2.3.5.11 subgroup: Difference between revisions

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The '''2.3.5.11 subgroup''' (AKA as ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 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 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.

The '''2.3.5.11 subgroup''' (AKA ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 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 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.

In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].

Revision as of 09:53, 19 April 2026 view source Eufalesio (talk \| contribs) autopatrolled 647 edits color notation Tag: Visual edit ← Older edit		Revision as of 09:54, 19 April 2026 view source Eufalesio (talk \| contribs) autopatrolled 647 edits mNo edit summary Tag: Visual edit Newer edit →
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	The '''2.3.5.11 subgroup''' (AKA as ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 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 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.		The '''2.3.5.11 subgroup''' (AKA ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 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 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.

	In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].		In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].