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On the Horizontal and Vertical Presentation of Musical Ideas and on Musical Space (II)

Published online by Cambridge University Press:  04 February 2010

Regina Busch
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Extract

The difficulties connected with the idea of synthesis do not originate with the fact that as soon as he starts to elucidate the laws that have been formulated in general terms, Schoenberg postulates a musical space that only has two dimensions, the horizontal and the vertical. The scientific origin of these concepts could tempt one to think of this space (strictly geometrically) as a plane surface, and then to imagine it as comprising the paper on which music is notated, the dimensions then comprising the directions of the notation itself or of reading. But this is not yet musical space, and only if one tries to imagine a synthesis on this plane surface does one tend towards the concept of a diagonal. The inadequacy of the ‘diagonal’ seems to have been sensed by those authors who directed attention to the temporal aspect of music and who (perhaps by a popularizing analogy with the idea of time as the fourth dimension) attempted to locate the synthesis within the domain of ‘time’—say, the rhythmic domain. Schoenberg—and Webern followed him in this—distinguishes with terminological exactitude: wherever vertical and horizontal appear as concepts on their own, the explanation is always added: ‘The elements of a musical idea are partly incorporated in the horizontal plane as successive sounds and partly in the vertical plane as simultaneous sounds’; or: ‘In accordance with this [law], harmony and melody, vertical and horizontal, form a musical unit, a space, in both of whose dimensions the musical substance is deposited’, and similarly in the draft for the Princeton lecture. The conception of the dimensions of musical space is therefore connected with ‘harmony and melody’—without ‘vertical’ and ‘harmony’, or ‘horizontal’ and ‘melody’, thereby being identical. But how do matters stand on this plane with the ‘unit(y)’ that primarily interested Schoenberg and with the ‘synthesis’ upon which Webern apparently directed his attention?

Type
Research Article
Information
Tempo , Issue 156 , March 1986 , pp. 7 - 15
Copyright
Copyright © Cambridge University Press 1986

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References

31 ‘Composition with Twelve Tones (1)’, Style and Idea, p.220. The word ‘plane’ is not represented in the original German text (‘… in the horizontal as …’, etc.); Regina Busch has pointed out that its introduction into Schoenberg's English version is both surprising and revealing

32 ‘Discussion on the Berlin radio’, Cesammelle Sdirifien, p. 277f.—M.G.translation.

33 Perspectives of New Music, Fall—Winter 1974, pp. 82–3.

34 Style and Idea, loc cit.

35 Perspectives, loc. cit.

36 ‘Einheit (lichkeit)’.

37 Perspectives, loc. cit. The translation is mine. The following is Claudio Spies's elegant but somewhat free translation as printed in Perspectives: ‘whereby the vertical and the horizontal, harmonic and melodic, the simultaneous and the successive were all in reality comprised within one unified space. It followed from this that whatever occurs at one point in that space, occurs not only there but in every dimensional aspect of the spatial continuum, so that any particular melodic motion—for instance, a chromatic step—will not only have its effect upon the harmony, but on everything subsequent that is comprised within that spatial continuum.’ The word ‘einheitlich(en)’, translated by Spies as ‘unified’ (hence my phrase ‘unified nature’ above), does not carry the English implication of the subsequent unification of initially disparate elements; rather, it carries the connotations ‘unitary’, ‘uniform’, ‘of a single essence throughout’—M.G.

38 Loc. cit.; my translation. Claudio Spies's version is as follows: ‘This circumstance, moreover, especially enables the composer to assign one part of his thinking to—or to store part of his thinking in—the vertical, and another in the horizontal domain.’ Note ‘ab(zu)lagern’ = to deposit (as in geology), to lay down (in a storage space); ‘Gedanken’ = literally ‘thought’, but in the context of the present discussion, Schoenberg clearly means his musical idea (cf. the title of the present paper), not his ‘thinking’ in the general or philosophical senses—M.G.

39 ‘Zusammenhang’: coherence, cohesion, connexion, continuity.

40 Stephan, Rudolf, ‘Der musikalische Gedanke bei Schonberg’, Osterreichische Musikzeitschrift 37 (1982), pp. 530–540 Google Scholar.

41 ‘abgelagcrt’: see footnote 38.

42 ‘Composition with Twelve Tones (1)’, Style and Idea, p. 220.

43 ‘1= scale’—Claudio Spies's footnote. This implication is not found in Schoenberg's text: ‘key’ implies hierarchical relationships not implied by ‘scale’.

44 Perspectives, loc. cit., pp. 86–7. The words up to ‘diatonic scale’ are Claudio Spies's translation of Schoenberg's German text. From ‘For always’ onwards, however, Schoenberg's own English version exists alongside his German, and it is this that appears above and in Perspectives. In the sentence translated by Spies, Schoenberg's German text does not refer to ‘the diatonic scale’, but merely to ‘the scale’. More importantly, ‘Gesetzmassigkeit’ could be translated ‘laws to which to conform’ rather than ‘legitimacy’. In the second sentence quoted above, Schoenberg's original German has ‘in the earlier music’, the words ‘the earlier’ being omitted in Schoenberg's own English translation, though they are partly implied by ‘always’—M.G.

45 Halm, August, Beethoven (Berlin, 1927 Google Scholar; facsimile reprint Darmstadt, 1971), p. 92—M.G. translation.

46 ‘Vorstellungen’.

47 ‘Begriffe’.

48 ‘Raum’: Schoenberg means ‘upper region’, i.e. the region occupied by the topmost voice in a texture in which the upper voice predominates—M.G.

49 ‘Neueund veraltete Musik, oder Stil und Gedanke’ is published as an appendix to Schoenberg, Arnold, Gedanke, Stil und (= Gesammelte Schrijlen 1), ed. Vojtech, Ivan (Frankfurt, 1976), pp. 466—477. The foregoing quotations (from pp. 4660 have been translated by Michael Graubart. Readers are referred to the detailed commentary in this appendix for the complex history of this text, which is a revision of a lecture delivered in Prague in 1930, founded upon many other writings going back as far as 1923. Schoenberg's subsequent English version, after further revisions, was published in the 1950 Style and Idea; a German translation of this is included in the main text of Gesammelte Schrijten. (Ed.)Google Scholar

50 ‘Erfassung’: this word can also mean ‘comprehension’—M.G.

51 ‘Tonbereich’. This can also mean ‘domain of notes’ or—more generally—‘domain of sound’—M.G. (Leo Black's translation in The Path to the New Music, ‘tonal field’, is even less happy. Regina Busch maintains that ‘note’ or ‘tone’ is in this context a better translation than ‘pitch’, and that Webern's use of Ton here is in any case an allusion to Schoenberg's famous sentence in Harmonielehrr. ‘Der Ton ist das Material der Musik’. The official English translation— Theory of Harmony trs. Carter, Roy E. (London: Faber, 1978), p. 19 Google Scholar—renders this as ‘The material of music is the tone’.—Ed.)

52 Translations of this and following extracts by M.G.

53 ‘Ton’: see note 51.

54 Guido Adler, Der Stil in der Musik (Style in Music), Leipzig, 1911.

55 Children's song.

55 Children's song.

56 Mathematically speaking, Schoenberg understates his case here. The number of n-note melodies that can be made from a 12-note scale is 12n−1 (if transpositions of the same melody are not considered to be different melodies); the number of combinations of two n-note melodies in counterpoint (similarly not counting transpositions of the whole structure as different, but taking account of the 12 different possible intervals between the starting notes of the two lines) is, therefore, 12n−1 x 12n. The number of n-note melodies that can be made from a 24—note scale is 24n−1, which equals 12n−1 x 2n−1, or 12n−1 x ½(2n). Since ½(2n) is always (much!) smaller than 12n if n is equal to or greater than 1, it follows that the number of ideas derived from a 12-note scale and presented in 2-part counterpoint with one another is very much greater than (not equal to, as Schoenberg says) the number of monophonic n-note melodies that can be derived from a 24–note scale.—M.G.

57 M.G. translation.

58 ‘Festigung’: making firm, solid or compact; settling, establishing, confirming, etc.

59 Musikpsychologie (Psychology of Music), 1930; Voraussetzungen der theoretischen Harmonik (Bases of Theoretical Harmony), 1913.

60 Musikpsychologie, p. 294 (of the 1947 edition).

61 Ibid., p. 122—M.G. translation.

62 Cf. Frobenius's, Wolf article ‘Polyphon und polyodisch’ in Handwörterbuch der musikatischen Termiuologie ed. Eggebrecht, Hans Heinrich (Wiesbaden, 1980)Google Scholar.

63 Vischer, Friedrich Theodor, Aesthetik oder Wissenschaft des Schönen (III. Theil. Die Kunstlehre. 2. Abschnitt: ie Kunste. 4. Heft: Die Musik) (Stuttgart, 1857) p.939 Google Scholar.