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PANTONALITY GENERALISED: BEN JOHNSTON'S ARTISTIC RESEARCHES IN EXTENDED JUST INTONATION
Published online by Cambridge University Press: 17 April 2015
Abstract
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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References
1 Johnston, Ben ‘On Bridge-Building’ (1977), in Maximum Clarity and Other Writings on Music, ed. Gilmore, Bob (Urbana and Chicago: University of Illinois Press, 2006), p. 147Google Scholar.
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.
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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.
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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? http://newdissonance.com/2008/07/02/who_is_ben_johnston/ (accessed 24 November 2014).
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19 http://eamusic.dartmouth.edu/~larry/misc_writings/out_of_print/op_option_etc./tenney_OP.pdf, accessed 13 October 2014.