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All-interval twelve-tone row
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All-interval twelve-tone row : ウィキペディア英語版
All-interval twelve-tone row

In music, an all-interval twelve-tone row, series, or chord, is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11. A "twelve-note ''spatial set'' made up of the eleven intervals (consecutive pitches )."〔Schiff, David (1998). ''The Music of Elliott Carter'', second edition (Ithaca: Cornell University Press), pp. 34–36. ISBN 0-8014-3612-5. Labels added to image.〕 There are 1,928 distinct all-interval twelve-tone rows.〔Carter, Elliott (2002). ''Harmony Book'', p.15. Nicholas Hopkins and John F. Link, eds. ISBN 9780825845949.〕 These sets may be ordered in time or in register. "Distinct" in this context means in transpositionally and rotationally normal form (yielding 3856 such series), and disregarding inversionally related forms.〔Robert Morris and Daniel Starr (1974). "The Structure of All-Interval Series", ''Journal of Music Theory'' 18/2: pp. 364-89, citation on p. 366.〕
The sum of numbers 1 through 11 = 66 and thus the chord contains a tritone between its outer notes〔Slonimsky (1975), p.iv.〕 and as its sixth (middle) interval, and between the two notes directly outside of those, etc.
==Examples==


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