A061920 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the 7 pairs of complementary target ratios needed to express the 12 unsymmetrical steps of the untempered (Just Intonation) scale known as the Duodene: 3/2 and 4/3, 5/4 and 8/5, 6/5 and 5/3, 9/8 and 16/9, 10/9 and 9/5, 16/15 and 15/8 and 45/32 and 64/45.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 19, 22, 31, 34, 41, 53, 118, 171, 289, 323, 376, 441, 494, 559, 612, 1171, 1783, 2513, 3684, 4296, 12888, 16572, 20868, 25164, 44249, 48545, 52841, 57137, 69413, 73709, 78005, 151714, 229719, 307724, 537443, 714321

Offset

1,2

Comments

The sequence was found by a computer search of all the equal divisions of the octave from 1 to 714321. The numerical value of each term represents a musical scale based on an equal division of the octave. The term 12, for example, signifies the scale which is formed by dividing the octave into 12 equal parts.

Links

Table of n, a(n) for n=1..46.

Formula

Recurrence Rule: The next term equals the current term plus one or more previous terms: a(n+1) = a(n) + a(n-x)... + a(n-y)... + a(n-z), etc.

Example

118 = 53 + [34 + 31]; Again, 69413 = 57137 + [4296 + 3684 + 2513 + 1783].

Crossrefs

A054540, A060525, A060526, A060527, A060528, A060529, A060233, A061918, A061919.

Sequence in context: A173925 A320319 A263363 * A062010 A071218 A215775

Adjacent sequences: A061917 A061918 A061919 * A061921 A061922 A061923

Keyword

nonn

Author

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

Status

approved