User:Squib/Drafts/5.7.11.13 subgroup: Difference between revisions

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The '''5.7.11.13''' subgroup is a subgroup.
The '''5.7.11.13 subgroup''' is a [[just intonation subgroup]] consisting of [[rational interval]]s where [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 5, 7, 11, and 13; this makes it a rank-4 system.
 
The subgroup can be very easily be collapsed into a rank-3 temperament by tempering out [[../847∕845|847/845]]
 
== Regular temperaments ==
=== Rank-1 temperaments ===
Some ED5s which are strong in this subgroup, by no particular criteria: {{EDs|equave=5|10, 29, 39, 57, 67, 96}}
 
=== Rank-2 temperaments ===
 
 
=== Rank-3 temperaments ===
 
== Music ==
[https://www.youtube.com/watch?v=TdkGD-yfNzY Nuusse] (5.7.11 subgroup)

Latest revision as of 14:18, 26 May 2026

The 5.7.11.13 subgroup is a just intonation subgroup consisting of rational intervals where 5, 7, 11, and 13 are the only allowable prime factors, so that every such interval may be written as a ratio of integers which are products of 5, 7, 11, and 13; this makes it a rank-4 system.

The subgroup can be very easily be collapsed into a rank-3 temperament by tempering out 847/845

Regular temperaments

Rank-1 temperaments

Some ED5s which are strong in this subgroup, by no particular criteria: 10, 29, 39, 57, 67, 96

Rank-2 temperaments

Rank-3 temperaments

Music

Nuusse (5.7.11 subgroup)