Kite's color notation/Temperament names
Color notation can name every regular temperament. The name is based on the comma(s) tempered out. The magnitude is part of the name: Schismatic is LyT and Diaschismic is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios in that row segment (i.e. of that magnitude and color): Mavila is Ly1T and Father is g2T. The degree is never needed if the comma is ≤ 90¢. The degree is also unneeded if the smaller ratio is a multiple of a simpler comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)2, tempering it out would simply result in zgT. Thus zzggT refers to tempering out the next largest ratio, 784/675 = 259¢.
[Idea to consider: the Wesley comma (-13,-2,7) has the awkward name of lasepyo-negative-two. Should there be a word for the 2nd biggest ratio in the segment? The degree doesn't matter much, and is tedious to calculate.]
Words like large, small, double, etc. are abbreviated to make the names a reasonable length.
- Double = bi- ("bee"), triple = tri- ("tree"), quadruple = quad-, quintuple = quin-
- 6-fold = tribi-, 7-fold = sep-, 8-fold = quabi-, 9-fold = tritri-, 10-fold = quinbi-
- 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc.
- Large = la-, small = sa-, double large = lala-, triple small = trisa-, etc.
Higher primes use their color word, but with the suffix -e for exponent: 11-fold = le- ("leh"), 13-fold = the- (unvoiced "th"). 17 = se-, 19 = ne-, 23 = twenty-the-, etc.
Even with these abbreviations, temperament names can get quite long. To make them quicker to say, "bee" and "tree" are preferred over "bye" and "try", and quadbi- is shortened to quabi-. If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.
La also means 11-all. The meaning will almost always be clear from context, however "this piece uses la notes" is ambiguous. To clarify, one should say either "large notes" (fifthward notes) or "ila notes" (11-limit notes). Likewise, sa also means 17-all, and "sa notes" should become either "small notes" or "isa notes".
La is also the La note in solfege, and Sa is the tonic in saregam. The meaning will always be clear from context. Notes are never large or small. In fixed-do countries, the chord ALw (81/64 3rd) is "La lawa".
Common examples: Porcupine = Triyo, Pajara = Sagugu, Augmented = Trigu, Diminished = Quadgu, Helmholtz = Layo. Many more examples can be found on the Commas page.
There are two obvious ways to name multi-comma temperaments. The odd name minimizes the double odd limit of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit Pajara is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y3&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between bicolored rank-2 temperaments better. The question of which name to use is not yet fully resolved.
Rules for naming remote colors and extreme magnitudes
There can be more than one way to name a comma. To avoid duplicate names, there are naming rules.
- Colors are always listed highest primes first.
- Multipliers affect all syllables up until the -a- delimiter occurs: trizogu = z3g3, but trizoagu = z3g.
- The "a" in la and sa acts as a delimiter: trilayo = L3y and trilatriyo = L3y3
- Multiplier syllables fuse into one multiplier word: tribizogu = (tribi) x (zogu) = z6g6, not (tri) x (bizogu) = z6g3.
- Avoid using the -a- delimiter if possible: z4gg = bizozogu, not quadzoagugu
Therefore if the name starts with a multiplier word, and there's no -a- delimiter, that first multiplier word indicates the GCD and thus the pergen's split(s). e.g. bizozogu = (P8, P5/2, /1). (In the following list, an asterisk marks cases where this isn't possible, and the GCD is hidden.)
Gugu is generally preferred over bigu (zogugu not zobigu). But bizo is preferred over zozo sometimes to indicate the GCD, e.g. bizogugu not zozoquadgu. Likewise, tribigu is preferred over trigugu, as is quabigu over quadgugu, and quinbigu over quingugu.
There follows examples of remote colors, for illustration. These examples don't all correspond to musically useful temperaments!
Bicolored examples
gg = gugu (Bug)
zgg = zogugu
zzgg = bizogu
zzg = zozogu
3g = trigu
z+3g = zotrigu (Starling)
zz+3g = zozotrigu
3z+3g = trizogu
3z+gg = trizoagugu
3z+g = trizoagu
4g = quadgu
z+4g = zoquadgu
2z+4g = bizogugu
3z+4g = trizoaquadgu
4z+4g = quadzogu
4z+3g = quadzoatrigu
4z+2g = bizozogu (Breedsmic)
4z+g = quadzoagu
5g = quingu
z+5g = zoquingu
2z+5g = zozoquingu
3z+5g = trizoaquingu
4z+5g = quadzoaquingu
5z+5g = quinzogu
5z+4g = quinzoaquadgu
5z+3g = quinzoatrigu
5z+2g = quinzoagugu
5z+g = quinzoagu
6g = tribigu
z+6g = zotribigu
2z+6g = bizotrigu
3z+6g = trizogugu
4z+6g = bizozotrigu
5z+6g = quinzoatribigu
6z+6g = tribizogu
6z+5g = tribizoaquingu
6z+4g = tribizoaquadgu*
6z+3g = trizozogu
6z+2g = tribizoagugu*
6z+g = tribizoagu
7g = sepgu
z+7g = zosepgu
2z+7g = zozosepgu
3z+7g = trizoasepgu
4z+7g = quadzoasepgu
5z+7g = quinzoasepgu
6z+7g = tribizoasepgu
7z+7g = sepzogu
7z+6g = sepzoatribigu
7z+5g = sepzoaquingu
7z+4g = sepzoaquadgu
7z+3g = sepzoatrigu
7z+2g = sepzoagugu
7z+g = sepzoagu
8g = quabigu
z+8g = zoquabigu
2z+8g = bizoquadgu
3z+8g = trizoaquabigu
4z+8g = quadzogugu
5z+8g = quinzoaquabigu
6z+8g = tribizoaquabigu*
7z+8g = sepzoaquabigu
8z+8g = quabizogu
8z+7g = quabizoasepgu
8z+6g = quabizoatribigu*
8z+5g = quabizoaquingu
8z+4g = quadzozogu
8z+3g = quabizoatrigu
8z+2g = quabizoagugu*
8z+g = quabizoagu
9g = tritrigu
z+9g = zotritrigu
2z+9g = zozotritrigu
3z+9g = trizotrigu
4z+9g = quadzoatritrigu
5z+9g = quinzoatritrigu
6z+9g = trizozotrigu
7z+9g = sepzoatritrigu
8z+9g = quabizoatritrigu
9z+9g = tritrizogu
9z+8g = tritrizoaquabigu
9z+7g = tritrizoasepgu
9z+6g = tritrizoatribigu*
9z+5g = tritrizoaquingu
9z+4g = tritrizoaquadgu
9z+3g = tritrizoatrigu*
9z+2g = tritrizoagugu
9z+g = tritrizoagu
Possible solution to the GCD problem:
bi- + -a- = double-all --> affects the whole name
6z+4g = tribizoaquadgu* = biatrizoagugu?
6z+2g = tribizoagugu* = biatrizoagu?
6z+8g = tribizoaquabigu* = biatrizoaquadgu?
8z+6g = quabizoatribigu* = biaquadzoatrigu?
8z+2g = quabizoagugu* = biaquadzoagu?
9z+6g = tritrizoatribigu* = triatrizoagugu?
9z+3g = tritrizoatrigu* = triatrizoagu?
Tricolored examples
if ilo is not doubled or tripled, it just gets tacked onto the beginning:
1o+z+2g = lozogugu
1o+2z+2g = lobizogu
1o+2z+g = lozozogu
1o+z+3g = lozotrigu
etc.
1oo+z+g = lolozogu
1oo+z+2g = lolozogugu
1oo+2z+2g = bilozogu
1oo+2z+g = bilozoagu
1oo+z+3g = lolozotrigu
1oo+2z+3g = bilozoatrigu
1oo+3z+3g = lolotrizogu
1oo+3z+2g = lolotrizoagugu
1oo+3z+g = lolotrizoagu
1ooozg = triloazogu
1ooozgg = triloazogugu
1ooozzgg = triloabizogu
1ooozzg = triloazozogu
1ooo+z+3g = triloazotrigu
1ooo+2z+3g = triloazozotrigu
1ooo+3z+3g = trilozogu
1ooo+3z+2g = trilozoagugu
1ooo+3z+g = trilozoagu
Quadricolored examples
if tho is not doubled or tripled, it just gets tacked onto the beginning:
3o1uzg = tholuzogu
3o1uzgg = tholuzogugu
3o1uzzgg = tholubizogu
3o1uuzzg = thobiluzoagu
etc.
3oo1uzg = thotholuzogu
3oo1uzgg = thotholuzogugu
3oo1uzzg = thotholuzozogu
3oo1uzzgg = thotholubizogu
3oo1uuzg = bitholuazogu
3oo1uuzgg = bitholuazogugu
3oo1uuzzg = bitholuzoagu
3oo1uuzzgg = bitholuzogu
etc.