Hostname: page-component-5db58dd55d-688nx Total loading time: 0 Render date: 2026-06-06T21:57:11.737Z Has data issue: false hasContentIssue false
  • English
  • Français

DIAHEMITONIC MODALITY: A QUARTER-TONAL COMPOSITION SYSTEM

Published online by Cambridge University Press:  01 September 2023

Simon Kaplan
Get access

Abstract

This article describes a design process for a composition system based upon the quarter-tone scale. As the semitone and quarter-tone scales share the same properties, a musical grammar based upon the former is used as a model to construct an analogous musical grammar based upon the latter. Within the scope of diatonic modal music, the organisation of pitches and durations is analysed from a scientific perspective. Several parameters are taken into consideration: scale, mode, chord, cadence, metre and rhythm. The one-to-one mapping of each facet of diatonic modality onto quarter-tonality results in diahemitonic modality.

Information

Type
RESEARCH ARTICLE
Information
Tempo , Volume 77 , Issue 306 , October 2023 , pp. 69 - 92
Check for updates
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1 Coined from the ancient Greek diahemitonikos, meaning ‘of semitones passed through (the heptachords)’ (from dia, ‘through’, + hemisys, ‘half’, + tonos, ‘tone’, + -ikos, ‘-ic’), upon the model of ‘diatonic’.

2 Coined from the ancient Greek hendekatonikos, meaning ‘of 11 tones’ (from hendeka, ‘11’, + tonos, ‘tone’, + -ikos, ‘-ic’), upon the model of ‘pentatonic’.

3 Wyschnegradsky, Ivan, Manual of Quarter-Tone Harmony, tr. Kaplan, Rosalie (New York: Underwolf, 2017), pp. 19–23Google Scholar.

4 Jedrzejewski, Franck, Dictionnaire des musiques microtonales, new revised and expanded edition (Paris: L'Harmattan, 2014), pp. 60–62Google Scholar.

5 d'Indy, Vincent, Cours de composition musicale, premier livre (Paris: Durand, 1912), pp. 91–106Google Scholar.

6 Ruland, Heiner, Expanding Tonal Awareness: A Musical Exploration of the Evolution of Consciousness – from Ancient Tone Systems to New Tonalities – Guided by the Monochord, tr. Logan, John F. (Forest Row: Rudolf Steiner, 2014), pp. 44–46Google Scholar.

7 Cowell, Henry, New Musical Resources (New York: Alfred A. Knopf, 1930; New York: Cambridge University Press, 1996), pp. 45–81Google Scholar. This reference is to the Cambridge edition.

8 Coined from the Latin octansdesesquialter, meaning ‘(in the ratio) of (one) and three-eighths (elements) to the other’ (from octans, ‘eighth’, + de, ‘off’, + semis, ‘half’, + -que, ‘and’, + alter, ‘other’), upon the model of ‘sesquialtera’.

9 Coined from the ancient Greek triogdoolios, meaning ‘(in the ratio) of the whole and three-eighths (to the whole)’ (from treis, ‘three’, + ogdoos, ‘eighth’, + holos, ‘whole’), upon the model of ‘hemiola’.

10 Emmanuel Bach, Carl Phillip, Essay on the True Art of Playing Keyboard Instruments, tr. Mitchell, William J. (New York: W. W. Norton, 1948), pp. 87–99Google Scholar; Quantz, Johann Joachim, On Playing the Flute, tr. Reilly, Edward R., 2nd edition (London: Faber & Faber, 2001), pp. 91–100Google Scholar.

11 Bach, Essay on the True Art, pp. 87–99; Quantz, On Playing the Flute, pp. 91–100.