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Complete data. Re-organize. - strange criteria for "patent edo tunings" |
m →Temperaments: the catakleismic extension is unrelated to the completely unexplained list of edos. it also should bother you that it's completely unexplained given it's not even a good selection of edos, so i fixed the list |
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== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 2.3.7.29 subgroup results in the rank-3 '''biminoric''' temperament, a.k.a. '''spoogalactic''' temperament. It tempers 28/27 and 29/28 together, as well as [[49/27]] and [[29/16]] together. [[7/6]] and [[29/24]] are separated by 29/28 as are [[36/29]] and [[9/7]], where 9/7 is 28/27 below [[4/3]] and 7/6 is 28/27 above [[9/8]], so tempering out this comma to extend the 2.3.7 subgroup to the 2.3.7.29 subgroup is of very high accuracy, yielding obviously distinct flavours of thirds, as a third-tone lies between the two minor thirds and between the two major thirds. | [[Tempering out]] this comma in the 2.3.7.29 subgroup results in the rank-3 '''biminoric''' temperament, a.k.a. '''spoogalactic''' temperament. It tempers 28/27 and 29/28 together, as well as [[49/27]] and [[29/16]] together. [[7/6]] and [[29/24]] are separated by 29/28 as are [[36/29]] and [[9/7]], where 9/7 is 28/27 below [[4/3]] and 7/6 is 28/27 above [[9/8]], so tempering out this comma to extend the 2.3.7 subgroup to the 2.3.7.29 subgroup is of very high accuracy, yielding obviously distinct flavours of thirds, as a third-tone lies between the two minor thirds and between the two major thirds. | ||
Relatively efficient [[edo]]s that [[support]] it include [[36edo]], [[41edo]], [[58edo]], [[77edo]] and [[99edo]], though because it's a multiple of 7edo (for 29) and 9edo (for 7/6), [[63edo]] is also a good tuning. | |||
A [[catakleismic]] extension is available in the 2.3.5.7.13.29 subgroup, with the notable [[S-expression]] of {S25, S26, S27, S28}. It is also tempered out in [[miracle]], [[magic]], [[newt]] extensions, and a [[septischismic]] extension. | A [[catakleismic]] extension is available in the 2.3.5.7.13.29 subgroup, with the notable [[S-expression]] of {S25, S26, S27, S28}. It is also tempered out in [[miracle]], [[magic]], [[newt]] extensions, and a [[septischismic]] extension. | ||
=== Biminoric === | === Biminoric === | ||