Diaschismic family: Difference between revisions
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atp just call it diaschismic |
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The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. The period is half an octave, and the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]], or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities. | The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. The period is half an octave, and the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]], or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities. | ||
== | == Diaschismic == | ||
{{Main| Diaschismic }} | {{Main| Diaschismic }} | ||
This temperament is also known as '''srutal''' in the 5-limit, but that name more strictly speaking refers to the [[Diaschismic family#Srutal|34d&46 extension]] to the [[7-limit]] that adds [[4375/4374]] to the comma list. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]]: 0.019915 | [[Badness]]: 0.019915 | ||
=== Srutal archagall === | === Srutal archagall === | ||
{{See also | Fiventeen }} | {{See also | Fiventeen }} | ||
The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}. | Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup, resulting in ''srutal archagall''. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}. | ||
Subgroup: 2.3.5.17 | Subgroup: 2.3.5.17 | ||
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Badness: 0.00575 | Badness: 0.00575 | ||
=== Overview to extensions === | |||
To get the 7-limit extensions, we add another comma: | |||
* Pajara derives from [[64/63]] and is a popular and well-known choice. | |||
* Diaschismic adds [[126/125]], the starling comma, to obtain 7-limit harmony by more complex methods, but with greater accuracy. | |||
* Srutal adds [[4375/4374]], the ragisma. It does no significant tuning damage, so we keep the 5-limit label srutal. | |||
* Keen adds [[875/864]]. | |||
* Bidia adds [[3136/3125]], the hemimean comma. | |||
* Echidna adds [[1728/1715]], the orwellisma. | |||
* Shrutar adds [[245/243]], the sensamagic comma. | |||
Pajara, diaschismic, srutal and keen keep the same half-octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as [[36/35]], the septimal quarter-tone) and echidna has a generator of 9/7. Bidia has a quarter-octave period and a fifth generator. | |||
== Srutal == | == Srutal == | ||