Consistency: Difference between revisions
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==Generalization to non-octave scales== | ==Generalization to non-octave scales== | ||
It is possible to generalize the concept of consistency to non-edo equal temperaments. Because octaves are no longer equivalent, instead of an odd limit we | It is possible to generalize the concept of consistency to non-edo equal temperaments. Because octaves are no longer equivalent, instead of an odd limit we might use an integer limit, and the term 2^n in the above equation is no longer present. Instead, the set S consists of all intervals u/v where u <= q >= v. | ||
This also means that the concept of octave inversion no longer applies: in this example, [[13/9]] is in S, but [[18/13]] is not. | This also means that the concept of octave inversion no longer applies: in this example, [[13/9]] is in S, but [[18/13]] is not. | ||
Alternatively, we can use "modulo-3 limit" if the [[equave]] is 3/1. Thus the tritave analogue of odd limit would allow integers not divisible by 3 under a given limit. | |||
==Links== | ==Links== | ||