

A060529


A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of three complementary pairs of simple musical tones: 7/6 and 12/7, 6/5 and 5/3 and 7/5 and 10/7.


7



1, 2, 3, 4, 12, 14, 15, 18, 19, 23, 27, 45, 68, 72, 99, 171, 346, 445, 517, 616, 688, 787, 1133, 1304, 3912, 7136, 8440, 9744, 11048, 12352, 18355, 19659, 20963, 22267, 26795, 28099, 29403, 30707, 40451, 41755, 69854, 71158, 72462, 143620, 216082
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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 216082. The selfaccumulating nature of this sequence fails once, between the fourth and fifth 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 sequences A054540, A060526 and A060527. 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..45.


CROSSREFS

A054540, A060525, A060526, A060527, A060528, A001149, A000045.
Sequence in context: A285618 A062946 A210584 * A048073 A002447 A275067
Adjacent sequences: A060526 A060527 A060528 * A060530 A060531 A060532


KEYWORD

nonn


AUTHOR

Mark William Rankin (MarkRankin95511(AT)Yahoo.com), Apr 12 2001


STATUS

approved



