2.3.7.11 subgroup: Difference between revisions

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The '''2.3.7.11 subgroup''' ('''~~laza~~''' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 7, 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, 7, 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 [[3/2]], [[7/4]], [[9/7]], [[21/16]], [[11/9]], [[22/21]], and so on.

The '''2.3.7.11 subgroup''' ('''zala''' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 7, 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, 7, 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 [[3/2]], [[7/4]], [[9/7]], [[21/16]], [[11/9]], [[22/21]], and so on.

The 2.3.7.11 subgroup is a retraction of the [[11-limit]], obtained by removing prime 5. Its simplest expansion is the 2.3.7.11.13 subgroup, which adds prime 13. It can also be retracted to the [[2.3.7 subgroup]] by removing prime 11.

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	The '''2.3.7.11 subgroup''' ('''~~laza~~''' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 7, 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, 7, 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 [[3/2]], [[7/4]], [[9/7]], [[21/16]], [[11/9]], [[22/21]], and so on.		The '''2.3.7.11 subgroup''' ('''zala''' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 7, 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, 7, 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 [[3/2]], [[7/4]], [[9/7]], [[21/16]], [[11/9]], [[22/21]], and so on.

	The 2.3.7.11 subgroup is a retraction of the [[11-limit]], obtained by removing prime 5. Its simplest expansion is the 2.3.7.11.13 subgroup, which adds prime 13. It can also be retracted to the [[2.3.7 subgroup]] by removing prime 11.		The 2.3.7.11 subgroup is a retraction of the [[11-limit]], obtained by removing prime 5. Its simplest expansion is the 2.3.7.11.13 subgroup, which adds prime 13. It can also be retracted to the [[2.3.7 subgroup]] by removing prime 11.