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A116475 Equal divisions of the octave with progressively increasing consistency limits and distinct approximations for all the ratios in the tonality diamond of that limit. 3
1, 3, 9, 27, 41, 58, 87, 111, 149, 217, 282, 388, 1323, 1600, 2554, 17461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Since the 1-division is distinct and consistent in the 1-limit, the sequence starts there. From a purely musical point of view one might prefer to begin the sequence at 3. - Gene Ward Smith, Mar 29 2006

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

9-EDO is consistent and distinct through the 5 limit because 6/5, 5/4, 4/3, 3/2, 8/5 and 5/3 map to 2, 3, 4, 5, 6 and 7 steps respectively and all the compositions of those intervals are consistent.

CROSSREFS

Cf. A116474, A117577, A117578.

Sequence in context: A045580 A070361 A056024 * A163791 A248078 A057829

Adjacent sequences:  A116472 A116473 A116474 * A116476 A116477 A116478

KEYWORD

nonn

AUTHOR

Keenan Pepper, Mar 17 2006

EXTENSIONS

More terms from Gene Ward Smith, Mar 29 2006

STATUS

approved

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Last modified June 17 15:07 EDT 2019. Contains 324185 sequences. (Running on oeis4.)