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%I #9 Dec 11 2013 23:01:56
%S 4,140,8472,157056,1629912,7050672,13962864,11951592,4526544,606408,
%T 23136
%N Number of ordered interval sequences in Schoenberg 12-tone rows that contain n unique intervals.
%C A Schoenberg 12-tone row is a permutation of the integers from 0 to 11. It is assumed the first element is 0 so there are 11! 12-tone rows. The ordered interval sequence is the 1st-order difference modulo 12.
%D S. Bauer-Mengelberg and M. Ferentz, On Eleven-Interval Twelve-Tone Rows, Perspect. New Music, (1965), 93-103.
%e There are 4 ordered interval sequences that contain only one interval: all 1s, all 5s, all 7s, and all 11s. One of the 140 that contain 2 unique intervals is [1,9,1,9,1,9,1,9,1,9,1,9], and one of the 8472 that contain 3 unique intervals is [5,4,5,4,5,4,4,3,3,3,4,4]. The 23136 sequences with 11 unique intervals are the famous All-Interval Sequences first determined by Bauer-Mengelberg and Ferentz in 1965.
%K nonn,fini,full
%O 1,1
%A _Ole Kirkeby_, Aug 17 2012
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