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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
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
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
KEYWORD
nonn
AUTHOR
Keenan Pepper, Mar 17 2006
EXTENSIONS
More terms from Gene Ward Smith, Mar 29 2006
STATUS
approved