Kite's color notation/Temperament names: Difference between revisions

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Rule #3 says that if the upward extension is weak and the downward extension is the best, the name must reflect that by excluding the lower prime. For example, za Liese is called Latriru, after its comma |-9 11 0 -3>. The best downward extension of Liese has commas 81/80, 686/675 (z3gg) and 1029/1000 (z3g3), all lower odd limit than the Latrilu comma. But Yaza Liese is called neither Gu & Trizo-agugu nor Gu & Trizogu, but Latriru.

Some rank-2 temperaments have 3-limit commas, which are written as edos. Every edo implies other commas, which are simply the best strong extension of the 3-limit temperament to higher primes. 12-edo implies Gu and Ru. 5-edo implies Gubi and Zo (and also Ru, but Zo is the canonical comma). 7-edo implies Gu and Ru. 19-edo implies Gu and Lazo. 22-edo implies Triyo and Ru. '''Tweaks''' aka warts change the implied comma: 22c-edo implies Gu and Ru. [''needs checking: The best extension sometimes creates tweaks, e.g. 12-edo's best 11-limit extension is 33/32, not 729/~~702~~, thus 12-edo becomes 12e-edo.'']

Some rank-2 temperaments have 3-limit commas, which are written as edos. Every edo implies other commas, which are simply the best strong extension of the 3-limit temperament to higher primes. 12-edo implies Gu and Ru. 5-edo implies Gubi and Zo (and also Ru, but Zo is the canonical comma). 7-edo implies Gu and Ru. 19-edo implies Gu and Lazo. 22-edo implies Triyo and Ru. '''Tweaks''' aka warts change the implied comma: 22c-edo implies Gu and Ru. [''needs checking: The best extension sometimes creates tweaks, e.g. 12-edo's best 11-limit extension is 33/32, not 729/704, thus 12-edo becomes 12e-edo.'']

Edos become rank-2 in two ways. One way is by adding an untempered prime, as in Blackwood, which is 5-edo + Ya. The "+ Ya" means the Gu comma is no longer implied. The other way is to add a bicolored comma, e.g. 12-edo & Ruyoyo. Since Ruyoyo is yaza, the Gu & Ru commas are no longer implied.

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 Rule #3 says that if the upward extension is weak and the downward extension is the best, the name must reflect that by excluding the lower prime. For example, za Liese is called Latriru, after its comma |-9 11 0 -3>. The best downward extension of Liese has commas 81/80, 686/675 (z<sup>3</sup>gg) and 1029/1000 (z<sup>3</sup>g<sup>3</sup>), all lower odd limit than the Latrilu comma. But Yaza Liese is called neither Gu & Trizo-agugu nor Gu & Trizogu, but Latriru.
-Some rank-2 temperaments have 3-limit commas, which are written as edos. Every edo implies other commas, which are simply the best strong extension of the 3-limit temperament to higher primes. 12-edo implies Gu and Ru. 5-edo implies Gubi and Zo (and also Ru, but Zo is the canonical comma). 7-edo implies Gu and Ru. 19-edo implies Gu and Lazo. 22-edo implies Triyo and Ru. '''Tweaks''' aka warts change the implied comma: 22c-edo implies Gu and Ru. [''needs checking: The best extension sometimes creates tweaks, e.g. 12-edo's best 11-limit extension is 33/32, not 729/702, thus 12-edo becomes 12e-edo.'']
+Some rank-2 temperaments have 3-limit commas, which are written as edos. Every edo implies other commas, which are simply the best strong extension of the 3-limit temperament to higher primes. 12-edo implies Gu and Ru. 5-edo implies Gubi and Zo (and also Ru, but Zo is the canonical comma). 7-edo implies Gu and Ru. 19-edo implies Gu and Lazo. 22-edo implies Triyo and Ru. '''Tweaks''' aka warts change the implied comma: 22c-edo implies Gu and Ru. [''needs checking: The best extension sometimes creates tweaks, e.g. 12-edo's best 11-limit extension is 33/32, not 729/704, thus 12-edo becomes 12e-edo.'']
 Edos become rank-2 in two ways. One way is by adding an untempered prime, as in Blackwood, which is 5-edo + Ya. The "+ Ya" means the Gu comma is no longer implied. The other way is to add a bicolored comma, e.g. 12-edo & Ruyoyo. Since Ruyoyo is yaza, the Gu & Ru commas are no longer implied.