A060527 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of 8 musical tones: 8/7 16/11 5/4 4/3 3/2 8/5 11/8 7/4.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 15, 22, 26, 31, 41, 63, 72, 87, 109, 161, 202, 224, 270, 494, 612, 742, 764, 836, 1012, 1084, 1106, 1308, 1417, 1578, 3426, 4843, 6421, 6691, 10698, 12276, 18355, 19461, 21039, 22887, 25046, 26894, 31737, 33585, 35163

Offset

1,2

Comments

The sequence was found by a computer search of all of the equal divisions of the octave from 1 to over 35163.

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.

Links

Table of n, a(n) for n=1..49.

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

109 = 87 + the previous term 22. Again, 184417 = 121524 + the previous terms (54624 and 6691 and 1578).

Crossrefs

Cf. A054540, A060525, A060526.

Sequence in context: A284831 A261040 A087950 * A152493 A229028 A079002

Adjacent sequences: A060524 A060525 A060526 * A060528 A060529 A060530

Keyword

nonn

Author

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

Status

approved