31-limit: Difference between revisions
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{{Prime limit navigation|31}} | {{Prime limit navigation|31}} | ||
The '''31-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 31. It is the 11th [[prime limit]] and is | The '''31-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 31. It is the 11th [[prime limit]] and is a superset of the [[29-limit]] and a subset of the [[37-limit]]. | ||
The 31-limit is a rank-11 system, and can be modeled in a 10-dimensional lattice, with the primes 3 to 31 represented by each dimension. The prime 2 does not appear in the typical 31-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, an eleventh dimension is needed. | |||
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]]; | |||
* Mode 16, 17, and 18 of the harmonic or subharmonic series. | |||
== Music == | == Music == | ||
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== See also == | == See also == | ||
* [[No-twos 31-limit]] | * [[No-twos 31-limit]] | ||
* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals | * [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals | ||
Revision as of 15:42, 17 December 2024
The 31-limit consists of just intonation intervals whose ratios contain no prime factors higher than 31. It is the 11th prime limit and is a superset of the 29-limit and a subset of the 37-limit.
The 31-limit is a rank-11 system, and can be modeled in a 10-dimensional lattice, with the primes 3 to 31 represented by each dimension. The prime 2 does not appear in the typical 31-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, an eleventh dimension is needed.
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-, 33-, and 35-odd-limit;
- Mode 16, 17, and 18 of the harmonic or subharmonic series.
Music
- Soul Box (2020)
- Echo and Narcissus (2020)
- Theme for a primate-like creature (2024)
See also
- No-twos 31-limit
- User:Contribution/31-limit – Includes an enormous table of 31-limit intervals