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

# [[Negri]] = Laquadyo, [[Tetracot]] = Saquadyo, [[Vulture]] = Sasa-quadyo, [[Diminished]] = Quadgu.

Multipliers like bi-, tri-, etc. can be combined: 6-fold = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. Higher primes use their color word, but with the suffix '''-e''' ("eh") for exponent:  

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:   

* [[User:TallKite/Catalog of seven-limit rank two temperaments with Color names]]   

If the comma is wa, an edo is implied. The temperament is named after the edo, not the wa comma, because "12-edo" is more informative than "Lalawa". For example, tempering out the pythagorean comma and 225/224 makes 12-edo & Ruyoyo.   

== Finding the comma from the name and vice versa ==

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.   

== Naming multi-comma temperaments ==

Rule #1 ensures linear independence. It completely determines the first comma, except possibly for the edo problem (see Issues below).

The pivot product indicates the amount of splitting in the [[pergen]]. 2 means something is split in half. 4 means either one thing is split into quarters, or two things are split into halves. Some double-split pergens have more splitting than the pivot product implies, thus a quad- comma can make an 8-fold split, e.g. Laquadlo = (P8/2, M2/4). But M2 = P5 + P5 - P8. Thus if M2 has a genspan of 4, P5 has a genspan of 2, and the pivot product is 2 x 2 = 4. For a pergen (P8/m, (a,b)/n), where (a,b) is the multigen, the pivot product is m·n/|b|. Pergens with an imperfect multigen (|b| > 1) are fairly rare, only about 3% of all rank-2 pergens. For a rank-3 pergen (P8/m, (a,b)/n, (a',b',c')/n'), the pivot product is m·n·n'/|b·c'|.

Because of rule #2, <u>the color name always indicates strong vs. weak upward extensions</u>. A strong extension always has the same pivot product, and a weak extension never does. Thus a strong upward extension always adds a comma with a pivot of 1, and a weak upward extension always adds a comma with a pivot > 1. (See "Issues" for downward extensions.) Gugu = 27/25, and Zozo = 49/48, and each one is (P8, P4/2). Combining both commas, Gugu & Zozo is a bad name, because it looks like a weak extension of Gugu (and of Zozo) when it is actually strong. This is because Gugu & Zozo has torsion. We can't change the ya comma, because rule #1 completely determines the 1st comma. Instead we change the 2nd one, and call it Gugu & Zogu. The Zogu comma is 21/20, so this name also has the advantage of using a lower odd-limit comma. However, often the effect of avoiding torsion is to raise the odd limit. For example, Pajara is Sagugu & Ru (2048/2025 & 64/63), not Sagugu & Biruyo, even though the Biruyo comma 50/49 has a lower odd limit.  

=== Inheriting temperament names ===

Rule #3 is easy to apply. Any comma to be excluded will have a pivot of 1. Simply remove that comma's pivot color from any other commas on the list by adding/subtracting it from them. If given Gu & Trizo-agugu and told that Gu should be excluded, eliminate gu by subtracting two Gu commas from Trizo-agugu, making Satrizo. The cents become negative, so invert to get Latriru.

For some temperaments, the commas' odd limits are much smaller if one changes the order of higher primes: 2.3.5.7 becomes 2.3.7.5. This means the first comma is za and the second one is yaza. The 2nd comma's pivot is the ya-exponent.

A strong downward extension always removes the original name if the new comma's pivot is > 1. A strong upward extension never removes it.

EDO PROBLEM:

DEFINITION OF BADNESS:

The color name indicates the prime subgroup. For example, Ruyoyo (225/224, [[Marvel]]) is yaza (2.3.5.7) because it contains 2 explicit colors ru and yo (7 and 5) and 2 implicit colors wa and clear (3 and 2). For explicit colors, each color pair (yo/gu, zo/ru, ilo/lu etc.) indicates a single prime. For example, Sagugu & Biruyo has only 2 explicit color pairs, and is yaza.

The color name also indicates the pivot product, and thus hints at the [[pergen]]. The name only indicates the amount of splitting, not which wa interval is split. Because Sagugu has gu twice, it halves something, in this case the 8ve. Zozo halves the 4th, Bizozogu halves the 5th, and Latrizo splits the 5th into three parts. A name with a tribi color either splits something into six parts, or splits something into two and something else into three. (This is one rationale for using tribi and not hexa, to show the possibilities.) A strong extension of a temperament has the same pergen, and a weak extension has a different one. Thus adding either 2 or 3 to the subgroup is a weak extension. For example, Gu & Biruyo must be a weak extension of Gu, and a strong extension of Biruyo. The commas in a multi-comma temperament name are chosen to indicate strong & weak extensions.

The taxicab distance and the cents together roughly indicate the damage of the temperament. Gubi is > 90¢ and not far away, and thus high damage. Layobi is > 90¢ but somewhat far away, and is medium damage. Sasa-quadyo is < 204¢ and quite far away, and low damage.

=== Advantages over current temperament names ===

* Mavila is a Chopi village

* Orwell wrote "1984", in which Winston, Big Brother and Doublethink appear

Color names can be spoken without confusion, because there are no homonyms such as:

* Squares/Skwares