A060233 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to six complementary pairs of ratios which generate simple musical tones (scale steps): 8/7 and 7/4, 6/5 and 5/3, 16/13 and 13/8, 5/4 and 8/5, 4/3 and 3/2 and 11/8 and 16/11.

1, 2, 3, 4, 6, 7, 9, 10, 15, 19, 22, 24, 26, 31, 37, 41, 46, 50, 53, 72, 84, 87, 130, 137, 140, 171, 183, 217, 224, 270, 494, 764, 851, 1038, 1282, 1308, 1578, 2190, 2684, 3395, 4843, 5004, 5585, 6079, 8269, 14124, 14618, 17302, 20203, 22887, 31737

Offset

1,2

Comments

The sequence was found by a computer search of all the equal divisions of the octave from 1 to over 31737. The numerical value of each term represents a musical scale based on an equal division of the octave. 19, for example, signifies the scale which is formed by dividing the octave into 19 equal parts.

Links

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

Formula

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

Example

6 = 4 + the previous term 2. Again, 48545 = 46625 + the previous terms (1578 + 270 + 72).

Crossrefs

A054540, A060525, A060526, A060527, A060528, A060529, A001149, A000045.

Sequence in context: A187092 A076679 A339509 * A235203 A187102 A191991

Adjacent sequences: A060230 A060231 A060232 * A060234 A060235 A060236

Keyword

nonn

Author

Mark William Rankin (MarkRankin95511(AT)Yahoo.com), Apr 14 2001

Status

approved