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

[[Color notation]] can name every regular temperament. The name is the same as that of the comma(s) tempered out, but without the degree (unison, 2nd, etc.). For example, Semaphore is the Zozo temperament. The name of the temperament and the comma is always capitalized, to distinguish it from the color. Thus zozo refers to all zozo ratios, whereas Zozo refers to one specific zozo ratio, the zozo 2nd = zz2 = 49/48.   

The color defines a lattice row, and the magnitude (large, small, etc.) defines a '''segment''' of that row. A name without a magnitude, like Zozo, refers to the central segment. Each segment contains 7 ratios. The comma that is tempered out is the smallest in cents of those 7.  

* '''-bi''' or '''-tri''' at the end of a name indicates that the comma is the 2nd or 3rd largest ratio in that segment, e.g. Mavila = Layobi   

Some 5-limit examples, sorted by color depth. Many more examples can be found on the comma pages [[Comma|here]], [[Medium commas|here]], [[Large commas|here]] and [[Unnoticeable comma|here]].

Note that sep- means 7-fold, while se- means 17-fold. Multipliers affect all subsequent syllables until the '''-a-''' delimiter occurs: Trizogu = z³g³ and Trizo-agu = z³g. The "a" in la and sa acts as a delimiter: Trilayo = L³y and Trila-triyo = L³y³. More examples of temperaments: 

To make the names easier for non-Anglophones, and to make the names quicker to say, the 5 vowels are the basic vowels found in Spanish, ah-eh-ee-oh-oo. Quin is an exception. Quad may optionally be spoken as "kwah", and quin as "kwee" or "keen". In Spanish and many other languages, "th" would become "tr". See [[Color notation/Translations|Color Notation/Translations]]. Number words like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: sasa-'''gu'''gu, bi'''ru'''yo, bi'''zo'''zogu. In longer names, the 1st occurrence of sa/la and/or of lower primes may also be accented: '''sa'''sa-'''gu'''gu, '''zo'''zotri'''gu'''.  

Hyphens are used to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity. Hyphens are inserted before every -a- delimiter and after the magnitude (after the final la- or sa-). However, the hyphen after the magnitude is omitted if it would create a subunit of 1 syllable. Thus Layo, Lalagu and Sagugu are unhyphenated.

Any comma smaller than 256/243 = 90¢ is guaranteed to be the smallest ratio in its segment. Any comma bigger than 9/8 = 204¢ is guaranteed to <u>not</u> be the smallest, and -bi or -tri must be appended to the name. If a comma is 90-204¢, let S = the sum of all the numbers in the monzo except the first one. If and only if S mod 7 is 4 or 5, 256/243 can be subtracted without changing the magnitude, and the comma is the 2nd smallest ratio. Any 204-294¢ comma is -bi, and any 408-498¢ comma is -tri.  

Sometimes the smallest ratio in a segment is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/400. But since this is (21/20)², tempering it out would simply result in the Zogu temperament. Thus there is no Bizogu temperament, although there is a Bizogubi one.

Every ratio can be named either as a standard interval or as a comma/temperament, e.g. 128/125 is both the trigu 2nd and the Trigu comma. The latter is awkward for low-odd-limit ratios: 5/4 would be the Yobi "comma" and 6/5 would be the Gutri "comma". But the former is awkward for high odd-limit ratios, because there will be many 2nds and 3rds and even 4ths, and many of them will be negative. Unfortunately this makes identifying the comma a little more work.  

It's fairly easy to find the color name for a temperament. If the comma is < 90¢, the name can be found directly from the monzo. The color is obvious. The magnitude is the sum of all the exponents except the 2-exponent, divided by 7 and rounded off.

 

To find the comma from the color name, first find the ratio of the midpoint of the segment, which has a 3-exponent that is a multiple of 7. Then find the cents of this ratio, and use this chart, which is based on the 3-limit Dorian scale:

!If the midpoint ratio is

!do this to the 3-exponent

NAMING PROBLEM:

* Add another word: Lasepyo on yaza, or yaza-ish lasepyo