CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

INTERPRETIVE MODELS FOR MICROWGUS OF GUIDO OF AREZZO

A thesis submitted in partial satisfaction of the requirements for the degree of Master of Arts in

Music

by

Blair Sullivan

August 1988 The Thesis of Blair Sullivan is approved:

Dr. Alvin Ford

Dr. William Toutant

Dr. NanjY Van Deusen, Chair

California State University, Northridge

11 TABLE OF CONTENTS

ABSTRACf...... i v CIIAPIER 1...... 1 CIIAPIER 2...... 1 6 CHAP1ER 3...... 6 2 BffiLIOGRAPHY ...... 7 1

111 ABSTRACf INTERPRETIVE MODELS FOR MICROWGUS OF GUIDO OF AREZZO by Blair Sullivan Master of Arts in Music

Commentaries on the Micrologus of Guido of Arezzo, written ca. 1026-1032, began appearing as early as the second half of the 11th century. Throughout its 950 year lifetime this succinct treatise has continued to draw the attention of theoreticians and historians of music. These scholarly examinations of Guido's work vary in range from a few sections to the entire treatise and focus largely on the explication of specific points of theory. Several commentators have undertaken to identify the sources used by Guido, but none have attempted a comprehensive study of the nature of the ideas that Guido presents in terms of his intellectual heritage. It is the purpose of this paper to present such an analysis. Two analytical models are identified. The first is based on the Platonic cosmology of Timaeus as transmitted by Calcidius and Augustine and the second is derived from the grammatical-rhetorical tradition represented in the writings of Priscian and Augustine. Guido's analysis of the musical structure of chant is based on the first

iv or mner model and his analysis of chant as sung speech on the second or outer model. The two models are not developed independently but exist in an interactive state throughout the 20 chapters of Micrologus. Guido's particular adaptation of the tools of rhetorical-grammatical analysis to the study of chant is achieved through his identification of the sung syllable as a fundamental structural unit shared by both models.

v CHAPTER I Commentaries on Micrologus of Guido of Arezzo, written ca. 1026-1032, began appearing as early as the second half of the 11th century. Throughout its 950 year lifetime this succinct treatise has continued to draw the attention of theoreticians and historians of music .1 These scholarly examinations of Guido's work vary in range from a few sections to the entire treatise and focus largely on the explication of specific points of theory. Several commentators have undertaken to identify the sources used by Guido, but none has attempted a comprehensive study of the nature of the ideas that Guido presents in terms of his intellectual heritage. It is the purpose of this thesis to present such an analysis. In the Epistola Guidonis ad Theodaldum Episcopum, which precedes the Prologus of Micrologus, Guido writes of the utility to the church of training in the art of music: "Qua de re cum de ecclesiasticis utilitatibus ageretur. exercitium musicae artis ... " (Smits van Waesberghe ed. 82).2 Later in the same document he states his purpose to be that of presenting the rules of this art lucidly and lThe reader is referred to Smits van Waesberghe, De Musico­ Paedagogico et Theoretico, and the works by Oesch and Wolking for modern commentary on Micrologus. The first two works are, in addition, excellent sources for what is known of Guido's biography. For commentary from the past, see Smits van Waesberghe, Expositiones; Aribo, Aribonis de Musica; and Vivell, Commentarius Anonymus in Micrologus Guidonis Aretini.

2The Latin edition of Micrologus cited throughout this thesis is that of Smits van Waesberghe. Babb gives the following translation of this phrase: "Since it was a matter of usefulness to the church, your authority decreed that this way of training in the art of music ... " (57).

1 briefly, not in the style of the philosophers before him: "Offero sollertissimae paternitati vestrae musicae artis regulas, quanto lucidius et brevius potui explicatas philosophorum... " (84).3 The study of music, he admits, is difficult and has been explained in simple terms by no one: .. Ideo enim hoc studium hactenus latuit occultatum, quia cum revera esset arduum, non est a quolibet humiliter explanatum" (84 ). Guido concludes the prologue to Micrologus as follows: Cupiens itaque tam utile nostrum studium in communem utilitatem expendere, de multis musicis argumentis quae adiutore Deo per varia tempora conquisivi, quaedam quae cantoribus proficere credidi, quanta potui brevitate perstrinxi; quae enim de musica ad canendum minus prosunt, aut si qua ex his quae dicuntur non valent intelligi, nee memoratu digna iudicavi, non curans de his, si quorundam livescat invidia, dum quorundam proficiat disciplina (86-7).4

3 .. I offer to your most sagacious and fatherly self the precepts of the science of music, explained, as far as I could, much more clearly and briefly than has been done by philosophers ... " (Babb 58).

4"Desiring therefore to set forth my own so useful method of study for the general benefit, I summarized as briefly as I could, out of the copious musical theorizing which with God's help I have at various times collected, certain things that I believed would help singers. But I judged those musical matters not worth mention which are of little benefit for singing, as well as any of the things that are said but cannot be understood--not worrying about any who might turn livid with ill will so long as the training of others made progress" (Babb 58).

2 Again he stresses utility and practicality; his aim is to train young singers. He makes reference to his familiarity with treatises on music, but will adapt to his purpose only that which is necessary and understandable. A commentary on the twenty chapters of Guido's treatise will be presented in the second chapter of this thesis. But first, just as Guido sets his stage with epistle and prologue, ours will be set with a discussion of several fundamental points: What was Guido's training and intellectual heritage? What exactly was the 11th century conception of the "art" or "discipline" of music? And what sorts of analytical tools did Guido assemble in order to accomplish his dual purposes of clarification of treatises on music and discussion of the art and practice of chant? Consideration of Guido's training is a convenient starting point. He · would have been educated according to the seven liberal arts originally formulated by Cicero in De Oratore : the trivium, consisting of grammar, dialectic, and rhetoric; and the quadrivium, consisting of arithmetic, music, geometry, and astronomy. The early Latin fathers had observed the aims of Cicero as codified by Quintilian. But while Quintilian in lnstitutio Oratoria of 95A.D. describes the goal of liberal education as "vir bonus discendi peritus," Augustine in De Doctrina Christiana writes of "vir Christianus dicendi peritus" (Gilson 176). Indeed, the extensive psalm commentaries of Augustine provide an example of the early Christian reponse to Quintilian's belief that the main task of a professor of letters was the explication of the works of the great poets.

3 The Latin grammatical-rhetorical tradition was represented in the early Medieval curriculum by the works of Augustine himself, Bede, Donatus, Cassiodorus and Priscian (Chase 5-26). Evidence about the path of Latin culture in the 9th and 1Oth centuries is incomplete, but grammarians and humanists are known to have existed in the monasteries. Remi d'Auxerre (841-908 A.D.), for example, wrote commentaries on Donatus, Priscian, and Augustine. Gilson mentions, in fact, that during the 1Oth and 11th centuries the Italians were notorious for their preference for grammar above all other liberal arts (231). Micrologus , as will be demonstrated, shows the strong influence on Guido of this tradition. On the side of the quadrivium, it is beyond doubt that Guido had access to the works of Boethius and Cassiodorus and thus, indirectly at least, to the precepts of ancient Greek music theory. His exposure to Greek philosophy could have come indirectly through, for example, the works of Boethius and Augustine, or directly through the Latin translation of the first 53 chapters of Plato's Timaeus provided by Calcidius as the frrst section of his extensive commentary on that dialogue. The continuity of the Platonic tradition throughout the Middle Ages has been established by Klibansky, who writes of the major role of the Calcidius commentary in providing a blending of myth, science, and wisdom (74-77). A somewhat different transmission of Platonic doctrine is given through Plotinus and Augustine. Both aspects are present in Micrologus. As quoted above, Guido writes of the "multis musicis argumentis" to which he has previously turned his attention. That

4 this exposure included music treatises more recent to his time has been discussed by several authors.5 Prominently mentioned are Musica and Scholica E'nchiriadis and Dialogus. And, indeed, these treatises are all plainly marked by the intellectual heritage sketched above. It must be noted that the discussions to follow operate more in the background than in the foreground. Thus, in the main, the object is not to identify specific text borrowed by Guido but to suggest possible sources for his analytical framework. Examination of the nature of the art or discipline of music leads to the formulation of two different aspects. The first, pertaining to discipline, comes from a consideration of music as part of the quadrivium and deals with inner structure. The second, arising from a recognition of certain communalities between the spoken word and the sung word, pertains to practice and uses methods of analysis proper to the trivium to treat the outer structure. Guido, reflecting perhaps the Italian fondness for grammar and rhetoric, states a preference for the outer model; he wishes to discuss the practice of chant. But, as will be indicated, the inner model is present in Micrologus ; in fact, the interplay of these two models is at the foundation of this treatise. A process of abstraction from certain of the works mentioned above will lead to a more precise delineation of each model.

5See, in particular, Smits van Waesberghe, De Musico-Paedagogico; Oesch, Guido von Arezzo; and Wolking, Guido's Micrologus und seine Quellen.

5 Timaeus of Plato is the treatise which is fundamental to the inner model. In this dialogue Timaeus, a man trained in Pythagorean doctrine, describes the origin and nature of the physical world. Central to this cosmological drama is the Demiurge, a kind of primary arranger. Calcidius, a Christian, takes this arranger as his first principle, Deus. The Demiurge, referred to by Calcidius as Opifex or Fabricator, upon beginning his work, finds matter without form or quality in a state of primitive chaos. This matter (hyle ), translated as silva by Calcidius, is placed in a state of order through the use of definite shape and number. The numbers used by the Demiurge are the harmonic ratios originally described in Pythagorean theory, permitting an analogy between the ordering of the physical world and the ordering of pitches on a scale. Furthermore, no order exists without harmony and anything which is knowable must be in a motionless state of order, therefore in a state of harmony. The soul, whose nature consists of these same harmonic numbers, has a contradictory function in Plato which is not clarified by Calcidius. On the one hand, it is the source of life or motion, and on the other the source of theoretical reason and knowledge of that which is ordered and motionless. The senses, as instruments of the soul in its second function, provide important initial observations which can lead, through stimulation of the intellect, to the attainment of truth. Special importance is given to sight and hearing: sight as the primary source of sensible observation and hearing as the means of

6 appreciation of musical sound whose harmonic ratios are identical to those which order the universe.6 Augustine presents his version of the Platonic cosmology in De Ordine, described by Gilson as Platonism filtered through Plotinus and given a Christian orientation (137).7 The cosmological model given by Augustine is much the same as that described above. Augustine, however, postulates a creation ex nihilo from space, thus differing from the Calcidius doctrine of an ordering of original chaos. Plato, it should be noted, is not entirely clear on this point.S To summarize the inner model: 1. The basic material of the universe is ordered by certain unchanging and motionless ratios. a. A state of chaos preceded the ordering activity. b. The ordering was accomplished ex nihilo from space. 2. Since numbers are the principles of all things, arithmetic, which is the science of numbers, is the primary quadrivial art.

6For discussions of Timaeus the reader is referred to the Archer­ Hind edition and commentary, which presents the text in English and Greek, to the Lee edition of Timaeus and to Cornford, Plato's Cosmology. The work of Calcidius is available in the excellent Waszink edition. Commentaries on Calcidius are given by Boeft, Switalski, Waszink, and Winden.

7Courcelle concurs in stating that there is no evidence that Augustine was familiar with the work of Calcidius and that it is unlikely that Augustine read Timaeus directly (137-142). Klibansky postulates that Augustine's sources of Platonic doctrine were the Victorious Latin translations of Plotinus and Porphyry (22).

8For a complete discussion of Augustinian Platonism the reader Is referred to the O'Connell treatise.

7 3. Music, whose harmonic structure is given by these same ratios, provides an exemplum of these ratios and an analogy for the structure of the universe. Therefore the science of music is given a place next to the science of numbers in the quadrivial arts. 4. The senses, in particular sight and hearing, can stimulate the soul to perform its function of theoretical reason. Nothing, however, in the physical world is knowable, since it is constantly changing. 5. Only that which is ordered and unchanging can be known. 6. Music has a special role, in that it is both knowable and unknowable. Its knowable nature is its harmonic structure; however, its outer aspect, physical sound, can only suggest truth. It remains to derive a second model for analysis of the outer aspect of music. Cicero, in formulating the quadrivial and trivial educational scheme, had spoken of the dual importance of sapientia and eloquentia. Man, he argued, was uniquely gifted with the ability for rational speech. This rhetorical skill should not, however, be cultivated for its own sake but for the purpose of effective communication of wisdom. That is, according to his model, the trivial arts should serve the quadrivial. The paradigms that were constructed toward this end begin with the classification of types of physical sound and end with rules and procedures for logical and convincing discourse. Exemplification of the type of scheme that Guido adapted to his own purposes is provided by lnstitutio Grammaticarum of Priscian, a grammar treatise which codifies m Latin the writings of the Greek authors Apollonius and Herodianus; and De Doctrina Christiana of Augustine, a turning of ancient Latin

8 grammatical, rhetorical and dialectical principles toward the interpretation and exposition of Scripture.9 The Priscian treatise, given in the second and third volumes of Grammatici Latini, begins with the definition and classification of vox and littera. His second paragraph will serve to illustrate his style: Vocis autem differentiae sunt quattuor: articulata, inarticulata, literata, illiterata. articulata est, quae coartata, hoc est copulata cum aliquo sensu mentis eius, qui loquitur, profertur. inarticulata est contraria, quae a nullo affectu proficiscitur mentis. literata est, quae scribi potest, illiterata, quae scribi non potest. (Grammatici Latini 2: 5)1 O In orderly fashion, the treatise moves from voice and letters through syllables, feet, accents, parts of speech, and structure. In each section, the special character of each topic is carefully considered.

9Guido would have had access to many grammatical and rhetorical writings. Certain unique aspects of the Priscian treatise are particularly applicable to Micrologus ; however, any of the writings contained in the seven volumes of the Grammatici Latini series (works of Bede, Donatus, Cassiodorus, etc.) could have been studied by Guido. The order of presentation used by Priscian in 515 A.D. is that standardized by Donatus in 350 A.D. Chase writes, "Those who in the five centuries after the sixth essay the task of grammar base their productions more upon Priscian and Donatus than upon any of the other ancient writers of grammar" (15). lOMoreoever, there are four categories of voiced sounds: articulate, inarticulate, literate, and illiterate. Articulate voiced sounds, flowing together, are made up of separate linked elements which are intelligible. Inarticulate voiced sounds, on the other hand, are completely unintelligible. Literate voiced sounds are those that can be written; illiterate, those which cannot be written.

9 For example, littera is described as "pars minima vocis compositae," defined as "vox quae scribi potest individua," and characterized as "nota elementi," that is, the smallest spatial entity which serves as a sign of articulate sound ( Grammatici Latini 2: 6). Vowels and consonants are carefully distinguished, vowels having the character of animae, consonants that of corpora : "Multa enim est differentia inter consonantes, ut diximus, et vocales. tantum enim fere interest inter vocales et consonantes, quantum inter animas et corpora" (Grammatici Latini 2: 13).11 This particular characterization of vowels and consonants is unique to Priscian and will be of particular importance to the analysis of Chapter 17 of Micrologus. De Doctrina Christiana spends very little time on purely grammatical analysis; however, Augustine does present in Book Two a discussion of letters as signs of words. Man's speech, he argues, because of its ephemeral nature can be visible to the eyes only through the use of such signs: "Sed quia verberato aere statim transeunt nee diutius manent quam sonant, instituta sunt per litteras signa verborum. Ita voces oculis ostenduntur, non per se ipsas, sed per signa quaedam sua" (35).12 This passage is particularly

11 In translation: There is a great difference between consonants and vowels, as much as that between souls and bodies.

12AII quotations are taken from the Green edition of De Doctrina Christiana. The Robertson edition is a translation into English and contains in the introduction information about the treatise. Robertson gives the following translation of this passage: "But because vibrations in the air soon pass away and remain no longer than they sound, signs of words have been constructed by means of letters. Thus words are shown to the eyes, not in themselves but through certain signs which stand for them" (36).

10 suggestive, since ephemerality is one of the many common characteristics of man's spoken and sung word. The four books of De Doctrina Christiana are divided by Augustine into two parts as designated at the beginning of Book One: "Duae sunt res quibus nititur omnis tractatio scripturarum, modus inveniendi quae intellegenda sunt et modus proferendi quae intellecta sunt. De inveniendo prius, de proferendo postea disseremus" (8).13 Books One through Three deal with modus inveniendi , the way of finding or discovering that which is to be understood, and Book Four with modus proferendi, the way of advancing or teaching that which has been learned. In modus inveniendi Augustine discusses faith, signs in general (including the passage on letters given above), and the proper interpretation of ambiguous signs in Scripture. In Book Four he presents his adaptation of classical rhetorical principles. As given by Cicero the five separate tasks to be undertaken by an orator in preparing a speech are inventio , dispositio arrangement), elocutio (verbal expression), memoria, and actio (the art of delivery). Although Augustine declines to give specific rhetorical rules, saying that such precepts have no intrinsic value, he does not deny their utility to the Christian purpose and bases much of what he writes in Book Four on the Ciceronian model. He particularly stresses the following characteristics of style:

13"There are two things necessary to the treatment of the Scriptures: a way of discovering those things which are to be understood, and a way of teaching what we have learned. We shall speak first of discovery and second of teaching" (Robertson 7).

1 1 1. Clarity and simplicity Words which are technically correct but which teach nothing should be avoided: Quid enim prodest locutionis integritas quam non sequitur intellectus audientis, cum loquendi omnino nulla sit causa si quod loquimur non intellegunt propter quos ut intellegant loquimur? Qui ergo docet, vitabit verba omnia quae non docent, et si pro eis alia quae integra intellegantur potest dicere, id magis eliget. (135)14 The connection between this statement and Guido's concluding paragraph to the Prologue to Micrologus, quoted above, is immediately apparent. 2. Variety Writing of the three styles of classic oratory (rhetorical, moderate, and dialectical), Augustine advocates an appropriate mixture: "Nee quisquam praeter disciplinam esse existimet ista miscere; immo quantum congrue fieri potest, omnibus generibus dictio varianda est. N am quando prolix a est in uno genere, minus detinet auditorem" ( 159-60).15

I4"What profits correctness in a speech which is not followed by the listeners when there is no reason for speaking if what is said is not understood by those on whose account we speak? He who teaches should thus avoid all words which do not teach. And if he can find other correct words which are understood he should select those .. (Robertson 134).

1s "But no one should think that it is contrary to theory to mix these three manners; rather, speech should be varied with all types of style in so far as this may be done appropriately. For when one style is maintained too long, it loses the listener" (Robertson 158).

12 3. Effective presentation Augustine quotes Cicero to the effect that the eloquent man speaks in a way which teaches, attracts, and convinces:16 "Dixit ergo quidam eloquens, et verum dixit, ita dicere debere eloquentem ut doceat, ut delectet, ut flectat" (137).17 A fundamental statement of De Doctrina Christiana is that grammatical and rhetorical models are only as good as the uses to which they are put. The rules of these arts, as opposed to those of arithmetic, are made by man and as such are changeable and unknowable. The man who is skillful in the art of rhetoric but does not seek the source of truth may appear learned but is not wise: Quae tamen omnia quisquis ita dilexerit ut iactare se inter imperitos velit et non potius quaerere unde sint vera quae tantummodo vera esse persenserit, et unde quaedam non solum vera, sed etiam incommutabilia, quae incommutabilia esse comprehenderit, ac sic ab specie corporum usque ad humanam mentem perveniens -- cum et ipsam mutabilem invenerit, quod nunc docta, nunc indocta sit, constituta tamen inter incommutabilem supra se veritatem et mutabilia infra se cetera -- ad unius dei laudem atque dilectionem cuncta convertere a quo concta esse cognoscit, doctus videri potest, esse autem sapiens nullo modo. (73)18

16The reference given by Green is De Oratore 69.

17"Therefore a certain eloquent man said, and said truly, that he who is eloquent should speak in such a way that he teaches, delights, and moves" (Robertson 136) 18"But whoever delights in these things in such a way that he boasts among the unlearned, and does not seek to learn the source of the

13 To summarize the grammatical-rhetorical model suggested by

Institutio Grammaticarum and De Doctrina Christiana :19 1. Rhetorical-grammatical analysis begins with the sound of the human voice. Human sounds which are both articulate and understandable are the basis of rational discourse. 2. Letters are the basic elements of grammatical analysis. The two types of sounds of letters, consonants and vowels, differ in character and function. 3. Visible signs of letters are needed because of the ephemeral nature of physical sound. That man makes sounds which are articulate and can be made visible is a characteristic of his rationality. 4. All grammatical entities are constructed according to certain rules and all have distinct natures. 5. Rhetorical analysis is concerned with the effectiveness and appropriateness of speech. Rhetorical skill has no intrinsic value; it takes its value from that of its subject. truths which he has somehow perceived and to know whence those things are not only true but immutable which he has seen to be immutable, and thus, arising from corporal appearances to the human mind, when he finds this to be mutable since it is now learned and now unlearned, does not come to understand that it is placed between immutable things above it and other mutable things below it, and so does not turn all his knowledge toward the praise and love of one God from whom he knows that everything is derived--this man may seem to be learned. But he is in no way wise" (Robertson 73).

19 Again, it must be emphasized that these two works were chosen for illustrative purposes from the large number of treatises to which Guido would have had access.

14 6. The laws of grammar and rhetoric are made by man and are therefore changeable and unknowable. Two analytical procedures abstracted from Guido's training and intellectual heritage have been identified: a model for the inner structure of music derived from Platonic cosmology and a model for the grammatical-rhetorical analysis of man's speech derived from Greek and Latin tradition modified by Christian purpose. It is an assertion of this thesis that Guido uses both models in Micrologus.

15 CHAPTER2 In Chapter 1 reference was made to Guido's use, in the introductory material to his treatise, of words which stress the utility and the difficulty of training in the art of music. In statements which refer implicitly to the dual nature of music he says that his purpose is to teach the art of chant practice and to clarify and simplify the more difficult aspects of treatises on music which he has read. Through the medium of a detailed commentary it will be demonstrated that Guido's simplified presentation of musica disciplina is built on the framework of the Platonic model and that his discussion of the art and practice of chant is based on an adaptation of the rhetorical-grammatical model to the analysis of sung speech. These two models are not developed independently, but exist in an interactive state throughout the 20 chapters of Micrologus. The commentary on Micrologus which comprises this central chapter follows in sequence the twenty divisions of Micrologus ; general observations abstracted from this commentary are presented in the following chapter. For ease of reference, the Latin title of each of Guido's chapters is given along with an English version. The format of the commentary is one in which, within each chapter, key words and phrases used by Guido are identified and examined. The brief but important first chapter of Micrologus is given in its entirety:

Capitulum I Quid faciat qui se ad disciplinam musicae parat (91- 92)

16 (What one should do to prepare himself to study music) lgitur qui nostram disciplinam petit, aliquantos cantus nostris notis descriptos addiscat, in monochordi usu manum exerceat, basque regulas saepe meditetur, donee vi et natura vocum cognita ignotos ut notos cantus suaviter canat. Sed quia voces quae huius artis prima sunt fundamenta, in monochordo melius intuemur, quomodo eas ibidem ars naturam imitata discrevit, primitus videamus. (91-92)20 Vox. Just as Prise ian begins his treatise with the consideration of vox, so does Guido. The vox which Guido describes as fundamental to the art of music is analogous to vox articulata of Priscian, that is, an intelligible sound. These primary elements, according to Guido, have distinct character and strength or effect; each one must be learned separately, in similar fashion to the basic components of human speech. Parat. The importance of preparation is emphasized in D e Doctrina Christiana. Augustine encourages the beginning student of Scripture to read and memorize parts of the Old Testament, even though he may not as yet have understanding (41-42). The idea that

20"Let him who seeks our training learn some chants copied in our notation, let him train his hand in the use of the monochord, and let him frequently ponder these rules, until, having learned the effect and character of the notes, he can smoothly sing unfamiliar music as well as familiar. Since we learn the notes, which are the primary foundation of this art, more easily at the monochord, let us first see how science, imitating nature, has given them their separate places thereon" (Babb 59).

17 preparation of the body is a first step in the ordering of the soul is found in Platonic theory .21 Ars natura imitata. The monochord is an invention of human ingenuity which serves as a link between the inner and outer aspects of music. This idea will be fully developed in the commentary on Guido's third chapter. Considered as a whole, Guido's opening paragraph is dialectically sound; he has selected an unadorned style of prose appropriate to his instructive purpose and has identified the basic elements to be studied (inventio ) .

Capitulum II Quae vel quales sint notae vel quat (93-95) (What the notae are, of what nature, and how many)22 Nota. In the way that letters are employed as visible signs of human speech, Guido assigns letters to the voces which are the primary elements of sung speech. Nota is vox made visible to the human eye. Gravis and acutus (93 -94). The words with which Guido describes his registers are used in grammar to describe the quality of

21See, for example, the Lee edition of Timaeus , 58-61. A more extensive statement of this idea is given in the section of The Republic given in Strunk, 4-12.

22Generally, the Latin words vox and nota will not be translated. Guido observes a semantical distinction between the two which is obscured by the English word "note." The rules of Latin grammar will not be observed; thus, only two forms will be used in each case: vox , voces and nota, notae. For a different interpretation of the semantical distinction the reader is referred to the Bower review of Hucbald, Guido, and John on music.

18 the sounds of human speech. Priscian writes, for example, "ut puta a litera brevis quattuor habet soni differentias, cum habet aspirationem et acuitur vel gravatur ... "(Grammatici Latini 2: 7). Septem alphabeti litterae (93). Seven letters only are used (A,B,C,D,E,F,G) to notate Guido's 21 pitch gamut, although the signs for these letters are varied according to their placement. The number seven is important in Pythagorean numerology and is mentioned repeatedly in Timae us where, for example, Plato defines seven possible physical motions (Lee 45) and describes a process in which the mixture of the world's soul involves a seven part division of the Circle of the Different (Lee 49). A further example which is particularly relevant to our discussion of Guido's division of the monochord is the series of seven numbers on which Plato bases his division of the soul: 1, 2, 3, 4, 8, 9, 27 (Lee 48). The process of naming, ordering and locating voces which Guido is beginning to describe is analogous to the ordering of the basic material of the cosmos by the Platonic Demiurge.

Capitulum Ill De dispositione earum in monochordo (96-1 02) (On the location of notae on the monochord) Dispositio. This is the term for the second task of the rhetorician and refers to the orderly arrangement which follows the finding of materials, inventio. Guido is placing in order the elements of sung speech or chant, and the procedures he describes are exactly analogous to the procedures described by Plato for the division of the soul (Archer-Hind 105-15). The string of the monochord is divided according to ratios formed from the set of seven numbers given

19 above. The formulation of the tenets of the inner model of music given previously includes the statement that the harmonic structure of music is analogous to that of the universe; Guido illustrates the point in this chapter.23 What is particularly fascinating about this process of dispositio is that it involves the interaction of the inner and outer models of music through the medium of the monochord: The inner structure of music is given by harmonic ratios which are invisible and inaudible. Science imitates nature in the construction of the monochord with the result that from invisible and inaudible harmonic ratios are created audible voces. The final step, a procedure taken from the grammatical-rhetorical model, is the use of letters to create the now visible as well as audible notae. Posses in infinitum ita progredi sursum vel deorsum, nisi artis praeceptum sua te auctoritate compesceret (98). 24 Guido points out that theoretically the procedure for locating notae could continue in infinitum, but that the authority of the rules of art provides constraints. This curious passage is similar to one found in the first chapter of Musica Enchiriadis : "Verum quia, ut dictum est, eorum multiplicatio in immensum procedit, ex hac immensitatis confusione certum sibi numerum elegit

23The reader is referred to the Handshin article for an interesting derivation of a musical scale based on this section of Timaeus. The McClain Pythagorean Plato discusses musical references throughout the work of Plato.

24"You could continue up or down thus ad infinitum, did not the precept of art restrain you by its authority" (Babb 60).

20 ratio disciplinae, et in decem et octo sonis sibi speculationem posuit ... " (Gerbert 1:152-53).25 Although the wording is different, the basic thoughts are the same, that is, that an infinite amount of musical matter is available. Dialogus, a treatise which has a close relationship to the first 12 chapters of Micrologus and lies in time between Musica Enchiriadis and Micrologus, describes a procedure for dividing the monochord but says nothing about the possibility of infinite extension (Gerbert 1: 253-54). The Platonic concept of order is that of an arrangement of a finite amount of material within a fixed framework. Augustine expresses this concept in De Ordine: Namque illud quod in nobis est rationale ... vidit esse imponenda rebus vocabula, id est, significantes quosdam sonos; ut, quoniam sentire animos suos non poterant, ad eos sibi copulandos sensu quasi interprete uterentur. Sed audiri absentium verba non poterant; ergo illa ratio peperit litteras, notatis omnibus oris ac linguae sonis atque discretis. Nihil autem horum facere poterat, si multitudo rerum sine quodam defixo termino infinite patere videretur. Ergo utilitas numerandi magna necessitate animadversa est. (138-40)26

25 "While truly, as it is said, their increase proceeds endlessly, the judgement of custom has picked out of this bewildering quantity eighteen tones" (Music Handbook 2).

26Russell gives the following translation: Now that which is rational in .us ... saw that names, or meaningful sounds, had to be assigned to things, so that men might use the sense almost as an interpreter to link them together, inasmuch as they could not perceive one another's minds. But they could not hear the words of those not present. Therefore reason, having carefully noted and discriminated

21 The relationship between between this passage and the first three chapters of Micrologus is evident. Guido's use of the word auctoritas is interesting. Augustine, again in De Ordine, discussing the education of youth, introduces the concept of authority into Platonic doctrine as follows: "Ad discendum item necessaria dupliciter ducimur, auctoritate atque ratione. Tempore auctoritas, re autem ratio prior est. Aliud est enim quod in agendo anteponitur, aliud quod pluris in appetendo aestimatur" (120).27 Guido is saying that the authority of art can supersede that which is strictly rational Ad memorandum facillimus (102). Guido remarks at the close of this section that although one of the two procedures he describes is quicker to apply, the other is easier to memorize. The role of memory in the attainment of knowledge is a recurrent theme m Plato. Its particular role in the study of music is discussed extensively by Augustine, who argues in De Musica that because of its ephemeral nature, physical sound exists only in memory (345). Memoria is also one of the five basic tasks of the orator.

Capitulum IV Quod sex modis sibi invicem voces iungantur (1 03- 1 06) all the sounds of the mouth and tongue, invented letters. But it could have done neither of these, if the vast number of things seemed to extend endlessly without any fixed limit. Therefore the great utility of enumerating was brought to mind by its very necessity. (139-41)

27 "Likewise with regard to the acquiring of knowledge, we are of necessity led in a twofold manner: by authority and by reason. In point of time, authority is first; but in the order of reality, reason is prior .. ( Russell 121).

22 (That the voces should be joined together by six intervals) Jungantur, coniungitur (103, 105). Having identified, notated, and located his basic elements, Guido proceeds to the question of appropriate combination of voces . The schema he is following is exactly that of a classical grammar text as described in our first chapter. Priscian, for example, after discussing vox and letter turns to the joining together (coniungo ) of letters into syllables (Grammatici Latini 2: 44). Just as Priscian gives explicit rules for the formation of syllables, Guido identifies six joinings of voces which are utilized in the creation of chant. Vocum consonantias (105). This is the phrase used by Guido to denote the proper joinings of basic elements. The six consonances he identifies (semitonum, tonum, ditonum, semiditonum, diatessaron, and diapente ) are described in terms of distances derived from the Pythagorean-Platonic scheme he uses to locate notae on the monochord. This 1s another example of the interaction of the outer and inner models: the audible and visible voces are bound together m ways prescribed by their inaudible and invisible harmonic ratios. Cumque tam paucis clausulis tota harmonia formetur (105- 106). 28 The idea that a whole system can be built on a numeric ordering of a small amount of prima:y material comes from Timaeus By harmonia Guido means properly formed melody; the grammatical analogy is to the ultimate derivation of correct sentences from step-by-step considerations of vox, letter, syllable, and word. Clausula is a rhetorical term which refers to a well-

28"Since all melody is formed by so few formulas ... " (Babb 61).

23 formed section of a discourse, frequently the peroratio , although that is evidently not Guido's meaning in this case. Utillimum est altae eas memoriae commendare, et donee plencanendo sentiantur et cognoscantur, ab exercitio numquam cessare, ut his velut clavibus habitis canendi possis peritiam sagaciter ideoque facilius possidere (106).29 This is Guido's formulation of the acquisition of knowledge of music, in this case chant. The necessary steps are given as follows: 1. Observation 2. Memorization 3. Formation of correct habits through practice 4. Attainment of knowledge A Platonic framework is evident. Plato speaks of the role of the senses in suggesting truth to the soul; memorization is a step in this process (Lee 65). Augustine's ideas on the particular role of memory in the acquisition of knowledge of music were described in our commentary on Chapter 3. Correct habit, that is, proper training and maintenance of the body, according to Plato is a sine qua non of knowledge (Lee 58-61). The first three items are m the realm of the outer model of music and have to do with the acquisition of skill in the art of music; the last has to do with the only unchanging and

29 "It is most helpful to commit them firmly to memory, and, until they are completely perceived and recognized in singing, never to stop practicing them, since when you hold these as keys, you can command skill in singing intelligently, and therefore more easily" (Babb 61).

24 therefore knowable aspect of music, its inner rational formation. Again, the two models interact; physical skill is a path to knowledge.

Capitulum V De diapason et cur sept em tantum sint notae ( 1 07-12) (On the diapason and why there are only seven notae ) For the reader's convenience most of the text of this difficult chapter is given: Diapason autem est in qua diatessaron et diapente iunguntur; cum enim ab A sit D sit diatessaron, et ab eadem D m a acutam sit diapente, ab A in alteram a diapason existit. Cuius v1s est eandem litteram in utroque habere latere .... Sicut enim utraque vox eadem littera notatur, ita per omma eiusdem qualitatis perfectissimaeque similtudinis utraque habetur et creditur. N am sicut finitis septem diebus eosdem repetimus, up semper primum et octavum eundem dicamus, ita primas et octavas semper voces easdem figuramus et dicimus, quia naturali eas concordia consonare sentimus, ut D et d. Utraque enim tono et semitonio et duobus tonis remittitur, et item tono et semitonio et duobus tonis intenditur. Unde et in canendo duo aut tres aut plures cantores, prout possibile fuerit, si per hanc speciem differentibus vocibus eandem quamlibet antiphonam incipiant et decantent, miraberis te easdem voces diversis locis, sed m1mme diversas habere, eundemque cantum gravem et acutum et superacutum tamen unice resonare... .Item s1 eandem antiphonam partim gravibus partim acutis sonis cantaveris aut quantumlibet per hanc speciem variaveris,

25 eadem vocum unitas apparebit. Unde verissime poeta dixit: septem discrimina vocum, quia etsi plures fiant, non est aliarum adiectio sed earundem renovatio et repetitio. Hac nos de causa omnes sonos secundum Boetium et antiquos musicos septem litteris figuravimus, cum moderni quidam nimis incaute quattuor tantum signa posuerint, quintum et quintum videlicet sonum eodem ubique charactere figurantes, cum indubitanter verum sit quod quidam soni a suis quintis omnino discordent nullusque sonus cum suo quinto perfecte concordet. Nulla enim vox cum altera praeter octavam perfecte concordat. (107-13)30

30"The diapason is the interval in which a diapente and a diatessaron are combined; for while from A to D is a diatessaron and from that same D to acute a is a diapente, from A to the other a is a diapason. Its property is to have the same letter on both ends .... Just as both sounds are notated by the same letter, so both are held and believed to be in all respects of the same nature and the most absolute likeness. Just as when seven days have elapsed we repeat the same ones, so that we always name the first and eighth the same; so we always represent and name the first and eighth notes the same way, because we perceive that they sound together with a natural concord, as D and d. For from each of them you descend by a tone, a semitone, and two tones, and ascend by a tone, a semitone, and two tones. Thus in singing, if two or three or more singers, as may be feasible, begin and sing through the same antiphon, whichever it be, with the various notes separated by this interval, you will be amazed that you get the same notes at different pitches, but with a minimal difference of sound, and that the same melody resounds in the graves, acutae, and superacutae as if a single thing. Likewise if you should sing the same antiphon partly in a low and partly in a high register, or however else you transpose it at the interval of a diapason, that same unity of the notes will be apparent. Therefore the poet spoke very rightly of 'the seven different notes' because even if more occur it is not an addition of other ones, but a renewal and repetition of the same ones. For this reason Boethius and the

26 One of the properties of the inner harmonic structure with which Guido is working is that the harmonic ratio of a diatessaron, 4:3, when combined with that of a diapente, 3:2, produces that of a diapason, 2:1. Guido introduces his discussion of the diapason with a reference to this aspect of the inner model and then turns immediately to a discussion of notation. As the reader will recall, Guido, in notating the voces, has given the same sign or letter, with certain variations, to voces which are at the distance of a diapason from each other. In this chapter he reasons that the cyclical notational scheme is a visible manifestion of an audible identity. Two voces at the distance of an diapason sounding together form a natural consonance, argues Guido. (It should be remembered that the diapason is not one of the allowable joinings of voces in chant; therefore his previous discussion does not apply. ) He adds that the disposition of tones and semitones around each of the two voces is identical, so the relocation does not affect our perception of the sound. Further, that same unity of voces is observed if an antiphon is sung partly in one vocal range and partly in another vocal range at an diapason's distance. He concludes a reference to the scale of Musica Enchiriadis by saying that perfect concordance of voces exists only at the octave. musicians of old, indicate all musical sounds by seven letters. However some people nowadays incautiously employ only four symbols. They indicate every fifth sound always by the same symbol, though it is true beyond a doubt that some notes disagree completely with those a fifth away, and that no note agrees perfectly with its fifth. For no note agrees perfectly with any other except its octave" (Babb 61-2).

27 Guido is on difficult ground. Clearly, he needs to make the argument because, although octave leaps were not acceptable in chant melody, octave displacement of melody was a part of chant practice. The fact that he appeals directly to the authority of two other writers (Boethius and Vergil) may indicate his discomfort with his line of reasoning, as he does not normally credit his sources. His greatest inconsistency lies in arguing that displacement from gravis to acutus does not affect the unity of voces. He had previously indicated that different vocal ranges had different qualities of sound. His strongest point is his appeal to the identical disposition of tones and semitones around two voces which are an octave apart. This is actually the argument that is used in Musica Enchiriadis to construct a scale that has the property of duplication at the interval of a fifth. Generally speaking, Guido is introducing the concept of cyclicity or circular motion into his musical construct. In Ti mae us, of the seven possible motions described by Plato, circular is the most perfect. Further, the circle is a common Platonic symbol of the activity of thought (Archer-Hind 114). The concept was carried over into Christian Platonic thought in the work of Augustine. Guido's argument by analogy from the semantic cyclicity observed in naming the days of the week to the semantic cyclicity of names of voces is fine. But in extending the analogy to the audible identity of voces at the cyclic interval he commits a dialectical error that Augustine would not have made; what is true about the names of things is not necessarily true of the things themselves.

28 Capitulum VI Item de divisionibus et interpretatione earum ( 114- 16) (Also on the divisions of the monochord and their meaning) Alias vero divisiones praeter has quattuor invenire non poteris (114).31 Guido explains that the complicated procedures for dividing the monochord which he has described previously are based on four ratios only: 2:1, 3:2, 4:3, and 9:8. This is, of course, a reference to the inner model; the harmonic structure of music is given by the same ratios which order the basic material of the cosmos in Timaeus. Again the monochord is the physical manifestation of these invisible and inaudible ratios. Spatium (115). Not only are the basic ratios given the physical property of sound on the monochord, they are given dimension. They have certain lengths and include within their physical boundaries fixed numbers of tones. This procedure of moving from measurement in terms of ratios to measurement in terms of intervals is directly analogous to that described by Plato when he is speaking of the mixing of the soul of the world: "He first marked off a section of the whole, then another twice the size of the first ... " (Lee 48). Symphonia ( 116). Guido uses a standard term to denote the diatessaron, diapente, and diapason. These three intervals have harmonic ratios formed from the basic set of numbers (1, 2, 3, 4).3 2 In addition, the ratios for the first two combine to give that of the

31 "But you can find no other divisions than these four" (Babb 62).

32The harmonic ratios of the diatessaron, diapente, and diapason are, respectively, 4:3, 3:2, and 2:1.

29 third. It is for these reasons that the three intervals were given prominence in Greek music theory, the basis of the inner model. Augustine in Chapter 12 of Book I of De Musica gives the argument for the primacy of the first four positive integers and of the ratios based on these integers (195-202). Guido, who is always more concerned with chant practice, justifies the special place given to diapason, diatessaron, and diapente on the evidence of the ears: "Has tres species symphonias, id est suaves vocum copulationes memineris esse vocatas, quia in diapason diversae voces unum sonant. Diapente vero et diatessaron diaphoniae id est organi iura possident, et voces utcumque similes reddunt" (116).33 Again, he gives us the idea of two voices sounding as one to describe the diapason, a description which is certainly suggested by the harmonic ratio of the diapason, 2: 1. Diapente and diatessaron, he says, always give similar voces, but offers no explanation. Simile is a rhetorical term which describes an ornament of discourse; but it has the additional meaning of "parallel." Since these two intervals are fundamental to strict parallel organum, Guido is perhaps using this sense of the term.

Capuitulum VII De affinitate vocum per quattuor modos ( 117-21) (On affinities through the four modes)

33"You should remember that these three intervals are called 'symphonies,' that is, smooth unions of notes, because in the diapason the different notes sound as one and because the diapente and the diatessaron are the basis of diaphony that is, organum, and produce notes similar in every case" (Babb 63).

30 Modus. Guido argues that the seven fundamental voces occur in four different modes which he describes in terms of the disposition of tones and semitones. The word modus is used by Priscian and other grammarians to indicate the manner in which the action or state denoted by a verb is conceived. In this usage, the word carries the idea of specificity both in function and flavor. It is also a word used extensively by Calcidius, along with ordine, to describe an orderly arrangement within fixed bounds of the material of the universe. Affinitas. Guido describes affinities of the seven voces through the diatessaron and the diapente. Affinitas (adfinitas ) in its classic sense refers to a connection by marriage. Quintilian uses the word figuratively to describe joinings of letters (Lockwood and Smith 13). In Guido's model the affinities between voces are made through the diatessaron and the diapente. The idea is that the strongest and most important audible ties between voces are those which are based on primary harmonic ratios of the inner model: 4:3 and 3:2, respectively.

Capitulum VIII De aliis affinitatibus ( 122-29) (On other affinities) Figura ( 123). Guido illustrates his discussion of affinities with a figura . This particular figura has a dual function. First, in the way of letters which are signs of articulate sound, Guido's figura is a visible sign of certain audible relationships between voces. Second, it is an outer sign which turns man's reason inward toward the

3 1 contemplation of that which can be known, in this case, the unchanging harmonic structure. Tempera. Guido, discussing the problem of the tritone between F and b-natural, writes that neumes may be tempered or adjusted to avoid the use of b-flat. That is, F, G, a, b-flat may be tempered to G, a, b-natural, c. He is expressing the idea that the character of a neume lies in its dispositio and not in its location. De similitudine vocum pauca perstrinximus, quia quantum in diversis rebus similitudo conquiritur, tantum ipsa diversitas, per quam mens confusa diutius poterat laborare, minuitur; semper enim adunata divisis facilius capiuntur (126-27).34 Two Platonic concepts are given in this passage. The first, a dialectical principle, holds that reasoning consists essentially of judgments of sameness and difference. This principle permeates the structure of the Cosmos; for example, the Demiurge, after giving the appropriate mathematical structure to the soul of the world, divides the soul into a Circle of Sameness and a Circle of Difference (Lee 46-7).35 In writing of the need to find similarities between voces, Guido is applying the Platonic dialectic.

34 "We have confined ourselves to just a few things about the similarities between notes, because insofar as similarity is sought out between different things, to this extent is lessened that diversity which can prolong the labor of the confused mind, for organized material is always more easily grasped than unorganized" (Babb 64- 5).

35The Brisson treatise is a fascinating exposttton of the same-other principle in the ontological structure of Timaeus.

32 The second Platonic concept is an epistemological one: Only that which is ordered can be known. The application of the dialectical procedure gives a structure which is analogous to that of the soul and whic~ can therefore be judged to be true. In Guido's application, the physical observation of certain audible affinities between voces leads to the knowledge that these affinities are based on an underlying harmonic structure. Distinctio (127). Distinctio is a term from rhetoric which describes a figure of speech in which distinctions are made between two allied words or between two uses of the same word. Guido applies the rhetorical term as a "figure of sung speech," that is, an audible sign of differences in the dispositions of tones and semitones in each of the modes.

Capitulum IX Item de similitudine vocum quarum diapason sola perfecta est (130-32 ) (Also on the resemblance of notes which is perfect only at the octave) Supradictae autem voces prout similes sunt, .. .ita similes faciunt neumas adeo ut unius tibi cognitio alteram pandat (130-31).36 Again Guido is using the dialectical principle of same-different: 1. Thedispositio of each of the four modes is known. 2. A particular neume is studied through its dispositio.

36"Insofar as the above-mentioned notes are alike ... they will make neumes sound alike. Thus the knowledge of one makes another clear to you" (Babb 65).

33 3. By a process of success1ve comparison (same-different) with what is known of the four modes knowledge about the neume is obtained. Mox auditu perciperet quanta diversitatis transformatio fieret (131).37The visible distinctions of each mode, dispositio, can be known by their audible manifestations. Thus both sight and sound, as described in Timae us, provide important information to the intellect.

Capitulum X Item de modis et falsi meli agnitione et correctione (133-38) (Also on the modes and on recognizing and correcting a wrong melody) Naturali diversitate (133). The four modes or tropes, according to Guido, are inherently different and provide a complete and disjunct classification of neumes. A misclassified neume will be forced to change its fundamental structure to accord with the mode in which it has been placed. Guido's classification scheme is a further reiteration of the logic of same and different as found in Timaeus. The epistemological possibility of misclassification occurs, according to Plato, when the orbits of the circle of Same and Different in the human soul or intellect are disordered:

37"0ne would soon tell by ear how great a change was taking place" (Babb 65).

34 This and similar effects were produced in the soul's orbits, and when they encountered anything in the category Same or Different in the external world, they made wrong judgements of sameness or difference, and lapsed into falsehood and folly, having no governing orbit in control. (Lee 60) Dissonantia ( 134 ). The human voice, an imperfect instrument according to Guido, can turn a neume away from its inherent structure by singing it incorrectly. The word dissonantia carries a sense of confusion and disorder; that the human voice, which exists in the physical world, is not in a state of perfect order follows directly from Platonic doctrine in Timaeus. Ubi nulla vox est (137). Guido writes that displacing a neume or a chant by a tone or a semitone can result in its ending where there is no vox, as, for example, a tone below F. The idea is that the basic elements of the outer model, the voces, are themselves a complete and ordered system for the discussion of chant. Priscian, analogously, provides rules for the proper construction of words and phrases using only the basic material of his system, the articulate and literate sounds of human speech. Si motione opus est (138). If a chant must be moved, that is, laterally displaced on Guido's scale, !his motion should be to an affinity of the original first vox. Guido again makes the point that the character of a mode is manifested in its disposition of tones and semitones. Displacement to an affinity of the first vox will not, he indicates, disturb the dispositio. This is, of course, not strictly true. Only moti one through an octave leaves dispositio unchanged; any

35 other displacement will force either a change of dispositio or the singing of a vox which is not part of Guido's scale.

Capitulum XI Quae vox et quare in cantu obtineat principatum (139-46) (What note should hold the chief place in a chant and why) Vox tamen quae cantum terminat, obtinet principatum (139).38 Guido argues the primary importance of the last vox of a chant, and gives rules of chant practice and organization based on this importance. As will be indicated, the argument for the primacy of the ultimate vox has both grammatical and rhetorical interpretations. Ea enim et diutius et morosius sonat (139).39 Guido states that the last vox has a particular form of performance associated with it; it is prolonged and followed by a pause. The principle he is applying comes from classical rhetoric, in particular, from the rules which apply to the actio of a speech. It was customary to articulate divisions of a speech with a pause (mora ); the greater the importance of the division, the greater the pause. The rules concerning the duration of sound of the last vox will be clarified in the discussion of Chapter 15. Color (140). Guido states that all voces of a chant are affected by the last; that is, their style or external condition is altered by the power of this particular vox. This particular aspect of his argument is taken from grammar; the reference is made explicit in his

38"The note that ends it [a chant] holds the chief place" (Babb 66).

39"It sounds both longer and more lasting" (Babb 66).

36 penultimate paragraph: "Nee mirum regulas musicam a finali voce sumere, cum et in grammaticae partibus pene ubique vim sensus in ultimis litteris vel syllabis per casus, numeros, personas, tempora discernimus" (145).40 Distinctiones (145). Speaking of the organization of a chant, Guido states that all its phrases should most properly end with that vox which is the ultimate. Distinctio , a rhetorical term, refers in this case to a separation or a division in discourse.4I That the phrases of a chant should close at the same location and with the same sound is analogous to the rhetorical maxim pertaining to dispositio that all major divisions of a speech should relate directly to the final and most important division, peroratio. A finali itaque voce ad quintam in quolibet cantu iusta est depositio, et usque ad octavas elevatio (146).42 All voces of a chant, according to Guido, must stay within a certain range of the final: an octave above and a fifth below. For the reason that they have a central location on the monochord, he explains, D, E, F, and G have been designated as the finalvoces. These four voces are, of course,

40 "It is no wonder that music bases its rules on the last note, since in the elements of language, too, we almost everywhere see the real force of the meaning in the final letters or syllables, in regard to cases, numbers, persons, and tenses" (Babb 67).

41 Guido uses the word in it second rhetorical sense, as a figure of speech, in his Chapter 8.

42"In any chant it is right to go down [as far as] a fifth from the final note and up [as far as] an octave... " (Babb 67).

37 representative of the four affinities based on the primary harmonic ratios of the underlying model.

Capitulum XII De divisione quattuor modorum in octo ( 14 7 -49) (On the division of the four modes into eight) Qui naturaliter in vocibus erant quattuor in cantibus facti sunt octo (148-49).43 Guido explains that considerations having to do with vocal range require that the four modes, given by the underlying harmonic structure described above, be divided into eight. He insists, however, that the words used to denote the eight modes should reflect the fact that in truth there are but four. Thus he disallows what he refers to as the Latin usage of "first" through "eighth" modes and requires autentus protus, plagis proti, autento deutero, plagis deuteri, autento trito, plagis triti, autento tetrardo, and plagis tetrardi.

Capitulum XIII De octo modorum agnitione acumine et gravitate (150-57) (On the recognition of the eight modes by their height and depth) lgitur octo sunt modi... per quos omnis cantilena discurrens octo dissimilibus qualitatibus variatur (150).44 Guido, making an analogy with the eight parts of speech and the eight beatitudes,

43"These modes, which naturally were four according to their notes, have been made eight in chants" (Babb 67).

44 "Thus there are eight modes ... and every melodic line, as it moves to and fro among these, is diversified by eight dissimilar qualities" (Babb 68).

38 writes that all song is diversified by the particular qualities of the eight modes as it moves here and there among these modes. It is difficult to know exactly what he means, but the grammatical analogy he gives is helpful. Parts of speech, in a grammar text such as that of Priscian, occur on an organizational level just above the syllable; they form a disjunct and complete classification of the set of all words, in the way that Guido intends the eight modes to form a disjunct and complete classification of all chant. In addition, analogously to the modes, the different parts of speech have distinct character and quality and function accordingly within a phrase or sentence. (In modern texts on usage this scheme is reversed; function is taken to be the primary dimension.) When Guido writes that all song (cantilena ) moves among the eight modes, one can think by analogy of all phrases and sentences as having a potential existence in the set of all words. In both cases the possibility for diversity lies in the existence of eight subdivisions which are distinct m character. Neumae inventae sunt, ex quarum aptitudine ita modum cantionis agnoscimus ( 150-51 ).45 Guido explains that for each mode a certain neume has been found which is a true representative of that mode. Arguing by analogy from the fact that the ownership of a tunic can be determined by fit, he states that a chant can be correctly identified as to mode by finding to which of these neumes

45 "For ascertaining these modes in chants, certain neumes have been composed" (Babb 68).

39 it is best suited.46 He admits that classification can be difficult, as not all chants follow the modal rules with regard to range and final which are observed in the special neumes. The underlying structure of this argument proceeds from Platonic doctrine. In Timaeus Plato writes, "We must make a threefold distinction and think of that which becomes, that in which it becomes, and the model which it resembles" (Lee 69). The idea is that from basic material, objects of the physical world are created after certain models. The objects are imperfect and changeable copies of the models, which are perfect and unchanging. Only that which is unchangeable is knowable, but one can, through observation and proper use of the same-other dialectic, reason from copy to form. Guido assumes the existence of forms or ideal realizations of chant. The special neumes are meant to be reasonable embodiments of these forms. Thus, one can learn about any particular chant, created as it is from the basic material of sung speech, by comparing it to these neumes and making a reasonable decision.

Capitulum XIV Item de tropis et vi musicae ( 15 8-61) (On the tropes and on the power of music) Guido closes his discussion of the modes with remarks on the strength of music. He reiterates points that we have considered previously: the importance of training and practice in the acquisition of knowledge, the necessity of variety, the role of the senses in

46Auda discusses this process in detail (179ff.).

40 transmitting suggestions of truth to the intellect. Two arguments appear for the first time in this treatise and require amplification: 1. The modes have the power to affect man's behavior. To support this statement Guido alludes to three stories. Two of the stories are taken from Cassiodorus and the Bible and relate the soothing power of certain music.47 The third indicates that while some music is soothing, other music can be maddening. The argument for the ethos of the modes is derived from Greek theory and was widely transmitted in the writings of Plato and others. It holds that the distinct characters of the modes have a physical manifestation in their different effects on man's behavior. In particular, while some dispositions of tones and semitones produce rational conduct, others can, in certain men, produce disorder. The relative effect can be attributed to individual differences in men. This doctrine is intriguing in that it is an attempt to explain the psychology of music in terms of the dispositio given by the inner structure of music, but it contains a basic inconsistency. According to Platonic theory, disorder in man's behavior is an indication of disorder in his intellect or soul. Therefore, it follows that certain modes either create or do not affect this disorder. But since the construction of each mode is itself based on the order induced by the numerical principles which order the soul, it is

47The story of Asclepiades the Greek physician is found in Cassiodorus, Institutiones 5, 9. The story of David and Saul is taken from 1 Samuel 16:23 and is also given by Cassiodorus in Institutiones 5, 9.

41 impossible for the sound of a mode to create disorder. Therefore the remaining possibility that certain modes have no affect must be true, which would be in contradiction to our original assumption. A satisfactory resolution of this inconsistency in Platonic theory would be to allow for an impaired sense of hearing in a man who is led to irrational or disordered conduct by the sound of a mode. 2. God is the ultimate source of truth; only God has complete wisdom. This idea is fundamental to Christian Platonism. For example, in Chapter 18 of the second book of De Ordine Augustine writes: "Hie est ordo studiorum sapientiae, per quem fit quisque idoneus ad intelligendum ordinem rerum, id est ad dignoscendos duos mundos et ipsum parentem universitatis, cujus nulla scientia est in anima, nisi scire quomodo eum nesciat" (158).48

Capitulum XV De commoda vel componenda modulatione ( 162-77) (Concerning proper modulation and how it is accomplished)49 Modulatione. Having examined in Chapters 1 through 14 of his treatise the inner and outer structure of music and the modal classification of the existent body of chant, Guido turns in Chapter 15

48 "This is the order of wisdom's branches of study by which one becomes competent to grasp the order of things and to discern two worlds and the very Author of the universe, of Whom the soul has no knowledge save to know how it knows Him not" (Russell 159).

49Guido's Chapter 15 has been the subject of extensive commentary. The interested reader is referred to the Crocker article, the Vollaerts book (168-94) and the Smits van Waesberghe introduction to Aribonis de Musica (xvi-xxiv).

42 to a discussion of rules and principles governing modulatione , a term which is difficult to translate. In classical rhythmics it is used to denote methods of changing from one rhythm to another. The definition of music as bene modulandi scientia is given by many writers (e.g. Augustine, Cassiodorus, the author of Scolica Enchiriadis) ; Holzer has concluded that the term originates in the lost works of Varro on the liberal arts (6,14,15). The sense of measurement which is implicit in modulatione refers to precepts of rhythmics and metrics which Guido will present. lgitur quemadmodum in metris sunt litterae et syllabae, partes et pedes ac versus, ita in harmonia sunt phtongi, id est soni, quorum unus, duo vel tres aptantur in syllabas; ipsaeque solae vel duplicatae neumam, id est partem constituunt cantilenae; et pars una vel plures distinctionem faciunt, id est congruum respirationis locum. ( 162-3 )5o Guido's opening passage is presented in full, as it is the first time in Micrologus that he has made explicit reference to the analogy between the structure of speech and that of chant. This particular form of the idea is not by any means original to Guido, but can be found in the Calcidius commentary (92), in Disputatio de Somnio Scipionis of Favonius Eulogius (38), and in Musica Enchiriadis

50"Therefore, just as in poetry there are letters and syllables, words and feet and verses, so in harmony there are phtongi, that is, sounds, of which one, two or three are fashioned into syllables; and these, either alone or repeated, constitute a neume, that is a part of a song; and one or more parts make a phrase, that is a suitable place to breathe" (Crocker12).

43 (Gerbert 1, 152).51 The impetus for the analogy, which seems to have originated with Calcidius, is found in Timae us: For no one has yet explained their origin, but we talk as if people knew what fire and each of the others (earth, air water) are, and treat them as the alphabet of the universe, whereas they ought not really to be compared even to syllables by anyone with the least sense. (Lee 66) It is Guido's intention in this chapter to analyze chant as sung measured speech; to set his stage he has chosen a traditional analogy. The greatest part of Chapter 15 is devoted to the presentation of rules and standards for the analysis of melodic lines. Crocker in his article "Musica Rhythmica and Musica Metrica in Antique and Medieval Theory" examines this section from the point of view of classical metrics, rhythmics, and rhetoric. Citing as possible sources works of the grammarians, Quintilian, and Augustine, Crocker identifies Guido's implicit use of rhetorical and metrical techniques. Four examples will serve to illustrate his work; the first and last are taken from metrics, the second and third from rhetoric (Cf. 13): Let the phrases of the verses be equal exaequatum membris Let them be repeated or varied slightly prope aequatum Let them be changed in mode transitum in genus Let a neume return by the same path versus reciproci

51For a discussion of the source and use of the analogy in Musica Enchiriadis the reader is referred to Phillips (279-87).

44 In addition, Crocker finds in the science of rhythmics the rule which Guido gives explicitly in his second paragraph: Ac summopere caveatur talis neumarum distributio, ut cum neumae tum eiusdem soni repercussione, tum duorum aut plurium connexione fiant, semper tamen aut in numero vocum aut in ratione tenorum neumae alterutrum conferantur, atque respondeant nunc aequae aequis, nunc duplae vel triplae simplicibus, atque alias collatione sesquialtera vel sesquitertia.

(164-65)5 2 Guido's use of metrics and rhythmics no doubt proceeds from a desire to apply techniques with which he is familiar to the analysis of chant composition. Again the outer and inner models interact; the study of rhythmics and metrics deals with quantitative speech, a physical phenomenon made rational through its underlying numeric structure.53 In this particular case, the structure of man's speech provides an analogy with the basic structure of the Platonic cosmos

52"And special care is to be taken to produce such a grouping of neumes that they, whether made of one tone in repercussion or of two or more linked together, are always related to each other either with respect to the number of sounds or to the proportion of the lengths so that equals may correspond to equals, or duple or triple to units, and others by a relation of sesquialtera or sesquitertia" (Crocker 12-13 ).

53The underlying numeric structure of rhythmics is based on ratios, while that of metrics is based on intervals. The musical analogy is the difference between the fundamental ratios of the voces and their positions on a scale. Rational measurement is the more fundamental of the two in both cases and is, in fact, that measurement which orders Plato's cosmos.

45 in the way that music does in general. Seen in this light, Guido's choice of techniques is extremely appropriate. Ad principalem vocem, id est finalem (170).54 Guido returns to the discussion given in Chapter 11 of the importance of the final vox of a chant, that is, the principal vox of that chant's mode. Not only should phrases end with this vox , he writes; it is desirable for phrases to begin with the principal vox as well. The idea expressed is that of unity, and the underlying structure is Platonic. 55 To Plato, as to Pythagoras, the principle of numbers is given in the number one, the Unity from which all others evolve. Calcidius adopted this doctrine and identified God with Unity or Monad.56 Augustine in De M usica argues the importance of the return to one: Then, if you will, let us start considering numbers from the very beginning and see, as far as we can grasp such things with the mind's strength we have, what the reason is that, although as we have said numbers progress to infinity, men have made certain articulations in counting by which they return again and again to One, the beginning or principle of numbers. For in counting, we progress from one to ten, and from there we return to one. (194-95)

54"To the principal notes [of the mode], that is, the final ... " (Babb 71).

55It should be noted that Crocker finds in this passage an application of the principle of homeoteleuton or rime, both final and initial (34).

56Calcidius further identified matter with Duality or Dyad, but he argued that the Dyad was not engendered from the Monad (297ff.).

46 The relation between this passage and Guido's theory is clear. When Guido writes of the fundamental importance and strength of the one principal vox of a mode, he is applying Platonic doctrine to the organization of chant. In a later paragraph he applies the idea to the words of a chant as well, writing, "Item ut in unum terminentur partes et distinctiones neumarum atque verborum" (173~74).S7 Item ut rerum eventus sic cantionis imitetur effectus, ut in tristibus rebus graves sint neumae, in tranquillis iocundae, in prosperis exultantes et reliqua (174).S8 The notion that the voice should be regulated to conform to the meaning of the spoken word is rhetorical in origin. Crocker, in fact, cites Quintilian (15). Guido is applying that idea to the sung word. More important, this is a further binding together of word and melody. Not only must they come to a final unity, word and melody must have the same effect throughout the chant. Et omnia quae diximus, nee nimis raro nee nimis continue facias, sed cum discretione (177).S9 Guido ends his fifteenth

S7Likewise let the parts and phrases of neumes and text come to one together. Musica Enchiriadis gives in Chapter XIX, "Item ut in unum terminentur particulae neumarum atque verborum" (Gerbert 1: 172).

58"Let the effect of the song express what is going on in the text, so that for sad things the neumes are deep, for serene ones they are cheerful, and for auspicious texts exultant, and so forth" (Babb 72). Musica Enchiriadis, Chapter XIX, gives, "Nam affectus rerum, quae canuntur, oportet ut imitetur cantionis affectus, ut in tranquillis rebus tranquillae sint neumae, laetisonae in iucundis, moerentes in tristibus" (Gerbert 1: 172).

59"Do everything that we have said neither too rarely nor too unremittingly, but with taste" (Babb 73).

47 chapter with an omnibus principle: all that he has advocated should be observed not too rarely, not too continuously, but with discretione , a word which carries the sense of observing differences and making distinctions. With this statement he has surely ~aptured the essence of the artistic effort, for particular decisions which cannot be derived from a general maxim are at the basis of every great work of art. It is interesting to note also the relation of the verb discernere to the Platonic order. The numbers which are the principles of things in Plato's cosmos are ratios which are countable and discrete, that is, strictly distinct one from the other. Capitulum XVI De multiplici varietate sonorum et neumarum ( 178- 85) (On the manifold variety of sounds and neumes) Guido turns from his discussion of measurable motion (modulatione ) to a classification of motus vocum. Paucis vocibus ( 17 8). Guido remarks again that all of chant is formed from a few voces bound together by six consonant intervals. He reiterates the analogy with grammar and the binding together of letters into syllables and words. Just as the variety in quantitative verse is studied by grammarians, Guido proposes to investigate ~he ways in which different neumes can be arranged. Again, the underlying Platonic model is evident: the ordering according to numerical principles of a basic material. M otus vocum ( 179). Adopting the style of the grammarians, Guido turns to a highly schematic exposition of the possibilities for melodic motion. His approach is basically combinatorial, with possibilities at each juncture for motion upward (arsis ) or downward

48 (thesis ) by one of the six allowable melodic intervals, or for motion in place (repercussas ). Guido's framework is that of basic material, the seven voces, set iri motion by six forms derived from the underlying harmonic ratios which order music, a perfect exemplum of Platonic cosmology. Specifically, Calcidius describes the basic material of the cosmos as being without form, quality, or motion; motion is created when the intelligible, numerically structured forms are placed in matter (316-324). The concept of motion, which Guido addresses in this and the following chapter, is of fundamental importance in Platonic theory. Motion is a property of the material, changing world, as is time, the material extension of eternity against which motion is measured. Augustine describes in De Musica a linguistic cosmology in which the syllable is a unit of motion and time in a universe of quantitative verse. The· numbers which quantify Augustine's verse are of course the ratios which order Plato's universe and Guido's melodic structures. As will be demonstrated in Chapter 17, Guido's unit of time and motion is the sung syllable. Per oculos (182). To close his discussion of motus vocum Guido gives a diagram or visible representation of possible melodic motion. This is again the idea of making an audible phenomenon literate and available to the eyes.

Capitulum XVII Quod ad cantum redigitur omne quod dicitur (186- 95)

49 (That anything that is spoken can be made into song)60 Argumentum inauditum (186). In an introductory paragraph Guido says that he will present a line of reasoning never before heard through which a causa for all song will become clear. Causa in this context probably means a decision procedure or basis, although in its rhetorical sense it refers simply to subject matter. He moves immediately to the following logical derivation: Perpende igitur quia sicut scribitur omne quod dicitur, Ita ad cantum redigitur omne quod scribitur. Canitur igitur omne quod dicitur. (187) The sense of this chain of implications is the following: All articulate speech is literate. All that is literate can be reduced to song. Conclusion: All articulate speech can be sung. The conclusion of this derivation is a major point for Guido, for the statement that all speech can be sung, in combination with the self­ evident proposition that all sung text can be spoken, establishes a correspondence between cantus and oratio. The frrst line of Guido's derivation has already been established by the grammarians. Priscian, for example, writes: "literata est, quae scribi potest, illiterata, quae scribi non potest. inveniuntur igitur quaedam voces articulatae, quae possunt scribi et intellegi, ut: Arma virumque cano"

60For a different commentary on this chapter the reader is referred to the Smits van Waesberghe article, "Guido of Arezzo and Musical Improvisation." The author describes this section of Micrologus as a set of rules for the neophyte composer.

50 (Grammatici Latini 2: 5).61 Thus, it is the second line of the derivation to which Guido turns his attention. Vocales. Guidds next paragraph, a discussion of vowels, is given in its entirety: Sed in longum nostra regula producatur, ex hisdem litteris quinque tantum vocales sumamus sine quibus nulla alia littera, sed nee syllaba sonare probatur earumque permaxime casus conficitur, quotienscumque suavis concordia in diversis partibus invenitur, sicut persaepe videmus tam consonos et sibimet alterutrum respondentes versus in metris, ut quamdam quasi symphoniam grammaticae admireris. Cui si musica simili responsione iungatur, duplici modulatione dupliciter delecteris. Has itaque quinque vocales sumamus, forsitan cum tantum concordiae tribuunt verbis, non minus concinentiae praestabunt et neumis. ( 187 -88)6 2 All classical grammarians treat vowels and consonants, the components of syllables, separately. The idea that consonants

61Literate [voiced sounds] can be written; illiterate cannot. An example of articulate and literate voiced sounds is given by, "Arma virumque cano."

62"Not to draw out our method to great length, let us take from the letters only the five vowels. Without them, manifestly, no other letter or syllable can sound, and it is for the most part due to them whenever an agreeable blending is found in the different partes. Thus, in verse, we often see such concordant and mutually congruous lines that you wonder, as it were, at a certain harmony of language. And if music be added to this, with a similar interrelationship, you will be doubly charmed by a twofold melody. Let us take then these five vowels. Perhaps, since they bring such euphony to words, they will offer no less harmony to the neumes" (Babb 74).

51 without vowels are mute is found in many writers. Augustine, for example, writes in De Ordine : Progressa deinde ratio animadvertit eosdem oris sonos quibus loqueremur et quos litteris jam signaverat, alios esse qui moderato varie hiatu, quasi enodati ac simplices faucibus sine ulla collisione defluerent, alios diverso pressu oris, tenere tamen aliquem sonum; extremos autem qui nisi adjunctis sibi primis erumpere non valerent. Itaque litteras hoc ordine quo expositae sunt "vocales, semivocales et mutas" nominavit. (140)63 And Priscian, in his economical style, writes, ""Ex his vocales dicuntur, quae per se voces perficiunt vel sine quibus vox literalis proferri non potest, unde et nomen hoc praecipue sibi defendunt; ceterae enim, quae cum his proferuntur, consonantes appelantur" ( Grammatici Latini 2: 9).64 Guido makes the same point, but uses the verb sonare, which in its usual sense means to sound as a noise and in its metaphorical sense to sound as a tone. The word is

63"When reason had gone further, it noticed that of those oral sounds which we used in speaking and which it had already designated by letters, there were some which by a varied modulation of the parted lips flowed clear and pure from the throat without any friction; that others acquired a certain kind of sound from the diversified pressure of the lips; and that there were still other sounds, which could not issue forth unless they were conjoined with these. Accordingly, it denominated the letters in the order of their exposition: vowels, semivowels, and mutes" (Russell 141).

64Those letters without which voiced literate sounds cannot be produced are called vowels. The rest of the letters which are impelled by the vowels are called consonants.

52 carefully chosen to reinforce the correspondence that he is establishing between that which can be written and that which can be sung. He writes also of lines of verse tam consonos and of symphoniam grammaticae and closes the passage with an analogy between the concordia which the vowels bring to words and the concinentia, a singing and sounding together, which the vowels will bring to neumes. Donee unicuique sono sua subscribatur vocalis (188).65 Guido describes a procedure whereby voces of the monochord are each joined to one of the five vowels. The monochord again plays the role of intermediary between inner and outer models; in this case, however, the outer model makes explicit the correspondence between oratio and cantus. He continues with the following passage: "In qua descriptione id modo perpende, quia cum his quinque litteris omnis locutio moveatur, moveri quoque et quinque voces ad se invicem ut diximus, non negetur" (189).66 Guido is describing vowels as the source of motion in speech. The resemblance between this idea and the thoughts expressed by Priscian in the following passage is striking: Multa enim est differentia inter consonantes, ut diximus, et vocales. tantum enim fere interest inter vocales et consonantes, quantum inter animas et corpora. animae enim

65"Let them [the vowels] be placed in succession beneath the letters of the monochord ... " (Babb 75).

66Consider this representation. Since all speech is set in motion by these five letters (i.e. the vowels), it should not be denied that five voces also may be set in motion among one another, as we have said.

53 per se moventur, ut philosophis videtur, et corpora movent, corpora vero nee per se sine anima moveri possunt nee animas movent, sed ab illis moventur. vocales similiter et per se moventur ad perficiendam syllabam et consonantes movent secum, consonantes vero sine vocalibus immobiles sunt. (Grammatici Latini 2: 13)67 This conceptualization of the motive force of vowels is not found in Donatus or Bede and is clearly an ancestor of Guido's idea, making the Priscian treatise a likely source of inspiration. Syllaba (189). Taking a specific phrase, Guido now binds each of its syllables, through its vowel, to an identical vowel on the monochord and thus to a vox. Taking motion from its vowel and tone from its vox, each syllable is now a unit of sung speech. Apta (193). Having expanded his system through the binding of several vowels to each vox, Guido closes with a reference to artistic discretione : Cum itaque suis tantum vocalibus quidam aptam sibi adeo vindicent cantilenam, non est dubium quin fiat aptissiama, si in multis exercitatus de pluribus potiora tantum sibique aptius respondentia eli gas. (193 )6 8

67There is a great difference between consonants and vowels, as much as that between souls and bodies. Souls, for example, produce motion in themselves and in bodies. Bodies can do neither. Vowels, similarly, are self-moving and set in motion syllables and consonants. Consonants, indeed, are motionless without vowels.

68 .. Since certain texts command a suitable vocal setting simply from their own vowels, there is no doubt that the vocal setting will be most suitable if, after practice in many such, you select from the

54 The word apta is carefully chosen, carrying as it does the sense of a binding as well as that of appropriateness or suitability. The idea is that any text has many possible expressions in terms of its syllabic units of motion and tone. This set of possibilities is reduced to those expressions which observe the rules of melodic motion appropriate for cantus. And, finally, from this set the artist exercises discretione in the selection of a binding of littera and vox in which melody and text are jointly appropriate. With this final explication Guido has completed his demonstration of the proposition to which he turned his attention at the beginning of this chapter: All that is literate can be reduced to song. The conclusion follows immediately: All articulate human speech can be sung. The correspondence between oratio and cantus is thus established.

Capitulum XVIII De Diaphonia, id est organi praecepto ( 196-208) (On diaphony, that is, the principles of organum) Capitulum XIX Dictae diaphoniae per exempla probatio (209-27) (Testing this diaphony through examples) Diaphonia vocum disiunctio sonat (196). Guido turns in these two chapters to a discussion of that aspect of chant practice known by the Greek term diaphony or the Latin term organum. Diaphony, he writes, sounds as a disjunction or separateness of voces in the following manner: "Diaphonia vocum disiunction sonat, quam nos numerous possibilities only the more effective and those that fit together better" (Babb 76).

55 organum vocamus, cum disiunctae ab invicem voces et concorditer dissonant et dissonanter concordant" ( 196-97). 69 That is, organum is a sounding of two voces in union or harmony and a sounding of a union or harmony of two voces. Guido's neat syntactical framework refers to the following aspect of the harmonic structure of music. The sounding of two separate voces has an aspect of union and an aspect of disjunction; the former is based on the harmonic ratio of the two voces and the latter on the interval or distance between them. The sounding will be a concord or agreement if it corresponds to one of a specific set of intervals. The exact identity of these intervals will be discussed below following consideration of a Platonic aspect of the unity and duality of sound. As previously mentioned, a tenet of Pythagorean numerology embraced by Plato is that Unity or the Monad is the principle of all numbers. In particular, Duality or the Dyad proceeds from Unity. And, on the other hand, all numbers, in particular the Dyad, flow back or return to Unity. Simply put, every plurality contains an aspect of unity, and every unity is potentially plural. The sounding of two distinct voces provides an elegant exemplum of this doctrine.

69"Diaphony sounds as a separateness of (simultaneous) sounds, which we also call organum, in which notes distinct from each other make dissonance harmoniously and harmonize in their dissonance" (Babb 77). As indicated by Palisca in his introduction to the Babb translation of Micrologus, Guido's statement is related to that of M usica Enchiriadis , "Haec namque est, quam Diaphoniam cantilenam, vel assuete, organum vocamus. Dicta autem Diaphonia, quod non uniformi canore constet, sed concentu concorditer dissono" (54).

56 Durus and mollis. Guido describes a strictly parallel diaphonic procedure in which the organal vox lies at the constant interval of a diatessaron below the principal vox . Then he writes: Cum itaque iam satis vocum patefacta sit 4uplicatio, gravem a canente succentum, more quo nos utimur, explicemus. Superior nempe diaphoniae modus durus est, noster vero mollis, ad quem semitonium et diapente non admittimus, tonum vero et ditonum et semiditonum cum diatessaron recipimus, sed semiditonus in his infimatum, diatessaron vero obtinet principatum. His itaque quattuor concordiis diaphonia cantum subsequitur. (201-2)70 Guido describes the system for strictly parallel organum with the adjective durus ; his own procedure which allows for a variety of intervals is mollis . Principal meanings of these two adjectives are "harsh" and "smooth," respectively, and these are the translations frequently given. Neither is particularly satisfactory, however, since Guido's system gives primary importance to the same interval, the diatessaron, which is fundamental to the parallel system. Guido has used the word mollis previously in Chapter 8 to describe the proper use of b-flat: "b vero rotundum, quod minus est

70"Since the doubling of notes has now been made sufficiently clear, let us explain the low voice added beneath the singer of the original line in the way that we employ. For the above manner of diaphony is hard (durus ) but ours is smooth (mollis ). In it we do not admit the semitone or the diapente, but we do allow the tone, the ditone, the semiditone, and the diatessaron; and of these the semiditone holds the lowest rank and the diatessaron the chief one. With these four concords the diaphony accompanies the chant" (Babb 78).

57 regulare, quod adiunctum vel molle dicunt, cum F habet concordiam" (124). The b-flat is an adjunct to Guido's basic system of notae , required by the fact that the interval from F to b is a tritone. A secondary meaning of mollis is "changeable or flexible," which would give the following translation: "Moreover b-flat, which is less regular and which is called added or changeable, has a concord with F." This translation emphasizes the fact that Guido's scale allows for flexibility or changeability in the matter of b and b-flat, and in that regard is entirely satisfactory. Returning now to Guido's discussion of organum, we note that durus itself has the secondary meaning "inflexible." It now seems extremely likely that Guido is not describing the strictly parallel system as "harsh" but as "inflexible." Analogously, his own system, which allows for a variety of intervals, is "flexible" or "changeable." Occursus (204 ). In writing that both voce must meet at the final of the chant Guido applies to diaphony the principle established in Chapter 15 for monophic cantus. The Platonic framework is evident. As the Dyad returns recurrently and inevitably to the Monad, the two voces return to a unity at the principal of the mode. Diaphoniae praecepta donata sunt, quae si exemplis probes, perfecte cognosces (208).71 As a bridge between his two chapters on organum, Guido writes that the rules of diaphony which he has given will become known by means of their demonstration in

71 "The precepts of diaphony have now been given, and if you test them by the following examples, you will understand them perfectly" (Babb 79).

58 exemplary instances. And, in fact, Chapter XIX is given over entirely to the presentation of patterns and precedents. In rhetoric, probatio, the proof of statements made, follows their presention, and that is the paradigm which Guido follows. The pedagogical procedure of presenting special cases as a means of illustrating a general rule is derived from the dialectic of Same-Other fundamental to Timae us and described previously in this thesis.

Capitulum XX Quomodo musica ex malleorum sonitu sit inventa (228-34) (How music was discovered from the sound of hammers) Musicae artis (227). At the close of Chapter 19 Guido writes that he will now make known to his readers the origin of musicae artis, a term which has not been used by him since the introductory Epistola and Prologus. By returning to it now, Guido creates a sense of unity and allows himself to move smoothly into his concluding chapter in which he makes explicit for the first time in Micrologus the harmonic ratios of the inner model for musicae art is. Malleus. Through the medium of the hammers, Guido explains, God revealed to Pythagoras the science of music. This well known story, which he tells in detail, is the substance of Guido's final chapter, which can be viewed as an homage to Pythagoras and Boethius, who is mentioned briefly. Augustine, in fact, concludes De Ordine with praise of Pythagoras, but in so doing makes the following revealing remark to Alypius, a character in the dialogue: "Quod autem Pythagorae mentionem fecisti, nescio quo illo divino

59 ordine occulto tibi in mentem venisse credo" (170).72 Pythagoras, Augustine believes, is naturally associated in one's mind with the unseen divine order. In Book II of De Doctrina Christina Augustine gives this definition of signum "Signum est enim res, praeter speciem quam ingerit sensibus, aliud aliquid ex se faciens in cogitationem venire" (32).73 These ideas combine to clarify the sense of Guido's final chapter. Malleus is for Guido a signum . First, of course, the written word "malleus " is a sign for the object. But beyond that, the object malleus is a multiple signum according to the Augustinian definition: 1. It is a signum for an event in history, the discovery by Pythagoras of the harmonic ratios which order musical sound. 2. It is a signum for the unseen divine order of the universe, m accord with Augustine's statement to Alypius given above. 3. It is a signum for the moral order of the human soul, which in Christian Platonic doctrine is analogous to the order of the universe. 4. Finally, smce the historical event in which Pythagoras discovered the properties of music was the result of divine revebtion, malleus is a signum for God as the ultimate and only source of wisdom.

72"But that you mentioned Pythagoras--! truly believe it came to your mind through that unseen divine order, whatever it may be" (Russell 171 ).

73"A sign is a thing which causes us to think of something beyond the impression the thing itself makes upon the senses" (Robertson 34).

60 Thus, Guido's decision to close his treatise with a retelling of the story of the hammers is quite significant. He offers an explicit statement of the harmonic inner structure of music and a tribute to Pythagoras in a peroratio based on a signum suggestive not only of the historical event under discussion but also of three separate aspects of the Christian Platonic deity.

Explicit Micrologus, id est brevis sermo in musica (End of Micrologus, that is, the short treatise on music)

61 CHAPTER3 The sequential commentary given in Chapter 2 will serve in the present chapter as the basis for a process of abstraction in which the interplay throughout Micrologus of the inner and outer models for music, as described in Chapter 1, will provide a framework for a discussion of the structure and nature of Guido's brevis sermo in musica . The two analytical models, restated concisely, are the following: Inner Model: 1. The basic material of the universe is ordered by unchanging ratios of numbers. 2. Numbers are the principles of all things; the number one Is the principle of numbers. 3. The harmonic structure of music is given by the same ratios which order the universe. 4. The senses can act to stimulate the soul to perform its function of theoretical reasoning. 5. Only that which is ordered and unchanging can be known. 6. Music has a special role in that it is both constant and changing, therefore, knowable and unknowable. Outer Model: 1. Human sounds which are articulate and literate are the basis of rational discourse. 2. Letters are the basic elements of grammatical analysis. 3. Visible signs of letters are needed because of the ephemeral nature of physical sound.

62 1

4. All grammatical entities are constructed according to rules and all have distinct natures. 5. Rhetorical analysis is concerned with the effectiveness and appropriateness of speech. 6. The laws of grammar and rhetoric are made by man and are therefore changeable and unknowable. A summary of the presence of these two models, frequently in an interactive state, in Micrologus will serve as a basis for a final examination of the nature and structure of Guido's treatise. In Chapters 1 through 4 Guido identifies the basic elements of the art of music, the voces . He describes the written signs for the voces , locates them in musical space, and defines the intervals by which they may be melodically connected. The order of presentation or dispositio is that of a Latin grammar text, which proceeds from the basic component of human speech, the vox , to letters to the joining of letters in syllables. The location of the musical voces is accomplished through the medium of the monochord, which provides an audible representation of inner harmonic structure and allows the projection of the fundamental ratios onto an interval scale. Chapters 5 through 14 contain Guido's discussion of the modes, and, in the main, he uses arguments derived from the inner model. The three fundamental symphonies (diapason, diapente and diatessaron) are those which have the simplest harmonic ratios (2: 1, 3:2 and 4:3, respectively) and which exhibit the property of closure. That is, joining of a diatessaron and a diapente through a common endpoint produces a diapason. The modes are described in terms of dispositions of tones and semitones which are in turn determined by

63 inner structure. Methods of modal identification rely on Platonic dialectic and the argument given for the primary importance of the modal final is based on Platonic numerology. Chapter 13, however, includes an analogy between the eight modes and the eight parts of speech. The basis of the analogy is that in each case the eight classifications are disjunct and complete and that each is distinct in character and function. Chapter 14 continues the discussion of the distinct properties of the modes with arguments taken from Platonic theory. Chapter 15 opens with an explicit statement of the analogy between chant and speech, but now Guido is speaking specifically of measured speech, metrum. This allows him to use principles of analysis taken from rhetoric, rhythmics and metrics to discuss the construction of melodic lines. Since the rational and interval structure underlying these last two disciplines is in great part the same as that which underlies music, the interaction between inner and outer models is evident. Guido is analyzing chant as measured speech. He makes a reference in Chapter 16 to the study by grammarians of variety in quantitative verse, but develops his discussion of motus vocum along Platonic lines. Thus, the melodic lines are given structure and set in motion by forms which are derived from the inner model. Guido binds inner and outer models together in Chapter 17 by establishing a correspondence between spoken syllables and voces located on the monochord. The discussion of diaphony given by Guido in Chapters 18 and 19 can be viewed as an extention of Chapter 4, since the allowable organa! intervals form a subset of the melodic consonances presented

64 previously. The interplay of outer and inner models in these chapters is through the analogy of the joining of voces to form consonant intervals, determined by harmonic structure, to the joining of letters to form syllables. Guido's final chapter, centered on the story of the Pythagorean hammers, is based entirely on the inner model. At a higher level of abstraction Micrologus is seen to have the following framework: Section I. Chapters 1-14. Analysis of the musical structure of chant using Greek harmonic theory and the language and principles of grammar and rhetoric. Section II. Chapters 15-17. Analysis of chant as sung speech and establishment of the sung syllable as the basis of the correspondence between cantus and oratio . Section III. Chapters 18-19. Extension of the arguments of Section I to diaphony. Section IV. Chapter 20. Peroration based on the story of the Pythagorean hammers. In order now to assess the nature and importance of Micrologus some mention of prior treatises related directly or indirectly to Guido's work will prove useful, although an extensive examination along these lines is not intended. In the introduction to his study of Guido's Chapter 15 Crocker describes the task of the medieval theorist, who had inherited Greek music theory without exemplary music and sacred chant without a specific theory. He concludes his remarks as follows:

65 The history of early medieval theory may be seen as the working-out of a relationship between these two elements, a rationalization of the sounding art work -- the sacred chant -­ according to the intellectual methods of Greek theory. For the medieval theorist is immediately concerned with the art-work, which he must sing and teach others to sing from day to day throughout the cycle of the liturgical year. (2) That the writers of early medieval musical treatises felt the need to provide the sort of rationalization that Crocker mentions is one aspect of their common intellectual heritage, specifically, the Platonic tradition. Klibansky, for example, writes: Of great import for the history of thought m general, however, was the fact that in the Latin Timaeus the scholar of the early Middle Ages became acquainted with the classical formulation of the principle of causality, and through the commentaries on the dialogue became aware of its importance. (74-75) Without doubt Guido typifes the early medieval theorist described by Crocker. Micrologus shows the strong influence on Guido of Greek rationalism, a paradigm for which is the inner model. And the need to ask questions and seek causes, described by Klibansky, was certainly a motivating factor for Guido. It was his need to explain and codify chant practice that led him to adapt the tools of grammatical-rhetorical analysis summarized in our outer model to the musical structure given by the inner model. It 1s in the establishment of a correspondence based on the sung syllable between the spoken word and the sung word that the real originality of Guido's brevis sermo in musica lies.

66 Micrologus is not by any means the first medieval treatise to contain the language and methods of the trivium. Gushee, in the introduction to his edition of Musica Disciplina, cites Aurelian's use of a grammatical approach to the analysis of chant (13). This treatise from the middle of the ninth century was not, as far as is known, widely disseminated; thus it may not have been familiar to Guido. At any rate, Aurelian's use of this approach is quite limited. The grammatical analogy with which Guido opens his Chapter 15 had been used by the theorist of Musica Enchiriadis (ca. 900), although the two presentations differ (Gerbert 1, 152). Guido was undoubtedly familiar with this extensively copied treatise; two examples of text borrowing by Guido from Musica Enchiriadis have been cited previously. And Huglo argues that Guido refers to it explicitly in Epistola de ignoto cantu ("L'auteur du Dialogue 119-71 ). The use, however, of grammatical models in Musica Enchiriadis is largely schematic. The second paragraph of Guido's Chapter 15 (163-165) contains language which is related to that of the numerose canere section of Scolica Enchiriadis (Gerbert 1: 182-184). Phillips cites Augustine's De Musica as the Scolica theorist's source, making the point that Augustine describes metrical and proportional rhythm in relation only to words, while in Scolica the application is made to "vocal, sounding music" (338). Guido's application is also to vocal, sounding music, but it is difficult to say whether he was inspired indirectly by Augustine, or directly by the Scolica theorist. A treatise that is mentioned by many authors in connection with Micrologus is Dialogus de Musica from around 1000 A.D.

67 (Gerbert 1: 252-64).74 Indeed, much of the material included in Guido's first thirteen chapters shows a strong relation to that of the earlier treatise. Huglo has shown that Dialogus was written in Arezzo, so it is quite likely that Guido had access to it ("L'auteur du Dialogue, 119-71 ). However, this intersection of ideas does not include any of the material found in Chapters 15 through 17 of Micrologus. Four important medieval treatises prior in time to Micrologus have been mentioned. A complete comparison of these and other early treatises with Guido's work is beyond the scope of this study. But this cursory examination supports the contention that Guido, in his particular adaptation of grammatical-rhetorical principles to Greek harmonic theory, made an original contribution to medieval mus1c theory. An overview of that adaptation abstracted from the first seventeen chapters of Micrologus will serve as a conclusion to this study. In Chapters 1 through 14 of Guido deals with the musical sound of chant; text is not mentioned. His precepts are those of Greek theory as modified by chant practice. An implicit analogy is established between the elements of the structure of musical sound and those of grammatical structure. Since the structure of musical sound is itself an exemplum of the Platonic structure of the cosmos, the outer and inner models are developed in parallel throughout the first section of Guido's treatise.

74See for example Smits van Waesberghe, De Musico-Paedagogico, and Oesch.

68 Chapter 15 opens with an explicit statement of the analogy between the elements of musical sound and those of grammar. Guido then proceeds to apply the methodology of quantitative verse to the construction of neumes, which are in tum constructs based on the inner model. Text, mentioned in two paragraphs only, is not yet an important consideration.75 Chapter 16, which begins with a comparison between the potential variety in the structure of quantative verse and that of melodic lines, is a continuation of Chapter 15 with the additional consideration of musical contour. This is not a factor, of course, in spoken quantitative verse, so Guido has had to extend that methodology with his combinatorial approach to arsis and thesis. Finally, Guido turns in Chapter 17 to the consideration of chant text, proposing to demonstrate that anything which is spoken can be sung. From the voces of grammar he selects the five vowels, the source of the motion of sound in the spoken syllable, and binds them to the voces of chant. Located on the monochord, the composite unit has pitch, that is, musically organized sound, and potential motion. Since any Latin word can be broken into syllables and any syllable can be identified with its vowel, Guido's demonstration is complete. He has shown that any Latin text has a musical expression. In fact, since the binding of vowels to voces is a one-many relation, many possible expressions exist for any specific text. The most appropriate

75Jt is interesting to note that the two paragraphs in Guido's Chapter 15 which mention text are those which Guido has borrowed from M usica Enchiriadis .

69 one must be chosen according to the limits prescribed by chant practice and by taste. With the argument just gtven, Guido has established the sung syllable as the basis of the correspondence between cantus and oratio . Since the sung syllable is the union of a component of speech, the syllable, and a component of musical sound, the vox, he has found a structural unit which is common to both the Platonic inner model and the grammatical outer model. Guido has rationalized the sounding art work in an extremely original and inventive way.

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