses.^^

[Here] I claim what I said before. There is a diapente, con sisting of seven semitones from the seventh string to the sixth; a diatessaron, [consisting of] five semitones from the sixth to the fifth; a diapente from the fifth to the fourth; a diatessaron from the fourth to the third; a diapente from the third to the second; and a diatessaron from the second to the first. Shortly thereafter, Bermudo provides the pitch names for each course (G-d-g-d^-gl-d2-g2), and systematically labels each of the frets. As before, he bases his template on gamaut.^^ Figure 14, illustrates Bermudo's template for the 7-Course-B.

^^Ibid., folio xcv, r. Declarolo ya dicho. Desde la septima cuerda hasta la sexta ay un diapente, que son siepte semitones. Desde la sexta a la quinta ay un diatessaron, que son cinco semitones. Desde la quinta a la quarta ay un diapente; desde la quarta a la tercera un diate£aron. Desde la tercera a la segunda ay un diapente: y de la segunda a la prima un diatefiaron. S^lbid., folio xcv, r. Pintando esta vihuela poned en la septima una g, en la sexta d, en la quinta g, en la quarta d, en la tercera g, en la segunda d, y en la prima g. En la septima en el segundo a, en el tercero b pequena, en el quarto h quadrada, en el quinto c, en el septimo d, en el nono e, y en el decimo f: las quales letras aueys de poner en la quinta, tercera, y prima...En la sexta cuerda aueys de poner en el segundo traste e, en el tercero una f, en el quinto g, en el septimo a, en el octauo b pequena, en el nono b quadrada, y en el decimo una c. [In diagranruning this vihuela, place a g on the seventh (string), a d on the sixth, a g on the fifth, a d on the fourth, g on the third, d on the second and g on the first. On the second fret of the seventh (string), there is an a, small b on the third (fret), squared b on the fourth, c on the fifth, d on the seventh, c on the ninth and f on the tenth. You have to place these letters on the fifth, third and first...On the second fret of the sixth string you must place an e, an f on the third, a g on the fifth, an a on the seventh, a small b on the eighth, a squared b on the ninth, and a c on the tenth ] 101 frets 5 6 7 8 9 10

A Bb B e f 7 r C 6 d e f A a bk b c ’ 5 9 a bb b di e’ f ’ V 2 4 d' 9 ’ a ’ bi 3 i O f2 3 a b*’1 b' c ' d ' f2 b2 C3 2 d 2 g ' a2 bb2 b^ d® 6® f® 1 9^ é

Figure 14. Template for the 7-Course-B Disposition.

Bermudo considers this disposition to be advantageous, first, because it can accommodate the intabulation of a musical composition with a large ambitus, and second, because "harmony" can be had by striking some or all of the open strings. He statos:^^

All the strings of this vihuela are in such a disposition that when the open strings are plucked together, there is harmony [consonance]... For the 7-course-C disposition, Bermudo supplies only the disposition of the strings.54 Instead of designating letter names for the strings and frets, he asks the student to complete the diagram by applying his previous

®^Ibid., folio xcv, r. Todas las cuerdas desta vihuela quejan en tal disposicion, que siendo heridas junctas en vazio hazen harmonia... 54ibid., folio xcv, v. Desde la septima a la sexta ay un diapente, de la sexta a la quinta un diateGaron, de la quinta a la quarta un ditono, de la quarta a la tercera un diapente, de la tercera a la segunda un diatessaron, y de la segunda a la prima un semiditono. [From the seventh (string) to the sixth, there is a diapente, a diatessaron from the sixth to the fifth, a ditone from the fifth to the fourth, a diapente from the fourth to the third, a diatessaron from the third to the second, and a semiditone from the second to the first.] 102 knowledge on the 6-course vihuela. The result is a template, with the seventh course designated as gamaut : G-d-g-b-f#l-b^-d^, as seen in Figure 15.

frets 1 2 3 4 5 6 7 8 9 1 0

A Bb B c d e f 7 r 6 d e f q a b** b c ’’ 5 9 a b^ b d ' f ■ % «J 4 b c' d' f' 9' a' f#^ q' a' b'^ b' d^ e" § 3 2 2 b' d" Ç a" a2 b2 c3 1 d2 f2 q‘

Figure 15. Derived Template for the 7-Course-C Disposition.

Bermudo's last disposition of strings for the 7-course vihuela appears in the Advanced section. This disposition, designated 7-course-D, is his own "theoretical invention." To the courses, he systematically applies the names of the three Guidonian hexachords (deduciones): G, C, and F.55

Just as we have the letters on the [Guidonian] hand, we can "imagine" them on the vihuela. The seven courses of strings must be placed so that each one will form its ow n deduciôn. The seventh string will be the first deducidn, the sixth will be the second, the fifth will be the third, and so forth, until the first [course] which is the seventh deduciôn. The distance from one string to another is the same distance as there is from one deduciôn to another.

SSlbid., folio d i, v. Como lo tenemos en la mano: lo ymaginemos en la vihuela.. Para esto se han de poner siepte ordenes de cuerdas, y cada una formara su deduciôn. La septima cuerda sera la deducion primera, la sexta la segunda, la quinta la tercera, y assi procédera hasta la prima: la qual sera septima deduction. Distara una cuerda de otra, lo que dista una deducion de otra. Here, Bermudo is referring to the three Guidonian hexachords: natural (C,D,E,F,G,A), hard (G,A,B,C,D,E), and soft (F,G,A,Bb C,D ). 103 Bermudo names the courses and frets in the text, and supplies the following engraving (Figure 16) as an illustration. Although his diagram shows only diatonic pitches, his intentions involve much more. He presents this template as a prototype, demonstrating the advantages this particular disposition (in Pythagorean fret placement) has over the standard 6-course disposition—a concept that is discussed in Chapter V, below. He also specifies the chromatic pitches for his 7-course-D disposition only after placing those frets that represent the division of the whole tone (chromatic frets).^

Demoflracio dela vihuela dc fiete ordenes 5----- —8 3 f T* ( j __k ------1 — r c i-----3 t j------0 LL ( — t ) r L — 7 J k f — 5 I 5

Figure 16. Bermudo's Diagram of the 7-Course-D Disposition {Declaraciôn, folio ciiii, r).

In the context of Bermudo's three-tiered pedagogical schema, he gives the student four different dispositions for the 7-course vihuela. He considers

®^Ibid., folio ciiii, r. The chromatic pitches are systematically presented on folio ciii, r. Since this disposition appears in the Advanced section, Bermudo links it to related topics, such as fret placement, semitone theory, modes, faults and remedies. 104 7-course-A to be the standard; he proposes 7-course-B and 7-course-C as useful alternatives; and 7-course-D represents his own theoretical invention with a more refined system of tuning, in which alternate fingerings are more readily available.

Additional Templates for the Seven-Course Vihuela Bermudo's description of 7-course-A is somewhat cryptic in that he illustrates it indirectly through the standard 6-course disposition. He does not provide additional templates, presumably because the standard 6-course and 7-course-A dispositions share the same principles. Similarly, Bermudo suggests that additional templates for 7-course-B are possible, but not mandatory. He states:^^

Furthermore, conforming to what was already said, they [additional templates] may be constructed, if it is necessary, with one beginning on Are, another on bmi, until seven are completed. With this task in mind, he provides preliminary details for designing the templates. After apologizing to those who already know how to construct their own, he admits that some less accomplished musicians will need more details. In an effort to find a happy medium, he supplies the names of the courses and holds the musician responsible for creating his ovm templates. He statest^s

S^ibid., folio xcv, v. Mas si fuere menester: conforme a lo ya dicho se hagan començando una en Are, otra en bmi, hasta complir el numéro de siepte. ^Ibid., folio xcv, v. Para pintar estas seys vihuelas he dicho poco: porque me parece para todos bastar, y aun para algunos abiles sera fastidio y sera menester suplicar les que perdonen mis prolixidades, pues para otros seran menester. Afii que todos seran suffidentes (si bien lo estndian [sic]) para complidamente pintar las dichas vihuelas, y poner todas las letras: aGi las que yo dixe que se ponen al prindpio de las cuerdas: como las que se han de poner en los trastes. 105

I have said little about diagramming these six [additional] vihuelas [templates], because it seems to me that it is sufficient for some, and it would be fastidious for those who are more capable; and it will be necessary to ask them to pardon my prolixities, because they [the directions] are necessary for some. Therefore, all that was said previously will be sufficient (if they studied it well) for diagramming these vihuelas, and for placing all the letters. This includes those letters that must be placed at the beginning [left] of the string, as well as those that must be placed on the frets. Bermudo offers no assistance in diagramming the additional templates for 7-course-C either. He simply states that the conscientious and capable student will certainly know how to diagram them.59

From this and the previous statements, the curious, studious and capable player will know how to tune this vihuela many ways, and how to diagram it along with another six, if necessary. Bermudo presents the 7-course-D disposition on gamaut only, with no references to additional templates. Since he considers it to be such a perfect instrument, and sees no need to describe additional templates, he makes no reference to the possibility of creating them.

The Four-Course Guitar Bermudo presents three dispositions of strings for the 4-course guitar: G-c-e-a (a los nueuos), F-c-e-a (a los viejos), and C-f-g-c^ (andent). Descriptions found in the Elementary section are comparable to those given for the 6- and 7-course vihuelas. Here, Bermudo delineates only the intervals between the

^^Ibid., folio xcvi, r. Por esto y por lo ya dicho otras vezes podra el curioso, estudioso y abil tanedor templar de muchas maneras esta vihuela, y saberla pintar, y otras seys si fueren menester... 106 courses, without referring to the names of the strings or the frets. His continued use of the 6-course vihuela as the model for subsequent explanations is apparent when he describes the 4-course guitar simply as a 6- course vihuela with the two outer courses removed. He states:^°

There is a diatessaron from one string to another, which is a fourth. The exception is from the third string to the second where there is a major third. This guitar [disposition] is no more than a vihuela [disposition] with the sixth and the first strings [courses] removed. Therefore, there is a diatessaron from the fourth string of the guitar to the third, and from the second to the first; and from the third to the second, a ditone. Bermudo's description clearly implies the following disposition for the 4- course guitar, with the lowest course designated as gamaut: G-c-e-a. Let us refer to this tuning, which Bermudo labels the guitarra a los nueuos as the "4- course-A" disposition. Bermudo recognizes a second tuning for the 4-course guitar, a los viejos (in the old manner). It is very similar to the previous disposition, differing only in that the lowest string is a whole tone lower. Bermudo states:^^

The guitar with the old disposition would differ only from this guitar with the new disposition, in that the fourth string was usually lower by one tone. On the new one, there is a diatessaron from the fourth string to the third, and on the old one, there is a diapente.

^Ibid., folio xxviii, v. Desde una cuerda a otra ay un diatefiaron, que es una quarta: excepto desde la tercera a la segunda que ay una tercera mayor. No es otra cosa esta guitarra: sino una vihuela quitada la sexta y la prima. Luego desde la quarta de la guitarra hasta la tercera, y desde la segunda a la prima ay un diatefiaron: y desde la tercera a la segunda ay un ditono. In the comparison of the 4-course guitar and the vihuela, Bermudo is referring to the "new" 4- course disposition and the standard 6-course disposition. ^^Ibid., folio xxviii, v. El temple de la guitarra a los viejos no diffiere de esta a los nueuos: sino que la quarta cuerda suelen abaxar un tono. Auia desde la quarta a la tercera a los nueuos un diatefiaron: y a los viejos ay un diapente, que es quinta perfecta. 107 The disposition of strings that emerges from this text is: F-c-e-a, and it will be designated as "4-course-B." When these two dispositions reappear in the Intermediate section, Bermudo provides a few more details. The description of 4-course-A in the Intermediate section is almost the same as in the Elementary section; now, however, Bermudo provides the letter names for each course and directs the student to complete the diagram by using the 6-course vihuela as a model:^^

After having placed these letters at the beginning [left] of the strings, they [the letters] continue through the frets, representing the note names, in the form and manner that they were placed on the [6-course] vihuela... Close examination of the text reveals a descrepancy in Bermudo's ref erence to the fourth course of this guitar. Bermudo refers to the usual prac tice of calling this course the quinta (fifth), but states that he would prefer to call it the fourth course—its most logical label.^^ Obviously, he believes that the term requinta is a source of much confusion for many students. Translated simply, requintar means "to raise, or lower by five notes."^4 Bermudo's own uncertainty is apparent as he describes this phenomenon:^^

^^rbid., folio xcvi, r. Despues destas letras puestas al principio de las cuerdas: yran seguidas todas las otras por los trastes, que significan los signos: en la forma y manera que se pusieron en la vihuela... ^^Ibid., folio xcvi, r. Suelen a llamar a la cuerda mas baxa quinta, yo le llamaria quarta, y a la otra tercera, a la siguiente segunda, y a la mas alta prima. (They usually call the lowest string, quinta. 1 would call it the fourth, and the other, third, and the following, the second, and the highest, first.] According to the Vox New College Spanish and English Dictionary, the term, requintar literally means "to raise or lower by five points, or notes." But, it makes no distinction as to the distance between these points, or notes. ^Ibid., folio xcvi, r. Suelen poner a la quarta de la guitarra otra cuerda, que le llaman requinta. No se, si quando este nombre pusieron a la tal cuerda: formaua con la dicha quarta un diapente, que es quinta perfects: y por esto tomo nombre de requinta. Ahora no tienen este temple: mas forman ambas cuerdas una octaua: segun tiene el laud, o vihuela de Flandes. Este instrumento teniendo las très, o quatro ordenes de cuerdas dobladas, que forman entre si octauas: dizen tener las cuerdas requintadas. 108

Along with the fourth [string], they usually place another string, that they call requinta. I do not know if when this name was given to that string, it formed a diapente (that is, a perfect fifth) with the said fourth, and therefore, it took the name requinta. Guitars do not have this timing now. Furthermore, both strings form an octave, like the lute, or vihuela of Flanders. By having three or four courses of strings doubled at the octave, this instrument [lute] is said to have requintada strings. Bermudo's varied use of the term requintar suggests two possible interpretations of this phenomenon. Taking the definition of the verb requintar literally, as he does at the beginning of the statement above, he describes a disposition in which the two strings of the fourth course are placed a perfect fifth apart. Although Bermudo gives no dear specifications for creating the fifth higher or lower than the fourth course, the description would result in one of the following dispositions for the guitar: G(d)-c-e-a, or G(C)-c-e-a. However, as Bermudo continues the discussion, he negates this description by stating that, "now, guitars do not have this tuning," impling that perhaps this was an old disposition of strings for the 4-course guitar. Subsequent statements would seem to contradict this first interpretation, requiring a re-evaluation of the verb requintar and its use in this context. In the second interpretation, it is possible that requintar refers not to the relationship between the two strings of the fourth course, but rather to that between the third course and one string of the fourth. If one of the strings of the fourth course is doubled at the octave, it then creates a fifth above the third string. Thus, the result is the re-entrant tuning, G(g)-c-e-a. This second 109 interpretation proves to be consistent with Bermudo's specific statements referring to octave doublings in the lute and Renaissance guitar.^^ Although Bermudo provides the letter names for each course of the 4- course-A disposition, he does not name the notes on the frets. He reasons that the student should apply the principles already established for the vihuela.^7 Figure 17 shows the template for the 4-course-A disposition, created according to Bermudo's instructions. The octave difference in the fourth course is assumed and not displayed.

frets 1 2 3 4 5 6 7 8 9 10 4 r A Bb B c d e f c d e f g a b^ e f a b^ b di 8 2 g di a bb b c' e ’ f ' 9^

Figure 17. Derived Template for the 4-Course-A Disposition.

According to Bermudo, the disposition of strings for 4-course-B is so similar to that of 4-course-A that it warrants little description beyond the dis position of the fourth course. The principles related to 4-course-A, therefore, transfer directly to 4-course-B. Bermudo states:^®

^Bermudo further confuses the issue by providing additional templates for this disposition, in which he alternately labels the lowest course as the fifth and then the fourth. (See discussion below.) He also confirms the second interpretation in the tuning methods for this instrument (folio xcvi, v). ^^Ibid., folio xcvi, v. Para la verdadera inteligencia desta guitarra, y para saber cifrar en ella: aprouecha lo dicho en la vihuela. [For the true understanding of this guitar, and for knowing how to intabulate for it, one takes advantage of what was said about the vihuela.] ^Ibid., folio xcvi, v. Esta mesma guitarra suelen tafier a los viejos: y no ay otra différencia entre ambas: sino, que en la de los viejos abaxan la quarta un tono. 110 They used to play this same guitar in the old disposition. There is no other difference between the two, except that they lower the fourth string a whole tone in the old disposition. Although Bermudo never gives a complete description of the 4-course-B disposition, it is a simple matter to derive its template, as seen in Figure 18.

frets 34 567 8 9 10

4 F r A Bb B c d c d e f a bb I 3 9 e f 9 a b^ b o' di 82 a bb b o' d' e' 9^

Figure 18. Derived Template for the 4-Course-B Disposition.

Bermudo presents the "4-course-C" disposition in the Intermediate section, and designates it the "ancient" disposition. He introduces this disposition under the pretense of "resuscitating the guitar of the great

Mercury."69 Apparently, Bermudo sees this particular disposition as a historical, rather than a practical model, because he gives only the disposition of strings by intervallic relationship—two disjunct tetrachords. He uses this opportunity to acquaint the reader with some important historical theorists and musicians, such as Tubal, Boethius, Mercury, Orpheus, Nichomachus, and Ornithoparchus. Although he gives no other details regarding 4-course-C, letter names can easily be applied to the courses by placing gamaut on the lowest string. The result of Bermudo's directions is

^^Ibid., folio xcvii, r. For lo qual me paredo resuscitar la guitarra del gran Mercurio. I l l the disposition: G-c-d-g. Limited discussions of the 4-course guitar also appear in the Advanced section, but they are limited to the 4-course-A disposition and concern themselves primarily with fret placement.

Additional Templates for the 4-Course Guitar In the Intermediate section, Bermudo recommends that the student diagram six additional templates for each of his 4-course guitar dispositions.^^

Players may find it necessary to diagram not only the gui tar [disposition] in gamaut (that I have been discussing), but also another six of the same disposition, with different letters. To assist the beginner in diagramming the remaining six templates for this disposition, Bermudo gives the names of the courses for each. However, he confuses the reader by alternately designating the lowest course as "fourth" and "fifth" in his description:^^

Because beginners may not be too diligent in creating, or diagramming them [templates], I want to present a brief method for it. If the second guitar begins on Are, the fourth string will be on A re, the third on Dsolre, the second on F faut with the "square b" mark which means the string begins on that key between Ffaut and gsolreut. The first string ivill be "square b" [b natural]. This is done

^®Ibid., folio xcvi, v. Necessidad teman los tafiedores de pintar no tan solamente la guitarra de gamaut, de la qual hasta ahora he tractado: sino otras seys del mesmo temple, de letras différentes. ^^Ibid., folio xcvi, v. Y porque los principiantes no trabajen tanto en sacar las, o pintar las: quiero poner un breue modo para ello. Començara la segunda guitarra en Are, la quarta della sera Are, la tercera Dsolre, la segunda Ffaut con sefial de bquadrado, que quiere dezir començar la tal cuerda en la tecla negra de entre Ffaut y gsolreut, la prima sera el mi de bfabmi. De forma, que a la quinta se ponga una A, a la tercera una D, a la segunda una f con sehal de b quadrado y a la prima una b quadrada...He presents this description because he fears that the student may not completely understand the actual disposition, due to his explanation of the requintada strings. 112 in such a way that an A is placed on the fifth string, a D on the third, an f with the mark of square b [i.e. raised to f#] on the second and a "square b" on the first [course]... Using these partial descriptions, in which Bermudo supplies only the names of the strings, it is possible to create templates that would include the names of the frets, as well as the courses. When dealing with the 4-course-B disposition, Bermudo offers no supporting details for diagramming additional templates. As usual, he refers the reader to the previously established vihuela principles, so that the desired templates may be constructed. Bermudo alludes to the possibility of additional templates for the dis position of 4-course-C. Although this disposition may be of historical interest only, he suggests that the student may choose to use it for intabulating certain works. If this particular template is needed, the student who understands the vihuela and its principles, will presumably know how to diagram additional templates for this disposition of strings.73

The Five-Course Guitar The description of the 5-course guitar in the Elementary section is largely a corollary to the the discussion of 4-course-A. Indeed, Bermudo de scribes the 5-course disposition simply as a 4-course-A with one course added

^^ibid., folio xcvi, v. El estudioso taüedor por la inteligencia de lo ya dicho afii en las vihuelas, como en las guitarras puede pintar siepte en este temple de los viejos. [By understanding everything that has been said about the vihuelas and the guitars, the studious player can diagram seven (guitar templates) in the old disposition.] '3ibid., folio xcvii, r. El que de proposito mirare las distancias sobredichas la entendera facilmente y la sabra pintar, y otras a ella semejantes: que seran menester para cifrar. [He who will look, especially, at the above distances (on the ancient guitar) will understand it easily and will know how to diagram it, and others similar to it that will be necessary for intabulating.] 113 a perfect fourth above the first, i.e. G-c-e-a-d^.^^ Let us designate this disposi tion as 5-course-A. Bermudo's discussion of this tuning is uncharacteristi cally brief. Nonetheless, a template, as shown in Figure 19, can be created from his scanty directions. Bermudo also discusses the 5-course-A disposition in the Advanced section, but as stated earlier, this treatment centers entirely on fret placement.

frets 8 9 10

r A Bb B c d e f c çi Ç f g a bb e f q a bb b o' d' 1 a b" b Ç e' Q d' e' g ’ a' bb1 b' c2

Figure 19. Derived Template for the 5-Course-A Disposition.

In the Intermediate section, Bermudo proposes an alternate disposition of strings for the 5-course guitar: G-d-g-b-dL^^ It will be referred to as the "5-course-B" disposition, as seen in Figure 20.

7^Ibid., folio xxviii, v. Guitarra auemos visto en Espana de cinco ordenes de cuerdas. En este instrumento se puede poner la sobre dicha quinta cuerda.. .si le ponen otra cuerda, que este sobre la prima un diateEaron. [We have seen a guitar of five courses in Spain. The fifth string (course) can be placed on this instrument...Such music can easily be played on the guitar, if players place the other string a diatessaron above the first.] "Ibid., folio xcvii, r. De la manera que en el genero de las vihuelas (no solamente en el temple, sino en el numéro de las cuerdas) puse vihuelas nueuas: assi en el genero de las guitarras me parecio hazer. Ya puse guitarras de quatro ordenes nueuas y viejas: quiero poner una nuei’a en el orden y numéro de cuerdas. [In the same manner I diagram new vüiuelas (not only in. tuning, but in the number of the strings), therefore in the genus of guitars it seemed a good thing for me to do. I have already presented new and old dispositions for the 4-course guitar. Now I want to present one with a new number of strings and a new disposition ] 114 frets 6 7 8 9 10

5 r A Bb 8 c d e f bb 4 d e f 9 a b c' i 3 q a b^ b c' d' e’ f 1 ou o 2 b o' d' e' f' 9^ a' 1 f' g' a' b'

Figure 20, Derived Template for the 5-Course-B Disposition.

Bermudo presents yet another disposition of strings for the 5-course guitar in the Advanced section. It is similar to the 7-course-D disposition presented earlier in the same section. He proposes that each course be given a letter of one of the Guidonian deduciones, forming the disposition: f-g-c^- fl.gl.76

Musicians are able to create a disposition for the five- course guitar in which the five courses correspond to five deduciones. These strings would be low F faut, low Gsolreut, csolfaut, high ffaut and high gsolreut. Bermudo considers this disposition, "5-course-C," to be purely theoretical—a 5-course counterpart to his 7-course vihuela disposition (7-course-D). He does not supply the letter names for the frets, but (as usual) refers the reader to the principles already established that govern their derivation. Bermudo also suggests the possibility of creating another 5-course dis position, simply by renaming the lowest course with the name of another

Bermudo proposed new dispositions for the 6- and 7-course vihuelas earlier. Here, he devises an alternate disposition for the guitar. This template can be constructed from the description of the tuning method. ^^Ibid., folio cviii, v. Pueden hazer una guitarra de cinco ordenes correspondientes a cinco deduciones: y serian Ffaut y Gsolreut graues, csolfaut, ffaut, y gsolreut agudos... 115

deduciôn. Therefore, if one follows his directions, naming the fifth course Gsolreut instead of Ffaut, the result is a new disposition, or the "5-course-D": g_cl-fl-gl-c2, shown in Figure 2l7? Bermudo provides little detail about these

last two dispositions evidently presuming that the student vdll use them and derive their templates as needed.^® Figure 21 illustrates the templates appropriately.

frets 6 7 8 9 10

5 g a bb b d’ el f’ 4 d’ e’ f’ q' a’ Ç)O d2 3 f1 g’ a^ bb^ bi SCourse-C 2 8 ? q' a’ b"' b^ 6 f" 2 2 2 1 e f' _q a

frets 6 7 8 9 10

f 9 a bb b c ’ d ’ 1 q 9 b Ç d' ç’ f’ % ^ 1 1 c’ d' e’ f^ a i 3 q 5-Course-D 8 f' 9^ a’ b’ c' d' 9' a' bb’ b’ c" d' f2

Figure 21. Derived Templates for the 5-Course-C and 5-Course-D Dispositions.

27ibid., folio cviii, v. ...o se pueden ymaginar las dichas cinco cuerdas en otras dnco deduciones, que viniesse a tener una onzena. [These five strings can also be imagined on another five deductions that would encompass an eleventh ] 2®Ibid., folio cviii, v. Acerca desta guitarra de cinco ordenes no me quiero a largar: porque si alguno la quisiere usar: se, que bastata lo dicho, y lo demas engendraria fastidio. [Concerning this 5-course guitar, I do not want to overextend myself. If anyone wishes to use it, then use what I have said, because it is sufficient. Any more details would be superfluous ] 116

The Bandurria In his Elementary passages, Bermudo describes two dispositions of strings for the bandurria, which he designates as the standard disposition and the special disposition. Both involve the juxtaposition of a perfect fifth and a perfect fourth within an octave. The standard disposition places the perfect fourth on the bottom (between the second and third courses) with the perfect fifth on top (between the first and second courses). The special disposition reverses this order. Bermudo states:^^

One [bandurria disposition] is common [standard] and the other is special. The common disposition comprises a di atessaron from the third course to the second, and a dia pente from the second to the first. This disposition seems to be ancient, because, it places the diatessaron on the bottom as the ancient ones used it. Some players raise the second string one more tone. In this [special] manner, the diapente moves to the bottom with the diatessaron on top. Although Bermudo gives no further details, it is possible to determine the letter names for each disposition according to his references to the intervals between the courses. Therefore, the standard disposition for the bandurria (bandurria-A) is g-c^-g^, while the special disposition (bandurria-B) is g-d^-g^. Since Bermudo refers to these two dispositions briefly here, one would expect a more complete discussion of each in either the Intermediate or Advanced sections. Unfortunately, he only explains the bandurria-A dis position in detail. Bandurria-B recurs, while Bermudo discusses a method of

folio xxviii, V. El uno es coranun: y el otro particular. El temple conmun, es que desde la cuerda tercera hasta la segunda ay un diatefiaron: y desde la dicha segunda hasta la prima contdene un diapente. Este temple parece ser antiguo; porque pone por fundamento el diateEaron, segun que en el tiempo antiguo se usaua. Por lo qual algunos tafiedores sut>en la cuerda segunda un tono mas, y viene el diapente a la parte inferior: y el diatefiaron a la superior. 117 "re-tuning" yet another bandurria disposition in the Intermediate section (bandurria-C, below).®® In the Intermediate section, Bermudo describes a new disposition of strings for the bandurria, to be referred to as "bcindurria-C," but confuses the reader by labelling it as the standard disposition. In contrast to the disposition presented in the Elementary section, this "standard" arrangement consists of two conjunct perfects fifths, forming the disposition, g-d^-al. At the same time, it matches the disposition of an entirely different instrument in the Elementary section—that of the rabel.®^ Bermudo supplies few details about this disposition (giving letter names for neither the courses nor the frets), which is uncharacteristic of his presentations of the other instruments in this section. Figure 22 displays the template for bandurria-C that has been created according to Bermudo's principles.

frets 1 2 3 4 5 6 7 8 9 1(

) 3 q a b‘ b c' d' e' f' 1 b"^ 2 3 2 d' e' f' a C O £ O 2 f2 1 a' C d ' e g '

Figure 22. Derived Template for the Bandurria-C Disposition.

®®Ibid., folio evil, v. Abaxando la prima un tono: formara con la segunda un diateHaron, y con la tercera un diapasson. [By lowering the first string a whole tone, there will be a diatessaron between the first and second strings, and a diapason between the second and third.l ®^Ibid., folio xcvii, v. Communmente tiene la bandurria tres cuerdas en la forma del rabel...Esta una cuerda de otra por distancia de una quinta perfecta: segun el temple de algunos tanedores. [Usually the bandurria has three strings in the same disposition as the rabel...From one string to another, there is the distance of a perfect fifth, according to the tuning of some players.] The rabel will be discussed later in this chapter. 118 Following the disposition of bandurria-C, Bermudo presents what ap pears to be another disposition in the Intermediate section. He designates this one "the most ancient and common disposition that is used now," but supplies only the intervals between the courses. This is curious, since he usually offers copious details on the various instruments in the Intermediate section.®^ Bermudo's documentation here is confusing, because what he de scribes as the "ancient" disposition for the bandurria is, in reality, no more than that of bandurria-A: g-c^-g^—a disposition presented earlier in the Elementary section. Therefore, the template for the bandurria-A disposition, as seen in Figure 23, is a suitable illustration of what Bermudo describes as the standard and ancient disposition.®^

frets 1 3 4 6 7 8 9 10

9 a b' b c' d ' e* f1 g ' 52 2 c' d’ e f' 9’ a* 3 2 2 8 1 a’ b' C _ Ç, f'

Figure 23. Derived Template for the Bandurria-A Disposition.

®^Ibid., folio xcvii, v. Esta bandurria tiemplan otros tanedores de otra forma, y es temple antiquillimo, y el commun que ahora se usa. Ponen todas tres cuerdas en una octaua: pero no como acabo de dezir. Desde la tercera a la segunda hazen un diatefiaron: y desde la segunda a la prima un diapente. [Other players tune this bandurria in another form, and it is the most ancient tuning, and the common one that is used now. They place all three strings within an octave, but not as 1 have just finished saying. They make a diatessaron from the third string (course) to the second, and they make a diapente from the second to the first.] ®®Bermudo never details this template. Nevertheless, it is created for purposes of clarity, using his vihuela principles. 119 In the Advanced section, Bermudo describes the "standard" disposition of the bandurria as g-c^-g^ which is the one he has already given in the Elementary and Intermediate sections—bandurria-A.^^ The last two bandurria dispositions, which Bermudo labels as "new," appear in the Intermediate section, both consisting of two conjunct perfect fourths.^ Bermudo stipulates that these dispositions were designed to be used together to play music that would be normally played on the standard 6- course disposition. Following his directions, the player must first label one disposition, and construct the second one a major third higher. The result is a pair of dispositions, whose combined courses correspond to the six courses of the standard 6-course disposition; the first disposition (g-c^-f^) represents the fourth, fifth and sixth courses of the 6-course vihuela; and the second disposition (a^-d^-g^) comprises the first, second and third. As Figure 24 demonstrates, these bandurria dispositions are nearly identical, and will be designated as "bandurria-D" and "bandurria-E."^

®^Ibid., folio cix, r. El temple commun de la bandurria es puesto por las decudiones. Si ymaginamos la tercera de la bandurria en Gsolreut, y la segunda en csolfaut, y la prima en gsolreut agudo: sera conforme a lo que se usa en este instrumento. Es pues la bandurria en el temple commun cercana a la perfection musical. [The common tuning of the bandurria is placed in the deduciones. If we imagine the third string (course) of the bandurria on Gsolreut, the second on csolfaut, and the first on high gsolreut, it will conform to that which is used on this instrument.] ®^lbid., folio xcviii, r. Si estas tres cuerdas que tiene este instrument las quisieren poner una de otra un diatefiaron a imitacion de la vihuela: seria buen temple por remeda a su origen, que es la vihuela. [If they would want to place each of these three strings the distance of a diatessaron apart, like the vihuela, it would be a good tuning in that it copies its origin, the vihuela.] ^Ibid., folio xcviii, r. Si a la una bandurria le pusiefie tres cuerdas: las quales correspondiefien a la sexta, quinta, y quarta de la vihuela: y en la segunda bandurria pussiesse otras tres cuerdas mas delgadas: las quales correspondiefien a la tercera, segunda, y prima de la vihuela: seria complida vihuela con tal condicion que desde la prima de la primera bandurria hasta la tercera de la segunda auia de auer una tercera mayor: como la tiene la vihuela desde la quarta cuerda hasta la tercera. [If one would place three strings (courses) on one bandurria that would correspond to the sixth, fifth and fourth strings of the vihuela; and on the second bandurria he would place another three, much thinner, that would correspond to 120

frets 1 2 j3 4 1 6 7 8 9 10

P a b' b ç ’ d ’ fi 1 c ' Ç f^ a ’ b*^i Bandurria-D 2 f' b' C d"

frets 1 2 3 5 6 8 9 10 a ^ b** b fi 1 e’ fi 2«! 2 A a bM Bandurria-E 3 b^'i i S 1 a’ b’ 0 d' el f'

Figure 24. Derived Templates for the Bandurria-D and Bandurria-E Dispositions.

The Rabel Bermudo saves the rabel, a bowed instrument, until last.®^ In his dis cussions, he often refers to it in the context of its close cousin—the bandurria. There are two reasons why he pairs the rabel with the bandurria; they both have three strings or, in the case of the bandurria, three "courses" of strings; and their disposition of strings is identical. Bermudo uses the bandurria as the model, and frequently indicates that the same concepts are to be applied to the rabel. The fact that one instrument is plucked and the other is bowed is not an issue here. In the Elementary section, Bermudo reveals the disposition of strings for the rabel in the material on tuning methods. Here, he describes a rabel the third, second and first strings of the vihuela: it would be a complete vihuela with the condition that the first [string] of the first bandurria is a major third from the third [string] of the second, like the fourth string to the third on the vihuela.] ®7Sibyl Marcuse, Musical Instruments, 433. Both entries, rabel and rabel de area, refer to a small bowed instrument of Spanish origin, or rebec. 121 with the disposition, g-d^-a^—the same as for bandurria-C.®® One may question why the description of the rabel in the Elementary section is found in the tuning methods, and not in with the descriptions of the other instruments. Obviously, Bermudo feels that the rabel is so closely related to the bandurria that illustrating it, along with the bandurria, would be unnecessary and tedious. What appears to be a new disposition for the rabel in the Advanced section, is simply the bandurria-C disposition, set at a different pitch level. Instead of using gamaut as the fundamental for this disposition, Bermudo uses Ffaut, creating f-c^-g^.®^ He refrains from describing the tuning of the rabel further, since it is exactly the same as that of the bandurria.

Conclusions In summary, Bermudo uses the term vihuela in three different con texts. In tlie first context, it is a generic term, designating a particular category of instruments—those with strings and frets. We find that in this category he includes an array of instruments: 6-course vihuela, 7-course vihuela, guitars, bandurria and rabel. Bermudo concentrates primarily on the plucked instruments. Being bowed, the rabel is the exception, and therefore

®®Ibid., folio xxix, v. Como el rabel tenga tres cuerdas: pueden tener los mesmos nombres de las cuerdas de la bandurria.. .De una cuerda a otra ay un diapente. Para que la segunda venga en octaua de la tercera: sera hollada la dicha segunda en el quinto traste. Tasmbien hollareys la prima en el quinto: para que venga en octaua con la segunda. [Because the rabel may have three strings, they can also have the same names as the strings of the bandurria. From one string to another there is a diapente. So that the second string may form an octave with the thrid, the second will be depressed at the fifth fret. Also you will depress the first string on the fifth fret, so that is forms an octave with the second string.] ®^Ibid., folio cviii, v. Si ymaginaCemos la cuerda tercera deste instrumento en Ffaut, la segunda en csolfaut, y la prima en gsolreut agudo: seria el temple que muchos usan.. .[And if we would imagine the third string of this instrument on Ffaut, the second on csolfaut, and the first on high gsolreut, it would be the tuning that many use...] 122 the material on this instrument is limited. In the second context, Bermudo clearly indicates a specific instrument by the term vihuela. He describes two vihuelas, one with six courses and the other with seven, and distinguishes them from the guitar, bandurria and rabel. In the third context vihuela refers to templates that promote ease in intabulation. As Table 2 shows, Bermudo's descriptions of all the instruments are scattered throughout the three levels of study: Elementary, Intermediate, and Advanced. At times he offers an abundance of details, and at other times, next to none. He provides the most specific information in his discussion of the 6-course vihuela, and continually refers to it as the model for all the others. He requires the student to apply the principles of creating templates to the 7-course vihuela, the guitars, the bandurrias, and even the rabel. Table 2 summarizes Bermudo's descriptions of each of the instru ments. It shows the many dispositions of strings, Bermudo's descriptive names, my classification code, and references to the section in which the specific instrument was discussed. 123 Table 2. Summary of Bermudo's Instruments, from the Three Levels of Study: Elementary (E), Intermediate (I), and Advanced (A). Disposition Bermudo's Name Code Level

6-course vihuela G-c-f-a-d^-g^ standard E, I, A G-c-f-b-dLgi Italian E G-B-d”g-b“d ^ alternate I

7-course vihuela G-c-f-a-d^-g^-c^ standard A E, I G-d-g*dLgi-d^g^ alternate B I G-d-g-b-f#Lbl-d2 alternate C I G-C-f-g-cLfl-gl theoretical (invented) D A

4-course guitar G-c-e-a new A E, I, A F-c-e-a old B E, I C-f-g-cl ancient C I

5-course guitar G-c-e-a-dl standard A E, A G-d-g-b-d^ alternate B I F-G-c-f-g theoretical (invented) C A G-c-f-g-c^ theoretical (invented) D A bandurria g-c^-g^ standard A E g_dl-gl special B E g-dl-a^ standard C g < V ancient A I, A g-cl-fi new D al-d2-g2 new E g-d'-g^ re-tuned B rabel g-d^-a (same as Bandurria-A) B f-ci-gl (transposed) A CHAPTER V BERMUDO'S METHODS OF FRET PLACEMENT:

PYTHAGOREAN TUNING AND EQUAL TEMPERAMENT

Since Bermudo feels that precision in fret placement is mandatory, his methods are especially important to his theory. Using primarily the 6-course and 7-course vihuelas, he directs the student to apply the same principles to the other instruments discussed in Chapter Iv' and stresses the understanding of certain prerequisites: the diatonic scales, the manner of forming intervals, the use of movable frets, and the division of the whole tone. All of Bermudo's discussions of fret placement and theories of tuning and temperament are found in the Advanced section of the vihuela material. Here, he presents two basic schemes: Pythagorean tuning and an approximate equal temperament. He describes three methods for applying the Pythagorean scheme, and one for the approximate equal temperament.

Prerequisites for the Art of Fret Placement Prior to presenting his four methods of fret placement on the vihuela (discussions of el arte de entrastar in the Advanced section), Bermudo bemoans the general lack of mastery of this skill and science on the part of musicians of his day. While he acknowledges that some players obtain fine

124 125 results by ear alone, he feels that the average player lacks sufficient experience and expertise to accomplish this task effectively.^

You seldom will find this instrument fretted well. Yet, there are those singular players who can place the frets correctly by ear. There is a great difference in the music when one places the frets by ear only, and not by a combi nation of this craft and the ear...Not everyone has the ear and the experience for placing frets by ear. Ultimately, it would not be as accurate as it would be by using propor tions. Therefore, in order to ensure "good" performance standards, Bermudo insists on presenting his own placement methods, which are very accurate because they rely on a compass and mathematical proportions. He claims that these methods are new in Spain, and declares that he has never seen or heard of anything like them before.^ Before beginning the task of fret placement, the musician must meet certain requirements. One must thoroughly know the diatonic scales and how to implement them on the vihuela.^ One must be aware that, although

^Bermudo, Dedaraciôn, folio cii, r. Apenas hallareys este instrumento bien entrastado: sino son los que usan los singulares tanedores, que los ponen a compas de su buen oydo. Es grande la différencia en la Musica puestos los trastes con solo oydo: o con arte junctamente con el oydo.. .Poner estos trastes a bcnefficio de oydo: no todos los oydos son para ello suffidentes y padecen trabajo, y en fin no van tan dertos como por la cuenta de las proporciones. ^Ibid., folio dii, v. El arte de entrastar es cierto y nueuo. Digo ser cierto, porque los musicos andquissimos lo usaron, y ahora se ha experimentado. Digo ser nueuo, por el modo y estylo en que va puesto. Si en Espana alguno lo ha usado: yo no lo he visto, ni oydo. [The craft of fretdng is certain and new. 1 say that it is certain because ancient musidans have used it, and it is now in pracdce. I say it to be new because of the method and style in which it is done. If anyone in Spain has used it, I have neither seen nor heard of it.] ^Ibid., folio di, r. Para que todos los que tafien la vihuela commun (y aun los que no lo saben) endendan puntualmente como se han de poner los trastes: no ten una breue informadon. Desde un traste a otra ay un semitono. De forma, que el semitono se forma en dos trastes, el tono en tres...En esta cuenta va numerada la cejuela de la vihuela por traste...[So that all those who play the common vihuela (and even those who do not know how) may understand exactly how the frets must be placed, may they heed the brief information. From one fret to another there is a semitone. In such a manner, that the semitone is fomied in two frets, the tone in three...] In this list, the nut of the vihuela is given a number. However, the end result is the same as if the numbering began at the first fret. 126 the frets may appear to be equidistant on the vihuela, they indeed produce unequal semitones, because normally two sizes of semitone are used.^ Consequently, the musician must understand the division of the whole tone to be able to place the chromatic frets.^

Pythagorean Tuning Bermudo begins by first introducing his three placement methods based on Pythagorean tuning. This system employs a simple manipulation of three basic intervals: the octave (2:1), the perfect fifth (3:2), and the perfect fourth (4:3). The whole tone is thus expressed as the difference between the perfect fourth and the perfect fifth (3:2 divided by 4:3, or the sesquioctave pro portion 9:8); the ditone, or major third, is expressed as the addition of two whole tones ([9:8] 2, or 81:64); the diatonic semitone, then, is expressed by the difference between the ditone and the perfect fourth (4:3 divided by 81:64, or 256:243). Figure 25 illustrates the mathematical proportions used to construct the diatonic scale in the Pythagorean system.

^Ibid., folio di, r. Digo mas, que aunque el semitono se forme de un traste a otro, y todos los semitonos en la vihuela commun esten quasi yguales en compas de Musica; en menor compas y cuenta se fbrman unos, que otros. [I also say that, although the semitone is formed from one fret to another and all semitones on the common vihuela may be equal, in music, some indeed, are formed smaller than others.] ^Boethius presents the division of the whole tone in his treatise. De institutione musica. 127

3:2 4:3 81:64

G B C H h 4- + H 1 ratios 9:8 9:8 9:8 9:8 9:8 256:243 256:243 cents 204 408 498 702 906 1110 1200

Figure 25. The Pythagorean Tuning of the Diatonic Scale.

The pitches of this diatonic scale comprise part of a circle of fifths. If one continues the succession of fifths to include five chromatic pitches within the octave, the resulting circle, if closed, contains one fifth that is twenty-four cents smaller than the justly tuned perfect fifths (702 cents). This small fifth of 678 cents is referred to as the "wolf fifth." Figure 26 demon strates the inclusion of twelve pitches within the octave, with the wolf fifth placed between C# and Clearly, the rigidity of this system results in two sizes of semitone: the major semitone (114 cents) and the minor semitone (90 cents).

"wolf fifth" F 678 cents 114 294 612 792 996 C C# D Eb F F# G Ab A Bb B C I------1------1------1——I------h - 4----- 1-----1------1— 1- 4 -----1 cents 0 204 408 498 702 906 1110 1200

Figure 26. The Pythagorean Tuning of the Diatonic and Chromatic Pitches Within the Octave.

^Bermudo uses G#, instead of A*’, in all his discussions of the chromatic pitches—keyboard, vihuela and harp. Therefore, the "wolf fifth" in his system is found between G# and E^. 128

When this scheme is extended beyond the twelve diatonic and chro matic pitches of the octave, one finds a difference of twenty-four cents (or a comma) between the enharmonic pitches. Figure 27 illustrates this difference between enharmonic pitches such as G# (816 cents) and its counterpart. A*’ (792 cents).^

cents 114 294 612 792 996 C C # D Eb E F G Ab A Bb B C I ,1------1----- \------1------1------L------1------1------1 Db D# Gb G# A# cents 0 204 408 498 702 906 1110 1200 90 318 588 816 1020

Figure 27. Pythagorean System Showing the Enharmonic Pitches (and Cents).

Pythagorean Fret Placement for the Elementarv Student Bermudo evidently intends his first method of fret placement for the elementary student.^ He concedes that although this method appears first in the treatise, it is not superior to the others. Rather, it is uncomplicated, and well-suited for those who are inexperienced in fret placement.® He directs the student through a simple procedure of dividing a string by means of a compass and a "carpenter's square" (cartabdn). To accomplish this, he sug-

^The cent-values here are based on the 'Table of Intervals" in Helmholz' On the Sensations of Tone, 453-56. 8Although these methods of fret placement are located in the Advanced section, clearly, Bermudo is adhering to his pedagogical intentions, by first presenting an easier method for the elementary student. ®lbid., folio cii, r. Puso lo aqui en el lugar primero, y en modo no primo: para los que saben pcx:o...[l placed it (the beginning method) first, but it is not the superior method. It is for those who know little...] 129 gests that the student make all calculations and divisions on a straight line (comparable to the length of the vihuela string) drawn on a separate piece of paper.^o Although Bermudo supplies no letter names, we may assume that the string is called gamaut, with the frets named accordingly, to maintain consistency with the discussions in Chapter IV. A paraphrase of Bermudo's method follows:^ ^ Step 1. Divide the entire length into nine equal parts. The point nearest the nut (9:8) marks the second fret (A). The third point (3:2) marks the position of the seventh fret (D), forming a 3:2 proportion. Step 2. Divide the space from the newly established second fret to the bridge, into nine equal parts. The point nearest the second fret (9:8) places the fourth fret (B). The third point (3:2) places the ninth fret (E). Step 3. Divide the entire string into four equal parts. The point nearest the nut (4:3) marks the position of the fifth fret (C). Step 4. Divide the distance from the fifth fret to the bridge into four equal parts. The point nearest the nut (4:3) marks the position of the tenth fret (F). In Steps 1-4, Bermudo sets all of the diatonic frets. But, because he appears reluctant to deal with the complex problem of placing the chromatic

^Ojbid., folio cii, r. Para hazer todos los repartimientos que en este libre tracto: tomad el tamaho de las cuerdas en una régla bien labrada, en la qual repartireys las consonancias con cartabon quadrado. [In order to make all the divisions which describe in this book, transfer the length of the strings (of the vihuela) onto a well-constructed line. On this line, you will divide the consonances with a carpenter's square.] ^^Ibid., folio cii, r. For a translation of the steps used in Bermudo's elementary method, see the Appendix. 130 frets by mathematical proportions and a compass, he offers an appropriately uncomplicated solution for the elementary student. His concern for simplicity is obvious in his final step. Step 5. The first, third, sixth and eighth frets form the chromatic frets. Simply place them midway between those frets that form whole tones. Be advised that once these frets are placed between the whole-tone frets, each must be adjusted. If the fret must be fa, lower it by mov ing it toward the nut; if it must be mi, raise it by moving it toward the bridge.^ 2 por example, place the chromatic fret (fret 3) between the second (A) and the fourth (B), and adjust it accordingly; raise it for m i (A#); lower it forfa

(Bb). Although Bermudo's directions allow only an approximate placement of these chromatic frets, he implies the continuation of the Pythagorean system, by stressing the difference between a "mz-fret" and a "/a-fret." Figure 28 illustrates Bermudo's fret placement method for the elementary student. The figure shows the exact placement of the diatonic frets, and at the same time, the approximate location of the chromatic frets. It also demonstrates Bermudo's intention to make the comma distinction (24 cents) between enharmonic pitches, although his directions are inexact.

^^This step has often lieen misinterpreted to refer to a crude form of equal temperament. See Lindley, Lutes, Viols and Temperaments, 29. 131

r A B C D E F frets 4 5 9 10

step

1 9:8 3:2

9:8 3:2

4:3 1 1

4:3

Place frets 1,3,6, and 8 In the middle of the whole tones. nut bridge

Figure 28. Bermudo's Elementary Method of Fret Placement.

Evidence, discussed previously (Chapters m and IV), has shown that Bermudo often avoids complicated instructions when dealing with the elementary student. Therefore, in this case, he chooses not to encumber the beginner with complex string divisions—a procedure he reserves for the accomplished musician. Figure 29 illustrates the extent of the Pythagorean system being used in Bermudo's elementary method of fret placement, and the leeway in the placement of the chromatic frets. 132 not given + frets 2 4 5 7 9 10 11 12 G A B C D E 1— ------1------+------K----- —'— ------1-----'----- 0 204 408 498 702 906 996

90-114 294-318 588-612 792-816 996-1020

Figure 29. Extent of the Pythagorean System Used in Bermudo's Elementary Method of Fret Placement.

Fret Placement for Bermudo's Theoretical Seven-Course Vihuela Bermudo directs the second method of fret placement to the more ac complished musician, and designs it specifically for his "invented" theoretical disposition of the 7-course vihuela (7-course-D ).^3 He draws his method from the principles established by Boethius and Stapulensis, but indicates that, although their methods are precise, they are unnecessarily difficult and complicated. His intention here is to simplify the procedure.^ He prescribes the use of a compass for placing not only the diatonic frets, but the chromatic ones as well. He also gives directions for determining two locations for each of the chromatic frets (Frets 1, 3, 6, and 8). The result is a

Figure 16 for Bermudo's diagram of this disposition. ^^Bermudo, Declaraciôn, folio dii, r. El modo de poner los traste scriuen Boedo y Stapulense en modo difficultoso: pero derto. Dexirlo he por las mas daras palabras, que pudiere. [Boethius and Stapulensis write about the method of pladng the frets. It (the method) is difficult, but exact. (Here), I have said it in the clearest way that I can.] The sources Bermudo is referring to are Boethius' De institutione musica, and Pater Stapulensis' [Jacques LePebvre] Musica libris quatuor demonstrata (Paris, 1496). This is further evidence of Bermudo's concern for good pedagogy. He strives to condense and clarify many complicated procedures and theories already written. 133 vihuela equipped with "fixed" diatonic frets, and double positions for each of the chromatic frets. Again, Bermudo demonstrates this method of fret placement on a line comparable to the length of a vihuela string as in the elementary method.^® The line is designated gamaut. As Figure 30 below shows, Bermudo first es tablishes the diatonic frets by means of simple Pythagorean proportions. A paraphrase of Steps 1-6 follows: IG Step 1. Divide the entire string into four equal parts. The point nearest the nut (4:3) marks the position of the the fifth fret (C). Step 2. Divide the distance from the fifth fret to the nut into four equal parts. From the fifth fret, extend another three of these parts (toward the bridge). This point (16:9) marks the position of the tenth fret (F), Step 3. Divide the distance from the fifth fret to the nut into three equal parts. Add another from the fifth fret (toward the bridge). This point (3:2) marks the seventh fret (D).^^ To ensure the accuracy of this fret, measure the distance from the fifth fret to the seventh and then divide the remainder of the string (to the bridge) by this particular length. If there are eight equal lengths from the seventh fret to the bridge, and nine

^^Bermudo does not indicate the use of a line on a separate piece of paper at this point. However, it is logical to assume, since later on in this particular method, he directs the student to draw an "additional" line on the paper for the whole tone divisions. l^Ibid., folio ciii, r. For the translation of this method, see the Appendix. t^If one were to continue dividing the string by this length, there would be a total of twelve, creating a 12:8 proportion, or simply, 3:2. 134 from the fifth fret, then the 9:8 proportion reflects the accurate placement of the seventh fret. Step 4. Divide the distance from the seventh fret to the nut into three equal parts. The point nearest the nut (9:8) marks the second fret (A). To ensure that the second fret has been placed accurately, divide the distance from the second fret to the bridge by the same segment. If these form eight equal parts, the 9:8 proportion is

verified. Step 5. Divide the distance from the second fret to the seventh into three equal lengths. Add a fourth part from the seventh fret toward the bridge (forming a 3:2 proportion). This point marks the position of the ninth fret (E). To check this fret's accuracy, divide the distance from the ninth fret to the bridge into eight equal parts. If there are nine of these from the bridge to the seventh fret, then the ninth fret is accurately placed.^® Step 6. Divide the distance from the second fret to the ninth into three equal parts. The point nearest to the nut (9:8) marks the position of the fourth fret (B). To verify the placement of this fret, use the same procedure for checking the placement as in Steps 3,4, and 5.

l®Although Bermudo only indicates four small parts, the true proportion is found by continuing to divide the string by this particular length, resulting in a total of twelve, creating a 12:8, or 3:2 proportion. 135 lener name B C D E F frets 4 5 7 9 10

(43 1 4:3 2 3 2 f : 9:1s 3:2 5 9:A 6 nut bridge

Figure 30. Placement of the Diatonic Frets on Bermudo's Theoretical 7-Course Disposition.

Next, Bermudo prepares the way for placing the chromatic frets. He indicates the need to place the four frets that represent divisions of the whole tones. These frets correspond to the black keys on the keyboard, some representing mi, and others, fa. He states:^^

All of the Guidonian hand has been placed, except for the fa of bfabmi and its octave on the one hand, and mi on the other. The voices that must be placed are located on these two frets that represent each of the divisions of the four whole tones...Then, we must place four frets that divide the whole tones, and that correspond to the black keys of the keyboard. The first, sixth and eighth [frets] form mi, and the third fret, fa. Later, in the same discussion of whole tone division, Bermudo adds four more chromatic frets—an additional first, third, sixth and eighth frets. For these frets, he recommends making an extra line on the paper, on which he makes the additional marks indicating their precise locations. One

l^Ibid., folio ciii, r. Toda la mano queda puesta excepto el fa de bfabmi y de su octaua en una parte, y en otra el mi: las quales bozes se ban de poner en dos trastes, de quatre diuisiones de tone que restan de poner.. .Luego los quatro trastes que nos faltan per poner: son diuisiones de tone, correspondientes a las teclas negras de monachordio. El primero y sexto y octauo forma mi: y el tercero fa. 136 should bear in mind that Bermudo is not discussing double frets here; he is reinforcing the concept of movable frets:^®

We must place another four [frets] in opposition to those already placed. I wish to say, that if the [initial] line for the fret forms mi, we will make another that is lower, form ing fa; and if it [the line] forms fa, we will make another that is higher, forming mi. The following steps reflect Bermudo's method for placing all the chromatic frets in the Pythagorean system. To the diatonic frets placed in Steps 1-6, he adds the chromatic frets in Steps 7-14. Figure 31 shows the continuation of his method. His method (paraphrased) resumes:^^ Step 7. Divide the distance from the fifth fret to the bridge into eight equal parts. Add another part toward the nut. This point (9:8) marks the third fret (B^). Step 8. Divide the distance from the fourth fret to the bridge into nine equal parts. The point (9:8) nearest the fourth fret marks the sixth (C#). Step 9. Divide the distance from the sixth fret to the bridge into nine equal parts. The point (9:8) nearest the sixth fret marks the eighth (D#). Step 10. Divide the distance from the sixth fret to the bridge into three equal parts. This point (4:3) marks the first fret (G#). Step 11. Divide the distance from the third fret to the bridge into eight equal parts. Add another toward the

20ibid., folio ciii, v. Otras quatro auemos de formar contrarias de las sobredichas. Quiero dexir, si la raya del traste formaua mi: haremos otra a baxo, que forme fa: y si formare fa, hazed otra arriba, que forme mi: Ibid., folio ciii, r - ciii, v. See the Appendix for translation. 137 nut. This point (9:8) marks the alternate first fret (Fret lA —A*’, which is a comma lower than the original first fret, G#). Step 12. Divide the distance from the first fret to the bridge into nine equal parts. This point (9:8) marks the alternate third fret (Fret 3A—A#). Step 13. Divide the distance from the alternate first fret (Fret lA) to the bridge into four equal parts. This point (4:3) marks the alternate sixth fret (Fret 6A—D^). Step 14. Divide the distance from the third fret (Bb) to the bridge into four equal parts. The point nearest the third fret (4:3) marks the alternate eighth fret (Fret 8A—Eb).

letter Ab A# Db Eb name G# A Bb B C C#D D# E F

frets s 6 7 9 10 : i ' 7 1 8 1 "I 1 1 1 1 1 9 1 1 "1 1 1 1 1 <0 10 è 11 10 1 12 1 1 ....i l l II 13 14 nut bridge

Figure 31. Continuation of Bermudo's Method—Placement of the Chromatic Frets. 138 Bermudo adds three more frets, although he describes the common vihuela as having only ten, as presented in Chapter IV. Here, he places the thirteenth and fourteenth frets in relation to the twelfth, but gives no explicit directions for placing the twelfth fret. One can easily determine its position by applying a simple 2:1 proportion, creating an octave above gamaut. Figure 32 shows the placement of these last three frets (Steps 15-17). Bermudo's instructions (paraphrased) foliow:22 Step 15. Divide the string in half. The halfway point (2:1) marks the position of the twelfth fret (G).23 Step 16. Divide the distance from the first fret to the nut into two equal parts. Place the compass on the twelfth fret, and reach for the thirteenth (g#) with that length.24

Step 17. Divide the distance from the second fret to the nut into two equal parts. Place the compass on the twelfth fret, and reach for the fourteenth fret (a) with that length.

22lbid., folio ciii, r.- ciii, v. See the Appendix for translation. 2^The inclusion of more than twelve frets appears to be inconsistent with Bermudo's previous descriptions of the vihuela as having only ten. 24Although Bermudo does not make a distinction here between the two positions for the first fret as a starting point, he indeed may have considered either of them (A*> or G#) viable starting points. These implications may also indicate that these frets were glued to the fingerboard, and were unmovable. Therefore there is no need to give both positions. 139 letter Ab A« Db Eb name r G« A Bb B C C«D D«E F G g#a 1A 3A 6A 6A fret 1 I 3 4 5 S 7 8 9 10 1:!1 31 4 I • 15 S. 16 H— ------—

Figure 32. Continuation of Bermudo's Method—Placement of Frets 12,13 and 14.

Since Bermudo's illustration of all the vihuelas depict only ten frets, this placement of frets beyond the tenth seems to be atypical here. (Compare, for example. Figures 8 and 16.) He may have considered this procedure a theoretical exercise, since this disposition (7-course-D) is his own prototype, on which he demonstrates selected theories of tuning and intabulation. If Bermudo intended to place the practical frets through the fourteenth, he certainly would have given directions for the eleventh fret (F#) as well, but, as seen in previous instances (Figures 29 and 33), he consistently passes over the eleventh fret. This repeated omission, along with Bermudo's description of the vihuela as having ten "usable" frets, provides strong evidence that the treatment of frets 12-14 may indeed be a theoretical exerdse.25 Figure 33 illustrates the disposition of the frets (except the octaves), as they are placed on the lowest course, designated gamaut.

^W henever Bermudo uses this vihuela disposition, it is usually employed to demonstrate his own innovations; he uses it to test his system of fret placement which approximates equal temperament; he uses it to demonstrate a comparable concept of "split keys" on the vihuela. Perhaps these extra frets are possible on other related instruments, such as the guitar or bandurria, provided the neck is long enough. 140 not g iv e n ; frets 1 2 3 4 5 6 7 8 9 10 11 12 cents 114 318 612 816 1110 r r # A A# BC C# D D# E F F # G 1 h i h -4—— 4 -__J---- ' — 4- 1— -I cents 0 204 408 498 702 90 6 996 1200

Ab Bb Db Eb G b 90 294 588 792 1020

Figure 33. The Frets and Pitches on the Seventh Course (gamaut) of Bermudo's Theoretical Disposition.

With this theoretical disposition, Bermudo creates a system of tuning on the vihuela in which all diatonic and chromatic pitches are possible—a system comparable to that of keyboards with split keys.^^ If, for example, an Ab is inaccessible on one course, it can easily be reached on an adjacent course. (See Figure 34.) Having had his "invention" examined and tested by two musicians, Bermudo describes it as a very flexible and perfect disposition for the vihuela.27

I consider this new vihuela very excellent for matters; [it is] precise, perfect, copious and easy for the left hand. The two examiners of this book in Granada proved it, and recognized the beauties and many other things already summarized [before]... Figure 34 illustrates this disposition with ten "usable" frets Bermudo's own diagram ( Figure 16) gives only diatonic pitches, a limitation that ex plains the lack of letter names on the first and eighth frets, and other places.

26Bermudo appears to be creating an instrument similar to Vicentino's arcicembalo (1555). 27ibid., folio ciiii, r. Tengo esta nueua vihuela por cosas muy prima, cierta, perfecta, copiosa, y para la mano yzquierda descansada. Los dos examinadores deste libro en granada la prouaron y cognoscieron en ella los primeres ya sumados, y otros muchos... 141 The template offered here shows all the frets, diatonic and chromatic. Although Bermudo's system does not admit chromatic pitches beyond the designated flats (E^ and B^) and sharps (F#, C# and G#), Figure 34 includes the additional accidentals created by the two possible positions for each chromatic fret. Bermudo offers this template because of the advantages apparent in both the fret placement and the disposition of strings. Its flexibility lies in the fact that if the musician cannot play a certain note on a particular string and fret, he has options on the adjacent strings.

frets 1 2 3 4 8 9 10 Ab G# A Bb A# B c# d d# e 7 d z# d e ' d# e f g'’ f# g a** 3# a b" 6 b f# g a** g# a b'’ cb b c ’ d" :# d e" 5 g ak g# a b" a# b c’ d**’ G#’ di 1#’ e 1 f’ 4 =#’ d ’ e f ’ f#"' 9 ’ a ^ i j# ’ a ’ b ^ ' 3 f#^ g ’ a ^ g#’ a’ b^'i b’ 0 = d ® 2 g "' 1 1 1 1 2 f 2 a ^ i b^ a# d ^ e " ' j / « 1 □# a b C

Figure 34. Derived Template for Bermudo's Theoretical 7-Course Disposition Showing all Chromatic Frets.

Pythagorean Fret Placement for the Individual Six-Course Templates Bermudo's third method of fret placement in the Pythagorean system focuses on the peculiarities of the individual templates for the 6-course vihuela. Here, Bermudo stresses the importance of understanding the differences in each template. He states:^®

2®Ibid., folio cv, r. Tractare de todas las vihuelas que alii puse, y veremos la différencia que entre si tienen en los trastes. Trastes ay que haziendo la sexta gareaut, no viene con hazer la bmi, o uno de otros signos. Es menester saber que trastes estaran fixos, y quales se deuen mudar, y que tantos. 142 I will present all the vihuelas [templates] that I described earlier, and we will see the difference in frets that each one has. There are frets on the gamaut vihuela that do not appear on the bmi vihuela, or any of the others. It is necessary to know which frets are fixed, and which [frets] must be moved—and by how much. Bermudo indicates his intention to place frets on each template of the standard 6-course disposition. In the light of Bermudo's pedagogical system, one may confidently assume that the methods given for the 6-course disposition are also valid for any of the dispositions for the other instruments in this category: 7-course vihuela, 4-course guitar, 5-course guitar, bandurria and rabel. Bermudo begins by dividing the seven templates into three groups to facilitate fret placement.29 He sorts them by species of diatessaron, and matches them according to the succession of the whole tones and the semi tone. He begins by placing the templates of gamaut, Cfaut, and Ffaut in Group I, because all of them represent the "third species of diatessaron" (TTS).30 Group II comprises the templates of Are and Dsalre (TST), and Group m indudes Elami and bmi (SIT). Figure 35 summarizes Bermudo's classification of templates.^'

^^Bermudo does not to include the "sharp" and "flat" templates that are presented in Chapter IV above. ^Bermudo gives no clues as to why he begins with the third species of diatessaron. He appears to be maintaining a certain consistency by starting his discussion with the model on gamaut. ^^Ibid., folio cv, r. Siepte vihuelas puse, que son desde gamaut hasta ffaut. Todas estas siepte vihuelas podemos poner entres différencias. La vihuela de gamaut, de Cfaut, y de ffaut se parecen mucho: porque todas très tienen una manera de procéder, conueiene a saber que son los diateflarones de la tercera specie. Primero forman dos tonos y luego un semitono en ambos diateBarones. La différencia que ay en todas très vihuelas: al poner de los trastes se vera. La vihuela de Are y la de Dsolre se parecen muchos y la de bmi y la de Elami son semejantes. [1 described seven vihuelas (templates) from gamaut to ffaut. We can set all seven according to their differences. The vihuelas of gamaut, Cfaut and ffaut are very similar, in that all three follow the diatessaron of the third species. They form two whole tones and a semitone in both diatessarons. The differences in all three vihuelas (templates for gamaut, Cfaut and Ffaut) 143 Group Species of Diatessaron 1 TTS gamaut C Cfaut 0 " D —E—F Ffaut F—G” A"Bb II TST Are A—6—C—D Dsolre D—E—F"G III STT Elami B--G-D—E bmi E"F”G”A

Figure 35. Bermudo's Classification of the Templates According to Species of Diatessaron.

One should bear in mind that this system of classification does not ultimately determine the placement of the chromatic frets. Bermudo uses these groupings to facilitate his discussion, presenting the gamaut template as the model. Bermudo begins his third method with the gamaut template. As the following steps show, he sets the diatonic (fixed) frets first (following the pat tern in the two previous methods), by using a succession of sesquitertia and sesquioctave proportions. Having fixed these diatonic frets, he places the chromatic (movable) frets. In addition to placing the frets, Bermudo names the pitches produced on each string (as seen in the step below). In Figure 36, Steps 1-6 illustrate the placement of the diatonic frets (including letter names), and Steps 7-10 establish the position of four chromatic frets on the gamaut disposition only. A paraphrase of Bermudo's method follows:^^

will be seen in the fret placement. The vihuelas of Are and Dsolre are very much alike, and so are those of bmi and Elami.] ^^Ibid., folio cv, r- cv, v. For translation, see the Appendix. 144 Step 1. Divide the entire string into four equal parts. The point nearest to the nut (4:3) marks the fifth fret. The letter names for all the strings at this fret are: C (sixth), F (fifth), (fourth), d (third), g (second), and c (first). Step 2. Divide the distance from the fifth fret to the nut into four equal parts. Add another three of these parts (from fifth fret) toward the bridge. This point (4:3) marks the position of the tenth fret. The letter names for the strings at this fret are: F (sixth), (fifth), (fourth), g (third), c (second), and f (first). Step 3. Divide the distance from the fifth fret to the nut into three equal parts. Adding another part from the fifth fret toward the bridge (3:2), marks the seventh fret. The letter names for the strings at this fret are: D (sixth), G (fifth), c (fourth), e (third), a (second), d (first). To ensure the accuracy of this fret, divide the distance from the fifth fret to the bridge into nine equal parts. The 9:8 proportion should fall on the seventh fret.^^ Step 4. Divide the distance from the seventh fret to the nut into three equal parts. The point nearest to the nut creates a 3:2 proportion, and marks the position of the second fret. The letter names for all the strings at this fret are: A (sixth), D (fifth), G (fourth), b (third), e (second).

^^Bermudo gives few directions for testing the accuracy of the fourth, seventh and ninth frets. He gives basic directions for testing the second fret, which is then to be applied in the same manner to the other frets. 145 and a (first). To check the accuracy of this fret, divide the entire distance into nine equal parts. The mark nearest to the nut (9:8) should correspond to the second fret. Step 5. Divide the distance from the second fret to the seventh into three equal parts. Add another part from the seventh fret (toward the bridge). This point (4:3) marks the position of the ninth fret. The letter names for all the strings at this fret are: E (sixth), a (fifth), d (fourth), f# (third), b (second), and e (first). To ensure the accurate placement of this fret, divide the distance from the sev enth fret to the bridge into nine equal parts. The 9:8 pro portion should fall on the ninth fret. Step 6. Divide the distance from the second fret to the ninth into three equal parts. This point (3:2) marks the position of the fourth fret. The letter names for all the strings at this fret are: B (sixth), E (fifth), a (fourth), c# (third), f# (second), and b (first). To check the accuracy of this fret, divide the distance from the second fret to the bridge into nine equal parts. The 9:8 proportion falls on the fourth fret. In the following steps, Bermudo does not delineate the letter names for any of the strings, as he does in the earlier ones, since the chromatic frets are movable and vary for each of the templates. Therefore, the letter names shown in Figure 36 reflect only the pitches formed on the sixth course of the gamaut template. 146 Step 7. Measure the distance from the nut to the second fret. Placing the compass on the ninth fret, add this length (toward the nut), and place the sixth fret (C#> into position. To check the accuracy of this fret, divide the distance from the fourth fret to the bridge into nine equal parts. The 9:8 proportion confirms the location of the sixth fret. Step 8. Divide the distance from the sixth fret to the bridge into nine equal parts. This point (9:8) marks the position of the eighth fret (D#). Step 9. Divide the distance from the bridge to the sixth fret into three equal parts. Add another part (toward the nut) from the sixth fret (forming a 4:3 proportion), and place the first fret (G#). Step 10. Divide the distance from the bridge to the fifth fret into eight equal parts. Add another (toward the nut) from the fifth fret. This point (9:8) marks the third fret (Bb). 1 4 7 letter name G# A Bb B C C« D D«E F

frets 1 23 4 567 89 10

nut bridge

Figure 36. Bermudo's Method for Placing Diatonic and Chromatic Frets on the GamautTemplàte. A s Figure 36 shows, the first, sixth and eighth frets represent mi (G#, C# and [D#]), while the third fret stands for fa (Bh). Bermudo provides an engraving of the gamaut template, as seen in Figure 37. It includes all the diatonic and chromatic pitches available on the template.

r—1 - 4 - H n :|---- * Ik—< H u o - g j n ■ y .h % ------& —%—J U

Figure 37. Bermudo's Diagram of the Gamaut Template (Declaraciôn, folio cvi, r). 148 Those frets marked with sharps represent F#, G# and C#; those frets marked with flats represent and E^; and those frets that have no markings whatsoever represent letter names that lie outside the Guidonian hand. Bermudo therefore designates them as "faults." Although this third method of fret placement focuses on the gamaut template, Bermudo stipulates that these principles are also applicable to the remaining six templates.^^ This is especially true for that of Cfaut, because it not only comprises the same species of diatessaron but also uses the same dis position of chromatic frets. In fact, the fret placement is exactly the same as for gamaut, and one need only change the letter names to complete the tempi a te. 35 As Figure 38 shows, the Cfaut template retains themi-frets on the first, sixth and eighth frets, and the fa-fret on the third.

19 c j » ? t i Ï ;f J j a F 1, ... k o j 3 1 * n d 3 ET b i I 3 t .1 I

Figure 38. Bermudo's Diagram of the C/autTemplate (Declaraciôn, folio cvi, r).

3'^Ibid., folio cv, v. El como en esta vihuela de gamaut qucdan puestos los trastes es fundamento para todas las vihuelas...[The manner in which the frets have been placed on the vihuela of gamaut is fundamental for all the vihuelas (templates)...] 35jbid., folio cv, v. ... y por consiguiente siruen para la do Cfaut. Mudadas solamcntelas letras...[and consequently, they serve for the template of Cfaut. Only the letters are changed...] 149 A comparison of the templates in Figures 37 and 38 illustrates their similarities; the pitches represented on the first, sixth and eighth frets are major semitones (sharps); those on the third fret are minor semitones (flats). Although Bermudo includes the Ffaut template in Group I (TTS), it requires a different placement of the third fret, as seen in Figure 39. One should bear in mind that here Bermudo is merely dividing the second whole tone (Fret 2 to 4) differently; this has no affect on its diatonic relationship with the first two templates. Instead of placing the third fret as fa (as on gamaut and Cfaut), he now sets it as Having already established the fundamental template on gamaut, Bermudo needs only to give instructions for shifting the third fret—from fa to mi (as in Step 1 of Figure 42).

a |— M — ^ — fr — — 1 L — ^ ) j r 1 {, -----7 V/ pt gf « h — It ------3 — ^ — a - 4 — 4 - 4 - 1

Figure 39. Bermudo's Diagram of the Ffaut Template (Declaraciôn, folio cvi, r).

When dealing with the templates in Group II (TST), Bermudo follows the same procedure of using the gamaut template as the basis. The fixed dia-

%Ibid., folio cv, v. Tambicn siruen los trastes como quedan puestos para la vihuela de Ffaut: excepto, que tercero en las superiores vihuelas es fa: en esta ha de ser mi. [Also, the frets function as they are placed on the vihuela of ffaut, except that the third fret in the higher vihuelas is fa, but on this one, it must be mi.] 150 tonic frets for this group are placed in the same manner as in the first template.37 However, the placement of the chromatic frets varies for this group of templates. For the Are template, all four chromatic frets are designated as fa, which requires the shifting of the first, sixth and eighth frets a comma lower than their original positions on the gamaut template. Since the third fret is already fa on gamaut, one need only shift three of the chromatic frets (as in Steps 2-4 in Figure 42). The Dsolre template, on the other hand, calls for three fa-frets (first, third and eighth), and one mi (sixth). Working with the gamaut model, one need lower only the first and eighth frets (Steps 2 and 4 in Figure 42), leaving the third and sixth as they are.^ Figure 40 shows Bermudo's version of the Are and Dsolre templates.

37ibid., folio cvi, r. En las dos vihuelas semejarûes (conuiene a saber la de Are y Dsolre) los seys trastes que pusimos primero: estan fixos, que no ay necefiidad de mudarlos: pero algunos de los otras se mudaran. El traste primero en la vihuela de gamaut fue mi; y eh la de Are es fa. [On these two similar vihuelas (that is. Are and Dsolre), the six frets that we placed first are fixed, and there is no need to change them, but some of the others will be changed. The first fret of the vihuela of gamaut was mi, and on that of Are is fa.] ^Ibid., folio cvi, v. Para que los trastes de la vihuela de gamaut vengan apelo de los de la vihuela de Dsolre: solo dos se han de mudar, que son primero y octauo. Estos en la vihuela de gamaut formauan mi: y en esta han de formar fa. Mudarse han segun ya fue dicho en la vihuela de Are. [So that the frets of the gamaut template coincide with those of the Dsolre template, it is necessary to change only two—the first and the eighth. On the gamaut template, they formed mi, and on this template, they must form fa. They can be changed according to what was said about the Are template.] 151

—1> r - e 5------B ---- ^ —^ c „ —f Cl n L J K CL —t t r w - 4 - f —}---- K— 4 f f t —-V- a —h ---- ^ — — e t L 1 . >1 vv/ J -----k -J ----

Figure 40. Bermudo's Diagram of the Are and Dsolre Templates {Declaraciôn, folio cvi, v).

Group III (STT) comprises the last two templates — Elami and bmi.

Both require the shifting of the first, sixth and eighth frets from mi to fa (from the gamaut template). To achieve this fret placement, one simply follows the procedures for the Are template (Steps 2-4 in Figure 42).^9

39lbid., folio cvi, v. En la vihuela do bmi mudar se han 1res diuisiones de tono, conuiene al saber el traste primero, sexto y octauo. En la vihuela de gamaut formauan estos très mi: yen esta han de formar fa. El como se han de mudar ya fue dicho en la vihuela de Are...Para la vihuela de Elami se mudaran las mesmas tres diuisiones de tono que sc mudaron en la de hmi. [On the bmi vihuela (template), three divisions of the whole tone must be changed, that is, the first, sixth and eighth frets. On the gamaut template, these three frets formed mi, but on 152 Actually, the disposition of the chromatic frets on the Elami and bmi templates is the same as that of Are. The bmi template, however, requires a diatonic alteration. The fourth fret, (which is normally a fixed fret) must be moved a comma lower (as in Step 5 of Figure 42). Figure 41 shows Bermudo's version of the Elami and bmi templates.

------1------7 3 %r —J---- » —1 5---- ? r c I --T. .1. o —z f ' {. t 3 h — d -b - r if) 1 < * - J " 9} 3■ f- J ■ ' "A VI J Ld b ■J - j —« ----- ^lA 7 fH a L J

» . > b 0Î r r' - j i z r ■ Cl " 7 t: — F------Ü’ 0 LI ' ) — a L—— ------h 1, t -* - y — y; - 3 r,‘ — 1 J J II1 ^ h - -J — ft ___ t j - j 0 — -t ------h — d — * I - y —4s -41

Figure 41. Bermudo's Diagram of the Elami and bmi Templates (Declaraciôn, folio cvii, r)

To facilitate the placement of these "shifted" frets for the various tem plates, Bermudo gives a separate set of instructions, presented as a continua tion of his previous steps (displayed in Figure 36). At this point, he does not

this template, they must form fa...For the Elami vihuela (template) the same three divisions of the whole tone arc alterred as on the bmi template ] 153 give any letter names because he is dealing with several different templates at once. A paraphrase of his instructions follows:^^ Step 1. To shift the position of the third fret from fa to m i, divide the distance from the first fret (mi on gamaut template) to the bridge into nine equal parts. The first point (9:8—a whole tone above the m i on the first fret) sets the third fret on mi. Step 2. To shift the position of the first fret from mi to fa, divide the distance from the third fret (fa on

gam aut template) to the bridge into eight equal parts. Adding another part toward the nut (9:8) sets the first fret on fa. Step 3. To shift the position of the sixth fret from mi to fa, divide the distance from the new first fret (fa) to the bridge into four equal parts. The point nearest the nut (4:3) sets the sixth fret on fa. Step 4. To shift the position of the eighth fret from m i to fa, divide the distance from the tenth fret to the bridge into eight equal parts. Adding another part toward the nut (9:8) sets the eighth fret on fa. Step 5. To shift the fourth fret a comma lower on the bmi template, divide the distance from the sixth fret (fa) to the bridge into eight equal parts. Adding one more part toward the nut (9:8) lowers the fourth fret by a comma.

^Ibid., folio cv, r-cvi, v. For translation, see the Appendix. 154 Figure 42 illustrates Bermudo's instructions for redividing the whole tone, thereby moving the chromatic frets for the designated templates. The figure also shows the manner in which the fourth fret (ordinarily a fixed, diatonic fret) is shifted a comma lower.

1A 3A 6A 8A frets5 1 2 3 4 5 6 7 8 9 10 4A 1 1 > ; 1 1 1 1 ■

1 1 1 ' 1 1 §■ 3 1 1

------1------1------1------1------1------1——4------nut bridge

Figure 42. Method for Placing the Alternate Chromatic Frets, Including the Adjustment cf the Fourth Fret on the bmi Template.

Clearly, Bermudo's templates establish the comma distinctions among the chromatic frets (and one diatonic fret on bmi). These are the frets that must be moved to facilitate the proper intabulation (and interpretation) of certain compositions. As Figure 43 illustrates, the disposition of the chromatic frets on the gamaut and Cfaut templates is identical. The first, sixth and eighth frets are mi, while the third is fa. The Are and Elami templates are also identical in the disposition of chromatic frets, all of them representing fa. The Ffaut template more closely resembles those of gamaut and Cfaut, differing only in the placement of the third fret (mi, instead of fa). The Dsolre and bmi templates are more closely related to those of Are and 1 5 5 Elami: the Dsolre template differs by maintaining the sixth fret as a mi-fret; the bmi template differs by including an additional fret adjustment—tlie fourth fret is lower by a comma. In Figure 43, the letter names (and cents) are given for all the frets (up through the tenth) on the sixth course of each template.

nut 1 2 3 4 5 6 7 8 9 10 r r# A Bb B c c# d d# e f 1 {— - 4 — — 4— — f— — I— — !— —4— —H- — 1— —\ 0 114 204 294 408 498 612 702 816 906 996

c c# d e** e f f# g g# a 1------4=------1------1------1------1------1------i------1------1------1 0 114 204 294 408 498 612 702 816 906 996

f f# g g# a b** b c c# d ------1 1------1------1------:------i------1------1------!------1------1 0 114 204 318 408 498 612 702 816 906 996 A Bb B c c# d e f f# g ------1 1------1------1------1------1------1------1------1------1------1 0 9 0 204 294 408 498 588 702 792 906 996

d e f f# g g# a b*’ b c ------1 1------1------1------1------1------4------1------1------1 0 90 204 294 408 498 612 702 792 906 996

e f f# g g# a b^* b e c# d ------1 1------1------1------1------1------1------1------1------1---- -I 0 90 204 294 408 498 588 702 792 906 996

B e c# d e f g ^ g a 1------1------1------1------1------h ------1------1------1------1------1 0 90 204 294 384 498 588 702 792 906 996

Figure 43. The Placements (and Values in Cents) of the Frets on the Sixth Course of Each Template. 156 Figure 44 summarizes the disposition of the movable frets on Bermudo's templates in terms of mi- and /a-frets, and displays in the groups designated by Bermudo. Here, the similarities and disparities among the templates become more apparent.

Template Chromatic Frets 1 3 4 6 8 Group gamaut mi fa mi mi 1 Cfaut mi fa mi mi Ffaut mi mi mi mi Group Are fa fa fa fa II Dsolre fa fa mi fa Group III Elami fa fa fa fa bmi fa fa fa fa fa

Figure 44. Summary of the Disposition of M i- and Ffl-Frets on Bermudo's Templates.

By dedicating a large portion of the vihuela material to detailed explanations of Pythagorean fret placement and its use in intabulation, Bermudo evidently reflects a tendency of his day to favor this system. Clearly, he believes that Pythagorean tuning is a logical, viable system in use on the vihuela. He states: "Everything I have said about the vihuela is that which very knowledgeable and practical musicians have used to the present."^^

4tlbid., folio cviii, r. Todo quanto de la vihuela tengo dicho es los que hasta oy los muy sabios musicos practicos han usado. 157 Despite his concentration on the Pythagorean system, Bermudo refers to "new" theories of tuning for the keyboard as well as for the vihuela. In the Prologue to the Declaraciôn, he states his intention to present new and more practical theories of tuning and temperament for both vihuela and keyboard, but only after he deals with the old theories that are applicable to the instruments of his day.^z The "new" method of fret placement for the vihuela appears in the very last chapter of the vihuela material (Book IV, Chapter 86), where Bermudo offers an approximate equal temperament. He defers coverage of the new methods for the keyboard and harp to Books VI and Vn, neither of which was ever published. Perhaps, there, he would have advocated equal temperament for these instruments as well.^^

Method of Fret Placement Using Temperament Bermudo presents his final method of fret placement at the end of the vihuela material, using his theoretical "invention" (the 7-course-D disposition) to illustrate his points. His objective is quite clearly to create a tuning scheme in which "all the semitones are playable." Not only does this

■^Ibid., folio +vii, r. Afii tracto de la vihuela, y organos, y pongo muchos preceptos en el libro quarto: y en fin del dicho libro, and en el tratado ultimo del sexto libro escriuo en contrario. Consyderando el tiempo, y para quien scriuo, y el artificio de los instrumentes: no ay contradicion en mi doctrina: porque primero pongo lo que se usa en los instrmentos y artificio viejo, para el que lo quisiere usar: y despues paCo adelante para los estudiosos y curiosos. [Thus, I deal with the vihuela and the organ, placing many precepts in the fourth book. At the end of that book (Book IV), and in the last tractate of the sixth book, I write to the contrary. Taking into account the times, for whom I am writing, and the method for the instruments, there is no contradiction in my doctrine. Because, first, I place that which is used on the instruments and used in the old arts for ones who would want to use it, and then I progress further along for the studious and curious ones.] '*^He never broaches the subject of Pythagorean tuning when dealing with the keyboard or the harp (also Book IV). All references to tuning indicate that he planned to discuss this topic at length in Books VI and VÎT. 158 method reflect the needs of the musicians of this period, but it also shows Bermudo's ingenuity. Bermudo declares that this method is applicable to the keyboard as well as to all fretted string instruments, adding that if organ builders become familiar with it, they will be able to construct an organ that also has equally playable semitones. He also implies that there will be no "faults" on certain frets of the vihuela if one uses this tuning scheme.^^ Bermudo begins this final method of fret placement by instructing the reader to make all necessary calculations and measurements on a separate piece of paper—a procedure prescribed for all the previous methods. In fact, this time, he provides the line. (See Figure 45, below.)**^ Again gamaut is the fundamental name of the sixth string (line). He begins by placing five diatonic frets by means of the Pythagorean system: second (A), fourth (B),

^Ibid., folio cix, r. ...y poniendo ahora Ids trastes en nueuo modo y manera, haremos que en cada uno de los dichos traste tenga todas las seys bozes, que es lo sobredicho poderse taner todos los modos por cada uno de los irasfe, y (anerse todos los semitonos. [.. .and now we will be placing the frets in a new method and style, in which we will be able to play all the modes through each one of the frets (which will have all six syllables, no faults), and all the semitones will be played.] Bermudo indicates future discussions on the keyboard and its tuning in his references to Books VI and VII. See Chapter III above. 45ibid., dx, r. El modo que en este pusiere de poner trastes: no seruira para sola la vihuela de siepte ordenes, sino para todo instrumente de cuerda y trastes.. El que el sobredicho modo de preparar las sesquioctauas supiere exercitar en el hazer del organo: sacara el organo que se tangan todos los semitonos. [This method will work not only for this particular 7-course vihuela, but for all fretted string instruments...He who would know how to execute this method of preparing the sesquioctaves for making the organ, will create one (an organ) which plays all the semitones ] ^Ibid., folio cix, v. Tomad en una regia bien labrada y derecha el tamaho de las cuerdas de vuestro instrumente, y hazed una linea derecha sobre la regia por la qual leueys el compas en los repartimientos que hizierdes, y porque mejor se entienda: lo yre practicando en las lineas puestas en el margen desta pagina. [Take a well made and straight ruler, the size (length) of the strings of our instrument; make a straight line above the ruler, on which you will guide the compass through the making of the divisions. To make it better understood, I will demonstrate it on the lines placed in the margin of this page.] 159 fifth (C) and tenth (F), and twelfth (G). A paraphrase of Bermudo's method follows Step 1. Divide the entire string into four equal parts. The point nearest the nut (4:3) marks the position of the fifth fret (C). Step 2. Divide the distance from the fifth fret to the bridge into four equal parts. The point closest to the nut (4:3) marks the position of the tenth fret (F—a perfect fourth above the fifth fret, C). Step 3. Returning to the division made in Step 1, the point in the middle of the string, (2:1) marks the position of the twelfth fret (G—an octave above gamaut). Step 4. Divide the entire string length into nine equal parts. The point nearest the nut (9:8) marks the po sition of the second fret (A—a whole tone higher than

gamaut). Step 5. Divide the distance from the second fret to the bridge into nine equal parts. The point nearest the second fret (9:8) marks the position of the fourth fret (B— a whole tone above the second fret. A). Bermudo now informs the reader that certain frets must be adjusted. The first adjustment is to be made to the major third that consists of two sesquioctaves, from gamaut (open) to B (4th fret). Here, he states that one must subtract a "certain quantity" from the first sesquioctave (A to B) and then, from

^^Ibid., folio cix, v. For translation, see the Appendix. 160 the other (G to A) before placing the rest of the frets.^ As Figure 45 shows, Bermudo makes all divisions and adjustments on a single line. Step 6. Divide the entire string into five equal parts. From the point nearest to the nut (5:4) to the fourth fret (B) is a (syntonic) comma. Step 7. Divide the comma into three equal parts, and at the point nearest the B (Fret 4), place a mark. This process repositions the fourth fret (Fret 4A). Step 8. Divide the string from the new fourth fret (Fret 4A) to the bridge into eight equal parts. Adding one more length toward the nut (9:8), marks a point that lies a short distance beyond the second fret toward the nut. Step 9. Divide the distance determined in Step 8 into two equal parts. The point in the middle marks the "new second" fret (2A). Step 10. Divide the distance from the new second fret (Fret 2A) to the bridge into four equal parts. At the point nearest the nut (4:3), place the seventh fret (D—a perfect fourth above the newly adjusted A). Step 11. Divide the distance from the new fourth fret to the bridge into four equal parts. At the mark near-

^Ibid., folio cix, v. Pues quedan dos sequioctauas en esta cuerda una desde la h hasta la a y otra desde la a, a la b, y porque son muy subidas dos sesquioctauas para una tercera mayor: es menester preparar la dicha tercera con quitar cierta quantidad a cada una de las dos sesquioctauas, y puestos el traste segundo en la primera sesquioctaua preparada y el quarto en la segunda: con estos dos trastes preparados sacaremos todos los demas. [Thus, there are two sesquioctaves on this string; one from the h to the a, and another from the a to the b. Because the two sesquioctaves are very high for a major third, it is necessary to prepare that third by removing a certain quantity from each sesquioctave. Having placed the second fret on the first of the prepared sesquioctaves and the fourth on the second, we will determine the rest.] 161 est the nut (4:3), place the ninth fret (E—a perfect fourth above B). In Steps 1-11, Bermudo places all the diatonic frets for the vihuela. In the process, he adjusts the fourth fret (B) lower by one-third comma, and the second fret (A) lower by one-sixth comma. From these two adjustments, he places the two remaining diatonic frets—ninth and seventh—in their respective positions (each showing the comparable comma adjustments). With these frets in place, he continues his method by placing the chromatic frets—first, third, sixth and eighth (Steps 12-17). Step 12. Divide the distance from the tenth fret to the bridge into two equal parts. Extending toward the nut by one more length of the same size (3:2), place the third fret (Bh). (This fret has undergone no adjustments, since it is derived from an untempered tenth fret.) Step 13. Divide the distance from the third fret to the bridge into four equal parts. The point closest to the third fret (4:3) marks the position of the eighth fret (E^). (This fret also shows no comma adjustment, since it has been derived from the third fret.) Step 14. Divide the distance from the fourth fret to the bridge into nine equal parts. At the point nearest to the nut (9:8), place a mark. (Since this mark is derived from the fourth fret—already lowered by one-third comma—it will also reflect the same comma adjustment. As it is now, this point would locate the position of the 1 6 2 sixth fret (C#), but Bermudo does not label it so, because he intends to adjust it further.) Step 15. Divide the distance from the second fret to the bridge into five equal parts. At the point nearest the nut (5:4) place another mark. Step 16. Divide the distance between these two marks into three equal parts On the point nearest to the seventh fret, place the sixth fret (C#). (This fret shows a downward adjustment of one half comma from the Pythagorean third.) Step 17. Divide the distance from the sixth fret to bridge into three equal parts. Add one more from the sixth fret toward the nut which marks the position of the first fret (G#). (Since this fret is created from the sixth, it will also show the downward adjustment of one-half comma.) Bermudo provides an illustration of this final method, as seen reproduced in Figure 45. Here, he marks the placement of the frets on a single line (from h to 1), which, for the sake of convenience, is illustrated as two line segments running along the margin of the folio.

r A hC flJPfC * 7 - * .,"...41------. I H — m----- !----- i----- 1 t-----i— 1

Figure 45. Bermudo's Diagram of String Division in His Method of Fret Placement Using Temperament (Declaraciôn, folio cix, v). 163 Towards Equal Temperament The result of Bermudo's method of fret placement is an irregular tem perament that is a very close approximation of equal temperament. Consistent with his first three methods, he establishes the five diatonic frets in the Pythagorean system (second, fourth, fifth, tenth and twelfth), and follows with specific adjustments, as shown in Figure 46. To make these adjustments, he determines the syntonic comma (22 cents) at the fourth fret (B).'*^ After dividing it, he moves the fourth fret toward the nut by one-third comma (-7.33 cents), lowering it from its original Pythagorean value of 408 cents to its new value of 400.67 cents. From this fret, he can adjust the second fret (A). Here, he derives the position of the second fret by means of a proportion from the new fourth, and cuts the previous adjustment (one- third comma) in half, displacing the second fret (204) downward by only one- sixth comma (-3.66). Thus the whole tone from gamaut to Are (second fret) consists of 200.34 cents. From these two adjusted frets, he places the seventh and ninth frets by pure Pythagorean proportion. Consequently, the seventh fret (perfect fourth above the second fret) reflects the same downward adjustment of one-sixth comma as the second fret; the ninth fret (perfect fourth above the fourth fret) reflects the same downward adjustment (one- third comma) as the fourth fret. Since Bermudo determines the third and eighth frets from the tenth fret, which is pure by proportion, no adjustments are made to them. They remain Pythagorean.

^^The syntonic comma is the difference between a Pythagorean major third (81:64) and a pure third (5:4). This is the only context in which Bermudo uses the 5:4 proportion. He nevers makes a case for the just third as a basis for a system tuning (as in just intonation, or meantone temperament). He uses this proportion for the sole purpose of determining the syntonic comma. 164 To place the last two frets (first and sixth), Bermudo makes one more comma adjustment. In this case, he finds the location of the ditone above the fourth fret (B), which reflects the downward one third comma adjustment (-7.33 cents). Forming a 5:4 proportion, he determines a syntonic comma from the second fret (A), which he divides into thirds. This enables him to lower the sixth fret (C#) by a total of one half comma (11 cents).^^ This adjustment is reflected in the lowered position of the first fret (one-half comma), and would be seen in the eleventh, if Bermudo had given directions for placing it. Figure 46 shows the disposition of the frets, according to Bermudo's final method of fret placement.

not given 1 T frets 1 2 3 4 5 6 7 8 9 10 11 12

comma -1/2 •1/6 -1/3 -1/2 -1/6 -1/3 -1/2 G G# A Bb B C C# D Eb E F F# G h cents 0 294 498 792 998 1200 200.34 698.34 400.67 898.67 103 601 1099

Figure 46. Disposition of the Frets (and Cents) in Bermudo's System of Temperament.

^^Since the ditone already reflects the one-third comma adjustment, and the division of the second syntonic comma allows another one-sixth, the adjustment here totals one half comma (-1/3-1/6=-l/2). 1 6 5 Clearly, Bermudo is striving to achieve a more flexible system of tuning than the Pythagorean system. Although his system is irregular, it closely approximates equal temperament. Table 3 summarizes the fifths in Bermudo's system, and reveals that eight of them remain pure (702 cents); three are tempered to 698.33 cents; and the value of the "wolf fifth" (actually a diminished sixth—G#-Eh) is increased to 689 cents, nearly eliminating it.^i

Table 3. Summary of Fifths in Bermudo's System of Temperament.

Interval Cents Interval Cents C-G 702 Eb-Bb 702 D-A 702 [F#]-C# 702 F-C 702 G-D 698.34 E-B 702 A-E 698.33 Bb-F 702 B-F# 698.33 C#-G# 702 G#-Eb 689

An evaluation of the whole tones in Table 4 shows that four of them are Pythagorean (204 cents); six are tempered to approximately 200 cents—the whole tone in equal temperament—and two (actually diminished thirds) comprise 191 cents.^2

^^The cent-values calculated in these tables are derived from the 'Table of Intervals not Exceeding an Octave" in Hermann L. F. Helmholz, On the Sensation of Tone, 2nd ed., trans. and revised by Alexander J. Ellis (New York: Dover Publications, 1954), 453-6. ^^An interval of 191 cents comes very close to the whole tone of 193 cents in Aron's system (1523) of meantone temperament, or the whole tone of 191.5 in Zarlino's (1558). However, Bermudo does not acknowledge the possibility of any such system on the vihuela. 166 Table 4. Summary of Whole Tones in Bermudo's System of Temperament.

Interval Cents Interval Cents Bh-C 204 B-C# 200.33 Eb-F 204 C-D 200.34 F-G 204 D-E 200.33 [F#]-G# 204 E-[F#j 200.33 G-A 200.34 G#-Bb 191 A-B 200.33 C#-Eb 191 In the case of the major thirds in this system, as shown in Table 5, only one remains a Pythagorean ditone (408 cents); three are tempered slightly to 404 cents; four are the size of thirds in equal temperament (400 cents); and the enharmonic thirds (actually diminished fourths) vary from 391.33 to 395 cents.53

5. Summary of Major Thirds in Bermudo's System of Temperament.

Interval Cents Interval Cents Eb-G 408 F-A 404.34 G-B 400.67 Bb-D 404.34 A-C# 400.66 [F#]-Bb 395 C-E 400.67 C#-F 395 D-[F#] 400.66 G#-C 395 E-G# 404.33 B-Eb 391.33

Obviously, Bermudo's semitones exhibit the most variety of sizes. But, he manages to temper them so that they are neither as large as the major semitone (114 cents) nor as small as the minor semitone (90 cents). In fact, most of them are very close to the equal-tempered semitone of 100 cents.

^^All of these thirds are much larger than those found in systems of tuning contemporary with Bermudo. Aron's major third consists of 386 cents; Zarlino's, 383 cents; and Salinas', 379 cents— all of which represent values in meantone temperament. 167 Table 6. Summary of Semitones in Bermudo's System of Temperament.

Interval Cents Interval Cents G#-A 97.34 G-G# 103 B-C 97.34 A-Bb 93.66 C#-D 97.34 D-Eb 93.66 E-F 97.33 Bb-B 106.67 F-[F#] 103 Eb-F 106.67 C-C# 103 [F#]-G 101

Conclusions Bermudo's pedagogical intent is evident in his progressively refined schemes of fret placement. They parallel his graduated discussions of the vihuela itself. The first method is designed for those with little experience, and is uncomplicated. It should not be misconstrued as equal temperament, because such was not Bermudo's intention according to the front matter and to comments made elsewhere in his treatise. It is apparent that Bermudo advocates the Pythagorean system of tuning; he gives three different methods for placing frets in this system. It also functions as the foundation of his advanced method of tempering the disposition of the vihuela's frets, which approximates equal temperament, since he modifies the frets after they have been placed in the Pythagorean system. He acknowledges no other systems of temperament or tuning (meantone or just) for the vihuela. When he uses the 5:4 proportion (the ratio of the just major third), it only serves the purpose of deriving the syntonic comma—a necessary ingredient in making fret adjustments. Although Bermudo's division of the comma is not very accurate, it is obvious that his manipulation of the Pythagorean proportions and the "crude" comma divisions result in a diatonic scale that is very close to an 168 equal tempered scale.®** Bermudo achieves this scale by alterring just two of the frets, the second and fourth. As seen in all his other methods of fret placement, Bermudo consistently omits the eleventh fret. Since he describes the vihuela as having only ten frets, it is apparent that he believes that there is no need to place an eleventh fret. The placement of the twelfth fret often is part of the ritual of Pythagorean tuning, and in the case of Bermudo's third method, he adds the twelfth, thirteenth and fourteenth, while he continues to omit the eleventh. This evidence seems consistent with Bermudo's description of the vihuela as an instrument with ten tied (or movable) gut frets on its neck, and implies that the frets forming octaves and compound intervals are either theoretical exercises, or (as evidenced by surviving lutes and guitars of the period) fixed or glued frets on the table of the instrument, not subject to adjustment by the performer.

54vogel, Martin, Die enhamonische Gitane. (Bonn: Veriag fiir systematische Musikwissenschaft, 1986), 7-13. Vogel deals with the problem of achieving equal temperament on the modem guitar having frets constructed in one single piece. He then uses a guitar by Walter Vogts, in which there are individually adjustable "mini-frets" for each string, to illustrate "true" equal temperament on the guitar. The photograph shows that these "mini-frets" do not run across the fingerboard in a straight line. Clearly, Bermudo was able to create, in his own "crude" way, a very close approximation of equal temperament, using single strands of gut string for the frets. CHAPTER VI AN EVALUATION OF BERMUDO'S PYTHAGOREAN TUNING ON THE VIHUELA

The relevance of Bermudo's writings on fret placement and his theoretical constructs, called "templates," may be tested by applying them to the representative vihuela music of his era. An effective methodology proposed is a simple reciprocity test: If "A" (being a sixteenth-century vocal model) yielded "B" (a sixteenth-century intabulation of the same), will "B" successfully translate back to "A" using the appropriate template provided by Bermudo? If the procedure proves successful, then one can conclude that Bermudo knew what he was writing about and that he provided the appropriate theoretical "key" to unlock the door between vocal models and in tabulations. By allowing only those chromatic pitches provided on the designated template, with no enharmonic substitutions, one will see to what extent Bermudo's templates form a logical link in both directions between sixteenth century vocal models and contemporary vihuela transcriptions of them. Indeed this procedure also reveals that the intabulations of the Spanish vihuelists lie within—and work within—the Pythagorean system on the vihuela as proposed by Bermudo.

169 170

Intabulation Intabulation is the process of converting musical compositions from staff notation to vihuela tablature—a very graphic and practical notation in which the pitches are represented by a series of numbers placed on a set of lines. Literally, tablature is an illustration of the left hand fingerings for a particular composition. The horizontal lines represent the courses of the vihuela, and the numbers (or letters) placed on those lines indicate the designated fret to be played. Historically, tablatures have differed one from another among the various countries of Europe. There were three types of tablature for lute (vihuela) in use during the sixteenth century: Italian, French, and German.^ The Italian tablature, used in Spain as well, designates the top line as the sixth course (lowest pitched course), and uses numbers to indicate the fingerings (O=open, l=first fret, 2=second fret, etc.). French tablature inverts the order of the strings, labelling the bottom line as the sixth string, and employs letters (a=open, b=first fret, c=second fret, etc.) to indicate the fingerings.^ German tablature is totally different from both the French and Italian styles; it does not utilize the graphic display of lines, but rather designates each of the frets with its own special sign.^ Tablature may vary according to the particular composer as well. Such is the case with the tablature of Luis Milan, a Spaniard. In his collection of

^Willi Apel, The Notation of Polyphonic Music, 900-2600, 5th ed. (Cambridge, Massachusetts: The Medieval Academy of America, 1953), 55. ^Another brief description of these tablatures may be found in James Tyler's book. The Early Guitar: A History and Handbook, 63-65. ^Apel, Notation, 72-74. The complexities of this particular type of tablature require the player to memorize the location of each individual symbol on the fingerboard. 171

1536, El Maestro, Milan deviates from the normal Spanish/Italian type of tablature by designating the lowest line as the lowest course (as in French tablature), but at the same time, using numbers (as in Italian tablature). At the end of the Intermediate section, Bermudo explains the basic principles used in Spanish tablature: rhythmic signs, syncopa, ties, etc. He stipulates that the student, in preparing to intabulate, first diagram the necessary templates and study them carefullyW hen ready to intabulate, both the vocal music and the template should be situated in front of the student so that they are easily visible.^ Bermudo concludes his preparatory remarks with two of his own examples of a romance viejo, entitled "Mira Nero de tarpea" in which he supplies both tablature and vocal line. His first example is intabulated for the standard 6-course disposition on Are. In his second, he intabulates the same composition for his "invented" theoretical disposition—7-course-D. Bermudo recommends that the student who wishes to intabulate should study the music of famous composers, so that the necessary principles may be fully understood. Bermudo suggests the student begin with some villancicos, because of their simple, homophonie structure.^ These pieces

^Bermudo, Declaraciôn, folio xdii, r. Antes que comenceys a dfrar: sacad estas vihuelas, y estudialdas: porque es buen prindpio para ser un consumado tanedor. [Before you begin to intabulate, diagram these vihuelas (templates), and study them. It is a good beginning in order to be a consummate player.] ^Ibid., folio xcviii, v. Quando el tahedor quisiere començar dfrar: delante de si ponga la musica en una parte, y en otra la vihuela pintada por do ha de dfrar. [When the player wishes to begin intabulating, he may place the music in front of himself to one side, and to the other side, the vihuela (template) which he must use to intabulate ] ^Ibid., folio xdx, v. La Musica que aueys de començar a cifrar: seran unos villancicos (primero duos, y despues a tres) de Musica golpeada, que communmente dan todas la bozes junctas. [The music that you must begin intabulating, will be some villandcos (first, 2-voice, and then 3- voice) "measured "(homophonie) music, in which all the voices usually sound together.] 172 would require only a beginner's skill, since they are uncomplicated. Their simplicity does not develop one's ear. After gaining this initial experience, Bermudo proposes the intabulation of more challenging works. The compositions Bermudo prefers are those of Josquin, Morales and Gombert. The music of Josquin and Morales is especially abundant and representative of good examples for in tabula ting. ^

In the masses of the illustrious musician Christobal de Morales, you will find much music to intabulate, with so many and such good qualities, which I cannot explain...You will find few composers who keep the qualities and diferencias of the letters. And among the few is that author [Morales]. Amid the good foreign music for intabulating, do not forget that of the great musician Josquin, who began music. When the student has successfully intabulated the works of Morales and Josquin, he may attempt the works of Gombert. Since Gombert's works are more complicated, Bermudo reserves their intabulation for those who are experienced in intabulation.®

The last [music] which you must intabulate will be that of the excellent Gombert. Since one encounters difficulty in setting it on the vihuela, due to its "extravagance," I put it in the last place. Bermudo also recommends that the student examine the intabulations of those vihuelists who are already accomplished in this skill, so that they may learn from these experienced musicians. In the Elementary

^Ibid., folio xdx, v. En las misses del egregio musico Christoual de Morales hallareys mucha Musica que poner: con tentas, y tan buenas qualidades que yo no soy suffidente explicarlas.. .Pocos componedores hallareys, que guarden las qualidades, y differendas de las letras. Y entre los pocos, en un el sobredicho author. Entre la musica estrangera que hallareys buena para poner: no olvideys la de el gran musico lusquin que començo la musica. ®Ibid., folio xdx, V. Lo ultimo que aveys de poner sea Musica del excelente Gomberth. Por la difficultad que tiene para poner en la vihuela, por ser derramada: la ponga en el ultimo lugar. 173

section, he names Narvâez, Fuenllana, Mudarra and Valderrâbano as the notable musicians to be emulated,® while in the Intermediate section, he mentions only Fuenllana and Valderrâbano.

The Use of Templates As seen in Chapter IV, a template is literally a diagram of the fingerboard of the vihuela, illustrating the names of the strings and frets (up through the tenth fret). Each template is designated by the letter name on the open sixth course (gamaut, Are, bmi, etc.), and the courses and frets are labelled accordingly. The templates are designed so that musicians can easily convert the pitches of the vocal music into tablature, by finding the comparable letter name on the template. Thus, the designated fret number is placed on the appropriate line of the tablature. The result is a series of numbers (representing the frets) placed on any of the six lines (representing the courses)—or tablature. To assist the student in discerning which template must be used, Bermudo suggests a preliminary step which is wholly irrelevant to tablature notation but which, as a theoretical exercise, provides important support to the notion that templates such as his were actually used by musicians of the time in their intabulating activities. In effect, he directs the student to place clefs (key signatures, in so many words) at the beginning of each intabulated

®Ibid., folio xxix, v. folio ci, r. El que quisiere començar a cifrar...vea los libres de los seflalados musicos Anriquez de Valderauano, y de Miguel de fuenllana: y vera grandes primores para saber elegir modo primo y claro para las dfras que hiziere. [Let him who wishes to begin intabulating examine the books of the notable musicians Enriquez Valderrâbano and Miguel Fuenllana, and he will see the great beauties (necessary) for knowing how to first clearly select the manner of intabulating which he would use.] 174

composition." Usually the C- and F-defs were used to indicate the particular

template, while some preferred to use sparingly the G-clef .^2 Bermudo describes the manner of interpreting the locations of the defs, and thus determining the particular template to be used:^^

It [the music] uses the Are vihuela [template], and thus, the third fret of the fifth string [course] carries the ffaut def, and the first fret of the third carries that of csolfaut. Bermudo indicates the use of templates in all three levels of study, and each time the topic arises he adds more details. His discussion peaks in the Advanced section, where he presents their most important aspect—the movability of the chromatic frets. In the Elementary section, he hints at the existence of seven individual templates, but obscures the issue by indicating that most players prefer the gamaut and Are templates. This passage has led some scholars to believe that transcribers of vocal music used these two templates exclusively. Bermudo presents sufficient evidence to contradict this assumption. Interestingly, Bermudo reports that the templates may be transposed to any scale degree, in addition to gamaut and Are (including Ah);i4

^ ^Ibid., folio V. Si dixere en las dfras donde traen las daues (como algunos curiosos lo ponen) bastante seria esto para saber porque vihuela se dfro. [If it says where the defs are located in the tablature (like some curious ones place them) this would be suffident for knowing on which vihuela (template) it was intabulated.] ^^Charles Jacobs, "Introduction" to Orphenica Lyra by Miguel Fuenllana, xxxii-xxxv. ^^Bermudo, Declaraciôn, folio ci, r. ...va por la vihuela de Are, y por tanto tiene la claue de ffaut en la quinta en el traste tercero, y la de csolfaut en la tercera en el traste primero. The use of these clefs to designate the various templates appears not only in the tablatures of the noteworthy musicians, but also in the detailed descriptions that Bermudo gives in the Intermediate section. He methodically designates the location of csolfaut and ffaut for each. ^^Ibid., folio xxix, r. Comunmente los tahedores de vihuela que son diestros en el arte de dfrar, y de poner en este instrumente dfras: ymaginan començar la sexta cuerda en vazio en gamaut, y algunas vezes en Are. Verdad es, que dfras he visto de buen tahedor ser la sexta la tecla negra que esta entre Are y bmi...Sabiendo el compas de poner los trastes: pueden ymaginar la sexta en 175

Usually vihuelists who are dexterous in the art of intabulating and placing numbers on this instrument, imagine the open sixth string as gamaut and sometimes. Are. The truth is, I have seen the tablature of a good player with the sixth string being the black key between Are and bmi...By knowing the means of placing frets, they [the players] can imagine the open sixth string on whatever sign [letter] that they want. The open sixth string can be not only gamaut or Are (according to what we have said), but bmi, Cfaut, Dsolre, or whatever other different signs [letters]. Since beginners are not expected to know the peculiarities of each template, Bermudo abandons further consideration of this matter in the Elementary section. Such details are reserved for the more experienced musician. So far, templates are simple vehicles for intabulation. If one can diagram them, then one can use them to intabulate easily. In the Intermediate section, Bermudo describes each template for the standard 6-course disposition in greater detail. Since he is not concerned with the specific placement of frets for each template, he provides only the diatonic letters and therefore makes no distinction in the sizes of the semitones (as reflected in fret placement). Obviously, an interpretation of Bermudo's theories of tuning based on this section alone could mislead— and has misled—writers into considering Bermudo an advocate of equal temperament. However, the explicit details found in the Advanced section demonstrate how this interpretation distorts Bermudo's intentions. Bermudo waits until his exposition of the "third method" of Pythagorean fret placement, in the Advanced section, to demonstrate the

vazio en qualquier signe que quisieren. Puede ser la sexta en vazio, no solamente gamaut, o Are (segun dicho auemos) pero bmi, y Cfaut, y Dsolre, y qualquiera de los otros signos différentes. 176 difference between the major and minor semitones (exemplified in the chromatic frets).^®

Selecting the Proper Template Bermudo provides, in the Intermediate section, some basic advice for selecting the proper template for intabulation. However, he is tentative in his presention.^^

There is a great difficulty in the matter of knowing how to intabulate (and I do not know if I have the words for explaining myself), that is, which vihuela [template] we will use to intabulate; whether there will be music that can be intabulated on all seven of the illustrated vihuelas [templates], or whether there will be music that can be intabulated on one, but not another. First, he advises the reader to examine the ambitus of the vocal music, and find the lowest note of the contrabass. This note should be placed on the open sixth string. If, for example, the contrabass extends down to gamaut, then the musician obviously should select the gamaut template. This advice accommodates those compositions with an ambitus of more than two octaves.^ ^

^^The illustrations referred to here, are the diagrams that Bermudo gives in the Declaraciôn. (See Figures 37-41.) He uses them to show the results of fret placement, and whole tone division employed in his third method of Pythagorean fret placement. This method is discussed in Chapter V. ^Îbid., folio xcviii, v. Una difficultad ay grande en la materia de saber cifrar (y no se si teme palabras para en ella declararme) y es, por qual de la vihuelas cifraremos. Si aura Musica que por todas siepte vihuela pintadas se pueda cifrar: o si de tal manera se cifrara por una, que no por otra. Si qualquier musica por sola una se puede cifrar: basdia seria tantas. ^Îbid., folio xcvii, v. Cûiero dezir, que por tal vihuela cifrareys: qual fuere el signo mas baxo de la contra. Si el contrabaxo allegare hasta gamaut, tomareys la vihuela que yo pinte, que comiença en gamaut: si abaxare hasta Are, tomareys la segunda que comiença en Are: y aSi de todas las otras. Esto se entiende: si la obra que cifrays anda en mas de quinze puntos. [I wish to say, that you will intabulate on that vihuela which is named according to the lowest note of the contrafbass). If the contrabass reaches (down) to gamaut, you will take the vihuela that I 177

Second, if the composition consists of a range smaller than an octave, Bermudo advises the reader to place the lowest note of the contrabass on other frets of the fifth or sixth course.^® Third, he allows the intabulator to extend the fingerings up to the fifth fret of the first course, but not to pass the seventh.^^ Although these criteria are vague, Bermudo considers them an adequate starting point. Unfortunately, he gives little supplementary information. Bermudo does point, however, to music that has already been intabulated. He directs the student to the music of the accomplished musicians, Fuenllana, Narvâez, or Valderrâbanor^o

You will recognize the good players who use many vihuelas [templates], because they do not always place the clef on one fret. In the titles [of pieces] which are

diagrammed on gamaut; if it goes down to Are, you will select the second vihuela that begins on Are, and so forth. This may be understood, if the work you are intabulating covers more than fifteen notes.] ^®Ibid., folio xcviii, r. El segundo auiso dara mucha lumbre. Toda Musica que anda en doze puntos: podeys poner el mas baxo punto en la quinta en el tercero, o quarto traste: y alcançara en la prima en el mesmos traste, que en la quinta tomastes. Si anduuiere en treze puntos començara el mas l»xo en la mesma quinta en el primero, o segundo traste. Si anduuiere en quatorze puntos: ponerse ha el mas baxo en la quinta en vazio...[The second advice will shed much light. On all music that covers twelve notes, you can place the lowest note on the fifth (course) on the third, or fourth fret, and it will reach to the same fret (as on the fifth course) on the first course. If it covers thirteen notes, the lowest will begin on the same fifth (course), on the first, or second fret. If it covers fourteen notes, the lowest (note) may t>e placed on the open fifth.] He also includes the possibility of placing the low notes on the various frets of the sixth course. ^ ^ id ., folio xdx, r. El tercero sera, que podeys poner la obra que suba hasta el quinto traste de la prima: y si fuere necessidad, al sexto y septimo. El que quisiere taner buena Musica y descansada (pudiendo lo hazer) no pafie del septimo traste de la prima: aunque carezca de las alabanças de los aldeanos. [The third (advice) is, that you can place the work that may rise to the fifth fret of the first (course), and if it were necessary, to the sixth and seventh (frets). He who wishes to play good music easily (being able to do it) may not pass the seventh fret of the first (course), even though it lacks the praises of colleagues ] ^Ibid., folio xc, v. Cognoscereys usar los buenos tahedores de muchas vihuelas: por que no siempre ponen la claue en un traste. En los titulos que tienen las dfras una vez dize, la claue de csolfaut esta en la tercera en el traste tercero, y es vihuela de gamaut, otra vez en el primero de la dicha tercera, y es vihuela de Are. De forma, que como mudan las vihuelas por do cifran: assi seûalan el lugar de la claue. 178 intabulated, one time it says, "the csolfaut clef is on the third fret of the third [course]," and it is the gam aut vihuela [template]; and another time, [the csolfaut clef] is on the first [fret] of the third [course], and it is the Are vihuela [template]. Bermudo acknowledges that some vihuelists choose not to use clefs in their tablature. However, where these are lacking, one can still determine the particular template employed by the evidence in the tablature—namely, the position of the semitones. He states:^^

If there is a semitone on the first [course], count down through the frets until you find the name of the open string. Then you will determine on which illustrated vihuela that music was intabulated.

Faults on the Templates, and How to Fix Them Since in the process of intabulation one uses the templates in Pythagorean tuning, Bermudo acknowledges that certain conflicts, or "faults," may arise. A fault, according to Bermudo, is a note that creates a specific conflict with another, such as false octaves (A#-B^), or a note that is playable on the vihuela (D#, A#, A^, etc.) but not admissable in the hexachordal system.^ These faults are a result of the restrictions imposed by the Pythagorean system of tuning, which does not permit enharmonic equivalence. If the first fret position on the second course, for example, were designated mi (as it is on the gamaut template), the resulting pitch would be a D#, which is not allowable in the hexachordal system. This chromatic pitch

^^Ibid., folio c, V . Si en la prima ay un semitono: venid contando por los trastes a baxo hasta que halleys en que boz començo en vazio: y assi juzgareys porque vihuela pintada se cifro la tal Musica. 22Bermudo allows G# in his system, where others use instead. 179

lies in the position normally occupied by an E^. In Pythagorean tuning, the D# cannot be used in place of Eh. Therefore, Bermudo designates this D# as a "fault," and urges the musician to implement one of several solutions. In his discussions pertaining to the methods of Pythagorean fret placement, Bermudo offers six possible ways to overcome these faults:

1) find an alternate fingering. 2) alter the pitch by finger pressure (left hand). 3) slant the fret. 4) move the fret. 5) place a double fret. 6) re-tune one of the strings in the course.

In the Pythagorean system of tuning, Bermudo's first solution has a limited value—each template having a rigid placement of certain pitches. If indeed the musician wishes to use the Eh, he must seek an alternative to the

D# located on the first fret of the second course. The alternate note (Eh) is found on the tenth fret of the fourth course only, which may be unplayable if the remainder of the fingerings lie on the lower frets. Actually, on the gamaut template, there is no optional location for the Eh, due to the specific fret placement. (The Eh on the third fret of the fifth course will not suffice, since it is an octave lower.) Examination of Bermudo's diagram of this template shows this problem, and the difficulty in solving it. (See Figure 37.) In his second "remedy," Bermudo suggests that the player alter the pitch of the D# (second course, first fret, or third course, sixth fret). This is to be done by the player's left hand technique, either by increasing or decreasing the finger pressure on the fret. Bermudo describes this common solution:^^

23lbid., folio cv, v. Si en este decimo traste no pudiere formar el dicho fa, porque esta occupada la quarta, o porque ay otro impedimento: formarlo ha en el sexto en la tercera, o en el 180

If one cannot form the said fa on the tenth fret, because the fourth [course] is occupied, or because there is another impediment, one should form it [fa] on the sixth [fret] of the third [course], or the first [fret] of the second. [It must be done] by depressing lightly and far behind the fret, so that mi becomes fa. Bermudo's third solution for correcting faults on the vihuela is effected by slanting the problematic fret—a solution that he does not favor. He states that there are some players who claim this solution is possible, but he clearly does not advocate it as a suitable remedy. It only disguises a serious problem:^^

Some claim to remedy those faults by placing the frets, where the designated faults are located, at a slant, taking them out of perpendicular. I give as an example the first fret of the gamaut vihuela [template], which is mi for four strings [courses] and must be fa for the third and second. To make itfa, they place that fret at a slant, where at the first [course] it must be lower and the others [courses], mi, as needed. Let this not be a remedy, but a compromise. . Bermudo presents the fourth solution for more problematic faults. This remedy is necessary when there are discrepancies in the octaves and unisons. To explain, Bermudo demonstrates a typical unison fault on the gamaut template, and the way in which it can be solved. He states;25

primero de la segunda: con tal condidon que huelle muy atras del traste y floxo: para que de mi venga a ser fa. 24ibid., folio evil, r. ...las sobredichas faltas algunos pretenden remediarlas con poner los trastes donde estan las dichas faltas a costados, sacandolos del quadrado. Do por exempio el traste primero de la vihuela de gamaut, el qual es mi para quatro cuerdas, y auia de ser fa para la tercera y segunda. Y para hazer el dicho fa ponen el tal traste en viaje, y pierde la prima un poco, y las otras que lo auian menester mi. Que este no sea remedio sino emplasto... ^Ibid., folio cvii, v. Esta primero de la tercera subido una comma mas que el quinto de la quarta.. .Luego no son unisonus en esta vihuela el quiuto [sic] de la quarta y d primero de la tercera. Si el traste primero allegaGen a la ceJa que de mi lo h izie^n fa: sin falta ninguna estaiian unisonus, y como quedan puestos no son unisonus. 181 The first [fret] of the third [course] (A#) is a comma higher than the fifth [fret] of the fourth [course] (Bh)...Now, there is no unison on this vihuela [template] between the fifth [fret] of the fourth [ c o u r s e ’ and the first [fret] of the third [course]. If they [musicians] would move the first fret toward the nut, making the mi into fa, there would be no fault in the unison; but as they are placed now, they [the two pitches] are not in unison. Bermudo presents a fifth remedy, namely, adding to the instrument's neck an alternate "first fret" a comma away (higher or lower) from the original one. This solution applies only to special circumstances where once the frets are placed, there is no need to move them. Bermudo recommends this particular template for musicians who choose not to deal with subtle differences found in the seven individual templates. This optional vihuela would consist of "fixed frets," letter names (in gamaut), and a disposition of the chromatic frets that corresponds to the Are template. The result is a "combination" template with fixed frets (including a doubled first) in Pythagorean tuning.26 The last solution to faults on the vihuela template is reserved for the highly accomplished musician. Here, Bermudo suggests that if all else fails, the musician may "re-tune" one of the strings in the course to another pitch. One should not attempt to do this without plenty of practice and dexterity.27

^^This special template should not be misconstrued as a form of equal temperament, simply because it has "fixed" frets. Since it is in Pythagorean tuning, Bermudo must present methods for solving the faults, in addition to the normal remedies suggested for the individual templates. Although he also recommends the other solutions, the double fret is peculiar to this optional template. As a result of this "easy way out," players have the option of using only one set of letter names on this one template— gamaut, or on Elnmi. ^Ibid., folio xdx, r. Algunos curiosos y diestros tanedores quando viehe algun paGo, que no se puede con la mano alcançar: ponen la una boz en una cuerda en vazio, y la otra en la compahera desta cuerda hollada en el tercero, o en otro traste que la tal Musica pide. 182 When some curious and dexterous players come to a passage which they cannot reach with their hands, they place one voice [note] on an open string, and the other on the "companion" string [of that course], depressing the third or any other fret, according to the demands of the music. As is the case with all of Bermudo's presentations, the principles established for the vihuela, also apply "to the standard fretted string instruments."^^

The Application of Bermudo's Theories to Music Since most of Bermudo's writings focus on the use of Pythagorean tuning on the contemporary vihuela, it is only fitting to test his theories on the music of his day. The evidence shows that he understood Pythagorean tuning as the commonly-used system for the vihuela, and as an important factor in the process of intabulation, as well. He clearly indicates that "everything he has presented about the vihuela (including fret placement and intabulation) has been used by the very knowledgeable and practical musicians."29

The methodology employed here involves the selection of representative compositions by those "knowledgeable and practical musicians" mentioned above. Since Bermudo has proposed certain composers (Narvâez, Valderrâbano and Fuenllana) and their compositions as prime models for intabulation, and supplies his own examples as well, it

2®Ibid., xdx, r. Lo sobredicho se entienda en los instrumentos de cuerdas communes... 2^Ibid., folio cviii, r. Todo quanto de la vihuela tengo dicho es lo que hasta oy los m uy sabios musicos practicos ham usado. 183

is appropriate to examine these particular works most closely.^ The intabulations also must have clef markings, because Bermudo contends that these will indicate which template is being used. The works examined below were selected at random from among dozens exhibiting the aforementioned characteristics.^^ The temptation to expand the discussion of pieces beyond what was considered necessary to make convincing points about Bermudo's theories was resisted so as not to compromise the theoretical (in contrast to the répertoriai) focus of this investigation. It did prove useful, however, to classify the pieces examined in groups according to their degree of concordance with specified templates. In the first group, the entire intabulation maintains a complete concordance with the template; in the second, certain passages demonstrate minor problems that are easily solved by left-hand fingerings; and in the third group, the compositions are more problematic, and require more drastic means of correction, such as moving a fret. Fortunately, Bermudo has supplied the necessary means of correcting virtually any problem that one may encounter.

^ L u y s de Narvaez, Los seys Libras del Delphin de Mûsica, 1538; Enriquez Valderrâljano, Silva de Siretm, 1547; Diego Pisador, Libra deMtisica de Vihuela, 1552; and Miguel de Fuenllana, Orphenica Lyra, 1554. Although Bermudo does not mention Pisador, a few of his compositions were examined in conjunction with those of the other three composers, since he is contemporaiy with Bermudo and the other selected vihuelists. 3tJhis is not a répertoriai or statistical study, but rather an effort to assess the general relevance of Bermudo's theories to representative vihuela music of his day. 184

Complete Concordance With the Selected Template A logical and yet simple composition that falls into the first group is Bermudo's own intabulation of the romance viejo, "Mira Nero de tarpea." In the tablature, Bermudo supplies two clefs (C and F), along with written directions that indicate the use of the Are template.^2 On this template, all the chromatic frets (first, third, sixth and eighth) form fa. The placement of these chromatic frets automatically imposes certain restrictions because of the Pythagorean system. (For example, on the Are template, one does not find a G# on the first fret of the fourth course; since that fret is fa, that particular note is A^.) A transcription of Bermudo's romance viejo from tablature to modern notation verifies his sensitivity and adherence to the subtlties of the Pythagorean tuning system. As Figure 47 demonstrates, there are no voice- leading problems in his intabulation. The use and resolution of the minor (diatonic) semitones reflect the concordance with the template. It is especially important at cadences, and as seen in measures 5-6, the leading- tone, G# resolves properly to the A. Similar instances occur in other interior cadences (mm. 13-14,25-26, and 31-32).33 Clearly, the placement of the chromatic frets enhances the voice-leading and, in this case, creates no conflicts with enharmonic equivalence, nor "bad" octaves or unisons. Since this example remains very close to the diatonic mode (fourth), the Are

^^Ibid., folio d, r. . ..y va per la vihuela de Are, y per tanto tiene la claue de ffaut en la quinta en el traste tercero, y la de csolfaut en la tercera en el traste primero. [...and it (the tablature) uses the Are vihuela (template), in so much as it has the clef of ffaut on the third fret of the fifth course, and that of csolfaut on the first fret of the third ] ^In measures 25-26, the placement of the first fret as fa, strengthens the downward resolution of the minor semitone (in upper voice) to the octave. 185 template can efficiently accommodate a limited amount of chromaticism (especially at the cadences). The major thirds in the Pythagorean tuning system (408 cents) are larger than the equal-tempered thirds (400 cents), and therefore sound somewhat out of tune to the modern ear. However, they should not be dismissed as intolerable, nor should they be considered as non representative of Renaissance preference.^^

Uyibseli itJitttordtattjitiAnmaaetjitftfkt.

Figure 47. Tablature (above) and Transcription (below) of Bermudo's Version of the Romance viejo, "Mira Nero de tarpea," {Declaracion, folio ci, r).

3‘*This piece was played on a replica of a period instrument with the frets adjusted according to the Are template. As one would expect, the thirds tend to sound a bit "large." However, pitting the modem ear against that of the Renaissance should not become the criterion for judging Bermudo's theories. This piece lies on the fingerboard in such a way that the perfect intervals remain pure. 186

É J JinJ^-j'f r r r m rr - L j . IL

?n À = L i@_ T-T . j f r f

_2L rr rr ■ j U .

m w # ITf f

Figure 47. (continued)

One finds ths t through this process of re-transcription, several compositions maintain total agreement with Bermudo's templates; all perfect intervals remain pure, and the principles of voice-leading are retained. This full concordance is apparent in several in tabulations by Narvâez, Fuenllana, Pisador, and Valderrâbano. (See Table 7.) 187

Another example of a full concordance with the selected template is seen in Narvâez's intabulation of the "Sanctus" from Misa Hercules dux

ferarie, by Josquin.^s Here, Narvâez' "clef" is our clue that he probably used the gamaut template to convert this vocal notation into tablature. A comparison of the tablature and the vocal score shows that Narvâez appears to be selecting his template according to the lowest pitch of the contrabass (gamaut), as Bermudo recommends above. He also retains the same pitches as in the vocal music—a fact that further reinforces the link between the tablature and the vocal model.^^ As Figure 48 shows, there is a complete concordance between this intabulation and the designated template. Obviously, this composition remains close to the diatonic mode (first mode on D), as does the previous example. It employs only three accidentals (B^, C#, and F#) needed in this mode for the voice-leading and cadences, and which are easily accessible on the gamaut template. The result is an intabulation that reflects totally the implications of Pythagorean tuning.

^L u y s de Narvâez, Los seys libres del Delphin de Mûsica...1538. ^O ne should bear in mind that Narvâez is an accomplished vihuelist, and therefore his intabulations will reflect a certain amount of artistic license on the part of the vihuelist. With this understanding, one will expect to see instrumental ornaments and minor alterations—to the original pitches, and to the meter. To compare the intabulation with the vocal model, see Josquin Des Prés, Missen, In Werken 7, edited by Prof. Dr. A. Sniijers. (Leipzig: Fr. Kistner and C. P. W. Siegel, 1937), 30-32. n i I J J i 188 • . • f r -3-1 3 - f—2- T4"^ - w : • •.• S . 5 s A 4- 4 s S' • - 4- o( o z- ■z- ---- SS—~ o 2 5 -o 2- ■ - s- o 2-- Sinaae. (mtiK. fancius.

. i ! i 5 ^ ... (}-r T O Ll n * 1 !Z u ■■■Vo ------* * ' «--- »---- 1 . - f 3 —

É m J ' J j J' s — zr

m f f 10

$ F

g M>- f f r"r r 'fÿf f rm

Figure 48. Tablature and Transcription (mm.1-14) of Josquin's "Sanctus," (Narvâez, Los seys libros del Delphin de Mûsica, folio xxxiv).

A significant number of intabulations fall into this first group. In the following selections (Table 7), in which the designation of clefs calls for a specific template, there is full agreement with the template and Pythagorean tuning, because the voice-leading is good; the cadences resolve properly as in 189 the vocal model; and the intervals created by the Pythagorean system on the vihuela pose no problems w hatsoever.^^

Table 7. List of Intabulations With Complete Concordance With the Selected Template. Composer Title Template Fuenllana 3-voice "Agnus," Misa Ave Maria (Morales) Are "Deposuit," Magnificat Primi Toni (Morales) Dsolre Narvâez chanson (Combert) Are "Sacris solennis" Dsolre Pisador romance viejo Are Valderrâbano "Senora, si te olvidare" Dsolre "Ave Maria" (Loyset [Compere]) bmi

In addition to the vocal intabulations above, three instrumentally conceived compositions also fell into this first group, for all of the reasons above. The compositions tested include two Fantasias by Fuenllana; the first is paired to his transcription of Morales's three-voice "Agnus" (above), and thus uses the same template (Are); the second is paired to his transcription of Morales's "Deposuit," also retaining that same template (Dsolre). The last of these purely instrumental works (rather than intabulations proper) to be tested in this group, is a "Fugue" by Valderrâbano, which uses the Are template.

^^There compositions were transcribed by this author from the original tablature sources. ®®These compositions are not intabulations of vocal music, but instead are instrumentally conceived. 190

Minor Problems and Bermudo's Solutions There are some intabulations that deviate from an exact agreement with the designated template, and which therefore are placed in the second group. Many contain passages with minor problems (in the voice-leading or in intervallic relationships) for which Bermudo proposes specific "short term remedies" that can be applied simply and easily by increasing or decreasing the finger pressure on the fret in question during the performance of the composition. The first example in this group is Narvâez's intabulation of the "Ossana" from the Misa Hercules dux ferarie by Josquin. For the most part, the intabulation of this piece reflects a concordance with the designated template (gamaut). However, as Figure 49 shows, there is an obvious instance in Measure 2, where an A# (first fret of the third course—mi) is used instead of the expected (m. 2).3* Since there is no alternate fingering readily available in this position, Bermudo's solution to the problem is simple—decrease the finger pressure on the fret and place the finger slightly toward the nut. This procedure enables the vihuelist to achieve an approximate B^ while playing. One might suggest that a possible remedy to this situation would be to lower the first fret to fa (automatically creating B^), but as seen later in Measure 9, the F# (mi) on the first fret of the fourth course is necessary to maintain proper voice-leading. If the first fret had been moved downward to accommodate the first problem, it would now create an additional one by

3^The discrepancy is clear, since the bass line rises to A#, while the soprano line, in imitation, rises to B^. 191 forming on the first fret instead of F#. Clearly, the only option here is to adjust the pitch by decreasing the finger pressure.

i III. “r % 4 • • # = E ua V 0 % 1 * • è s J o ' ------o—W » J 1 0ffamiinttcc\Rf. 11 ! ------— , 2 -o---s 1 2 • . .JC__ 4 . r * 4 L I-. 2 — : f r \ ^ * Q • », 5 ^ ■ Q Q ' • • • -----2 — ^ — OS — ~r=- « ----- — - 4 - 4

S-i

$ i ? 10

§ Y ^ etc. — hif »

Figure 49. Tablature and Transcription (mm. 1-11) of Josquin's "Ossana," (Narvâez, Los seys libros del Delphin de Mûsica, folio xxxiv). 192

The intabulation of Pisador's villancico (also using the gamaut template) illustrates a similar situation. In Measure 19 of Figure 50, the third fret (/fl) of the fourth course transcribes as an where proper voice-leading in the music would call for a G# (mi). Since Bermudo strives to maintain the purity of the vocal model and Pythagorean tuning, his solution for this passage would be in the same vein as in the previous example, except that here, one must increase the finger pressure on the fret to approximate the desired G#.'^ The remainder of the intabulation conforms to the designated template.

I I I 4— T e e Z Z 4 — IIt

I m etc. Ü 3Z I f

Figure 50. Tablature and Transcription (mm. 17-23 of a villancico (Pisador, Libra de Mûsica de Vihuela, folio ix, r).

^ In reality, the A*’ in this passage would probably go unnoticed, since the third created here (384 cents) is very close to a just third (386 cents). 193

One should bear in mind that the conflicts described in this group tend to be rather isolated instances that warrant only minor adjustments during the performance of the music. Passages that contain similar problems, requiring the same type of corrections, are to be found in the intabulations in

Table

Table o. List of Intabulations Containing Minor Problems With the Selected Template. Composer Model Measure Template Narvâez "Mille Regres" (Josquin) 6-7,18 Are Pisador villancico (Juan Vasquez) 9 Are Valderrâbano "Exultet celum" (Sepulveda) 28 Cfaut

Problematic Passages and Bermudo's Solutions In the third group, the intabulations demonstrate consistent faults throughout the composition. These, as a practical matter in the event of performance, would require some kind of fret adjustment or other remedy on the part of the performer. Problems that appear to recur throughout the musical composition (usually on a particular fret) probably would be better resolved by moving the fret prior to playing, than by varying the left-hand finger pressure. An intabulation that contains a series of these problematic passages is Valderrâbano's setting of a motet by Willaert—"Augustine lux doctorum." The work requires the Ffaut template and is in the sixth mode. In Figure 51, it is apparent thtii the problems consistently recur on the third fret (mi). (See

Among these compositions tested, only one instrumental piece fell into this group: "Fantasia" by Narvâez (folio xxvii, r), using the Elami template. 1 9 4

the Ffaut template in Figure 39.) In Measures 5-7, the consistent use of the

third fret as rni disrupts normal voice-leading procedures by using A# (instead of B^) on the third course, and D# (instead of E^) on the second course, pitches which are atypical in an F-mode. The third fret of the third course (A#), also creates an obvious augmented octave with the open fifth course (Bb) in measures 8 and 11. For the sake of maintaining the purity of the vocal model, these faults must be corrected. To alleviate the faults created by the placement of this third fret as mi in this example, Bermudo would recommend the adjustment of the fret to fa, in order to achieve the appropriate voice-leading and pure octaves. Therefore, in Figure 51, by moving this fret "down" a comma to fa, the A# converts to B^, and the D# to E^—both of which are more acceptable in the F- mode. This adjustment of the third fret (from mi to fa) ultimately changes the disposition of chromatic frets on the Ffaut template. Before any adjustment is made, the chromatic frets are placed: mi-mi-mi-mi (See Figure 39.); after the third fret is lowered, the disposition changes to mi-fa-mi-mi and matches that of the gamaut and Cfaut templates (See Figures 37 and 38.). 195 ê I «U U Ut il T e # ■Q--- Î- ^ 2 - ^ ------f z t e — 2 0 - Auguftmc gu

é - L ^ — te------1 he — .—

S-}-

f r to etc.

Figure 51. Tablature and Transcription (mm.1-11) of Willaert's "Augustine lux doctorum/' (Valderrâbano, Silva de Sirenas, folio xvii, r).

Other compositions which pose comparable problems and invite comparable solutions are represented in the following two vocal intabulations: Fuenllana's intabulation of a motet by Gombert—"Beata Maria," using the gamaut template, and a villancico by Pisador, using the Ffaut template. A purely instrumental work was also tested, and the results were exactly the same as in the vocal compositions contained in this group. Narvaez's set of diferencias on "Conde claros" (a popular villancico), had 196 similar recurring situations on the third fret that were easily alleviated by shifting the fret a comma lower from mi to fa.

Conclusions The foregoing examples show clearly what is noteworthy about Bermudo's theories of intabulation and tuning/fret placement. First of all, they work. His templates address the hierarchical hexachord system of his day with a series of "grids" that correctly map notes to frets—and vice versa. Inasmuch as no theory of Renaissance music could fully account for the chromaticism that became increasingly common in the course of the sixteenth century, one must allow for "adjustments" in Bermudo's templates, as indeed he did himself. Second, Bermudo confronts head-on the practical problems of accommodating Pythagorean tuning—a given in sixteenth-century Spain— to live performance requirements. His repertoire of remedies to what he calls "faults" is imaginative enough to find echoes even tcxlay in the world of avant-guard guitar music. The so-called "enharmonic guitar" currently being revived in Germany, for example, has the double fretting (parallel frets a comma apart) that Bermudo recommended as a possible solution over four hundred years ago.^^ Yet it is being touted as a new invention or remedy, by authors who appear to be blissfully unaware of a vast segment of the history of fretted instruments.

^^Martin Vogel, Die enhamonische Gitarre, 21-24. CHAPTER VII SUMMARY AND CONCLUSIONS

Juan Bermudo the pedagogue, theorist, and vihuelist has generally not fared well in the scholarly literature addressing issues of tuning, temperament and the music of sixteenth-century Spain. It is hoped that major contributions of this study will be the exoneration of Bermudo's reputation as a theorist and acoustician, and the wider recognition that his writings are a surprisingly fertile source of information on the music and the performance practices of Renaissance Spain.

Tuan Bermudo the Pedagogue Juan Bermudo was, in a certain sense, a maverick priest. If Holy Orders was his vocation, music appears to have been an even stronger avocation. He persevered in the study of music, although this course of action was frowned upon by his religous order (as seen in Chapter n above). Sustained by an apparently profound knowledge of mathematics, he established himself as an important musicus—musical theorist—of his era despite this inimical climate. Bermudo's Declaracidn is a monument to his insights and to his calm perseverance. One of the most important—but often neglected—aspects of the Decïaraciôn is its pedagogical structure. A thorough examination reveals that

197 198 Bermudo presents his ideas appropriately in three levels of study; Elementary, Intermediate and Advanced. Not only do the individual books of the treatise exhibit a definite interconnectedness at many levels, but they also demonstrate a progressive sequence of materials as well. A major contribution of this dissertation has been to expose Bermudo's pedagogical method in the vihuela material, and to demonstrate how it undergirds all of the topics presented. Bermudo the pedagogue painstakingly presents many topics in a manner appropriate for the successive levels of study. Concepts presented at the Elementary level are often omitted later at the Intermediate and Advanced levels, implying that the student must master the fundamentals before attempting any of the advanced techniques. Likewise, since the elementary student is not expected to understand complicated theories, he is never exposed to sophisticated ideas at the elementary level. The result is a series of closely related discussions in which Bermudo systematically adds details appropriate to the level of study. This progression is apparent in his discussion of the vihuela. He begins with simple introductions to the instrument and its tunings (in Book II), and culminates with detailed prescriptions for in tabulation and fret placement (in Book IV). Seldom has Bermudo's pedagogical intent been considered by scholars addressing his texts. As a result pertinent theories for this instrument have often been misconstrued, and the documentation of the vihuela and related instruments has suffered from inaccuracies and distortions. Many theorists and historians have erred in attempting to report Bermudo's ideas, for the 199 simple reason that they have derived their findings by sampling only one or two of the teaching levels. Some of these instances were pointed out in Chapter I, especially in the documentation of the vihuela as described in the Decïaraciôn. James Tyler reported only two string dispositions for the 7-course vihuela,^ but Bermudo provided four. By reexamining the treatise in light of its pedagogical structure, we now realize that Tyler derived his findings from the Intermediate level only. As Chapter IV demonstrates, Bermudo proposed these two dispositions as alternates to the standard disposition (found in the Elementary and Intermediate sections) and to his own theoretical "invention" (in the Advanced). Diana Poulton recorded only three of Bermudo's 7-course vihuela dispositions—those found in the Intermediate and Advanced sections.^ Unwittingly she missed the standard disposition whose description, although rather cryptic, is found in both the Elementary and Intermediate sections. Clearly, any meaningful interpretation of Bermudo's reporting of the vihuela must take cognizance of Bermudo's pedagogical agenda.^

Tuan Bermudo the Theorist The literature review in Chapter I drew attention to a number of ways in which Bermudo's writings have been misunderstood and distorted, often due to the seeming disarray created by Bermudo's pedagogical modus operandi.

^Tyler, The Early Guitar, 23. ^Poulton, "Vihueia/" Tne New Grove Dictionary of Musical Instruments, 3:724-27.. ^Bermudo's agenda might best be characterized as "progressive revelation"—a concept admittedly more common in theology than in music. But if Bermudo had a theological grounding—which one assumes for clerics—might not this formation at least contribute in part to our understanding of his working methods? 200 One such instance is apparent in Mark Lindle/s interpretation of Bermudo's first fret placement method as representing equal temperament.^ This method, although roughly hewn and simplistic, is in fact purely Pythagorean in nature. Bermudo specifies it as a "method for beginners." But (pedagogue that he is) he avoids presenting complex ideas to the beginner, and allows a certain amount of leeway in the placement of the chromatic frets—"in the middle of the diatonic whole tones." Yet, at the same time, he indicates the need to adjust these frets "high" (for the major semitone) or "low" (for the minor semitone) according to the specific circumstances displayed in the music. One should bear in mind that all three of Bermudo's Pythagorean fret placement methods are very similar in procedure—the first of which is very simple. The highly detailed instructions for precise placement of the chromatic frets are found in the second and tliird fret placement methods. It is these areas of the treatise that Lindley evidently overlooked in reaching what now appear to be premature conclusions on the issue of equal temperament. In Book IV of the Declaracidn, Bermudo first presents the orthodox system of Pythagorean tuning, and culminates by proposing his own revolutionary system of tuning (an approximation of equal temperament). In his book. Lute, Viols and Temperaments, Lindley portrayed Bermudo as a confused theorist, and implied that Bermudo could not distinguish between Pythagorean tuning on the vihuela and meantone temperament on the keyboard.® By comparing Bermudo's fret placement for the vihuela with

^Mark Lindley, Lutes, '-'his and Temperaments, 29. ®Lindley, Lute, Viols and Temperaments, 15-16. 2 0 1

Other writers' theories for the keyboard, Lindley evidently assumed that Bermudo was advocating meantone temperament on the vihuela. However, Bermudo provides no grounds for this assumption. In the Prologue to the Decïaraciôn, Bermudo indicates his strategy in presenting his theories of tuning and temperament. He elects to treat first the "old systems still used on the instruments of his day," and then follow up with newer ones.^ In the case of the vihuela, the first three fret placement methods (which account for most of his discussion) deal with the old system—Pythagorean; the "last" method (at the end of the advanced vihuela material) represents a new one—approximate equal temperament.^ Might Lindley be trying to push Bermudo into the mainstream of Renaissance theoretical thought by "squeezing" portions of the Spanish friar's Pythagorean fret placements into meantone temperament? Perhaps another explanation is worth considering. Paradoxically, Bermudo—who was apparently well versed in the theoretical currents of his day—does not refer to other tuning systems, such as meantone temperament and just intonation. Oddly, he never mentions those contemporary theorists who propose meantone systems, such as Pietro Aron.® He also bypasses the theories of his fellow countryman, Ramos de Pareja (who was from the same province as Bermudo)—whether in the interests of saving space, or in fraternal charity, we may never know. Whatever the case, internal evidence

^Bermudo, Decïaraciôn, folio +vii, r. ^The discussion of both keyboard and harp in Book TV remains within the constructs of the Pythagorean tuning system. He promised these innovations for the keyboard and harp, but unfortunately, they were never realized, since they were supposed to appear in Books VI and Vn, (never published). ®In his treatise, Toscanello (1523), Pietro Aron devised a one quarter comma system of mean tone temperament. 2 0 2

in the Declaracidn suggests that Bermudo developed his "final" and most noteworthy theory of tuning, namely, his approximation of equal temperament, independently of the mainstream of European theoretical thought. One may ask how a well-read scholar of Bermudo's caliber could have disregarded his contemporaries. How could he commit such an oversight? Could it be that Bermudo's position was not a matter of oversight, but rather of intention? Evidence in the Declaracidn suggests that he was well aware of other tuning systems; he recognizes the importance of the 5:4 proportion (pure third); and he uses the 5:4 proportion in his last fret placement method. However, this particular third is employed for the sole purpose of determining the syntonic comma—an element vital to his last method of fret placement. Apparently, Bermudo considered his own systems of tuning (Pythagorean and approximate equal temperament) the only viable options on the vihuela. Evidently, as far as he was concerned, meantone temperament and just intonation were just not relevant or pertinent to his musical scheme. Clearly, Bermudo demonstrates a level of theoretical sophistication that was exceptional for his time. This is evident in his practical method for approximating equal temperament. He proposes this method as an innovative system applicable to all instruments—keyboard, as well as vihuela. In this system, the fifths, whole tones, major thirds, and semitones are either Pythagorean, equal-tempered, or very close to equal-tempered. Although his process of tempering results in a variety of sizes of semitones, it is clear that Bermudo has achieved his goal. In his final tuning 203 system, there are neither major semitones (114 cents) nor minor semitones (90 cents). The semitones here range from as narrow as 93.66 cents to as wide as 106 cents. However, despite the various sizes of semitones, most musicians accustomed to equal temperament would probably find the differences inconsequential.

Tuan Bermudo the Vihuelist In the Decïaraciôn, Bermudo shows himself to be an innovative practitioner as he leads the reader through a structured program of explanations, illustrations and theories for the vihuela. Indeed, there are relatively few theorists whose knowledge of techniques for the musical instruments of their era is as thorough and convincing as is Bermudo's. His expertise seems to span all aspects of the vihuela as he provides practical advice regarding tunings, intabulation, fret placement and, ultimately, performance. Bermudo's ever-present pedagogical agenda intrudes time and time again in this treatise, even in sections which are otherwise nothing if not "practical." Witness the seemingly endless series of templates that he uses to provide students with precise, practical instruction for intabulation. Not only does he describe the standard disposition of strings for the vihuela and related instruments, but he is knowledgeable enough about the instrument to propose his own alternate tunings and to describe meticulously the many templates for each of them. Another instance that highlights Bermudo's practicality is apparent in his manner of tuning two vihuelas to each other by using sympathetic 204 vibration. Although he realizes that there are some players who can accurately tune by ear alone, he provides the reader with a helpful, practical procedure using pieces of straw.® Contrary to the mainstream theories of keyboard tuning, Bermudo establishes a flexible system of Pythagorean tuning on the vihuela by means of movable frets. Fully aware of the problems inherent in Pythagorean tuning, he supplies practical solutions to the performer. These solutions vary according to the specific problem being addressed. Bermudo's "remedies" certainly evidence a seasoned performer's practical survival skills: 1) find an alternate fingering; 2) increase or decrease the finger pressure on the string; 3) move the fret up or down a comma; 4) slant the fret (not a good solution); 5) place a double fret at the problematic location; and 6) re-tune one of the strings of the course. To demonstrate the workability of the Pythagorean system even further, he invents a theoretical vihuela that enables the musician to play both enharmonic counterparts, such as and G#. This vihuela disposition is comparable to Vicentino's famous arcicembalo —a keyboard instrument having split keys.^o Endeavors of this type have recently come into favor—have been unwittingly "rediscovered," as it were—in the twentieth century as seen in Martin Vogel's book Die enharntonische Gitarre. Here, instrument makers, performers and composers are urged to revive the Pythagorean system of

®Bermudo, Declaracion, folio cix, r. ^^Nicola Vicentino also developed the comparable ardorgano. He presents his theories in his treatise, Lantica musica ridotta alia moderna prattica (Rome, 1555). 205 tuning on the modem guitar by using double frets.O bviously, their ideas are not new, for Bermudo preceded them by four hundred years. The fact that the "clefs" that correspond to or signal Bermudo's templates appear only in Spanish tablatures seems to imply that the use of clefs, templates and movable frets is an Iberian phenomenon. So far the examination of Italian and French lute tablatures has revealed no such markings. They neither indicate clef nor do they designate templates—or specific fret dispositions—for a particular intabulation.^^ Evidence suggests that the Spanish vihuelists were quite cognizant of the relationship between the vocal music and the instrumental intabulations. Their sensitivity is exemplified in their use of templates and clef indications in their intabulations. These conventions evidently were not Bermudo's own theoretical creations. They were in use both before and after Bermudo's publication dates. Prior to publication of the Decïaraciôn, these markings appear as early as 1538, in Luis de Narvâez's collection of in tabulations, Delphin de Mûsica. They also appear in the tablatures of Valderrâbano (1547), Pisador (1552), Fuenllana (1554), and as late as 1576 in Esteban Daza's Lihro de Mûsica. However, Bermudo appears to be the only theorist to deal with them.

Martin Vogel, Die enharmonische Gitarre, 21-24. ^^The sources examined here contain a variety of compositions, but none makes use of clefs, or refers to a specific template. See Vincenzo Capirola, Lute Book (c. 1517), edited by Otto Gombosi (New York: Da Capo Press, 1983); Vincenzo Galilei, Fronimo (1584), trans. and edited by Carol MacClintock. In Vol. 39 of Musicological Studies and Documents (Neuhausen- Stuttgart: Hanssler-Verlag, 1985); and Preludes, Chansons and Dances for Lute, edited by Daniel Heartz (Neuilly-sur-Seine: Société d'Autrefois, 1964). The French tablatures were published by Pierre Attaingnant circa 1529, and likewise contained no references to the use of tem plates. 206 The application of Pythagorean tuning to musical instruments has always posed certain problems during performance. Bermudo supplies the means to overcome the system's limitations by specifying the placement of certain frets on the vihuela. The ingenious nature of Bermudo's insight provides a ground-breaking link between Renaissance vocal music and Spanish instrumental in tabulations. As a self-taught scholar, Bermudo showed little timidity in striving for the advancement of important practical theories for the Renaissance vihuela—theories still relevant to those who today might wish to recapture the splendor and subtleties of sixteenth- century Spanish vihuela music. APPENDIX TRANSLATION OF BERMUDO’S METHODS OF FRET PLACEMENT

Fret Placement for the Elementary Student (Decïaraciôn, folio di, r)

Divida lo largo de las cuerdas en Divide into nine equal parts, the nueue tamanos yquales: que se string’s length which is understood entiende desde la puente de la from the bridge to the nut...Having vihuela hasta la ceja...Diuiso pues el divided that space, you will place a dicho spado, en el punto primero de fret on the first mark of division la diuision, cercano ala ceja, porneys nearest the nut, and it will be the un traste, y sera segundo: en el second fret. On the third point of tercero punto de la diuision pone the division, place another (mark), otro, y sera el septimo. and it will be the seventh fret.

Bolved a diuidir el espacio que ay Return to divide the space which desde el dicho segundo traste hasta exists from the second fret to the la puente en otros nueue tamanos, y bridge into another nine lengths. en el punto primero de la diuision On the first mark of division, place a poned un traste, y sera quarta: y en fret, and it will be the fourth. On el punto tercero de la diuision the third mark of division, place poned otro, y sera el nono. another, and it will be the ninth.

Diuida se luego toda la cuerda en Let the entire string be then divided quatro tamanos, y el primero terna into four lengths. The first mark [sic] desde la ceja al quinto traste. from the nut is the fifth fret.

207 208

Otra diuision se haga semejante de Similarly, another division into quatro desde el quinto traste hasta la four may be made from the fifth fret puente, y el tamano primero to the bridge. The first portion will alcançara al decimo traste. reach to the tenth fret.

Para poner en medio destos trastes To place other frets in between these otros que for men semitonos, que frets which will form semitones, seran primero, tercero, sexto, y and will be the first, third, sixth and octauo: tomad este auiso. En medio eighth frets, take this advice. In the de los trastes que forman tono middle of the frets which form poned uno: y si fuere fa, auia de ser whole tones, place one. If it is to be llegado hazia la ceja: y si fuere mi fa, it must be moved toward the allegadc a la parte de la puente. nut, and if it is to be mi, it must be moved toward the bridge.

Fret Placement for the Theoretical Seven-Course Vihuela (Declaraciôn, folio ciii, r)

Diuidid el spacio que ay desde la Divide the space from the bridge of puente de la vihuela hasta la ceja en the vihuela to the nut into four quatro partes, y en el punto primero parts, and on the first point of the de la diuision cercano a la ceja division nearest the nut, place the poned el quinto traste: en el qual se fifth fret, on which a diatessaron will formara diateCaron. be formed.

Diuidid el spacio desde la ceja hasta Divide the space from the nut to the el quinto traste en quatro tamanos, y fifth fret into four parts, and go up subid desde el dicho quinto hazia el by three from that fifth (fret) toward nascimiento de las cuerdas con tres, the bridge of the strings. That point, y donde viniere el punto de los to where the three sizes reach, dichos tres: sera el decimo traste. marks the tenth fret.

Diuida se el spacio que ay desde el Let the space from the fifth fret to quinto treate hasta la ceja en tres the nut be divided into three tamahos, y poned el compas en el lengths. Place the compass on the dicho quinto: y donde alcançare sera fifth fret, and where the compass septimo. reaches with another length will be the seventh fret. 209

Para prouar si este septimo queda To prove that the seventh fret is bien puesto: tome el dicho compas, well-placed, take the compass, sin abrirîo, o cerrarlo, y diuida desde without changing its opening, and el nascimiento de las cuerdas hasta divide the string from the seventh el dicho septimo, y si vinieren fret to the bridge by this distance. If justos ocho tamaftos: queda bien the result is eight, then the seventh puesto. fret is placed well.

Buelua a diuidir desde el septimo a Return to divide from the seventh la ceja en tres, y poniendo el compas [fret] to the nut into three, and en la dicha ceja: donde alcançare placing the compass on the nut, it sera segundo traste. will reach out to the second fret.

Para examinar si este segundo queda To determine whether this second puntualmente puesto: tomad el fret is placed exactly, take the dicho compas como esta, y medid compass as it is (open to the same desde el nascimiento de las cuerdas length) and measure out eight parts hasta el dicho segundo ocho from the bridge to the second fret. If tamahos: y si vinieren yguales, en these parts are equal, then it (the su perfection esta. second fret) is in its perfection.

Diuida se el spacio que ay desde el Let the space between the second sgundo al septimo en tres tamaftos, and seventh frets be divided into y poniendo el compas en el dicho three equal lengths. By placing the septimo: alcançara al nono. Para compass on the seventh fret, reach ver por demonstracion si queda bien for the ninth fret. To see by puesto: hazed lo sobredicho de los demonstration if it is well-placed, do ocho tamaftos desde el traste hasta el the same process of dividing the nascimiento de la cuerda. string from this fret to the bridge into eight equal lengths.

El spacio que ay desde el segundo Let the space between the second fret hasta el nono se diuida en très and the ninth be divided into three tamaftos, y poniendo el compas en equal lengths, and by placing the el segundo: alcançara al quarto. compass on the second (fret), it (the Examinaldo si esta bien puesto: compass) will reach to the fourth. segun ya es dicho con ocho tamaftos. Examine it for accuracy according to what has already been said about dividing the portions of string into eight lengths. 210

Placement of Chromatic Frets on the Theoretical Seven-Course Vihuela (Dedaracidn, folio ciii, r - civ, r)

Poned el compas en el quinto traste, Place the compass on the fifth fret, y diuidid el sspacio, que ay desde el and divide the string from there to dicho quinto hasta el nascimiento the bridge into eight lengths. Then de las cuerdas en ocho tamaflos. place the foot of the compass on that Poned el un pie del compas en el fifth fret, and where it reaches with sobredicho quinto traste, y donde another length (toward the nut), alcançare con el otro: sera el tercero. there is the third fret.

El spacio que ay desde el The length from the fourth fret to nascimiento de las cuerdas hasta el the bridge may be divided into nine quarto traste diuida se en nueue parts, and where the eighth (from tamaflos, y donde allegaren los the bridge) is located, there will be ocho: sera el traste sexto. the sixth fret.

Diuidid desde el dicho sexto hasta el Divide the string from that sixth fret nascimientos de las cuerdas en to the bridge into nine parts. On the nueue tamanos: y el punto primero first mark of the division (nearest de la diuision poned el octauo. the nut), place the eighth (fret)

Diuidase otra vez desde el sexto Again, let the distance from the hasta el principio de las cuerdas en sixth fret to the bridge be divided tres tamaflos, y puesto el compas en into three lengths. By placing the el dicho sexto: donde alcançare sera compass on the sixth fret, you can traste primero. reach (with the same length) to the first fret.

Poned el compas en el traste tercero, Divide the string from the third fret y diuidid la distanda que ay desde el to the bridge into eight lengths. By dicho tercero hasta la puente en placing the compass on the third ocho tamahos: y poniendo el fret, twist the compass and make a compas en el tercero, donde mark which will be the (alternate) alcançara la buelta hareys una sehal: first fret that forms fa. la qual sera traste primero que forme fa. 211

Diuidase el interualo que ay desde el Let the space between the first fret traste primero, que forma mi, hasta that forms mi and the bridge be el nascimiento de las cuerdos [sic] en divided into nine lengths. Place the nueue tamaftos, y poniendo el compass on this first fret and where compas en el sobredicho traste, it extends will be that mi or the third donde alcançare sera la seftal del fret. dicho mi, traste tercero.

Para hazer una seftal abaxo del, que To make a mark lower than that forme fa, para quando fuiere (sixth) fret, divide the space from menester: diuidid el interualo que the first fret, which is fa, to the ay desde el traste primero, que es fa, bridge into four equal parts; place hasta el nascimiento de las cuerdas the compass on the first fret and en quatro partes yguales y poniendo where it reaches, make a mark that el compas en el dicho traste will form fa. primero, donde alcançare hareys una seftal: la qual formara fa.

Para hazer una seftal abaxo del, que To make a mark lower than it (the pueda form ar el fa: se diuida el eighth fret) that will form fa, divide espado que ay desde el traste tercero, the string from the third fret, which traste que era fa, hasta el is fa, to the bridge into four parts. nascimiento de las cuerdas en otras Place the compass on that third fret, quatro partes, y poniendo el compas and where it reaches, make a mark en el dicho tercero donde alcançare for the eighth fret, which will be fa. hareys la seftal para el fa traste octauo.

Placement of Frets 12. 13 and 14 on the Theoretical Seven-Course Vihuela

Si teniendo disposicion la vihuela If the disposition of the vihuela has de tener mas de doze trastes, y el more than twelve frets, and the taftedor los quisiere poner: guarde player wishes to place them, keep la regia siguiente. Puestos los doze the following rule. Having placed trastes tomo el compas, y diuida en the twelve frets take the compass, dos tamaftos yquales el espacio que and divide the length between the ay desde la ceja de la vihuela hasta nut of the vihuela and the first fret el traste primero, y un tamafto into two parts. One of these two destos dos formara semitono parts will form a semitone beyond despues de los doze, y sera traste the twelfth. This will be the treze. thirteenth fret. 212

Y si se diuidiere la distanda desde la And if the distance from the nut to ceja al segundo traste en otros dos the second fret were to be divided tamaüos: el uno dellos formata into another two lengths, one of tono despues de los dichos dose, y es those will form a tone beyond the traste quatorze. twelfth fret, and it is the fourteenth.

Fret P la c e m e n t for the Individual Templates (Declaracidn, folio cv, r - cv, v)

Diuida se en quatro partes toda la Let the entire string be divided into cuerda (segun otras vezes es dicho) y four equal parts. On the first point en el primero punto de la diuision of the division, place the fifth fret, pongan el quinto traste: el qual en which will be Cfaut on the sixth la sexta sera Cfaut, en la quinta string, Ffaut on the fifth, fa of bfabmi Ffaut, en la quarta el fa de bfabmi, en on the fourth, dlasolre on the third, la tercera dlasolre, en la segunda high gsoireut on the second, and gsoireut agudo, y en la prima csolfa. csolfa on the first.

Diuida se en quatro tamanos el Let the distance between the fifth spacio que ay desde la ceja de la fret and the nut be divided into four vihuela hasta el dicho quinto traste: equal lengths, and by placing the y poniendo el compas en este traste compass on this fret, add three den tres tamaftos, y donde lengths to reach the tenth fret. This alcançaren sera el decimo traste. fret at the sixth fret will be Ffaut, on Este traste sera en la sexta Ffaut, en the fifth, the fa of bfabm i, on the la quinta el fa de bfabmi, en la quarta fourth, the fa of elami, on the third, el fa de elami, en la tercera gsoireut high gsoireut, on the second, csolfa, agudo, en la segunda csolfa, y en la and on the first, ffaut. prima ffaut.

Diuidid el espacio desde la ceja al Divide the space from the nut to the quinto traste en tres tamaftos y fifth fret into three lengths. By poniendo el compas en el quinto placing the compass on the fifth fret, traste: donde alcançare es septimo: it will reach to the seventh with the el qual en la sexta es Dsolre, en la same length, forming Dsolre on the quinta Gsoireut, en la quarta sixth string, Gsoireut on the fifth, csolfaut, en la tercera elami, en la csolfaut on the fourth, elami on the segunda alamire, y en la prima third, alamire on the second, and dlasol. dlasol on the first. 213

Diuidid el spacio que ay desde la ceja Divide the distance between the nut hasta el septimo traste en tres and the seventh fret into three tamaftos, y poniendo el compas en lengths. By placing the compass on la ceja, donde alcançare sera el the nut, reach for the second fret, segundo traste: el qual en la sexta which will be Are on the sixth string, sera Are, en la quinta Dsolre, en la Dsolre on the fifth, Gsoireut on the quarta Gsoireut, en la tercera el mi fourth, the m i of bfabmi on the third, de bfabmi, en la segunda elami, y en elami on the second, and alamire on la prima alamire. the first.

Tomad en el compas el spacio que ay Taking the compass, divide the desde la ceja hasta el segundo traste string from the second fret to the y ha de auer nueue tamaftos desde bridge into (eight) equal parts. el nascimiento de las cuerdas hasta Adding the space from the second la dicha ceja. fret to the nut, makes it nine.

Diuida se el spacio que ay desde el Let the distance between the second segundo traste hasta el septimo en fret to the seventh be divided into tres: y poniendo el compas en el three. Placing the compass on the dicho septimo, donde alcançare sera seventh fret, another length of the el nono: el qual sera en la sexta same size will reach to the ninth Elami, en la quinta alamire, en la fret, which will be Elami on the sixth quarta dlasolre, en la tercera no (course), alamire on the fifth, dlasolre tiene signo, en la segundo el mi de on the fourth, no name on the bfabmi, y en la prima ela. third, mi of bfabmi on the second, and ela on the first.

Lo mesmo hareys desde el quarto al You will do the same from the segundo y desde el septimo al fourth (fret) to the second, from the quinto y desde el nono al septimo. seventh to the fifth, and from the ninth to the seventh.

Diuidid el spacio que ay desde el Divide the distance from the second segundo traste hasta el nono en tres fret to the ninth into three lengths. tamaftos: poniendo el compas en el Placing the compass on the second dicho segundo, donde alcançare sera fret, the first length will reach to the el quarto: el qual en la sexta es bmi, fourth fret, which will be bmi on the en la quinta Elami, en la quarta sixth string, Elami on the fifth, alamire, en la tercera el sustentado alamire on the fourth, the sus-tentado de csolfaut, en la segunda el de ffaut, ofcsolfaut the sustentado oi ffaut on y en la prima el mi de bfabmi. the second, and the mi of bfabmi on the first. 214

Tomad en un compas desde la ceja Take the compass and measure hasta el segundo traste, y poned el from the nut to the second fret. dicho compas en el nono, y donde Then place the compass on the alcançare sera el sexto. Para requérir ninth fret and reach by the same si este sexto esta bueno tomad el length for the sixth. In order to compas desde el sexto al quarto, y si investigate whether this sixth fret is ay nueue tamaftos desde el good, divide the string from the nascimiento de las cuerdas hasta el fourth fret to the bridge by the dicho quarto: bueno esta el sexto. distance between the fourth fret and the sixth. If there are nine lengths, then the sixth fret is good.

El spacio que ay desde este sexto Let the space between the sixth fret hasta el nascimiento de las cuerdas and the bridge be divided into nine se diuida en nueue, y donde (lengths), ard at the eighth point, vinieren los ocho tamaftos: poned place the eighth fret, which must be el octauo traste: el qual queda por mi, as I have said. necefiidad (como dicho he) mi.

Repartid en tres tamaftos el spacio Divide the string from the sixth fret que ay desde el nascimiento de las to the bridge into three lengths, and cuerdas hasta el traste sexto y donde the fourth length of the same size alcançare con el quarto tamafto: sera will reach the first fret. el traste primero.

Repartid el spacio que ay desde el Divide the string from the fifth fret nascimiento de las cuerdas hasta el to the bridge into eight lengths. traste quinto en ocho tamaftos, y Returning the compass [to the fifth bolviendo el compas: donde fret], reach for the third fret, which alcançare sera el traste tercero: el will be fa. qual formara fa. 215

Placement of Alternate Frets on Certain Templates (Declaracidn, folio cv, v

[Fret 3A] Para mudar este traste To change this fret, take the compass tomad el compas que ay desde el and divide the string from the first primero traste hasta el nascimiento fret to the bridge into nine lengths, de las cuerdas, y diuidase en nueue and the point nearest the first fret tamahos: y el uno dellos dareys will be the third. desde el dicho primero al tercero.

(Declaracidn, folio cv, r)

[Fret lA] Poned el compas en el Place the compass on the third fret tercero, y diuidid el espacio que ay and divide the distance from there desde el nascimiento de las cuerdas to the bridge into eight lengths. hasta el dicho tercero en ocho Where it reaches toward the nut tamahos: y donde alcançare con un with another length, will be the first compass: sera el primero, y formara fret, and it will form fa. fa.

[Fret 6A] Mudareys el sexto, si You will change the sixth fret by poniendo el compas en el primero: placing the compass on the first. diuidierdes el espacio que ay desde You would divide the string from el nascimiento de las cuerdas hasta the first fret to the bridge into four el dicho primero en quatro tamahos. lengths. By reaching from the first Donde alcançare el compas desde el fret toward the bridge with the primero: sera sexto, y formara fa. compass, the sixth fret will be placed, and it will form fa.

[Fret 8A] El octauo en la vihuela de The eighth fret on the vihuela of gamaut era mi: y en esta ha de ser g a m a u t was m i, and on this one fa. Fuede se formar, si diuidis el (Are), it must be/a. It can be formed espacio que ay desde el nascimiento as you divide the distance from the de las cuerdas hasta el decimo en tenth fret to the bridge into eight ocho tamahos: y donde alcançare el lengths. Extending by one more uno desde el dicho decimo: sera el toward the nut reaches the eight octauo. fret. 216

[Fret 4A] Para hazerlos fa, se diuida To make it (the string) fa. let the en ocho tamaflos desde el string from the sixth fret to the nascimiento de las cuerdas hasta el bridge into be divided into eight sexto, y donde allegare con uno: lengths. Reach toward the nut with sera el quarto. the same length and place the fourth fret.

Fret Placement—Temperament iDeclaraciôn, folio cix, r - dx, v)

Es pues la cuerda desde la h hasta la Therefore, I divide the string, from 1: la qual diuido en quatro tamaftos, the h to the 1 into four lengths, and y con uno alcança desde la h, a la c: where that one reaches from the h la qual d, es el quinto traste. to the c, that c is the fifth fret.

Diuido otra vez desde la 1, hasta la c, Again, I divide from the 1 to the c, en otros quatro tamanos y alcançara into another four lengths, and with con los tres a la f, y sera decimo three, it will reach to the t, and it traste. will be the tenth fret.

...con los quatro primeros compases ...with the first four lengths, you sacareys el traste dozeno, y sera con will derive the twelfth, and it will be los dos tamaftos que allegara a la g: where two lengths meet at the g. donde es el dozeno traste. There will be tlie twelfth fret.

...diuido toda la cuerda en nueue ...I divide the entire string into nine tamanos y con ocho allegara a la A,... parts, and eight comes to A,...

...y diuisa otra vez desde la 1 hasta la ...and with the string from the 1 to A en nueue tamaftos, allegara con the A, divided again into nine parts, ocho a la b quadrada. b will be at eight.

Hazed una diuision desde la 1, hasta Divide from the 1 to the h into five la h de cinco tamaftos y con quatro parts, and with four, you will reach allegareys adelante de la seftal de la for the mark nearest the nut. The h. La distanda que ay desde la h, a la distance between the b and this new sobredicha seftal es una comma... mark is a comma... 217

...ia qual se diuida en tres tamaftos, ...which may be divided into three dexando los dos a la parte de la h, lengths, leaving the two (parts) que es la cejuela de la vihuela: nearest the nut. You will make a hareys una seftal qucdando el un mark nearest the b, which will be tamafto cercano a la h: la qual seftal the (new) fourth fret. sera el quarto traste.

Sea diuisa la cuerda desde la 1, hasta Let the string from the 1 to this este quarto traste en ocho tamaftos, y (new) fourth fret be divided into donde alcançare con uno hazia la h: eight lengths, and where one more hareys una seftal, y sera un poco (the ninth) reaches toward the nut, adelante la a. you will make a mark, which will be in front of the a (second fret).

El spacio que ay entre la dicha seftal The space between the indicated y la a, se diuida por medio y la seftal mark and the a is divided in half, que en este medio se pusiere sera le and the mark placed in the middle traste segundo. will be the second fret.

Desde este traste segundo se diuida The rest of the string from this el resto de ia cuerda hasta la 1, en (new) second fret to the i is divided quatro tamaftos, y en el punto into four lengths, and on the first primero de la diuision sera el traste mark, it will be the seventh fret. septimo.

Hazed otra diuision de quatro desde From the fourth fret to the 1, make el quatro traste hasta la 1, y en el another division into four. On the punto primero de la diuision poned first point of the division, place the el traste nono. ninth fret.

Diuida se desde la 1, hasta el decimo From the 1 to the tenth fret is traste en dos tamaftos, y donde divided into two lengths, and where alcançare con uno hazia la cejuela one reaches toward the nut with sera el traste tercero. one more, will be the third fret.

En quatro tamaftos se diuida desde From that (third) fret to the 1 is el dicho traste hasta la 1, y en el divided into four lengths, and on punto primero de la diuision sera el the first point of the division, it will octauo traste. be the eighth. 218

Sacad una sesquioctaua desde el Determine a sesquioctave from the traste quarto hasta la 1, y donde fourth fret to the 1, and where that alcançare la sobredicha sesquioctaua sesquioctave is located, make a mark. hazed una sehal.

Luego diuidid desde la 1, hasta el Then, divide the string from the segundo traste en cinco tamaflos, y second fret to the 1 into five lengths. donde alcançaren los quatro hareys Where the four parts reach, you will una senal: y sera un poco adelante make a mark, and it will be a little de la otra de las dos sesquioctauas beyond (to the left of) the previous hazia la cejuela. mark for the sesquioctave.

Diuisa en tres partes la distancia de Having divided the distance las dos seflales en la primera cercana between these two marks into three al setimo [sic] traste, sera el sexto. lengths, on the mark nearest to the seventh fret, will be the sixth fret.

Diuidase desde la 1, hasta este sexto Let [the distance] between the 1 to traste en tres tamanos, y donde the sixth fret be divided into three alcançare con el quarto sera el traste lengths, and where the fourth prim ero. length reaches, there will be the first fret. BIBLIOGRAPHY

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