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

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== Regular temperaments ==
== Regular temperaments ==
=== Rank-1 temperaments ===
=== Rank-1 temperaments ===
 
Some ED5s which are strong in this subgroup, by no particular criteria: {{EDs|equave=5|10, 29, 39, 57, 67, 86, 96}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===

Revision as of 13:02, 24 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, 86, 96

Rank-2 temperaments

Rank-3 temperaments