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

Author

Keenan Pepper, Mar 17 2006

Keywords

• nonn

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

Examples

			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.

Extensions

More terms from Gene Ward Smith, Mar 29 2006