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Abstract
The climax of the chorus ‘The Heavens are Telling’ from Haydn’s oratorio Die Schöpfung (The Creation) employs a harmonic progression that Beethoven later adapted to conclude the first movement of his Symphony no. 2. An earlier (pre-Haydn) version of the progression might be found in a keyboard rondo by C. P. E. Bach. This harmonic unit is regarded as consisting of a sequence of musemes (musical memes): each is a replicated pattern serving as the cultural analogue to the gene. The neural encoding of such patterns is considered in terms of William Calvin’s hexagonal cloning theory, in order to adduce ‘memotypic’ (meme-encoding) evidence to support the ‘phemotypic’ (meme-product) evidence gleaned from musical score-analysis.
Notes
1 I employ this term, after Tagg’s somewhat different use (Tagg 1999, 32), as a contraction of ‘musical meme’. My coining here of several mus-prefixed and gene-derived neologisms stems not from a desire for obfuscation, or from a wish to pour old wine into new bottles; rather, it is grounded in a belief that the expansion of conceptual horizons is often best served by new terminology.
2 Although my case study here draws exclusively from the western musical canon, it should be clear from the foregoing that this is not be taken to indicate that only this repertoire conforms to the precepts of memetics. Although constraints of space prevent my offering evidence, it is my contention that all human culture, including non-western musics, are subject to its claims. Indeed, were this not the case, then memetics would be invalidated, for it could not logically encompass only part of human culture.
3 ‘Die Himmel erzählen die Ehre Gottes, und seiner Hände Werk zeigt an das Firmament’/‘The heavens proclaim the glory of God, and the labour of his hands is shown in the firmament’.
4 One might question Temperley’s use of the term ‘modulations’, for even the most reluctant Schenkerian prolongationist or Schoenbergian monotonalist might readily concede that both passages represent circular chromatic motion within a firmly established key area — treading water, rather than swimming the Channel.
5 See also (Tovey 1981, Exx. 11a, 11b, p. 368). The figured bass and Roman numeral notation in Example 1 iii and v reinterpret certain pitches enharmonically in order to clarify the similarities and recurrences in the harmonic sequences. Some symbology in Example 1 v is after (Russ 2007, Example 1, p. 113). See (Jan 2007, 49–52), for an explanation of the musemic analysis symbols.
6 Significant differences between the passages are indicated by appending the museme’s letter designations in Beethoven with a following numeral (b1, c1, etc.). Museme components are also labelled in Example 1 i, ii, iii, v and vi, as b/1, c1/2, etc.
7 In the P[ermutation]m,n symbology, the number of perturbations by semitonal motion is represented by m and the number of perturbations by whole-tone motion is represented by n. When two pitches are moved, c and s represent contrary and similar motion respectively.
8 Nevertheless, in contrast to this view, it is clear that both Haydn and Beethoven use a somewhat generic tutti texture here, lacking any real melodic identity.
9 One might speculate that motor-kinaesthetic representations (the hand on the piano keyboard, shifting some fingers while holding others) might have been prevalent. As Russ’s article makes clear, there is no shortage of examples of Pm,n-based passages in the literature of the nineteenth century. His Example 10 (132) shows the closest perturbation structure to that represented in Example 1 vi, a passage from Chopin’s Mazurka op. 68 no. 4 (?1846), in which a P2s,0–P1,0 progression occurs in bb. 4–5.
10 Constraints of space and the fear of infinite regress prevent my exploring antecedent coindexes for Bach’s passage, or indeed consequent coindexes of Beethoven’s passage. Often highly rewarding when conducted manually, such exploration can be facilitated by computer-aided pattern searching (Cope 2003; Jan 2004; Conklin and Anagnostopoulou 2006; Lartillot and Toiviainen 2007), which arguably offers the only practical means of gathering the type of wider evidence referred to in note 2.
11 After (Kramer 1985, Example 8b, p. 576). Errors of bar numeration in this source are corrected here; and the vertical dotted lines indicate textural changes. Studies have examined the nature of C. P. E. Bach’s modulations and their relationship to contemporary music theory. See (Mitchell 1970; Kramer 1985; and Ferris 2000).
12 In making such determinations, it is important to bear in mind the issue of the units of selection, which stipulates that one should look for the smallest indivisible units (Pocklington and Best 1997). I contend that, whereas at least three sequential pitches are required for a pattern to function as a melodic museme, at least two chords (minimally four to six pitches) are required for harmonic musemes (Jan 2007, 61).
13 As with the Haydn and Beethoven passages, Bach’s progression is situated at the shallow-middleground level. To a greater extent than its evolutionary derivatives, Bach’s is animated (strictly, generated) by distinct foreground-level musemes.
14 By analogy with gene-alleles, a museme-allele is a rival but (functionally/structurally) analogous form of a museme (Jan 2007, 137). Mutant forms of musemes may function as alleles of their antecedents, such as is the case with Musemes d and d1.
15 See (Johnson, Tyson, and Winter 1985) for a comprehensive overview.
16 For a list of ‘sketchbooks in facsimile, or in complete or substantial transcription’, see (Kerman 2010, Bibliography, Section I (ii)).
17 Categorizations are from (Mikulicz 1972, 28). Pages 23–4 of Landsberg 7 are missing. Underlined page numbers in (Mikulicz 1972), starting at p. 25, represent the original numbering sequence.
18 The minicolumnar grid upon which the triangular arrays are placed in this figure, wherein raised circles represent minicolumns, is taken from http://williamcalvin.com/Demo2.htm (accessed 22 March 2012).
19 Pitch designations here use the Helmholtz system, where c is one octave below (middle) c1 and c2 is one octave above.
20 ‘This game is played on a tall rod-studded surface that is almost upright, and it is played with discs that are dropped one at a time from a position above the multi-rodded surface. Each disc falls (by gravity) and bounces off the rods in its path until it reaches the bottom and drops into one of nine receptacles’ (Fremantle 2012).
21 I somewhat skirt around the issue of conscious choice in memetic replication here. While it appears clear that Beethoven’s replication of Haydn’s musemes was intentional (in the sense that Beethoven was aware of the specific source of his material), it is difficult to prove that the same is true for Haydn’s apparent use of C. P. E. Bach’s material. From the ‘memes’ eye view’ (Blackmore 2000) this is probably insignificant; and if one subscribes to Dennett’s atomistic, memetic view of consciousness (Dennett 1993), the problem ultimately dissolves.
22 This segmentation and grouping is largely accomplished before information reaches the cerebral cortex [at the level of ‘echoic memory’, ‘feature extraction’, and ‘perceptual binding’ (Snyder 2000, 6)], and is therefore not specifically encompassed by the HCT — although hexagons embedded in the connectivity can favour one of two or more ambiguous segmentations of incoming data, the coindexation-determined segmentation noted in Section 2·2 (see also Snyder 2000, 32–3).
23 Figure 2, as with Example 1, represents another simplification, in that the passages are in two different keys. The tendency of most listeners to represent music using relative pitch (via encoding of scale-degree and intervallic sequence) rather than absolute pitch suggests an additional level of abstraction/translation, not shown here.
24 See also the animated simulation at http://williamcalvin.com/Demo3.htm (accessed 22 March 2012).
Additional information
Notes on contributors
Steven Jan
Before joining the Music Department at the University of Huddersfield in January 2001, where he is currently Senior Lecturer, Steven Jan taught at the University of East Anglia and in the School of Academic Studies at the Royal Northern College of Music, Manchester. His research interests concern the application to music of theoretical and analytical perspectives drawn from evolutionary theory, particularly the meme paradigm, and the use of computers to expedite such investigations. His The Memetics of Music: A Neo-Darwinian View of Musical Structure and Culture was published in 2007 by Ashgate, and he has contributed articles to Music Analysis, the International Journal of Musicology, the Journal of the Royal Musical Association, Computer Music Journal, Musicae Scientiae, and Music Theory Online.
Correspondence to: Steven Jan, Department of Music and Drama, Creative Arts Building, The University of Huddersfield, Queensgate, Huddersfield HD1 3DH, UK. Email: [email protected].