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TUNING AND TEMPERAMENT IN SOUTHERN GERMANY TO THE END OF THE SEVENTEENTH CENTURY. VOLTM I JOSEPH VICTOR POLLARD Submitted in accordance with the requirements for the degree of Doctor of Philosophy. University of Leeds, Department of Music. April, 1985. i ABSTRACT. In an age when consistency between the macro and the micro were believed to indicate sure signs of God1s eternal truth, the anomalies which crop up as soon as a comprehensivet interdependent theory of consonance and harmony is attempted must have been a source of bewilderment and embarr-assment,to Renaissance and Baroque theorists and musicians. Composite instruments such as human voices in concert have no difficulty in making pitch adjustments necessary to achieve consonance, but the keyboard with its twelve pre-set notes is inhibited. The history of temperament is an account of the struggle to endow the keyboard with something approaching the versatility of the human voice. German theorists and musicians were leaders in the recognition of the need to compromise between purity of interval and harmonic freedom. Part 1 of the dissertation traces the development of temperament from Schlick to Werckmeister, but concentrates on the seventeenth century. It attempts to show how temperaments became obsolete as musical vocabulary widened, and how, at least in Werckmeister's casey temperaments were assessed not only for their faithfulness to the accepted standards of consonancet but for their ability to give to certain keys certain affective characteristics. The music of several southern and central German composers is considered in varying degrees of detail. The most detailed study is of the music of Froberger, an important predecessor of, and influence upon, J. S. Bach. Almost exclusivelyt Froberger was a composer of keyboard music, and a musician most probably familiar with temperaments used in other musical centres of Europet because he travelled widely as a celebrated keyboard artist. As the research progressed, a need to assess in objective terms the qualities of different temperaments when applied to the keyboard music of the time became increasingly insistent. Part 2 of the dissertation shows a method of solving this problem. The psychological effects of musical sound received by the human ear are considered. By dissecting a piece of music into its smallest interacting partst i. e. its intervals and their duration, objective comparison can be made between the in temperament piece played one and played in another or other temperaments. The complete process is laborious, but is greatly alleviated by transferring data to a suitably programmed computer, which can then process the data in relation to any ii temperament applied. Some of the music of Froberger has been examined in this way and conclusions drawn. The final chapter looks back over the ground covered, outlines some issues which still require investigationt and makes suggestions for further research., using the information, arguments and techniques to be found in this dissertation. iii CONTE24TS VOLME ONE Preface xi Introduction xiii PART I ChaDter 1 Concepts of Consonance, Ancient and Modern. 1 The Pythagorean concept of consonance Post-Pythagorean developments 3 Modern concepts of consonance 5 Purity of interval 9 ChaDter 2 Consonance, a Dilemma of the Renaissance. 11 Pythagorean principles applied 12 The encroachment of pure thirds 16 Just-intonation 20 The rise of the triad 23 The pure scale 25 The Pythagorean systems extended 27 Just-intonation extended 29 Keyboard deficiencies 30 Chapter 2 The Semantics of Temoerament. 32 Tuning and temperament - monochord - tuning note 32 Laying the bearings - checks - the tuning pipe 34 Categories of temperament the wolf - subsemitonal intervals 37 Chai3ter 4 Tunings and Temi)eraments. 42 Early Pythagorean tunings: Gf - Eýj transpositions, Ramos, Agricola: Erlangen., Grammateus 42 Pure intervals abandoned 50 Schlick's tuning instructions 53 Meantone temperaments 55 Praetoriusts tuning instructions 59 The meantone variants: regular variantsp Schneegass 64 Just-intonation monochords. Kepler, Reinhard 68 Tuning schemes reconstructed. Ammerbachy Keller 71 iv Chapter 4 (continued) Multiple division of the octave 76 The well-tempered concept; Bendeler, Werckmeister 78 A Werckmeister tuning scheme 85 Equal temperament 88 Chapter 5 Temperamental Expedients applied to the Instruments, of the Period. 91 Keyboard inadequacy 91 Schlick's evidence 92 Praetorius's evidence 94 Kircherts evidence 96 Other German evidence 98 Werckmeisterts evidence 99 Super-duodecuple keyboards elsewhere in Europe 100 Chapter 6 The Suitability of the Temperaments for the Music of the Earlier Part of the Period- 105 Renaissance composers 105 Arnolt Schlick 114 Elias Ammerbach 117 Chapter 7 Meantone Temperament, and its Suitabilitv for Froberger's Music. 120 Froberger's background and personality 121 Sideways shift 124 Frobergerts note vocabulary 126 Froberger's exposure to Italian and French influence 141 Mersenne's temperaments for Froberger's music? 143 Chapter 8 Temperament and Note Vocabulary towards the end of the Seventeenth Century. 146 Alessandro Poglietti 146 Nicholas Adam Strunck 150 Kerllq Techelmannt Richter 152 Georg Muffat 154 Johann Pachelbel 155 V PART II ChaDter 1ý An Objective Method of Temperament Assessment. 163 Psychological considerations 165 The intervhls of just-intonation defined 173 The idea of a templet 175 The construction of a templet 176 The application of a templet 181 Expedient templet-changes, 187 Working definitions 190 Chai)ter 10 An Analysis of the Computer Calculations. 192 Froberger's music under scrutiny 194 The arrangement of a printout of results 195 Absonances and absonance levels 199 Arpage: absonance and duration correlated 203 Arpages of regular meantone temperaments 206 - Meantone arpages of organ works 209 Maverick organ works 211 Meantone arpages of the harpsichord works 213 Arpage results of other historical temperaments 216 Conclusions 217 Chapter 11 Temperament in PersDective. 231 Temperament in historical perspective 231 Temperament in psychological perspective 232 Temperament: the prospects 234 Bibliography 236 Appendices Volume 2 vi CONTENTS VOLUMETWO APPENDICES Ap-oendix 1 Transjýjtions 245 Extracts from: Agricolag Martin. Musica Instrumentalis Deutsch. 246 Schlick, Arnolt. Spiegel der Orgelmakher und Organisten. 248 Praetorius2 Michael. Syntagma Musicume 254 Werckmeister2 Andreas* Erweiterte und verbesserte Orgelprobe. 270 Printz, Wolfgang Caspar. Sing= und Kling=kunst. 274 Appendix Temaets of Froberaerts Music 278 Canzona,6 280 Capriccio 15 290 Fantasia 1 298 Fantasia 8 318 Lamentation for Ferdinand 111 324 Ricercar 1 330 Ricercar 2 340 Ricercar 3 348 Ricercar 4 360 Ricercar 5 368 Ricercar 6 378 Ricercar 9 384 Ricercar 12 398 Suite 1 in A minor 404 Suite 4 in F major 410 Suite 6 in G major (cromatica) 416 Suite 8 in A major 418 Suite 12 in G major 426 Suite 19 in C minor 436 Suite 26 in B minor 446 Toccata 5 452 Toccata 6 460 Alo-pendix 3 A User-Manual for Temperament Assessment Programs-468 Program: HTEMPLET511 487 Program: "IMPURITY" 492 Program: "ABSONANCE" 495 Program: 11MEANTONES11 500 vii LIST OF DIAGRAMS, ETC. Figure Page Number Number 1 Consonant and Dissonant Intervals 5 2 Helmholtz's Hierarchy of Consonances 6 3 The Overtones of three Consonances 7 4 Combination Tones of Helmholtz's Consonances 8 5 Basic Pytha-Orean Intervals 13 6 The Monochord of Ornithoparchus 15 7 Hugo von Reutlingen's Monochord 16 8 Pythagorean and Just-Intonation Proportions compared 21 9 Ptolemaic Proportions as drawn by Zarlino 22 10 The Pure Major Scale 25 11 The Pythagorean Spiral 27 12 Werckmeister's Chain of Thirds 28 13 Some Just-Intonation cent values for G major 29 14 The Divisions of a Tone, according to Kircher 39 15 Pythagorean Monochord, G4, - Eý 43 16 Pythagorean Tuning transposed to B- Gý 44 17 RamosIs Just-Pythagorean Temperament 45 IS Agricolats Just-Pythagorean Temperament 46 19 Erlangen Just-Pythagorean Monochord 47 20 Grammateusts Temperament 48 21 Grammateusts Chromatic Pipe Length 49 22 Agricola's Pythagorean Temperament 50 23 Schlick's Temperament 54 24 Quarter comma Meantone Temperament 58 25 Meantone with two wide fifths 62 26 Quarter comma Meantone Temperament, 1ý -G 64 27 Regular Meantone Temperaments before 1700 65 28 Schneegass's Monochord 67 29 Schneegass (theoretical) 67 30 Two ninths Meantone Temperament 68 31 Keplerts No. 1 Monochord 69 32 Keplerls No. 2 Monochord 69 33 Reinhard's Monochord 70 34 Ammerbach: conjecture No. 1 73 35 Ammerbach: conjecture No. '2 73 viii Figure LQRe Number Number 36 Keller's Temperament 76 37 Well-Tempered Distribution of Thirds 80 38 Bendeler's No. 3 Temperament 82 39 Werckmeisterts Correct No. 1 Temperament 82 40 Werckmeister's Correct No. 3 Temperament 82 41 Bendeler's No. 1 Temperament 83 42 Bendeler's No. 2 Temperament 83 43 Werckmeister's Correct No. 2 Temperament 83 44 The Identification of Werckmeister's Temperaments 84 45 Werckmeister's Irregular one seventh Ditonic comma Temperament 85 46 Werckmeister's 'Continuo Temperamentt 88 47 Equal Temperament 90 48 A Broken Octave 93 49 Kircher's Eighteen-note Keyboard 97 50 Praeambulum super G (Buxheim organ book) 107 51 Praeambulum in mi (Tablature of Kleber) 107 52 Praeambulum in re (Tablature of Kleber) 108 53 Meffen's Calculations of comma Mistunings 110 54 Paumann:, Mit ganezeraWillen ill 55 Kotter: Praeambulum in fa 113 56 Ein fro"hlich Wesen 113 57 Schlick's Harmonic Vocabulary 114 58 Schlick: Da Pacem 11 116 59 Schlick: Maria zart 117 60
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