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Towards A Metamusic

Published online by Cambridge University Press:  04 February 2010

Iannis Xenakis
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Extract

Today's technocrats and their followers treat music as a message which the composer (source) sends to a listener (receiver). In this way they believe that the solution to the problem of the nature of music and of the arts in general lies in formulae taken from information theory. Drawing up an account of bits or quanta of information transmitted and received would thus seem to provide them with ‘objective’ and scientific criteria of aesthetic value. Yet apart from elementary statistical recipes this theory—which is valuable for technological communications—has proved incapable of giving the characteristics of aesthetic value even for a simple melody of J. S. Bach. Identifications of music with message, with communication and with language are schematisations whose tendency is towards absurdities and desiccations. Certain African tom-toms cannot be included in this criticism, but these are exceptional. Hazy music cannot be forced into too precise a theoretical mould. It may be possible later, when present theories have been refined and new ones invented.

Type
Research Article
Information
Tempo , Issue 93 , Summer 1970 , pp. 2 - 19
Copyright
Copyright © Cambridge University Press 1970

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References

1 Cf. Graresaner Blatter, No. 29, ed. H. Scherchen, Gravesano, Tessin, Switzerland.

2 Cf. Gravesanet Blatter, Nos. 1 & 6, and the scores of Metastaseis (1954) and Pithoprakta (1956) (Boosey & Hawkes) recorded on Chant du Monde LDX A 8368, and Cardinal. See also sketches, designs and texts in my fiverecord album by Erato, Paris (1969). Pithoprakta is also recorded on Nonesuch H 71201.

3 We are not here concerned with quarter-tone and sixth-tone music as currently practised, for these remain within the same tonal-diatonic field.

4 Cf. My book Musiques Formelles, ch.V (Richard-Masse, Paris).

5 Tinctoris, Johannis, Terminorum Musicae Diffinitorium (Richard-Masse, Paris)Google Scholar.

6 ‘Le mythe des modes grecs’, Chailley, Jacques, in Acta Musicologica vol. XXVIII, fasc. IV, 1956 (Barenreiter Verlag, Basel)Google Scholar.

7 Aristoxenos von Tarent, Melik and Rhythmik, Westphal, R., Leipzig, 1893 Google Scholar, (Verlag von Ambr. Abel (Arthur Meiner) German introduction, Greek text.)

8 Mathematiques by Guilbaud, G. Th., vol. 1, Presses Universitaires de France, 1963 Google Scholar.

9 Kointilianou, Aristidou, Peri Mousikes Proton, Teubner, Leipzig, 1963 Google Scholar.

10 The Aristoxenian scale appears to be one of the experimental versions of the ancient diatonic which corresponds to the theoretical versions neither of the Pythagoreans nor of the Aristoxenians: X.9/8. 9/8 = 4/3, 6 + 12 + 12 = 30 segments respectively. Archytas's version (X.7/8. 9/8 = 4/3) or that of Euclid are significant. On the other hand the so-called 'Zarlinian scale‘ is none other than the so-called ‘Aristoxenian scale’, which in fact goes back only as far as Ptolemy and Didymos.

11 Stichtodi Mathimata Byzantinis Ekklisiastikis Moustkis, Avraam Evthimiadis, O.X.A. Apostoliki Diakonia, Thessaloniki, 1948.

12 In Quintilian and Ptolemy the fourth is divided into 60 equal tempered segments.

13 In Westphal, op. cit. pp. XLVII Google Scholar etc. we have the formation of the tetrachord mentioned by Ptolemy: lichanos (16/15) - mese (9/8) - paramese (10/9) - trite (harmonics 2, 1 p. 49)

14 In Ptolemy the names of the chromatic tetrachords were reversed: the soft chromatic contained the interval 6/9 and the hard or syntonon the interval 7/6, cf. Westphal, , op.cit. p. XXXII Google Scholar.

15 Examples in Westphal, , op. cit. p. XLVIII Google Scholar, selidion 1, mixture of syntonon chromatic (22 : 21, 12 : 11, 7 : 6) and toniaion diatonic (28 : 27, 8 : 7, 9 : 8); selidion 2, mixture of soft diatonic (21 : 20, 10 : 9, 8 : 7) and toniaion diatonic (28 : 27, 8 : 7, 9 : 8); etc.

16 Wellesz, Egon, A History of Byzantine Music and Hymnography, O.U.P., 1961, p. 71 Google Scholar etc. On page 70 he too repeats the myth of the ancients' descending scales.

17 The same neglect can be found in the antiquising Hellenists, such as Laloy, Louis in the classic Aristoxense de Tarente, 1904, p. 249 Google Scholar etc.

18 Alain Daniélou went to live in India for a number of years and learnt to play Hindu instruments. The same goes for Mantle Hood with Indonesian music, and we should also mention Tan Van Khe, theoretician and composer practising traditional Vietnamese music, etc.

19 Cf. the author cited in fn.16, also the transcriptions by C. Hoeg, another eminent Byzantinist to have ignored the problems of structure, etc.

20 The ‘specialists’ were surprised to discover Byzantine script in the notation of Rumanian folk-music; see Rapports Complementaires du XIIe Congres International da Etudes Byzantines, Ochride, 1961, p. 76. Doubtless these specialists do not realise that an identical phenomenon exists in Greece.

21 Cf. My text to the record, published by Chant du Monde, LDX A 8368. See also Gravesaner Blatter, No. 29, La Revue d'Esthetique No. 2-3-4, 1969 (Librairie Klincksieck, Paris)Google Scholar and my book already cited.

1 A stop = a point in musical space-time (translator's note)

22 Elementary displacements are like whole numbers among themselves, in other words they are defined as the elements of one and the same axiomatics.

23 Daniélou, Alain, Northern Indian Music, Halcyon Press (Barnet), 1954, Vol. II, p. 72 Google Scholar.

24 This corresponds perhaps to Edgar Varese's wish for what he calls a spiralling scale = cycle of fifths not related to the octave. This information, sketchy though it unfortunately is, was given me by Odile Vivier.

25 These latter structures have been used in Akrata (1964), for 16 wind instruments (recorded on Nonesuch H 71201), in Nomos Alpha, for solo cello (1965), recorded on H.M.V., ASD 2441, and in Nomos Gamma for large orchestra (1968).