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

Author

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

Keywords

• nonn

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.

Examples

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

Crossrefs

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

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.