This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141598 #34 Oct 10 2018 12:08:57 %S A141598 2,8,24,192,2880,46272,1250592,44095488,1865756160 %N A141598 Total number of all-interval rows for systems with 2n notes in the octave (2n-edo). %C A141598 This sequence and A141599 are based on the idea of "all-interval rows" from a musical techniques called dodecaphony and serialism. %C A141598 Twelve tones from an octave (c, c#, d, d#, e, f, ..., b) are marked by numbers 0, 1, ..., 11 (c is 0, c# is 1, etc.). %C A141598 The "interval" between two notes n1 and n2 is calculated as the difference n2-n1 modulo 12. For example, if note 1 is c# (1) and note 2 is f (5) the interval is 5-1=4, interval between 5 and 1 is 8 (1-5=-4, -4=8 mod 12), etc. %C A141598 The "all-interval" row is any sequence of twelve notes containing all notes of an octave (0..11) and all intervals (1..11) between adjacent positions. For example, the row 0 1 3 2 7 10 8 4 11 5 9 6 has intervals 1 2 11 5 3 10 8 7 6 4 9, i.e., it is an all-interval row. %C A141598 There are 46272 such rows from all possible 479001600 (12!) permutations. %C A141598 Rows with the same interval structure are equivalent in dodecaphony, for example the rows 0, 1, ..., 10, 11 and 1, 2, ..., 11, 0 both have the same intervals (all 1s), the second row is only transposed (moved) one step higher. There are 12 possible transpositions of one row, therefore there are 3856 (46272/12) "non-equivalent" unique all-interval rows. %C A141598 My generalization is an extension of this principle to microtonal systems - equal divisions of octave, EDO. Rows can be constructed for the tuning systems with any number of notes in the octave, not only 12. As it can be easily proved, the all-interval rows exist only in systems with even number of notes in the octave. %C A141598 Also the number of permutations of 1..2n which have distinct differences [Gilbert]. - _N. J. A. Sloane_, Mar 15 2014 %H A141598 E. N. Gilbert, <a href="http://www.jstor.org/stable/2027267">Latin squares which contain no repeated digrams</a>, SIAM Rev. 7 1965 189--198. MR0179095 (31 #3346). Mentions this sequence (see Q(n)). - _N. J. A. Sloane_, Mar 15 2014 %H A141598 Milan Gustar, <a href="http://www.uvnitr.cz/music_theory/rady.html">More information</a> %H A141598 Milan Gustar, <a href="http://www.uvnitr.cz/downloads.html">Programs</a> %F A141598 a(n) = 2*n*A141599(n). - _Leo C. Stein_, Nov 26 2016 %Y A141598 Cf. A067601, A141599, A155914. %K A141598 nonn,more %O A141598 1,1 %A A141598 Milan Gustar (artech(AT)noise.cz), Sep 03 2008 %E A141598 a(9) is calculated from A141599(9) after _David V. Feldman_. - _Jud McCranie_, Oct 07 2018