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.

1, 3, 9, 27, 41, 58, 87, 111, 149, 217, 282, 388, 1323, 1600, 2554, 17461

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 * A337948 A163791 A248078

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