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MUSIC T H E O R Y T R A N S L A T I O N SERIES CLAUDE V . PALISCA, EDITOR

Other published volumes in the Music Theory Translation series: The Practical Harmonist at the Harpsichord, I 708, by Francesco Gasparini, translated by Frank S. Stillings, edited by David L. Burrows. The Art of Counterpoint, Part Three of Le Istitutioni harmoniche, I 558, by Gioseffo Zarlino, translated by Guy A. Marco and Claude V. Palisca. Hucbald, Guido, and John On Music, Three Medieval Treatises, translated by Warren Babb, edited with Introductions by Claude V. Palisca. The Art of Strict Musical Composition, 177 1-1779, by Johann Philipp Kirnberger, translated by David Beach and Jurgen Thyrn. Introductory Essay on Composition, I 782- I 793, by Heinrich Christoph Koch, translated by Nancy Kovaleff Baker. Quintilianus On Music, in Three Books, translated, with Introduction, Cornmentary, and Annotations, by Thomas J. Mathiesen.

ON THE MODESPart Four of Le Istitutioni Harmoniche, 1 5 5 8

GIOSEFFO ZARLINO

TRANSLATED B Y

VERED COHENEDITED WITH AN INTRODUCTION BY

CLAUDE V . PALISCA

YALE UNIVERSITY PRESS, NEW HAVEN A N D LONDON

The preparation of this volume was made possible by a grant from the Translations Program of the National Endowment for the Humanities, an independent federal agency Copyright 6 1983 by Yak University. 3 All rights reserved. This book may not be reproduced, in whole or in part, in any form (beyond that copying permitted by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press), without written permission from the publishers. Designed by James J . Johnson and set in Garamond Roman by The Composing Room of Michigan, Inc. Printed in the United States of America by Murray Printing Company, Westford, Massachusetts.

Library o Congress Cataloging in Publication Data f Zarlino, Gioseffo, I 5 17- I 590. [Istitutioni harmoniche. 4a pt, English] On the modes. (Music theory translation series) Bibliography: p. Includes index.I.

Music-Theory-16th

century.111. Title.

2.

Musical intervals

and scales-Early

works to I 800.

I. Cohen, Vered.IV. Title: 83-2477

11. Palisca, Claude V. Institution! harmoniche. MT5.5.23813 1983 ISBN 0-300-02937-3

V. Series. 781'.221

ContentsIntroduction List of abbreviationsI.2.

vii xxiii

What is a mode The different terms that have been used for modes and the reasons for them The inventors of the modes

3. The name and number of the modes4.

5 . The nature or properties of the modes

6. The order of the modes7. The Hypermixolydian of Ptolemy is not that which we call the eighth mode

8. The manner in which the ancients indicated the notes of their modes9. The manner in which the diapason should be harmonically or arithmetically divided10.

There are necessarily twelve modern modes; and how it may be proved Another way of demonstrating that the number of the modes is twelve The division of the modes into authentic and plagal

II.

I 2.

13. The final note of each mode; and how far it is permissible to ascend or descend above and below it

14. Common modes and mixed modesI5.

Another way of classifying the modes; and what should be observed in each mode in composing vocal music Whether by removing the tetrachord Diezeugmenon from any composition and

I 6.

CONTENTS

putting in its place the Synemmenon while the other tetrachords remain immovable, one mode can be changed into another

17. Transposition of modes 18. A discussion of the first mode in particular:its nature, its initial notes, and its cadencesI 9. Second20.2 I.

mode

Third mode Fourth mode Fifth mode Sixth mode Seventh mode Eighth mode

22. 23. 24. 25.

26. Ninth mode27. Tenth mode 28. Eleventh mode29.

Twelfth mode when composing, and how the modes should be judged

30. What the composer should observe

31. The parts of a vocal composition:how they should be arranged, their range, and how far the highest note of the composition may be from the lowest note

32. How harmonies are accommodated togiven words 33. How to assign note values to the words 34. Ligatures 35. What anyone must know who desires to arrive at some perfection in music 36. The senses are fallible, and judgments should not be made solely by their means, but should be accompanied by reason Bibliography Index of classical passages cited General index

Introduction

Of the four books of Gioseffo Zarlino's Le Istitutioni barmontche, Part 111, on counterpoint, and Part IV, on the modes, are oriented toward the practicing composer and musician, while Parts I and I1 establish the theoretical foundation on which the later books are built. Part 111 was published in translation in this series in 1968. We are now able to complete Zarlino's Practica with this translation of Part IV, which in the original lacks a title and we are calling simply On The Modes. We aim with this translation, as with Part 111, The Art of Counterpoint, to enrich the resources both of the historian of theory and of the musical analyst who seeks to apply contemporary criteria to the music of the mid-sixteenth century. The book on the modes marks a new stage in Zarlino's thought. Whereas the book on counterpoint was wholly rooted in the practice taught by Adrian W i l l a e ~ the chapters on the modes emerge largely from Zarlino's own researches into sources often external and somewhat alien to the rest of the Istitutioni. Willaert's works remain the most quoted examples for modal practicethirty-two citations in these chapters-but the most important source is a theoretical work that Zarlino never acknow1edges:Heinrich Glarean's Dodekacbordon (Basle, I 547). Glarean, long dissat-..---- -----isfied with the received doctrine on the eight modes of plainchant as a tonal system for polyphony, completed in 1539 his exposition of the system of twelve modes.1 Adding to the modes of plainchant that had been recognized as early as the ninth century-the eight on the finals D, E, F, and &he canonized four more that in practice had existed in the guise of modes with cofinals or irregular finals. These four are the authentic and plagal modes whose finals are A an& C . Several concepts derived from the classical music theory transmitted by Boethius and Gaffurio helped Glarean to legitimize these four modes. One concept was the species of consonance, which takes into account the arrangement of tones and semitones within the span of a consonance. For example, the consonant interval ofI. For a history of Glarean's work, see Clement A. Miller, "The Dodecachordon: Its Origins and Influence on Renaissance Musical Thought," M d c a Dzsciplina 15 (196 I): I 5 5-66. See also Miller's translation of Glareanus: Dodecachodon, translated, transcribed and edited by Clement A. Miller, Musical Studies and Documents 6 (American Institute of Musicology, 1965), p. 9. 2. Boethius, De institutions musica, ed. Gottfried Friedlein (Leipzig, 1867), 4. 14, p. 337. Boethius figured the species descending, i.e., fourths, a-e, g-d, f-c; and fifths: b-e, a-d, g-C, f-B; the octaves: a'-a, gt-g, etc., to b-B.

vlll

*.

.

INTRODUCTION

the fourth is a compound of two tones and a semitone, which may be arranged ascending in three ways: tone-semitone-tone, semitone-tone-tone, and tone-tonesemitone. Consequently the fourth is said to have three species. Similarly the fifth has four species, and the octave, seven species. Glarean followed Gaffurio in numbering the octave species from A, the species of fifth from D, and the species of fourth from A.3 Thus Glarean built each authentic modal octave on its final with a fifth as the base and a fourth above it. Since there are four species of fifth and three of the fourth, twelve combinations are possible, but only six are diatonic, those in which semitones are separated by at least two but not more than three whole tones. The potential combinations are shown in Table I . The plagal modes were conceived as joining at the final a fourth below and a fifth above. Again out of twelve such combinations, only six are usable. Thus twelve modes are possible, six authentic, and six la gal.^ Another concept that Glarean derived from classical theory is the division of the octave by arithmetic and harmonic means.5 If the octave is expressed as the ratio between two string lengths, as 1 2 (for the lower note) and 6 (for the higher), then the arithmetic mean is 9 and the harmonic mean, 8.6 Measured up from the lower limit3. Franchino Gaffurio, De burmonia musicorurn instrumentorum opus (Milan, 15 18), Book I, chaps. See the translation by Clement Miller in Musicological Studies and Documents 33 (1g77), pp. 58-60. The tradition of numbering the fourths from A, fifths and octaves from D stems from Hermannus Contractus, Musica, ed. Leonard Ellinwood (Rochester, 1g52), pp. 26-31. It persists in music theory through the middle ages and Renaissance, including Marchettus of Padua, Lucidarturn, and Aron, Trattuto delta nutura et cognitione di tutti gli tuuni di canto figurato (Venice, 15251, chap. I . Glarean, evidently, did not know their work. Cf. Dodekacbordon, Book I, chap. 8; 11, 3. 4. Glarean, Dodekacbordon, Book 11, chaps. 3, 7. 5. Boethius, De inst. m .2 . 12-17. s 6. Zarlino describes the method for finding the harmonic mean between two terms of a ratio in Part I, chap. 39. First find the arithmetic mean, which is half the sum of the two terms. Then multiply both terms by the arithmetic mean to get the ratio in larger whole numbers. Finally multiply the two original terms to get the harmonic mean between the larger numbers. Thus, if the interval is a fifth in the ratio 6 4 , then the arithmetic mean is 5; the convened l