2.5 subgroup: Difference between revisions
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CompactStar (talk | contribs) Created page with "The '''2.5 subgroup''' is just intonation subgroup consisting of rational intervals where 2 and 5 are the only allowable prime factors, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are 5/4, 8/5, 25/16, 32/25, and so on. {{stub}}" |
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The '''2.5 subgroup''' is [[just intonation subgroup]] consisting of [[rational interval]]s where 2 and 5 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 and 5. This is an infinite set. Some examples of intervals in this subgroup are [[5/4]], [[8/5]], [[25/16]], [[32/25]], and so on. | The '''2.5 subgroup''' is [[just intonation subgroup]] consisting of [[rational interval]]s where 2 and 5 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 and 5. This is an infinite set. Some examples of intervals in this subgroup are [[5/4]], [[8/5]], [[25/16]], [[32/25]], and so on. | ||
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The 2.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 3. Its simplest [[expansion]] is the [[2.5.7 subgroup]], which adds prime [[7/1|7]]. | |||
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[[Category:Just intonation subgroups|#]] | |||
[[Category:Rank-2 temperaments|#]] | |||
[[Category:5-limit|#]] | |||
Latest revision as of 06:25, 21 October 2026
The 2.5 subgroup is just intonation subgroup consisting of rational intervals where 2 and 5 are the only allowable prime factors, so that every such interval may be written as a ratio of integers which are products of 2 and 5. This is an infinite set. Some examples of intervals in this subgroup are 5/4, 8/5, 25/16, 32/25, and so on.
The 2.5 subgroup is a retraction of the 5-limit, obtained by removing prime 3. Its simplest expansion is the 2.5.7 subgroup, which adds prime 7.
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