Kite's color notation: Difference between revisions

{{nowrap|'''Lo''' {{=}} 11-over|'''lu''' {{=}} 11-under}}, and {{nowrap|'''la''' {{=}} 11-all}} = 2.3.11. Because "lo C" sounds like "low C", lo when by itself becomes '''ilo''' ("ee-LOW"). But when with other syllables, it doesn't need i-, as in {{nowrap|11/7 {{=}} loru 5th}}. La when by itself becomes '''ila''', to avoid confusion with the solfege note La, and also with La for large. Sans serif fonts like the one you're reading right now conflate upper-case-i with lower-case-L, so ilo and ila are capitalized as iLo and iLa rather than Ilo and Ila. iLo and lu are abbreviated to '''1o''' and '''1u''' both on the score and in interval names and chord names, e.g. ilo A = 1oA, ilo 4th = 1o4 = 11/8, and C ilo seven = C1o7 = 1/1 - 11/9 - 3/2 - 11/6. Lolo is written 1oo. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only [[243/242 |7.1{{c}}]] apart. Lavender is a '''pseudocolor''' that implies the [http://x31eq.com/cgi-bin/rt.cgi?ets=24_17&limit=2_3_11 Lulu aka Neutral] temperament. iLo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.   

Note that 23/16 = 628{{c}} is a 5th, not a 4th (but see po & qu below). Furthermore, 31/16 = 1145{{c}} is a 7th not an 8ve, and 37/32 = 251{{c}} is a 3rd not a 2nd. For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo:

'''<u>Converting a ratio</u>:''' Find the  PCV by prime factorization. To find the color, combine all the appropriate colors for each prime > 3, higher primes first. To find the degree, first find the [[stepspan]], which is the dot product of the PCV with the "pseudo-edomapping" discussed above <7 11 16 20 24 26 29 30...]. Then add 1, or subtract 1 if the stepspan is negative. To find the magnitude, add up all the prime counts except the first one, divide by 7, and round off. Combine the magnitude, color and degree to make the color name. If the interval is > 1200{{c}}, octave-reduce as desired (e.g. a 9th may or may not become a compound 2nd). Add one co- prefix for every octave removed. Combine repeated syllables so that three yo's becomes triyo, etc. For the exact combination "grammar", see [[Color notation/Temperament Names]].     

The [[4:5:6:7|y,z7 chord]] is called the har7 ("har-seven") or h7 chord, because it's part of the harmonic series. {{nowrap|[[4:5:6:7:9|Ch9]] {{=}} Cy,z7,9}} and {{nowrap|[[4:5:6:7:9:11|Ch11]] {{=}} Cy,z7,w9,1o11}}. The [[60:70:84:105|sub7 ("sub-seven") or s7 chord]] is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. {{nowrap|[[140:180:210:252:315|Cs9]] {{=}} Cr,g7,9}} and {{nowrap|Cs11 {{=}} C1o11(1or5,1og9)}}. Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ''ascends'' from the root, but in a sub9 chord it ''descends'' from the top note, and becomes the new root. Thus the s7 chord is contained in the ''upper'' four notes of the s9 chord, not the lower four.   

Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that omits the degree. [[81/80]] is the Gu comma, with the "G" capitalized to distinguish it from the gu ''color'', which includes many ratios. Tempering out Gu creates [[Meantone]] or Guti or gT, where "-ti" and "T" stand for temperament. [[2048/2025]] is the Sagugu comma sgg2, and [[Srutal]] is Saguguti or sggT. [[Porcupine]] is Triyoti or 3yT. Certain commas over 90{{c}} use the -bi- syllable (see the[[Color notation/Temperament names | main article]] for details). For example, [[Schismic]] is Layoti or LyT, but [[Mavila]] is Layobiti or Ly#2T.  Certain wa commas use yet another alternate format, e.g. [[Mercator's comma]] is Wa-53 or w-53.           

Multi-comma temperaments have multiple commas in their name. [[Meantone family#Septimal meantone | Septimal Meantone]] is Gu &amp; Ruyoyo and [[Meantone family#Dominant | Dominant Meantone]] is Gu &amp; Rugu (-ti can be omitted when the ampersand is used). Untempered primes are included with a plus sign. The 2.3.5.7 prime subgroup with 81/80 tempered out is Guti + za = gT+z, and [[Blackwood]] is Sawa + ya = swT+y.           

Color notation merely renames ratios more conveniently, and strictly speaking, it only applies to just intonation. However, ratios are often used to loosely describe intervals in [[EDO | edos]], and colors can be used as well. A more precise notation uses [[Ups and downs notation |'''ups''' '''and''' '''downs''']] (^ and v) as "virtual colors", inflections that always map to exactly one edostep. Ups and downs are used on the score just like color inflections are. Notes are named e.g. up C sharp = ^C#. [[Sharpness | Sharp-1 and flat-1]] edos don't require ups and downs.                 

<u>Pronunciation</u>: exponent syllables like bi or tri are always unaccented. To emphasize the prime limit, the first occurrence of the highest prime is always accented: 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'''.

! colspan="2" | Word

| har

| sub

| po

| qu

| -ti

| changes a comma name to a temperament name

| Gu = 81/80, Guti = meantone

| -bi

| style="text-align: center;" | #2

| Guti = gT is Meantone, but Gubiti = g#2T is [[Father]] (16/15 vanishes)

| Wa-

| [[Mercator's comma]] = Wa-53 = w-53