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Aristides Quintilianus and Constructions in Early Music Theory

Published online by Cambridge University Press:  11 February 2009

Andrew Barker
Andrew Barker
Affiliation:
University of Warwick
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Extract

Aristides Quintilianus' dates are not known, but he can hardly be earlier than the first century A.D. or later than the third. Several passages in the early pages of his deMusica1 purport to record facts about the practice of much older theorists, in contexts which make it clear that his references are to the period before Aristoxenus. Since our knowledge of music theory in that period is extremely sketchy, it is obviously worth trying to assess the reliability of Aristides' information. Two of his references have often been recognized as being of special interest, and there is a third, to which, I shall argue, the other two are intimately related. The first (12. 12 to the end of the diagram on 13) records two systems of notation, alleged by Aristides to have been used by oί ⋯ρχαîoι. The second (18. 5 to the end of the diagram on 20) is the famous, or notorious, account of certain ‘divisions of the tetrachord’ which were employed by oί π⋯νυαλαιότατoι πρ⋯ς ⋯ρμoνίας. It is these, Aristides tells us, which are mentioned by Plato in the Republic.2 The remaining passage (15. 8–20) is superficially rather less exciting: it records the names and initial notes of the ⋯ρμoνίαι, or forms of octave scale, said to have been distinguished by oί παλαιoί, and says something about a method by which the πoιότης of each can be made clear. The information given here about the nature of the ⋯ρμoνίαι is familiar: it is to be found, for example, in Cleonides Eisagoge 19. 4 ff., where rather more detail is given, and where the names of the ⋯ρμoνίαι are again ascribed to oί ⋯ρχαîoι (19. 7: cf. also ‘Bellerman's Anonymous’ 62). I shall suggest, however, that Aristides' version has independent interest. What he tells us in the first two passages is found nowhere else.

Type
Research Article
Information
The Classical Quarterly , Volume 32 , Issue 1 , May 1982 , pp. 184 - 197
Copyright
Copyright © The Classical Association1982

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References

1 The most recent edition is that of Winnington-Ingram (Teubner, Leipzig, 1963). All references to Aristides in this paper are to the pages and lines of that editon.

2 Rep. 398 e 2–399 a 4.

3 The details are discussed in Winnington-Ingram, R. P., Mode in Ancient Greek Music (Cambridge, 1936), pp. 21–30. See also the works referred to in his n. 2, 22.Google Scholar

4 A careful exposition of the differences between Pythagorean and Aristoxenian approaches to the expression of intervals will be found at Ptolemy, Harmonics, 1. 5 and 9 (11–12 and 19–21, During).

5 See e.g. the Euclidean Sectio Canonis, proposition 14.

6 Very frequently, e.g. lines 4–9, and throughout Bk. III.

7 Following the example set by Timaens 35bl-36d7. Cf. the qualified approval given to Pythagorean musical theory at Rep. 531 c 1-d 4, and Plato's contempt for their ‘empiricist’ rivals, 531a4-b9.

8 Named after Alypius (probably third century A.D.), whose Eisagoge sets out the tables of this notation in full. But its origin is certainly much earlier.

9 The ‘fixed’ notes (τ⋯ ⋯ρεμo**ντα, πθόγγoι ⋯κίυητoι, μένoντες) are those which do not change with changes of genus, and thus provide a constant framework within which variations may occur. The intervals between them are determinate, whereas those involving the ‘movable’ notes are flexible. See e.g. Aristoxenus, Harm. 21. 32 ff., 33. 32–4, 46. 19–23.

10 J. Chailley, ‘La notation archaïque grecque d'après Aristide Quintilien’, Revue des Etudes grecques 86 (1973), 17–34. More briefly in his La Musique Grecque Antique (Paris, 1979), 121–5: see especially 123, n. 2.Google Scholar

11 Aristoxenus 2. 7–25. Aristides is not explicit on this point.

12 See the edition of R. da Rios (Rome, 1954), app. crit. to 46. 9, and her translation, p. 53, n. 2. Chailley's proposal (op. cit. p. 38) to retain the MSS reading runs into difficulties which I shall discuss later.

13 Asserted by e.g. Nicomachus, Enchiridion 9; cf. Aristides Quintilianus 15.8–10, Plato, Rep. 617b6–7. But there is some vacillation about this: cf. Aristotle, Metaph. 1093a 14. The supposedly older heptachord scales were at least sometimes called ρμoνίαι, e.g. in ps.-Ar. Problems, 19. 7,918 a 13, and 25.919 b 21. The divisions of Aristides Quintilianus 18–20 constitute another kind of exception (see 18. 6, 19. 8).

14 The Harmonics of Aristoxenus ed. Macran, H. S. (Oxford, 1902), pp. 229–32. What I shall call his ‘reconstruction’ is constituted by the tables of notes on 231.Google Scholar

15 By Ruelle, following Meibom's note. See da Rios op. cit., app. crit. to 36. 5–6.

16 He argues that they have not discussed the question whether bifurcation of the series may take place after just any form of the (enharmonic) fourth (e.g. q, d, q) or only after one privileged form (this will be q, q, d). Various propositions in Bk. III seem expressly designed to fill this gap, and to prove the impropriety of disjunction after any other arrangement of the fourth (see 65. 30–66. 8, 66. 9–17, 71. 23–72. 11). But Aristoxenus does not say, and almost certainly does not mean, that the Eratocleans posited disjunction at any points which he himself does not recognize: he means that they have omitted to show why such rogue disjunctions are impermissible.

17 Ptolemy, Harmonics 2. 5 (51, During). On the importance of relations between mesai cf. Cleonides, Eisagoge 23. 14 ff.

18 Macran, op. cit. pp. 262–6. See also Cleonides 26. 19 ff. and Aristides Quintilianus 22. 11–26.

19 Macran, op. cit. p. 266.

20 The notes of the conjunct versions of these harmoniai will be as follows: Mixolydian, 6, 7, 8, 16, 17, 18, 26; Lydian. 5, 6, 14, 15, 16, 24, 25; Phrygian, 4, 12, 13, 14, 22, 23, 24; Dorian, 3, 4, 5, 13, 14, 15, 23; Hypolydian, 2, 3, 11, 12, 13, 21, 22; Hypophrygian, 1, 9, 10, 11, 19, 20, 21; Hypodorian, 0, 1, 2, 10, 11, 12, 20. Thus 10 and 20 are supplied by Hypophrygian and Hypodorian, 21 by Hypolydian and Hypophrygian.

21 The only seven-note scales generally referred to are those of the conjunct system, spanning five tones. The alleged innovator who ‘added the eighth note’ is commonly thought of as thereby completing the octave. See e.g. Nicomachus, Enchiridion 5. The main exception is ps.-Ar. Problems 19. 32, 920a 14–18; cf. 7, 918a 13–18 and 47, 922b3–9, which display some uncertainty on the matter. But the ⋯ρμoνίαι to which these passages refer are evidently thought of as much older than any which are our present concern.

22 The closest analogy is provided by Ptolemy's limitation of the τόνoι to seven, ruling out repetition at the octave (2. 8). But his argument is evidently a new one: in the thirteen Aristoxenian τόνoι the last is at an octave from the first (Cleonidcs 25. 4–26. 15).

23 cf. Aristoxenus 34. 8–11.

24 Aristoxenus 7. 10–8. 3.

25 Cleonides loc. cit. Cf. Aristoxenus 7. 23, 37. 8–38. 5.

26 Aristoxenus 7. 10–8. 3.

27 The importance of this for the character of the melody is emphasized at 7. 13–16. It is arguable that in this respect Aristoxenus is claiming for his τόνoι some of the ethical significance earlier assigned, as Aristides Quintilianus (15.19–20) and many others tell us, to the old ⋯ρμoνίαι He seems, however, to have avoided the wilder excesses of certain versions of this theory (cf. 31. 16–29).

28 I have argued this in ‘ oί καλo⋯μευoι ⋯ρμoνικoί: the predecessors of Aristoxenus', Proceedings of the Cambridge Philological Society n.s. 24 (1978), 1–21, especially 15–17.

29 67. 10–25.

30 Plato, Rep. 531 a4-b 1 comments on the pursuit of the least interval. Cf. Aristotle, Metaph. 1016b 18, 1052b20, 1083b33. Contrast Aristoxenus' implication that theoretically (not melodically) speaking there can be no least interval, 15. 7–12.

31 Macran, op. cit. pp. 252–3.

32 On their failure to give demonstrations see especially 32. 27–31. For his criticism of the thesis that the aim of harmonics is notation see 39. 4–41. 24.

33 The New Oxford History of Music, vol. I ed. Wellesz, E. (London, 1957), 349 n. 4.Google Scholar

34 This paper has not attempted to give a general account of the ancient harmoniai and their development. The subject is difficult and controversial. For a select bibliography see Michaelides, S., The Music of Ancient Greece, An Encyclopaedia (London, 1978), pp. 128–9.Google Scholar