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  • Marc Sabat

This article explores the use of innovatory tonal relations in the music of the American composer Ben Johnston (b. 1926). Johnston's use of a microtonal tuning system employing scales and intervals in extended just intonation is described, and passages from several of his compositions (especially String Quartets nos 2 and 5) are analysed to show the use of these pitch resources in practice. The article also situates Johnston's contribution in the context of older theories of harmony and the mechanics of pitch perception.

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1 Johnston, BenOn Bridge-Building’ (1977), in Maximum Clarity and Other Writings on Music, ed. Gilmore, Bob (Urbana and Chicago: University of Illinois Press, 2006), p. 147.

2 Ben, Johnston, ‘Without Improvement’ (1995), in Maximum Clarity and Other Writings on Music, p. 168.

3 Equal ‘tempered’ semitones are defined as the irrational frequency proportion (1:12√2), which may be combined to approximate the most common rational intervals within varying degrees of tolerance. Most significantly, the perfect fifth (3:2) and perfect fourth (4:3) are represented to within a small degree of error, measuring approximately 1/600 of an octave (2:1).

4 The Tierce de Picardie and the chromatic alteration of sixth and seventh degrees in minor are clear indications that a completely symmetric understanding would be incomplete.

5 Hauptmann, Moritz, Die Natur der Harmonik und der Metrik zur Theorie der Musik (Leipzig: Breitkopf und Härtel, 1853), pp. 2833.

6 von Helmholtz, Hermann, Die Lehre von den Tonempfindungen als Physiologische Grundlage für die Theorie der Musik (Braunschweig: Friedrich Vieweg und Sohn, 1863), p. 451.

7 von Oettingen, Arthur, Harmoniesystem in dualer Entwickelung (Dorpat and Leipzig: W. Gläser 1866), pp. 31–2.

8 Riemann, Hugo, Musikalische Syntaxis (Leipzig: Breitkopf und Härtel, 1877), pp.121–3.

9 Debussy's choice of pitches evokes the traditional enharmonic diesis by changing spelling between chords from G# to A@, which may be interpreted to suggest a microtonal difference.

10 Cristiano Forster, Musical Mathematics. 2000–2014. Ch. 10 Part VI.

11 James Tenney distinguishes between harmonic space, in which every prime number generates its own tonal axis, and projection space, in which pitches any number of octaves apart are considered as equivalent pitch-classes.

12 Euler, Leonhard, Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae (Petropolis: Typographia Academiae Scientiarvm, 1739), p. 147.

13 The difference between a perfect fifth 3/2 and a perfect fourth 4/3 is called a Pythagorean whole tone 9/8. A syntonic comma, 81/80, is the difference between two 9/8 whole tones (81/64) and a 5/4 major third (5/4 = 80/64).

14 The diesis 128/125 is the difference between three 5/4 major thirds and an octave. It comprises approximately two commas and is the characteristic enharmonic difference between sharps and flats.

15 Ben Johnston. Who Am I? Why Am I Here? (accessed 24 November 2014).

16 von Gunden, Heidi, The Music of Ben Johnston (Metuchen, N.J. and London: The Scarecrow Press, 1986), pp. 7685.

17 Accidentals by Marc Sabat and Wolfgang von Schweinitz; for further information please visit the website

18 James Tenney, ‘John Cage and the Theory of Harmony’ (1982). (accessed 24 November 2014).

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  • ISSN: 0040-2982
  • EISSN: 1478-2286
  • URL: /core/journals/tempo
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