3.5.11 subgroup: Difference between revisions
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The '''3.5.11 subgroup''' is a [[non-octave]] [[just intonation subgroup]] consisting of [[rational interval]]s where 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 3, 5, and 11. This is an infinite set. Some examples of intervals in this subgroup are [[5/3]], [[11/9]], [[15/11]], [[33/25]], and so on. Due to the lack of octaves, it would most obviously be approached by using [[3/1|tritave]]-equivalence. | The '''3.5.11 subgroup''' is a [[non-octave]] [[just intonation subgroup]] consisting of [[rational interval]]s where 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 3, 5, and 11. This is an infinite set. Some examples of intervals in this subgroup are [[5/3]], [[11/9]], [[15/11]], [[33/25]], and so on. Due to the lack of octaves, it would most obviously be approached by using [[3/1|tritave]]-equivalence. | ||
The 3.5.11 subgroup is a [[retraction]] of the [[11-limit]], obtained by removing primes | The 3.5.11 subgroup is a [[retraction]] of the [[11-limit]], obtained by removing primes 2 and 7. Its simplest [[expansion]] is the [[3.5.11.13 subgroup]], which adds prime [[13/1|13]]. | ||
It could perhaps be considered the simplest place to look in the no-2s world after the [[3.5.7 subgroup]]–it is to the [[3.5.7 subgroup]] as the [[2.3.7 subgroup]] is to the [[5-limit]]. | It could perhaps be considered the simplest place to look in the no-2s world after the [[3.5.7 subgroup]]–it is to the [[3.5.7 subgroup]] as the [[2.3.7 subgroup]] is to the [[5-limit]]. | ||