User:Squib/Drafts/5.7.11.13 subgroup: Difference between revisions
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The '''5.7.11.13''' 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)