2.3.7 subgroup: Difference between revisions
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* Ratios without a 7 are pythagorean and sound much like 12edo intervals | * Ratios without a 7 are pythagorean and sound much like 12edo intervals | ||
* Ratios with a 7 in the numerator (7-over or '''zo''' in color notation) sound [[Supermajor and subminor|subminor]] | * Ratios with a 7 in the numerator (7-over or '''zo''' in color notation) sound [[Supermajor and subminor|subminor]] | ||
* Ratios with a 7 in the denominator (7-under or '''ru''' in color notation) sound supermajor | * Ratios with a 7 in the denominator (7-under or '''ru''' in color notation) sound [[Supermajor and subminor|supermajor]] | ||
This subgroup is notably well-represented by [[5edo]] for its size, and therefore many of its simple intervals tend to cluster around the notes of 5edo: [[9/8]]~[[8/7]]~[[7/6]] representing a pentatonic "second", [[9/7]]~[[21/16]]~[[4/3]] representing a pentatonic "third", and so on. Therefore, one way to approach the 2.3.7 subgroup is to think of a pentatonic framework for composition as natural to it, rather than the diatonic framework associated with the [[5-limit]], and a few of the scales below reflect that nature. | This subgroup is notably well-represented by [[5edo]] for its size, and therefore many of its simple intervals tend to cluster around the notes of 5edo: [[9/8]]~[[8/7]]~[[7/6]] representing a pentatonic "second", [[9/7]]~[[21/16]]~[[4/3]] representing a pentatonic "third", and so on. Therefore, one way to approach the 2.3.7 subgroup is to think of a pentatonic framework for composition as natural to it, rather than the diatonic framework associated with the [[5-limit]], and a few of the scales below reflect that nature. | ||
=== Scales === | === Scales === | ||
* | |||
* | ==== Minor ==== | ||
* zo pentatonic: 1/1 7/6 4/3 3/2 7/4 2/1 | |||
* | * zo [[wikipedia:In_scale|in]]: 1/1 9/8 7/6 3/2 14/9 2/1 (the in scale is a minor scale with no 4th or 7th) | ||
* | * zo: 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 | ||
* 2 | * za harmonic minor: 1/1 9/8 7/6 4/3 3/2 14/9 27/14 2/1 (zo scale with a ru 7th) | ||
==== Major ==== | |||
* ru pentatonic: 1/1 9/8 9/7 3/2 12/7 2/1 | |||
* ru: 1/1 9/8 9/7 4/3 3/2 12/7 27/14 2/1 | |||
==== Misc ==== | |||
* [[diasem]]/Tas[9] ([[Chiral|left-handed]]): 1/1 9/8 7/6 21/16 4/3 3/2 14/9 7/4 16/9 2/1 | * [[diasem]]/Tas[9] ([[Chiral|left-handed]]): 1/1 9/8 7/6 21/16 4/3 3/2 14/9 7/4 16/9 2/1 | ||
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<nowiki />* In 2.3.7-targeted DKW tuning | <nowiki />* In 2.3.7-targeted DKW tuning | ||
==== | ==== Slendric ==== | ||
''' | '''Slendric''' temperament, also known as [[slendric|gamelic]], tempers out the comma [[1029/1024]] = S7/S8 in the 2.3.7 subgroup, which splits the perfect fifth into three intervals of [[8/7]]. It is one of the most accurate temperaments of its simplicity. While semaphore and archy equate each middle interval of each triplet with either the major or the minor, gamelic makes it a true "neutral" intermediate between them. | ||
The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 699.126c, and therefore ~8/7 to 233.042c; a chart of mistunings of simple intervals is below. | The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 699.126c, and therefore ~8/7 to 233.042c; a chart of mistunings of simple intervals is below. | ||