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