A061416 A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the pair of ratios 11/8 and 16/11 which generate two complementary musical tones.

1, 2, 6, 7, 9, 11, 13, 24, 37, 505, 542, 579, 616, 653, 690, 727, 764, 801, 838, 875, 912, 949, 986, 1935, 2921, 4856, 11647, 16503, 148527, 181533, 214539, 219395, 235898, 252401, 268904, 285407, 301910, 318413, 334916, 351419, 367922, 384425

Offset

1,2

Comments

The sequence was found by a computer search of all the equal divisions of the octave from 1 to 384425. The numerical value of each term represents a musical scale based on an equal division of the octave. 24, for example, signifies the scale of quartertones which is formed by dividing the octave into 24 equal parts. The recurrence in this sequence breaks down three times, between the 2nd and 3rd terms, between the 9th and 10th terms and between the 28th and 29th terms, but the sequence is of interest because 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, composite sequences. The examples of proper recurrence which do occur in this sequence are of the same type as is seen in sequences A054540, A060526, A060527, A060529 and A060233.

Links

Table of n, a(n) for n=1..42.

Crossrefs

A054540, A060526, A060527, A060529, A060233, A001149 and A000045.

Sequence in context: A278999 A190784 A344167 * A190247 A020897 A020898

Adjacent sequences: A061413 A061414 A061415 * A061417 A061418 A061419

Keyword

nonn

Author

Mark William Rankin (MarkRankin95511(AT)Yahoo.com), May 02 2001

Status

approved