Diaschismic family: Difference between revisions
→Pajara: move paja to the bottom as it's the least accurate |
m →Srutal archagall (2.3.5.17): note relevance of fiventeen |
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[[Badness]] (Sintel): 0.507 | [[Badness]] (Sintel): 0.507 | ||
=== 11-limit === | === Undecimal pajara === | ||
==== 11-limit ==== | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness (Sintel): 0.673 | Badness (Sintel): 0.673 | ||
==== 2.3.5.7.11.17 subgroup ==== | ===== 2.3.5.7.11.17 subgroup ===== | ||
Subgroup: 2.3.5.7.11.17 | Subgroup: 2.3.5.7.11.17 | ||
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=== Pajarous === | === Pajarous === | ||
==== 11-limit ==== | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness (Sintel): 0.937 | Badness (Sintel): 0.937 | ||
==== 2.3.5.7.11.17 subgroup ==== | ===== 2.3.5.7.11.17 subgroup ===== | ||
Subgroup: 2.3.5.7.11.17 | Subgroup: 2.3.5.7.11.17 | ||
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{{See also | Fiventeen }} | {{See also | Fiventeen }} | ||
This extension of 5-limit diaschismic adds prime 17, and can be seen as the trivial tuning of [[MVP archagall]] in its minimal prime subgroup by equating [[85/64]] with [[4/3]] by tempering out their difference of [[256/255]] (S16). Therefore it also tempers out [[289/288]] (S17) and thus equates [[17/15]] with [[9/8]] due to tempering out [[136/135]] (S16⋅S17). It could be described as the 10 & 12 temperament with strong emphasis on 12edo being the better tuning on the 2.3.5.17 subgroup, implying ideal tunings of 34edo, 46edo or 80edo. | This extension of 5-limit diaschismic adds prime 17, and can be seen as the trivial tuning of [[MVP archagall]] in its minimal prime subgroup by equating [[85/64]] with [[4/3]] by tempering out their difference of [[256/255]] (S16). Therefore it also tempers out [[289/288]] (S17) and thus equates [[17/15]] with [[9/8]] due to tempering out [[136/135]] (S16⋅S17). It could be described as the 10 & 12 temperament with strong emphasis on 12edo being the better tuning on the 2.3.5.17 subgroup, implying ideal tunings of 34edo, 46edo or 80edo, and if we note that 46edo is the least ideal tuning of these, it is especially good as a realization of [[fiventeen]], for which it can be seen as completing the subgroup from 2.3.17/5 to 2.3.5.17 by splitting the octave period in half, as ~24/17~17/12 (via S17). | ||
Subgroup: 2.3.5.17 | Subgroup: 2.3.5.17 | ||