Keresés

18. Ératoclès s'est bien efforcé d'énumérer ces divers points, mais sans donner de démonstration et seulement en partie; il n'a rien dit [de vrai].: toutes ses opinions sont erronées. Il s'est complètement trompé même à l'égard des faits qui se manifestent aux sens. Nous nous sommes expliqué là-dessus précédemment lorsque nous avons examiné cette question en elle-même. Quant aux autres questions, en général, comme nous l'avons dit précédemment, nul ne s'en est occupé. Dans un seul genre, Eratoclès voulut énumérer les diverses formes d'un seul système, à savoir l'octave, qu'il produisait démonstrativement par la circulation des intervalles (18) ; il ne remarquait point que si l'on n'expose pas auparavant les diverses formes de la quarte et de la quinte, et ensuite la nature de la composition suivant laquelle (19) ces [intervalles] se combinent mélodiquement, il est évident que l'on aura [exclusivement] des [intervalles] multiples de sept (20); or nous avions établi qu'il en était ainsi; en conséquence qu'on laisse de côté cette question et qu'on aborde les autres. Après avoir énuméré les systèmes, suivant chacun des genres et suivant toutes ces variétés dont nous avons parlé, il deviendra nécessaire de traiter de nouveau des genres mélangés entre eux, car on n'a pas même étudié la nature de ce mélange.

(18) Περιφορᾷ. Ce mot nous rappelle assez naturellement la marche ou conduite circulaire, ἀγωγὴ, περιφερής, laquelle procède, on le sait, par séries de sons alternativement montantes et descendantes.
(19) On verra au troisième livre que l'auteur indique deux sortes de composition des systèmes tétracordes, deux modes, τρόποι, modi, qu'il est arrivé à quelques modernes de confondre avec les modes ou tropes résultant du choix de la première corde d'une échelle mélodique.
(20) Il est évident que, autant il y a de genres et de diversités ou variétés de genre, autant il y aura de fois sept intervalles, si l'on ne considère que la formation de l'octave.

17. Après avoir montré, au sujet des intervalles incomposés, comment ils se combinent entre eux, il faudra parler des systèmes qui s'en forment, du système parfait (17) et des autres, de manière à montrer quel nombre et quelle sorte [de systèmes] en résultent, et à faire connaître leurs différences en grandeurs, leurs diverses grandeurs à chacun, leurs différences de composition et leurs différences de forme, de manière à ce que nulle question relative au chant: grandeur, forme, composition, position, ne soit [laissée] sans démonstration ; or c'est là tout un côté de la doctrine (musicale) dont presque personne ne s'est occupé.

(17) II y a le grand système parfait et le petit système parfait; l’un correspond à l'échelle naturelle des sons de notre voix, l'autre se compose seulement des trois tétracordes conjoints; le premier comprend deux octaves, l'autre une quarte redoublée. Noir la planche I.

14. Personne n'eut jamais la moindre idée de toutes ces questions; et il nous a fallu les traiter nous-même toutes pour la première fois, car nous n'avions rien trouvé à leur sujet qui fût digne d'être pris en considération.
15. Il faudra aussi s'occuper des intervalles incomposés, puis des intervalles composés.
Il sera nécessaire, lorsque nous étudierons les intervalles composés, auxquels il arrive en quelque sorte d'être des systèmes en même temps que des intervalles, de dire quelque chose sur la combinaison des intervalles incomposés, question dont la plupart des harmoniciens ne se sont pas même aperçus qu'il fallait parler, comme nous eu avons acquis précédemment la conviction.
16. Les disciples d'Ératoclès ont seulement dit à ce sujet que le diatessaron (la quarte), dans l'un et l'autre sens (aigu et grave), partage en deux le chant (16), et cela sans déterminer si ce partage a lieu à partir d'un intervalle quelconque; [sans examiner], à l'égard des intervalles autres que la quarte, comment ils se combinent entre eux ; sans observer s'il y a une relation déterminée dans la composition d'un intervalle quelconque avec un autre intervalle quelconque ; [sans dire] de quelle manière les systèmes peuvent ou ne peuvent pas résulter des intervalles; ou bien [s'ils en parlent] rien n'est précisé. Car personne n'a jamais donné à ce sujet aucune explication soit avec, soit sans démonstration. Malgré l'ordre admirable qui règne dans la constitution du chant, on lui reproche quelquefois d'être tout à fait désordonnée. C'est la faute de ceux qui ont travaillé cette matière, car aucune des autres études expérimentales ne possède un ordre aussi parfait, aussi compliqué. Ce fait deviendra évident pour nous lorsque nous serons engagé dans l'examen même du sujet. Pour le moment il faut parler des autres parties.

(16) Meybaum explique très ingénieusement celte phrase qui, suivant son expression, l'a torturé longtemps (page 81). Mais nous croyons remplacer avec avantage son interprétation par une conjecture qui a reçu l'adhésion de M. Vincent. Peut-être s'agit-il ici d'un système heptacorde composé de deux tétracordes conjoints et dont le chant se trouve partagé en deux par chacun des tétracordes, c'est-à-dire deux tétracordes conjoints dont les différentes grandeurs partielles se trouvent chantés musicalement ou si l'on veut harmonieusement avec un repos observé à la moitié de cette sorte de gamme, qui est la mèse.

7. Ces déterminations une fois bien précisées, il sera convenable de parler sommairement de l'intervalle; puis il faudra le diviser en autant d'espèces qu'il y a moyen de le faire.
8. En ce qui touche le système, après en avoir donné une explication sommaire, il faudra montrer en combien d'espèces il est naturel de le partager.
9. Ensuite, à l'égard du chant, il faudra faire voir assez rapidement et esquisser la propriété du chant musical; car il y a plusieurs espèces de chant; l'une d'elles consiste dans l'accord de l'échelle musicale, et la mélodie. Mais pour être amené à cette espèce de chant, et pour la distinguer d'avec les autres, il sera nécessaire de dire aussi quelque chose des autres espèces de chant.
10. Après avoir déterminé le chant musical (ou accordé) comme il est admissible de le faire, sans rien examiner particulièrement, mais plus tôt en procédant par aperçus et par généralités, il faudra le diviser sommairement en autant de parties qu'on le jugera nécessaire.
11. Après cela il faudra parler de la continuité et de la succession, et dire quelle en est la nature et comment elles fonctionnent dans les systèmes.
12. II faudra montrer quelles sont les variétés de genres, lesquelles résultent [du déplacement] des sons mobiles.
13. II faudra montrer aussi les lieux dans les limites desquels s'effectue ce déplacement des sons mobiles (15).

(15) Sur la mobilité de certains sons, voyez notre Étude sur Aristoxène et son école, note 39. dans la Revue archéologique, année 1857.

5. Il sera nécessaire en outre, pour l'intelligence de ces questions, de dire en quoi diffèrent le relâchement, la surtension, la gravité, l'acuité et la tension. Car personne n'a rien dit [de bon] sur ces questions. Tantôt elles étaient tout à fait Ignorées, tantôt elles ont donné lieu à des confusions.
6. Après cela il faudra parler de la distension (14) dans le sens du grave et de l'aigu, dire si elle s'accroit ou se réduit à l'infini, et sous quel rapport elle est ou n'est pas possible.

(14) 'Ἄνεσις signifie le relâchement des cordes ou le décroissement de leur tension, ἐπίστασις, la surtension, c'est-à-dire l'accroissement de la tension des cordes (on nous passera les néologismes surtension et surtendre, qui ont leurs analogues, et que l'un ne pourrait remplacer que par une périphrase). La tension, τάσις, ce sera l'état d'une corde qui est tendue et dont la tension ne reçoit ni accroissement ni décroissement. Ce mot désigne par suite le degré d'intonation ou la valeur d'un son : ainsi tomber ou venir dans la même tension se dira de deux notes musicales chantées à l'unisson. Par exemple la paranète des conjointes chromatique toniés et la paramèse « tombent dans la même tension » ; de même en musique moderne, sur un instrument tempéré, le la # et le si b, etc. - La distension, διάτασις, est la distance sonore ou si l’on veut l'écart qui se produit ou peut se produire entre deux sons dont la tension est différente. (Quelques manuscrits donnent διάστασις.) M. Vincent qui, du reste, était loin de désapprouver les dénominations que nous adoptons, traduit toujours ἄνεσις par abaissement, ἐπίστασις par élévation, τάσις par les mots ton ou intonation, enfin διάτασις, par extension ou étendue. - Au moyen âge, le mot ἄρσις, qui de la rythmique était passé dans l’armonique (accent aigu), correspondait à l’ἐπίτασις, et se traduisait elevatio ou intentio; θέσις correspondait à ἄνεσις (accent grave) et se rendait par depositio ou remissio. Voy. dans l'Hist. de l'Harmonie au moyen âge, par M. E. de Coussemaker (Paris, Didron, in-4°,1852), le texte et la traduction de Hothby n° 58, p. 328.

Il n'est jamais arrivé à personne de signaler la différence qui règne entre ces deux mouvements, et cependant, si cette distinction n'est pas faite, il n'est pas du tout facile d'expliquer la nature du son.
4. Il sera indispensable, si l'on ne veut pas faire comme Lasus (11) et quelques autres musiciens, disciples d'Épigonus (12), qui pensaient que le son a une sorte de largeur (13), de parler à ce sujet avec un peu plus d'exactitude [qu'ils n'ont fait]; car une détermination précise [de la nature du son] rendra la suite beaucoup plus claire.

(11) Lasus, natif d’Hermione, ville d'Argolide, vivait sous Darius, fils d'Hystape, entre le sixième et le cinquième siècle avant notre ère. Suivant Meursius, il fut le premier qui écrivit sur la musique: on rapporte qu'il lit un hymne à Cérès et une ode sur les Centaures ou il n'y avait pas de Σ. Plutarque parle de lui comme d'un novateur : « Lasus d’Hermione, ayant transporté les rythmes dans la poésie dithyrambique et multiplie les sons de la flûte dont il l'accompagnait, causa par cette variété des sons trop désunis un grand changement dans l'ancienne musique. » (De musica, § 29.) Voy. aussi Athénée, Deipnosoph., I. X , p. 455.
(12) Epigonus d'Ambrasie, le premier, fit usage de la lyre sans plectrum, et inventa un instrument appelé l'epigonium, composé de quarante cordes, lesquelles, dit Burette, étaient accordées deux à deux à l'unisson.
Meybaum donne à l'occasion de Lasus et des disciples d'Épigones quelques détails remplis d'érudition : on y remarque une citation de Porphyre (Comment. in Harm. Plotemaei) sur les doctrines musicales qui ont précédé celles de notre auteur.. « Il y a eu bien des écoles; avant Aristoxène il y avait eu celle d'Épigonus, de Damon, d'Eratoclès, d'Agénor et d'autres encore dont il fait mention. Après lui, etc. »
(13). Πλάτος. Voyez, sur ce passage, les mémoires de Burette (ancienne Acad. des Inscriptions, t. XV. p. 328).

La voix n'a pas une manière unique de se manifester; lorsque nous parlons aussi bien que lorsque nous chantons, elle reçoit le mouvement précité (suivant le lieu). Evidemment le grave et l'aigu se rencontrent dans l'un et dans l'autre cas; or c'est un mouvement suivant le lieu que celui dans lequel se produisent le grave et l'aigu: seulement ce double mouvement n'est pas d'une seule et même espèce (10).

(10) C'est-à-dire que ce mouvement est tantôt continu, ce qui arrive quand nous parlons, et tantôt discontinu, lorsque nous chantons. Voir plus loin, § 26. - Il suffisait chez les Grecs, comme il surfit chez nous, de changer le mouvement de la voix pour que la parole pure et simple devienne un chant : c'est ainsi que Philippe de Macédoine, dans Plutarque (Démosthène, § 23), chante en battant la mesure le début du décret que Démosthène fit rendre pour le combattre.

3. Avant toute chose, si l'on veut faire un ouvrage sur le chant, il faudra déterminer le mouvement de la voix, lequel est un mouvement suivant le lieu (09).

(09) On sait qu'Aristote distingue le mouvement suivant la qualité, suivant la quantité et suivant le lieu. Voir sa Physique, livres V, 1, VII, 2 et VIIl, 7.

c'est une chose dont nous nous sommes convaincu précédemment lorsque nous examinions les opinions des harmoniciens (08). Du reste on le comprendra mieux encore si nous passons en revue successivement toutes les parties de l'harmonique pour en faire connaître le nombre et pour montrer la valeur de chacune d'elles. Nous verrons que les unes ont été totalement négligées par les musiciens, et les autres traitées imparfaitement ; de cette manière notre assertion sera rendue évidente et nous envisagerons en même temps d'un coup d'oeil le plan de notre travail.

(08) On peut supposer qu’Aristoxène fait allusion à quelque autre de ses nombreux ouvrages, notamment à son Histoire de l'Harmonique, citée par Plutarque, De musica, § 16.

mais ils ne contenaient que des systèmes octocordes enharmoniques: quant aux autres genres, aux autres formes [d'intervalles] qui se rencontrent dans l'enharmonique et dans les autres genres, personne n'a cherché à les approfondir. Au contraire, ils détachaient dans la mélodie tout entière un seul genre qui en forme la troisième partie (06), et une seule grandeur, le diapason ou l'octave (07), qui devenait l'objet exclusif de leurs traités. Ils n'ont étudié aucune question, en aucune manière, même relativement à l'art dont ils s'occupaient;

(06) Meybaum traduit : « Quin tertiae partis ex tota modulandi ratione resectae unum quoddam cognovere genus; cujus magnitudo erat diapason. » Il observe en outre que ce passage obscur concerne soit le genre, troisième partie de la mélodie, dont les systèmes et les tons forment les deux premières, - soit l'harmonique qui, avec la rythmique et la métrique, constitue la science musicale. Cp. dans les Notices, le second anonyme, p. 15. - Notons que dans le livre II, § 14, l'étude des genres forme la première partie de l'harmonique. Mb., p. 35.
(07) Plutarque (De musica, § 34) dit à peu près la même chose ; « Quoique l'harmonique se divise en trois genres égaux quant à la grandeur des systèmes et quant à la puissance des sons et des tétracordes, les anciens n'ont cependant traité que d'un seul de ces genres. En effet, ils n'ont porté leur vue ni sur le chromatique ni sur le diatonique; ils n'ont considéré que l'enharmonique et cela, dans le seul système de l'octave ou diapason; car ils étaient en désaccord sur la constitution du chromatique et s'accordaient pour reconnaître un seul genre enharmonique. » - Voir aussi plus loin, livre Il, § 15.

2. Il faut établir aussi que les musiciens antérieurs voulaient être seulement harmoniciens.
En effet, ils ne s'occupaient que du genre enharmonique et ne considéraient aucunement les deux autres; la preuve, c'est que, chez eux, les diagrammes ne sont composés que de systèmes enharmoniques; pour les diatoniques et les chromatiques, personne ne les a jamais vu [exposer]. Toutefois leurs diagrammes (05) indiquaient la marche entière de la mélodie;

(05) Aristoxène, à l'occasion de ce passage, est vivement critiqué par Proclus, dans ses Commentaires sur le Timée (liv. III, p. 192, éd. de Schneider). Meybaum cherche à l'excuser, et M. Vincent lui rend pleine justice (Notices, etc., p. 80) : « Pour reproduire les autres genres, dit-il, il suffit d'élever d'une manière convenable la parhypate et l'indicatrice de chaque tétracorde. » C'est précisément ce que dira plus loin notre auteur (livre lll, § 34, p. 68 de Meyb.).

En effet, c'est la première des études [musicales] théoriques, je veux dire la première de celles qui servent à former la théorie des systèmes et des tons. Il convient de ne rien demander de plus à celui qui s'est acquis la science de l'harmonique; car tel est le terme d'un traité de ce genre, et les questions qui s'élèvent plus haut n'appartiennent plus spécialement à cet ordre d'études (la [musique] pratique (04) se sert déjà des systèmes et des tons), mais à la science qui embrasse et l'harmonique et toutes les autres parties composant l'ensemble des connaissances musicales, j'entends par là tout ce qui constitue le musicien.

(04) Τῆς ποιητικῆς. - S'agit-il ici de la musique en tant qu'exécutée, comme nous le supposons dans notre traduction, ou bien, comme Meybaum l'entend dans la sienne, de la partie de la musique appelée la poétique ? - Voir sur ce mot la note de Meybaum, p. 75.

1. Comme la science du chant (01) se compose de plusieurs parties (02) et se divise eu plusieurs espèces, il faut établir que l'une de ces parties, appelée l'Harmonique (03), occupe le premier rang et possède une valeur tout élémentaire.

(01) Le chant, en grec τὸ μέλος. De ce mot, on a formé μελοποιία, mélopée, qui signifie « application des règles du chant, soit vocal, soit instrumental, composition » ; et μελῳδία, mélodie, c'est-à-dire « musique chantée, musique vocale » - Sur le mot μέλος, voir dans les Notices et Extraits des manuscrits, tome XVI, 2e partie (1847), l'ouvrage de M.. A.-J.-H. Vincent sur la Musique des anciens Grecs, p. 6 et passim.

(02) Savoir l'Harmonique, la Rythmique, la Métrique, l'Organique, la Poétique, l’Hypocritique. - Voir Vincent, Notices, etc., p. 33.

(03) On trouvera de nombreuses définitions de l'Harmonique dans les Notices, etc., p. 15. Voir aussi Plutarque, Questions platoniques. § 2.

http://remacle.org/bloodwolf/erudits/aristoxene/table.htm

ARISTOXÈNE



Oeuvre numérisée par Marc Szwajcer













INTRODUCTION : AVERTISSEMENT.

LIVRE PREMIER.

CHAPITRE PREMIER. ÉTAT DE L'HARMONIQUE AVANT L'AUTEUR.
CHAPITRE II. PLAN D'UN TRAITÉ D'HARMONIQUE.
CHAPITRE III. DES DIVERSES SORTES DE MOUVEMENTS DE LA VOIX.
CHAPITRE IV. DES LIMITES DE LA DISTENSION.
CHAPITRE V. DÉFINITION DU SON.
CHAPITRE VI. DÉFINITION DE L'INTERVALLE.
CHAPITRE VII. DÉFINITIONS DU SYSTÈME. - OBSERVATION SUR CES TROIS DÉFINITIONS.
CHAPITRE VIII. DES DIVERSES ESPÈCES D'INTERVALLES ET DE SYSTÈMES.
CHAPITRE IX. DE LA COMPOSITION DU CHANT ACCORDÉ.
CHAPITRE X. DES GENRES.
CHAPITRE Xl. LIMITES DE LA CONSONANCE EN GRANDEUR ET EN PETITESSE.
CHAPITRE XII. DÉFINITION ET DIVISION DU TON.
CHAPITRE XIII. GÉNÉRATION DES NUANCES OU COULEURS.
CHAPITRE XIV. POSITIONS RELATIVES DES CORDES MOBILES.
CHAPITRE XV. NATURE DE LA CONTINUITÉ ET DE LA SUCCESSION.
CHAPITRE XVI. DIVERS PRINCIPES DE MÉLODIE.

LIVRE DEUXIÈME.

CHAPITRE PREMIER. CONSIDÉRATIONS SUR L’HARMONIQUE.
CHAPITRE II. DES SEPT PARTIES DE L’HARMONIQUE; TERME DE CETTE ÉTUDE.
CHAPITRE III. AUTRES TERMES ASSOCIÉS A L’ÉTUDE DE L’HARMONIQUE.
CHAPITRE IV. CONDITIONS A REMPLIR POUR FAIRE UN TRAITÉ D’HARMONIQUE.
CHAPITRE V. DES GENRES.
CHAPITRE VI. NOMBRE DES CONSONANCES.
CHAPITRE VII. DÉFINITION ET DIVISION DU TON.
CHAPITRE VIII. SUR LA DÉNOMINATION DES SONS ET DES INTERVALLES.
CHAPITRE IX. GÉNÉRATION DES NUANCES.
CHAPITRE X. DISTANCES RELATIVES DES CORDES MOBILES.
CHAPITRE XI. USAGE DE LA CONTINUITÉ ET DE LA SUCCESSION.
CHAPITRE XII. PRINCIPE DE LA COMBINAISON DES INTERVALLES.
CHAPITRE XIII. FIXATION DES DISSONANTS PAR LE MOYEN DES CONSONANCES.

LIVRE TROISIÈME.

CHAPITRE PREMIER. DE LA SUCCESSION DES TETRACORDES.
CHAPITRE II. MOBILITÉ DE LA CONJONCTION. STABILITÉ DE LA DISJONCTION.
CHAPITRE III. NATURE DES INTERVALLES INCOMPOSÉS.
CHAPITRE IV. PROPRIÉTÉ DES INCOMPOSÉS DE LA QUINTE.
CHAPITRE V. DE LA SUCCESSION DES INCOMPOSÉS ÉGAUX.
CHAPITRE VI. DE LA SUCCESSION DES INCOMPOSÉS INÉGAUX.
CHAPITRE VII. DÉTERMINATION DES PROCÉDÉS A PARTIR DES DIVERS INCOMPOSÉS.
CHAPITRE VIII. PROPRIÉTÉS DES SONS DU PYCNUM.
CHAPITRE IX. NOMBRE DES INCOMPOSÉS DANS CHAQUE GENRE.
CHAPITRE X. DES ESPÈCES OU FORMES DES CONSONANCES.
FORMES DE LA QUARTE.
CHAPITRE XI Emprunté au second anonyme. FORMES DE LA QUINTE ET DE L’OCTAVE.
APPENDICE EXTRAITS DIVERS A RAPPROCHER DES ÉLÉMENTS HARMONIQUES D’ARISTOXENE.

Aristoxene de Tarente et Aristote, le Traite d'harmonique (Etudes et commentaires) (Paperback)
by Annie Belis

science harmonique, saisie des principes, genre enharmonique, genre diatonique, faits musicaux, mouvement discontinu, intervalles musicaux, questions musicales, les intervalles, ses devanciers, des intervalles, deux tons, sons mobiles, des diagrammes, dans son commentaire, les commentateurs, parties constitutives, les deux termes, notre texte, pour notre part, trois genres, grecque antique, mouvement continu, les tons, livre premier

The Science of Harmonics in Classical Greece
Andrew Barker
University of Birmingham

(ISBN-13: 9780511365287)



The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians and astronomers as well as by musical specialists. This book examines its development during the period when its central ideas and rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists' methods and purposes and the controversies that their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists' work draws on and in some cases influences that of philosophers and other intellectuals.

• Proposes new interpretations of important texts • Relates the musical theorists' work to that of philosophers and other intellectuals • Written by a world-renowned authority in the field
Contents

Part I. Preliminaries: Introduction; 1. Beginnings, and the problem of measurement; Part II. Empirical Harmonics: 2. Empirical harmonics before Aristoxenus; 3. The early empiricists in their cultural and intellectual contexts; 4. Interlude on Aristotle's account of a science and its methods; 5. Aristoxenus: the composition of the Elementa harmonica; 6. Aristoxenus: concepts and methods in Elementa harmonica Book 1; 7. Elementa harmonica Books 2-3: the science reconsidered; 8. Elementa harmonica Book 3 and its missing sequel; 9. Contexts and purposes of Aristoxenus' harmonics; Part III. Mathematical Harmonics: 10. Pythagorean harmonics in the fifth century: Philolaus; 11. Developments in Pythagorean harmonics: Archytas; 12. Plato; 13. Aristotle on the harmonic sciences; 14. Systematising mathematical harmonics: the Sectio canonis; 15. Quantification under attack: Theophrastus' critique; Postscript: The later centuries.

Bryn Mawr Classical Review 2006.07.46
Sheramy Bundrick, Music and Image in Classical Athens. Cambridge: Cambridge University Press, 2005. Pp. xvi, 256; b/w figs. 110. ISBN 0-521-84806-7.

Reviewed by Sophie Gibson (sophie.gibson@oxon.blackwellpublishing.com)


Bundrick (henceforth B.) presents a thorough discussion of the iconographical evidence for the role of music in Athens in the fifth century, during which the rise of democracy coincided with rapid advances in musical performance and a flourishing of musical imagery in the visual arts. The author notes that pictorial evidence for many aspects of musical activity in the fifth century is more plentiful than literary evidence, much of which dates from the fourth century or later. This gives us the opportunity to expand our understanding of the classical perception of music from that which can be drawn from literary sources alone. The book produces some measured conclusions about how and why the presentation by Athenian artists of various aspects of music-making changes through the course of the fifth century.

The introductory Chapter 1, "Music and Image in Fifth Century Athens" sets out B.'s premise. Athens, arriving on the musical scene after some other Greek states, in the sixth century laid the foundations for the rapid development of musical activity and discussion in the fifth. Musical imagery on vases in the sixth century had a limited number of contexts and subjects -- mainly Apollo and a few other musicians, Panathenaic contests, and symposia. As Athens becomes a centre for musical innovation in the fifth century (witnessing the rise of the technically challenging "New Music"), the iconography of music also changes. B. argues that this alteration of subjects and scenes is not coincidental, and presents three concepts central to the change: first, the discipline of mousike and its social role in the increasingly institutionalised education amongst the elite in Athens; second, the theory of ethos and its context in the Athenian perception of character; and third, the idea of harmonia, reflected in the tuning of a musical instrument and used as a metaphor for the stability of the polis. While none of these concepts works entirely independently from the literary evidence, B. shows how our understanding of the attitudes to music in fifth-century Athens can by dramatically expanded by the visual material.

Chapter 2, "Representing Musical Instruments" systematically covers images and the significance of stringed instruments (chelys lyre, kithara, barbitos, phorminx, Thracian kithara, and harp), wind instruments (aulos, syrinx, and salpinx), and percussion. In relation to stringed instruments, the author notes that while the terminology in literary sources can be imprecise, the visual evidence is consistent and clear in the associations of particular instruments. For example, the chelys lyre has connotations of the elite and the amateur, the kithara of competitions and virtuosi. Further, the semantic value of particular instruments in literature can be expanded by the visual sources. In particular, the aulos' negative image in some fourth-century literature (especially in Plato Republic 399d and Aristotle Politics 1341a) is contrasted with its appearance in vase paintings in a wide variety of contexts in the fifth century. It occurs in scenes depicting the respectable education of boys of the elite, but it is present also in raucous and erotic scenes. Where our literary evidence for the fifth century is limited, B. argues that there is significant visual material. By the fourth century the aulos is strongly associated with New Music and the increasing professionalism of music, which possibly explains Plato and Aristotle's lack of enthusiasm for it.

With the significance of each instrument established, the third chapter "Mousike: The Art of the Muses" turns to the first of the three concepts anticipated in the introduction. It outlines how mousike formed the backbone, along with athletics (gymnastike), of the traditional education (archaia paideia) associated with the elite classes, and then uses visual imagery to interpret changing attitudes to music in education. B. arranges her discussion for this and the following two chapters into scene types. The discussion first focuses on the art of the Muses (instrumental music, dance and the singing of poetry), and the introduction of new iconography representing the Muses not just as companions for Apollo, but as musical virtuosi. They promote the benefits of music as a cultural and educational good, but they appear less frequently on vases by the end of the fifth century. The role of music as a social good is supported by images representing the idea of a mousikos aner (a phrase used by Plato in the Laws), suggesting one who is in possession of an elite education and, among other things, is capable of contributing an appropriate performance at a symposion. Presentations of this idea become less frequent during the fifth century with the rise of the power of the demos and the refocusing of education on rhetoric and literacy. Other types of scene include those depicting Herakles and Linos, the music teacher he murdered. These scenes further emphasise the civilising nature of mousike in contrast with Herakles' behaviour. Representations of mousike and gymnastike together on the same vase reflect the combined role they play in Athenian education. B. discusses the changing attitude to music in the fifth century in her discussion of music and the symposion. During the course of the fifth century, B. argues, the symposion becomes more democratic, and the elite education required to participate musically as a guest is considered old fashioned compared with a new style of symposion which increasingly employs professional, often female, entertainers. The chapter closes with a discussion of citizen women and their relationship to mousike. Although the literary sources make no reference to women receiving musical education, we do find images of them making music in domestic settings amid the general increase of images of women during the fifth century. B. argues that although these women may represent hetairai, Muses or other mythological figures, the domestic setting of many of these images suggests that these are respectable citizens, and she effectively examines this evidence in the light of what we can know about the lives of Athenian women.

Chapter 4, "Ethos and the Character of Musical Imagery" opens with a discussion of the idea of ethos, which considers how music affects character or behaviour. Although the concept occurs early in Greek literature (B. uses the example of the Sirens in the Odyssey), there is little literary material until theoretical discussion in the fourth century. Again, the lack of fifth-century literary sources is contrasted with the range of visual evidence. The chapter focuses on the musical iconography of four mythological figures: Dionysos, Orpheus, Thamyris, and Marsyas. In the discussion of images of Dionysos, B. recalls the opposing associations of Dionysos with the aulos and Apollo with the lyre and argues that modern scholars have exaggerated the Greeks' view that the aulos is something wild to be rejected by the polis. She argues, as she does in Chapter 2, that the aulos had a legitimate place in Athenian society and that music (and drinking) in the context of the symposion are seen to have kathartic function and are therefore beneficial in moderation. The images of Orpheus demonstrate again the issue of the effect of music on listeners: they primarily focus on Orpheus' death at the hands of the Thracian women and, later in the fifth century, on Orpheus with the Thracian men. B. suggests that both scene types refer to music's ability to arouse the emotions. Two further figures which appear regularly in the iconography, Thamyris and Marsyas, are depicted as examples of how a lack of moderation in musical matters is devastating. The third and final of B.'s essential concepts is the subject of Chapter 5, "Harmonia and the Life of the City", in which she argues that harmonia, an idea connected primarily with music in the sixth century, develops social and political connotations in the fifth. Visual images of instruments and performance in scenes of sacrifice, musical contests, and weddings represent a broader idea of harmonia of the household and the polis. B. highlights the role of Apollo as a musician, who appears profusely on vases in the fifth century and embodies ideas of harmonia and eunomia, and suggests how images of Apollo can be seen to promote and support democratic values. Further, the rise in representations of cult ritual -- including images of musicians, for example in processions and in the rituals associated with sacrifice -- exemplify the civic associations of music and harmonia. Similarly, changes during the fifth century to representations of musical contests show a shift from elitist to democratic priorities. They coincide with and confirm the rise and popularity of professional musicians and virtuosi, reflected in the emphasis on the individuality of performers on some vase scenes. B. argues that these and other changes to the iconography (representations of Nike, judges of musical competitions, aulodic contests, and changes in vase shapes), reflect changes that Perikles made to the musical competitions of the Panathenaia. Continuing her discussion of representations of music in institutional performance, B. examines depictions of music in the theatre (with due caution about the possibilities of identifying theatre productions with certainty), in which the aulos was the principal instrument. Similarly, B. emphasises the civic and social function of harmonia in her discussion of representations of music as part of different stages of the wedding ritual. The final type of scene examined is that of Harmonia personified, as a bride (of Kadmos), with Aphrodite or the Muses, with Eunomia, and in domestic scenes. The brief, concluding chapter 6, "Musical Revolution in Classical Athens", suggests that the sudden fall in the representation of certain types of musical scene on vases at the end of the fifth century reflects again a change in social attitudes.

The book is beautifully presented and richly illustrated with over 100 black and white photographs, mostly of vases (which have been well reproduced), and is practically free from typographical errors (I noticed only one, "annd" on p. 51). There is a brief but useful glossary which includes both musical and Greek cultural terms -- it might also have been helpful to include further terms relevant to material culture for those more familiar with literary and philosophical evidence. There is an extensive bibliography.

Music and Image in Classical Athens provides a valuable contribution to the discussion of the social significance of music in Ancient Greece. With a thorough examination of a wide range of visual evidence, B. constructs a coherent narrative about the significance of musical images. While some sections are more compelling than others -- the chapter on harmonia as metaphor for the stability of the democratic polis is less consistently convincing than the sections on mousike and ethos -- each chapter contains stimulating discussion about the semantic value of each type scene. B. demonstrates clearly the dangers of overlooking the visual evidence in favour of literary sources, and thereby encourages a cross-disciplinary approach to the study of ancient music.

Aristoxenus of Tarentum and the Birth of Musicology
by Sophie Gibson

The Harmonics of Aristoxenus of Tarentum, Pythagorean and student of Aristotle, sealed his reputation as master of musical theory, especially harmonic science. Despite his many writings, it is this text that makes him stand out from Greek philosophy as the father of musicology. In her dissertation, Sophie Gibson presents a detailed and specialised analysis of the structure and aguments of the Harmonics and another treatise, the Rhythmics, enveloped by discussions of musical theory before and after Arostoxenus. The text includes many Greek terms and extracts, translations of which can be found in the extensive notes. The study presupposes knowledge of Greek and musical theory. 264p (Routledge 2005)
ISBN 9780415970617. Hardback. Price GB £45.00

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Sophie Gibson, Aristoxenus of Tarentum and the Birth of Musicology. Studies in Classics, vol. 9. New York and London: Routledge, 2005. Pp. ix, 264. ISBN 0-415-97061-X. $70.00.

Reviewed by Otto Steinmayer, Independent Scholar, Kampong Lubok Gayau, Lundu, Sarawak
Word count: 1929 words

Antiquity knew Aristoxenus [fl. 4th c. BCE] as ho Mousikos, THE authority on music. While he was not the first person to write whole books dedicated specifically to music, he is the earliest musical writer whose work has survived in bulk.

I must clarify. Aristoxenus's surviving work, and this is especially true of his Harmonics, does not deal with actual music, but with the material of music -- not with the nature of sound but with the nature of musical intervals and scales. In our days, the investigation of such things comes under the rubric of musicology. Sophie Gibson in her excellent study makes a convincing case that Aristoxenus was the inventor of this discipline.

For sheer abstruseness, Aristoxenus's writings must lie near the top in ancient Greek. Aristoxenus's subjects, the nature of the musical material and of rhythm, are of themselves difficult. Scientific investigation of them at the time he wrote was at its very beginning, speculative, and confused.1 Though Gibson demonstrates that Aristoxenus followed Aristotle in method, she makes it clear that in the musical sphere he was determined not to owe anything to anybody. He lashed his predecessors, and elsewhere even Aristotle, says the Suda, when the former passed him over as successor for leadership of the Lyceum. Intellectual perplexity and odium scholasticum give his books a double edge; irritation is added to difficulty, rather like the Clarke-Leibniz correspondence.

Furthermore, the most substantial piece of Aristoxenus's work we have, the Harmonics, survives in three incomplete books, of which Book I appears written at hazard, and Book II is a recasting of the same material, though exhibiting contradictions with Book I. Book III breaks off just when we might have been getting to something to do with real melody. From Books I and II of his Rhythmics there survive chunks, and only much smaller fragments from the rest of Aristoxenus's work.

Notwithstanding these problems of fragmentation and opaqueness, Aristoxenus is an extremely important source for the study of ancient Greek music, where the evidence is so scarce that we need to squeeze out all we can anywhere we find it. I was delighted to read Sophie Gibson's excellent discussion of Aristoxenus's work, and I am most grateful for her heroic labor in elucidating it. Lucid indeed her exposition is, though necessarily requiring constant and diligent attention. A secondary work such as Gibson's is vital to the study of Aristoxenus, for in many places in his text it is not in the least obvious what he is trying to do, and in such a technical subject we need plenty of context.

Gibson examines Aristoxenus's work minutely, point by point in a chain of many complex small arguments, and her book is best reviewed chapter by chapter.

In her Introduction Gibson states Aristoxenus's principal influences -- his musical training (the Suda says he was the son of a musician), Pythagoreanism, Aristotle -- and his ambition, not simply to describe music empirically, but to "establish an autonomous science" [p. 4]. Others had looked at music before Aristoxenus, notably the Pythagoreans, who were less concerned with music itself than "about its position in a mathematically coherent universe." [p. 6] The same might be said of Plato, and both Plato and Aristotle are mainly interested in music's effect on character, again not in music itself. Aristoxenus in his Harmonics ignores both cosmology and ethics, and examines music -- at least its pitch structure -- as a system in itself. Here, says Gibson, musicology was born.

Gibson gives Chapter One to a survey of harmonic theory before Aristoxenus. Music theory began when Pythagoras discovered that the fundamental consonances of ancient Greek music, the octave, the fifth, and the fourth, can be expressed in numerical ratios, 2:1, 3:2, and 4:3 respectively. Later the tone was found to be 9:8. (The elegance of this series quickly got spoiled when the semitone and diesis, a fraction of the semitone kin to the modern quartertone, were found not to be so tidily definable. Theorists up to Claudius Ptolemy kept fiddling with the numbers.)

And yet, though basic consonances could be represented in number, that they were consonances was judged by the hearing. Music theory quickly began to busy itself with the antithesis of reason versus perception. Aristoxenus rejected the mathematical approach as the absolute criterion of defining sound as musical, Gibson explains, because "we do not perceive musical sound as ratios or relative speed." [p. 16] Aristoxenus prefers to study the relationship between notes "as multiples of a particular unit of measurement" [p. 18]:

"... for example, the interval of a fifth as three and a half tones without reference to the ratio of 3:2 and in this way it is more compatible with the way that the human mind perceives music." [p. 18]

Earlier empiricists had accepted a similar logic, and tried to identify the "atom" (so to speak) of musical space from which they thought to build larger intervals. Plato ridicules these harmonikoi listening intently over their monochords in Republic 531a-c. Aristotle takes the diesis as his "least element." This Aristoxenus rejects; how, he says, can one comprehend 28 dieses in a row when one cannot sing even three? [Harm. I.28.6ff.] Gibson notes that Aristoxenus tends to use the tone as his unit of measure. By this he avoids the impossibility of mathematically dividing a superparticular2 ratio such as that of the tone, 9:8 -- "... a semitone could be perceived as an interval half the size of a tone" [p. 18].

In Chapter Two Gibson examines Aristotle's influence on Aristoxenus. Aristotle said almost nothing about music itself -- he mentions music as it relates to other subjects and never devoted a work to it. It was Aristotle's method that Aristoxenus took over, especially from the Posterior Analytics, and "applied [it] with a diligence unseen in Aristotle" to music [p. 31]. Aristoxenus worked by the book: he limits his subject, he considers what is observed by the hearing and what can be established by reason, he defines parts, he searches for first principles, he constructs axioms and draws demonstrations from them. He even follows Aristotle's injunction to pay attention to things of value in predecessors' work, though he did that in order to trash it.

Considered as an intellectual structure, Aristoxenus's exposition looks neat. However, Gibson concludes, the attempt to apply the Aristotelian axiomatic method to harmonic science is not "entirely appropriate" [p. 38], and in her following chapter she demonstrates how this more geometrico reasoning breaks down when applied closer and closer to real music as Aristoxenus tries to bull his way through contradictions. Even though flawed, such a method was (she says) a program that later theorists could and did extend and refine.

In Chapter Three, the focus of her book, Gibson surveys the Harmonics, explicates the work's contents and develops her discussion of Aristoxenus's Aristotelian method. The state of the text is problematic, and so Gibson attends usefully to the relationship of Books I and II, and the organization of the whole. To broadly characterize Gibson's approach to the Harmonics, she is what Aristoxenus so badly needed, a good, "blue-pencil" editor.

The heart of this heart-chapter, in my opinion, lies in Gibson's explanation of Aristoxenus's concept of dynamis, that is, how any note, bounded by intervals, is what it is by how it functions within the whole scale. This way of looking at the note liberates it from the ungiving rigor of mathematical definition: "the perception of a structure is more important than its measurement" [p. 46]. Gibson is right to consider this Aristoxenus's most important conceptual contribution; it is as though in treating the note he had discovered the existence of the "phonemic" as something apart from the "phonetic."

In Chapter Four Gibson turns to the fragments of Aristoxenus's Rhythmics. Here too Aristoxenus attempted to organize his theory axiomatically. He makes a separation between rhythmics and metrics, between rhythm in the abstract and as it is embodied in the rhythmizomena. He again rejects earlier views which based rhythm on the syllable or analyzed it by feet, and posits instead a prôtos chronos, a least unit of time, which, however, can be of any length according to the tempo. By this provision he gets around the objection he himself leveled at the harmonikoi who tried to compose intervals out of dieses whose size was rigidly fixed at the minimum of perceptibility by hearing. Feet are constructed out of khronoi, both asynthetoi, incomposite, or synthetoi, composite, in certain ratios which are perceived as rhythmical, other ratios not being so perceived. Gibson clearly demonstrates the Rhythmics' methodological kinship with the Harmonics.

Aristoxenus's other works occupy Chapter Five. Only fragments survive, and a few titles of the 453 books the Suda says Aristoxenus wrote. Later authors cite Aristoxenus mainly for his pronouncements on music, dance, instruments, tragedy. What remains of his work on music and education shows his conservatism and his attachment to Pythagorean ethics. Aristoxenus wrote the life of Pythagoras and his disciples, and on Pythagorean doctrine. He was also known in antiquity as a skillful, albeit often harsh and sour-tempered, biographer of other philosophers and poets.

None of Aristoxenus's other works ever approached the influence and important of the Harmonics. Gibson in her final chapter surveys the transmission and development of Aristoxenus's ideas throughout antiquity, and their reception by Boethius, through whose De Institutione Musica they passed to the Middle Ages and in some sense to the present.

Here, and in her general conclusion, Gibson sums up Aristoxenus's contributions to musicology. First, he invented musicology as a discipline in itself, not subservient to cosmology or ethics. He brought method to the investigation of harmonics, and, even though the method he used was flawed, his example suggested how it could be used better. Aristoxenus devised essential conceptions: that musical sound is that which proceeds by stepped pitches; that note is the first element of melody and that how it functions in a scale is what makes it musical; that larger intervals can be put together from the tone and smaller intervals defined as parts of a tone.

Aristoxenus did not abjure mathematics altogether. Later ancient theorists blended his synthetic approach to intervals with the Pythagorean method, and this is very much what every musician accepts today, a Both/And way of thinking: a fifth is both pitches in a ratio of 3:2 as to their frequencies, and also three tones and a semitone. The concept of dynamis seems intriguingly close to the way the modern theory of harmony defines notes of the scale as "tonic," "dominant," and so forth, and how they change functions in modulation, say in a classical sonata.

Aristoxenus is responsible for the limitation of scales, which at times threatened to proliferate uselessly, to the seven possible species of the octave.

Most of all, says Gibson, Aristoxenus created a language in which the empirical discussion of music could take place. Surely, if we had a good sample of the music itself whose harmonic material Aristoxenus attempted to described, we would understand him much better, and perhaps even admire how well he managed in his pioneer attempt. Unfortunately, when Aristoxenus speaks, it as if we are hearing a lecture on biology without a fish on the plate; we hear much about what Aristoxenus thinks about his personal approach to harmonics, but have no music to relate his opinions to. Yet it is important to understand these brotôn doxas even while the pistis alêthês may be escaping us, and I applaud Gibson for bringing light to a very difficult author on a very difficult subject.
Notes:


1. P. 20. As I read Gibson here, I had a small insight on a conceptual problem which hindered ancient harmonicists from a clear understanding of the nature of pitch. This will I hope confirm Gibson's characterization of early harmonic theory as "confused," and I would be grateful for the liberty to air it here. Gibson [p. 16] quotes Aristoxenus's dismissal of those who define notes and sound as "movements," and she refers us [note 45] to Archytas's [Fr. 1 (KD 47B1)] theory that difference in pitch was due to difference in force of breath. Other theorists speculated on the "speed" of high and low pitches. Much confusion, I conjecture, came into acoustics because the Greeks lacked, though perhaps were groping for, the concept of "frequency." The English word itself is late, 1838 [OED]. It may be telling that the Greek words for "low" and "high" pitch, barus and oxus are not antonyms, but words describing two utterly different qualities, viz., "heavy" and "sharp." This disjointedness is very striking, as it comes from a people who relished and cultivated antithesis, and may mean that the Greeks were not sure whether low and high sounds were quite of the same nature, or that they sat at different ends of a spectrum.
2. Or "epimoric": a "ratio ... such that the greater term is equal to the smaller term plus an integral 'part' or 'factor' of the smaller term. All such ratios have the form n+1:n." (Chapter One, note 15).

Aristoxenus of Tarentum and the Birth of Musicology (Studies in Classics) (Hardcover)
by Sophie Gibson

epimoric intervals, rhythmic treatise, harmonic treatise, primary chronos, tetrachordal divisions, moveable notes, musical enquiry, chronos protos, natural theoretical science, epimoric ratios, enharmonic pyknon, harmonic science, musical methodology, enharmonic genus, disjunctive tone, musica greca, vocabulorum differentia, octave species, greater perfect system, irrational intervals, musical investigation, axiomatic science, disjunct tetrachords, enharmonic genera, rhythmic theory
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Aristides Quintilianus, Peri Mousikes, Sectio Canonis, Posterior Analytics, Martianus Capella, Aristoxenus of Tarentum, Bacchius Geron, Middle Ages, Ptolemy's Harmonics, Book Ill, Kai Tas, Plato's Timaeus, Porphyry's Commentary

http://www.amazon.com/Aristoxenus-Tarentum-Musicology-Studies-Classics/dp/041597061X#sipbody

I am a composer music-theorist, lexicographer, author, software developer, teacher, performer, arranger, artist, cartographer, locksmith, bicyclist, motorcyclist, and pacifist.

Since 1984, my main interest has been microtonal and just-intonation music theory and its application on computers.

Some other things I'm interested in: languages, writing systems, history, philosophy, religions and mythologies, astronomy and cosmology.

I'm available in Southern California, at your home, for piano tuning, private music lessons in theory, composition, conducting, woodwinds (clarinet, sax, oboe, bassoon, recorder), piano/keyboard, MIDI sequencing, and (of course) tuning theory, and tutoring in CakewalkTM and Microsoft WordTM and ExcelTM. Click on the appropriate link to email me.

My cell phone number is easy to remember: 619-CAR-KEYS. Give me a call if you're in San Diego and let's get together at a coffee shop.

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If you don't understand any of my music theory, start here
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email: monz@juno.com

REFERENCES ----------

Aristoxenus. c 330 BC. _Harmonika stoicheia_. Athens?

Cleonides. c 100 AD. _Eisagoge_. [English translation in Strunk 1950.]

Plutarch. _de Musica_. [English translation in Volume 1 of Barker 1989]

Boethius, Anicius Manlius Severinus. c 505 AD. [English translation in Bower 1989]

M - Codex Venetus. c 1150. Constantinople. (with corrections from many hands) Ma - the original script Mb - corrections before 1300 Mc - corrections 1300 or later Mx - unidentified corrections In Library of St Mark, Venice.

V - Codex Vaticanus. 1200-1400. Va - original script Vb - corrections by another hand

H - Codex from Protestant Seminary, Strassburg. 1400s? Destroyed in war 1870.

Valla, Georgius. 1497. Cleonides: _Eisagoge_. Latin translation of Cleonides. Venice.

S - Codex Seldenianus. c 1500. In Bodleian Library, Oxford.

R - Codex Riccardianus, 1500-1600. Florence.

B - Codex Berberinus. 1500-1550. Bibliotheca Berberina, Rome.

Meibom, Marcus. 1652. _Antiquae musicae auctores septem, Graece et Latine_. Apud Ludovicum Elzevirium, Amsterdam. (Contents: Vol. 1: I. Aristoxeni Harmonicorum elementorum libri III. II. Euclidis Introductio harmonica. III. Nicomachi Geraseni, Pythagorici, Harmonices manuale. IV. Alypii Introductio musica. V. Gaudentii Philosophi, Introductio harmonica. VI. Bacchii senioris Introductio artis musicae Vol. 2: Aristidis Quintiliani De musica libri III & Martiani Capellae de musica liber IX.) [Contains Greek texts and Latin translations.]

Marquard, Paul. 1868. _Die Harmonischen Fragmente des Aristoxenus_ Greek text and German translation. With critical notes and explanatory commentary. Berlin.

Westphal, H. 1883 (volume 1), 1893 (volume 2). _Aristoxenos von Tarent: Melik und Rhythmik des Classischen Hellenentums_. Translated and explained. [Attempted reconstruction of Aristoxenus's alleged original work] Leipzig. Reprint: 1965, Georg Olms Verlagsbuchhandlung Hildesheim.

Macran, Henry Stewart. 1902. _The Harmonics of Aristonexus_. Edited with translation, notes, introduction, and index of words. Clarendon Press, Oxford. Reprinted 1974, Hildesheim; New York: G. Olms Verlag. [Contains complete English translation.]

Laloy, L. 1904. _Aristoxène de Tarente et la musique de l'Antiquité_. (Includes _Lexique d'Aristoxène_.) Paris.

Strunk, Oliver. 1950. _Source Readings in Music History_. Selected and annotated [and translated]. W. W. Norton. New York. [English translation of Cleonides on p 34-46.]

da Rios, R. 1954. _Aristoxeni Elementa harmonica_, edited. Rome. [Includes Latin introduction and Italian translation.] [Text of Aristoxenus used by Barker 1989.]

Crocker, Richard L. 1966. 'Aristoxenus and Greek Mathematics'. In _Aspects of Medieval and Renaissance Music: A Birthday Offering to Gustave Reese_. Ed. Jan LaRue. W. W. Norton, New York. p 96-110.

Burkert, Walter. 1972. _Lore and Science in Ancient Pythagoreanism_. English translation by Edwin L. Minar, Jr. Cambridge, Harvard University Press. (original German edition 1962)

Mathiesen, Thomas J. 1976. 'Problems of Terminology in Ancient Greek Theory: `APMONIA', in _Festival Essays for Pauline Alderman: a musicological tribute_. Ed. Burton L. Karson. Brigham Young University Press; Provo, Utah. p 3-17.

Barker, Andrew. 1978. 'Music and Perception: A Study in Aristoxenus'. _Journal of Hellenistic Studies_, v 98, p 9-16.

Litchfield, Malcolm. 1988. 'Aristoxenus and Empiricism: A Reevalutation Based on his Theories'. _Journal of Music Theory_, v 32 # 1, p 51-73.

Barker, Andrew. 1989. _Greek Musical Writings_, volume 1: volume 2: 'Harmonic and Acoustic Theory'. Translated and edited. Cambridge University Press, New York. [Contains complete English translation of Aristoxenus _Elementa harmonica_ in vol 2, p 126-184.]

Bower, Calvin M. 1989. Boethius: _Fundamentals of Music_. English translation of Boethius. Yale University Press, New Haven.

Landels, John G. 1999. _Music in ancient Greece and Rome_. Routledge, London and New York.

concerning observations on the change of preference from the enharmonic genus to the chromatic, see: yahoo tuning group, message 6947 [Wed Dec 15, 1999 6:46 pm].

[1.25.26-30]
> He de barytate diatonos ... epi men gar ten tou hemioliou chromatos
> lichanon | hemitonion en ap' autes,
>
>> The lowest diatonic _lichanos_ ... is a semitone from the _lichanos_
>> of the hemiolic chromatic

[2.51.29] syntonou de,
> en he to men hypates kai pa-[30]rypates hemitoniaion;
> ton de loipon to-[31]niaion hekateron estin.
>
>> [2.51.29] [The division] of the tense diatonic is that
>> in which the interval between _hypate_ and [30] _parhypate_ is a semitone,
>> and each of the others [31] is a tone.

[2.51.11 ...] Mechri men oun tautes tes di-[12]aipeseos > amphoteroi kinountai hoi phthon-[13]goi. > meta tauta d' he men parypate me-[14]nei; > dieleluthe gar ton hautes topon; > he de [15] lichanos kineitai diesin enarmonion. > kai [16] gignetai to lichanou kai hypates > diaste-[17]ma ison toi lichanou kai meses. > hoste me-[18]keti gignesthai pyknon en tautei tei diai-[19]pesei. > symbainei d' hama payesthai to py-[20]knon, > synistamenon en tei ton tetrachor-[21]don diairesei > kai archesthai gignomenon to [22] diatonon genos. > >> [2.51.11 ...] Up to [the tonic chromatic] division, >> [12] both the notes [_lichanos_ and _parhypate_] move, >> [13] but after this _parhypate_ stays still, >> [14] since it has travelled through its whole range, >> while [15] _lichanos_ moves through an enharmonic diesis, >> and [16] the interval between _lichanos_ and _hypate_ >> [17] becomes equal to that between _lichanos_ and _mese_, >> so that [18] in this division the _pyknon_ no longer occurs. >> [19] The _pyknon_ disappears [20] in the division of the tetrachord [21] simultaneously >> with the first occurrence of the [22] diatonic genus.

> [2.51.24 ...] malakou men oun esti diatonou diai-[25]pesis, > en he to men hypates kai parypa-[26]tes hemitoniaion esti; > to de parypates kai [27] lichanou trion dieseon enarmonion; > [28] to de lichanou kai meses, pente dieseon. > >> [2.51.24 ...] The division of the soft diatonic is that >> [25] in which the interval between _hypate_ and _parhypate_ [26] is a semitone, >> that between _parhypate_ and [27] _lichanos_ is three enharmonic dieses, >> and [28] that between _lichanos_ and _mese_ is five dieses.

[1.25.26-30]
> He de barytate diatonos ... epi men gar ten tou hemioliou chromatos
> lichanon | hemitonion en ap' autes,
>
>> The lowest diatonic _lichanos_ ... is a semitone from the _lichanos_
>> of the hemiolic chromatic

[1.24.28-30] > pempton de pros toi autoi, to ex hemitoniou kai hemioliou > diastem|matos synestekos systema eilephtho; > >> fifthly, from the same note [_hypate_] take the _systema_ composed >> of a semitone and an interval one and a half times as great, ...

[1.25.26-28] > He de barytate diatonos tes barytates chromatikos hemitonioi > kai dodekatemorioi tonou oxytera estin. > >> The lowest diatonic _lichanos_ is higher than the lowest chromatic >> by a semitone and a twelfth part of a tone.

[1.25.30-31]
> apo de tes hemioliou epi ten enarmonion diesis,
>
>> from the _lichanos_ of the hemiolic chromatic ... to the enharmonic
>> _lichanos_ is a diesis ...

> [2.51.1 ...] hemioliou de chromatos di-[2]aipesis estin, > en he to te pyknon hemiolion [3] esti, tou [t'] enarmoniou, > kai ton dieseon heka-[4]teras ton enarmonion. > >> [2.51.1 ...] The division of the hemiolic chromatic [2] is that >> in which the _pyknon_ is one and a half times [3] that of the enharmonic, >> and each of its dieses is [4] one and a half times the corresponding enharmonic diesis.

And again, extracting from the more elaborate phrase previously quoted, that which is relevant to this genus:

[2.51.4-7] > the hemiolic _pyknon_ ... falls short of being a tone by > an enharmonic diesis