31-limit: Difference between revisions
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Like the [[23-limit]], the 31-limit implies a substantial increment in its harmonic contents compared to previous prime limit. Specifically, these things are contained by the 31-limit, but not the 29-limit: | Like the [[23-limit]], the 31-limit implies a substantial increment in its harmonic contents compared to previous prime limit. Specifically, these things are contained by the 31-limit, but not the 29-limit: | ||
* The [[31-odd-limit|31-]], [[33-odd-limit|33-]], and [[35-odd-limit]]; | * The [[31-odd-limit|31-]], [[33-odd-limit|33-]], and [[35-odd-limit]]; | ||
* Mode 16, 17, and 18 of the harmonic or subharmonic series. | * Mode 16, 17, and 18 of the harmonic or subharmonic series; this means it completes the 5th octave of those series. | ||
The 31-limit intervals of the 2.3.31 subgroup are mainly [[interseptimal]], with [[32/31]] being a quartertone, [[36/31]] and [[31/27]] being semifourths, and [[31/24]] being a naiadic, with their [[octave complement]]s classified accordingly. While interseptimal intervals are abundant in lower limits, [[31/1|31]] is the first prime where such intervals occur without combining primes higher than 3. As such, the intervals of 31 are difficult to classify diatonically, but add a contrasting character to the lower limits, in particular [[11/1|11]] and [[13/1|13]], which are mainly neutral in quality. | |||
== Edo approximations == | == Edo approximations == | ||