Kite's color notation: Difference between revisions

Yo and ru intervals tend to be major, and gu and zo ones tend to be minor. But interval quality is redundant (if a third is yo, it must be major), it's not unique (there are other major thirds available), and quality isn't used with color names (see [[#Color Names for Higher Primes]] below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), written as L and s, and abbreviated as '''la''' and '''sa'''. '''Central''', the default, means neither large nor small. The general term for large/small/central/etc. is '''magnitude'''. When discussing magnitudes in general (e.g. tempering out a large comma usually flattens the 5th), the full words large and small are used to avoid confusion with solfege's La and saregam's Sa.

A ratio's magnitude is the sum of all the monzo exponents except the first one, divided by 7, and rounded off. 0 = central, 1 = large, 2 = double large, etc. 81/64 = Lw3, 135/128 = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees do: w2 + w2 = Lw3. Only intervals have a magnitude, notes never do, and L and s never appear on the staff.

Colors can be doubled or tripled, which are abbreviated '''bi-''' ("bee") and '''tri-''' ("tree"): 49/25= bizogu 9th = zzgg9 and 128/125 = trigu 2nd = g³2. Bi- is only used if it shortens the name: 25/16 = yoyo 5th not biyo 5th. Likewise with magnitudes: double-large is lala and triple-large is trisa. For quadruple, etc., see [[#Exponents]].  

Colors using only one prime above 3 are called '''primary''' colors. Thus gu and yoyo are primary and ruyo is non-primary.

[[File:Lattice41a.png|833x833px]]

Degrees can be negative: 50/49 = biruyo negative 2nd = rryy-2. It's a negative 2nd because it goes up in pitch but down the scale: zg5 + rryy-2 = ry4. Negative is different than descending, from ry4 to zg5 is a descending negative 2nd. There are also diminished unisons, which raise the pitch but diminish the quality. For example, if 11/8 is notated as a P4, two of them are a m7 of 121/64 = 1102¢. Going from a yo M7 = 1088¢ up to this m7 raises the pitch, and 121/120 is a dim unison.

Compound, abbreviated '''co-''' or '''c''', is a conventional term that means widened by an octave. 15/4 is a compound yo 7th = coyo 7th = cy7. 5/1 is a double-compound yo 3rd = cocoyo 3rd = ccy3. 9/1 is a tricowa 2nd = c³w2. More examples in the [[Gallery of just intervals#Intervals larger than an octave|Gallery of just intervals]]. Mnemonic: co- as in co-pilot means auxiliary, thus a 9th is a co-2nd. See [[#Prime Subgroup Names]] below for another mnemonic.

'''Lo''' = 11-over, '''lu''' = 11-under, and '''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 words, it doesn't need i-, as in 11/7 = loru 5th. La when by itself becomes '''ila''', to avoid confusion with the solfege note La, and also with la for large. Lo and lu are abbreviated to '''1o''' and '''1u''' 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 on C. Lolo is 1oo, trilu is 1u³, etc. The associated color is lavender (mnemonic: "e-leven-der"), which refers to both ilo and lu, since they are only 7.1¢ 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. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.  

Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Temperament Names]] below). Setho means 13¹⁷-over, so it can't mean 73-over. So starting at 71, one might use the longer form: 71o is seventy-wo, 73o is seventy-tho, etc. Or one might use these terms:     

Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that omits the degree. [[Meantone]] is the Gu temperament. [[Srutal]] is Sagugu. [[Porcupine]] is Triyo. Certain commas over 90¢ use the -bi suffix, e.g. [[Mavila]] is Layobi, because Layo is [[Schismic]]. Certain wa commas use yet another alternate format, e.g. Mercator's comma is Wa-53 or w-53.