Abstract
As mentioned in the introduction, the perhaps defining feature of the etudes of Book 3 is the restricting of the gamut of PCs used at any one time, as opposed to the freer chromatic saturation of his previous piano etudes. There is perhaps no more radical example of this than Etude 15, White on White, which for the majority of its duration does not stray at all from the white-note set—and the few black notes that do appear towards the end of the piece come across as specks of pepper in a sea of salt.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
Namely, as opposed to Tymoczko’s use—see the discussion on page 21.
- 3.
Many of the graphs are shown in landscape orientation for better readability, where these axes are thus flipped at 90°.
- 4.
Letters for sets with vertical bars around them (i.e. |S| and |Sn|) represent the cardinality of those sets/subsets.
- 5.
When using radians, 2π = 360°, meaning that 30° = π/6.
- 6.
This is also explained, though in somewhat different terms, by Quinn’s Multiplication Principle: “on Fourier Balance n, the PC p is located at (n*p) o’clock, where n and p are integers modulo 12 and should be multiplied accordingly” (Quinn 2007, 36).
References
Sources
Browne, R. 1981. Tonal Implications of the Diatonic Set. In Theory Only. 5: 3–12.
Clough, J. 1979. Aspects of Diatonic Sets. Journal of Music Theory. 23: 45–61.
Egmond, R. and D. Butler, 1997. Diatonic Connotations of Pitch Class Sets. Music Perception: An Interdisciplinary Journal. Vol. 15 No. 1: 1–29.
Gauldin, R. 1983. The Cycle-7 Complex: Relations of Diatonic Set Theory to the Evolution of Ancient Tonal Systems. Music Theory Spectrum. 5: 39–55.
Quinn, I. 2007. General Equal-Tempered Harmony: Parts 2 and 3. Perspectives of New Music. Vol. 25 No. 1 (Winter): 4–63.
Santa, M. 2000. Analyzing Post-Tonal Music: A Modulo 7 Perspective. Music Analysis. Vol. 19 No. 2 (July): 167–201.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Namoradze, N. (2022). Alternating Diatonic Qualities in Etude 15, White on White. In: Ligeti’s Macroharmonies . Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-030-85694-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-85694-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-85693-9
Online ISBN: 978-3-030-85694-6
eBook Packages: Computer ScienceComputer Science (R0)