A060526 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of six simple musical tones: 8/7 5/4 4/3 3/2 8/5 7/4.

1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 21, 22, 31, 53, 84, 87, 94, 99, 118, 130, 140, 171, 270, 410, 441, 612, 935, 966, 1053, 1106, 1277, 1547, 1578, 2954, 3125, 3566, 6691, 9816, 11664, 14789, 18355, 39835, 48545, 54624, 58190, 59768, 63334, 81689, 84814

Offset: 1

Author

Mark William Rankin (MarkRankin95511(AT)Yahoo.com), Apr 01 2001

Keywords

• nonn

Comments

The sequence was found by a computer search of all of the equal divisions of the octave from 1 to over 84814.

The numerical value of each term represents a musical scale based on an equal division of the octave. 12, for example, signifies the scale which is formed by dividing the octave into 12 equal parts.

Examples

			84 = 53 + the previous term 31. Again, 291152 = 103169 + the previous terms (84814 + 81689 + 11664 + 9816).
		

Crossrefs

Cf. A054540, A060525, A060257.

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.