OFFSET
1,3
COMMENTS
"Inequivalent" effectively means that the permutation begins with 0 and the second item is <= n. (Working modulo 2n, s1+k,s2+k,s3+k,... is equivalent to s1,s2,s3,...; and -s1,-s2,-s3 is equivalent to s1,s2,s3,...)
The references all deal with length 12.
LINKS
Stefan Bauer-Mengelberg and Melvin Ferentz, On Eleven-Interval Twelve-Tone Rows, Perspectives of New Music 3, no. 2 (Spring-Summer 1965): 93-103
Sean A. Irvine, Java program (github)
Robert Morris and Daniel Starr, The Structure of All-interval Series, Journal of Music Theory 18, no. 2 (Fall 1974): 364-389.
David Schiff, Elliott Carter's Harvest Home, Tempo 167 (December 1988): 7-13.
FORMULA
a(n) = ceiling(A141599(n)/2). - Leo C. Stein, Nov 26 2016
EXAMPLE
0 1 3 2 has first difference, mod 4, of 1 2 3;
0 2 1 4 5 3 has first difference, mod 6, of 2 5 3 1 4;
0 4 5 8 3 1 7 9 2 11 10 6 has first difference, mod 12, of 4 1 3 7 10 6 2 5 9 11 8.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Eugene McDonnell (eemcd(AT)aol.com), Jan 31 2002
EXTENSIONS
Edited by Don Reble, Oct 31 2005
a(9) from Sean A. Irvine, Dec 22 2023
STATUS
approved