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

Line 65:

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 not Gu & Trizo-aquadgu or Gu & Trizogu, but Latriru.

(This rule could possibly be extended to include when the upward extension is weak, and the downward extension is strong but not the best strong one. For example, Injera is Gu & Biruyo, but under this rule, it would become Gu & Laruru. However, this would greatly increase the odd limit.)

Some rank-2 temperaments have 3-limit commas. These commas are written as edos, because "12-edo" is more informative than "Lalawa". 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.

@@ Line 65: / Line 65: @@
 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 not Gu & Trizo-aquadgu or Gu & Trizogu, but Latriru.
-(This rule could possibly be extended to include when the upward extension is weak, and the downward extension is strong but not the best strong one. For example, Injera is Gu & Biruyo, but under this rule, it would become Gu & Laruru. However, this would greatly increase the odd limit.)
 Some rank-2 temperaments have 3-limit commas. These commas are written as edos, because "12-edo" is more informative than "Lalawa". 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.