

A061921


A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the 11 pairs of target ratios needed to express the 22 steps of the theoretical Hindu scale known as the 22 Srutis: 45/32 and 64/45, 27/20 and 40/27, 4/3 and 3/2, 81/64 and 128/81, 5/4 and 8/5, 6/5 and 5/3, 32/27 and 27/16, 9/8 and 16/9, 10/9 and 9/5, 16/15 and 15/8, 256/243 and 243/128.


0



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 28, 29, 30, 32, 34, 37, 39, 40, 41, 53, 118, 171, 323, 335, 376, 388, 441, 494, 506, 559, 612, 1171, 1783, 2513, 3072, 3125, 3684, 4296, 12276, 16572, 20868, 40565, 44861, 48545, 52841, 57137, 61433, 69413, 73709
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OFFSET

1,2


COMMENTS

The sequence was found by a computer search of all the equal divisions of the octave from 1 to 73709. The numerical value of each term represents a musical scale based on an equal division of the octave. The term 32, for example, signifies the scale which is formed by dividing the octave into 32 equal parts.


LINKS

Table of n, a(n) for n=1..51.


FORMULA

Recurrence rule: The next term equals the current term plus one or more previous terms: a(n+1) = a(n) + a(nx)... + a(ny)... + a(nz), etc.


EXAMPLE

118 = 53 + [34 + 31]; Again, 229719 = 78005 + [73709 + 69413 + 4296 + 3684 + 612].


CROSSREFS

A054540, A060525, A060526, A060527, A060528, A060529, A060233, A061416, A061918, A061919, A061920.
Sequence in context: A257738 A039210 A243020 * A071786 A151766 A004852
Adjacent sequences: A061918 A061919 A061920 * A061922 A061923 A061924


KEYWORD

nonn


AUTHOR

Mark William Rankin (MarkRankin95511(AT)Yahoo.com), May 15 2001


STATUS

approved



