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A060525 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to four of the simple ratios of musical harmony: 5/4, 4/3, 3/2 and 8/5. 10
1, 2, 3, 7, 9, 10, 12, 19, 22, 31, 34, 53, 118, 289, 323, 441, 494, 559, 612, 1171, 1783, 2513, 3684, 4296, 12276, 16572, 20868, 25164, 48545, 69413, 73709, 78005, 151714, 229719, 689157, 792326, 944040, 1022045, 1173759, 1251764, 2733247, 3985011 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence was found by a computer search of all the equal divisions of the octave from 1 to over 3985011. The self-accumulating nature of this sequence fails once, between the third and fourth terms. The sequence therefore does not meet the rigorous definition of 'impeccable' recurrence. The otherwise perfect recurrence in this sequence is of the type seen in A054540.

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..42.

CROSSREFS

Cf. A054540, A060526, A060527.

Sequence in context: A140221 A046668 A047533 * A152863 A047359 A027700

Adjacent sequences:  A060522 A060523 A060524 * A060526 A060527 A060528

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 27 22:01 EDT 2015. Contains 257884 sequences.