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

If the comma is wa, an edo is implied. For the most common cases of 5-edo, 7-edo and 12-edo, the temperament is named after the wa comma (Sawa, Lawa and Lalawa respectively). For example, tempering out the pythagorean comma and 225/224 makes Lalawa & Ruyoyo. Every other wa comma is named after the edo it implies, thus [-30 19> is Wa-19, not the difficult-to-decipher Trila-wabi. Note that multi-ring edos such as 10-edo can't be implied by a wa comma, and Wa-10 is not a valid comma name. However 10-edo can be created with a non-wa comma, or by a wa comma plus a non-wa comma, e.g. Sawa & Yoyo.

If the commas don't include every prime in the subgroup, some primes are untempered. These primes are added with a plus sign: [[Blackwood]] is Sawa + ya. The 2.3.5.7.11 subgroup with 81/80 tempered out is Gu + zala. Primes 2 and 3 are always assumed to be present in the subgroup, even if the commas don't contain them. They are never added, but are sometimes removed. Prime 3 is removed with the term "Nowa", and prime 2 with "Noca" (ca for clear). Thus 2.5.7 with 50/49 is named Biruyo Nowa. "Nowaca" removes both 2 and 3.  

A non-wa comma can also imply an edo, but that edo isn't part of the temperament's name. Tempering out 128/125 from 2.3.5 makes Trigu, not 3-edo + wa. This avoids a non-wa comma having the same name as a wa comma.  

Temperaments can be abbreviated using "T": Zozo = zzT, Triyo = y³T, Gu & Rugu = g&rgT, Layobi = Ly#2T, Sawa + ya = sw+yT, Gu + zala = g+z1aT, and Biruyo Nowa is rryy-wT.