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A061919 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the pair of ratios 6/5 and 5/3 which generate two complementary musical harmonies, the Minor 3rd (6/5) and the Major 6th (5/3). 2
1, 2, 3, 4, 11, 15, 19, 95, 232, 251, 270, 289, 308, 327, 346, 365, 384, 403, 422, 1285, 1707, 2129, 3836, 19180, 28981, 32817, 36653, 40489, 44325, 48161, 51997, 259985, 3591629, 3643626, 3695623, 3747620, 3799617, 3851614, 3903611, 3955608 (list; graph; refs; listen; history; text; internal format)



The sequence was found by a computer search of all the equal divisions of the octave from 1 to 3955608. The numerical value of each term represents a musical scale based on an equal division of the octave. 19, for example, signifies the scale formed by dividing the octave into 19 equal parts. Within the terms shown, the self-accumulating nature of this sequence breaks down five times, between the 4th and 5th terms, between the 7th and 8th terms, between the 8th and 9th terms, between the 23rd and 24th terms and between the 32nd and 33rd terms, but the sequence is of interest because it shows the terms generated when this pair of target ratios stands alone.

Later, in other sequences, this pair of target ratios will appear in combination with other pairs of target ratios, resulting in new, different (and often recurrent), composite sequences. The examples of proper recurrence which do occur in this sequence are of the same type which is seen in sequences A054540, A060526, A060527 and A060233.


Table of n, a(n) for n=1..40.


A054540, A060525, A060526, A060527, A060528, A060529, A060233, A061416, A061918.

Sequence in context: A176541 A171376 A141704 * A192613 A002098 A162969

Adjacent sequences:  A061916 A061917 A061918 * A061920 A061921 A061922




Mark William Rankin (MarkRankin95511(AT)Yahoo.com), May 15 2001



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Last modified January 16 23:43 EST 2017. Contains 280872 sequences.