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A215606 Number of ordered interval sequences in Schoenberg 12-tone rows that contain n unique intervals. 0
4, 140, 8472, 157056, 1629912, 7050672, 13962864, 11951592, 4526544, 606408, 23136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

REFERENCES

S. Bauer-Mengelberg and M. Ferentz, On Eleven-Interval Twelve-Tone Rows, Perspect. New Music, (1965), 93-103.

LINKS

Table of n, a(n) for n=1..11.

EXAMPLE

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.

CROSSREFS

Sequence in context: A002917 A235536 A229453 * A119038 A048432 A332114

Adjacent sequences:  A215603 A215604 A215605 * A215607 A215608 A215609

KEYWORD

nonn,fini,full

AUTHOR

Ole Kirkeby, Aug 17 2012

STATUS

approved

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)