Kite's color notation: Difference between revisions

The next table lists all the intervals in this lattice. See the [[Gallery of Just Intervals]] for many more examples.   

!'''ratio'''

!'''cents'''

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 "Higher Primes" below for why). Instead of augmented and diminished, remote intervals are '''large''' (fifthward) and '''small''' (fourthward), written L and s, and sometimes abbreviated '''la''' and '''sa''' (especially in temperament names). '''Central''', the default, means neither large nor small. The '''magnitude''' is the sum 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.

[[File:Lattice41a.png|833x833px]]  

'''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''' and '''19u'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu key" from "the new key". 12edo implies yasana = 2.3.5.17.19.  

Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.   

For any prime P, the degree of the ratio P/1 is determined by its 8ve-reduced cents, and how it relates to 12edo: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37...|. (An alternate method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, less convenient than the 24edo boundaries used here.)

Often a ratio can be converted by breaking it down into simpler, familiar ratios. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. The magnitude is <u>not</u> summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = |-5 2 1>, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.     

Example: interval = sgg2, S = 2 - 1 = 1 step, M = small = -1, monzo = |a b -2>, X = <7 11 16| dot |0 0 -2> = -32, b = (2·1 - 2·(-32) + 3) mod 7 + 7·(-1) - 3 = 69 mod 7 - 7 - 3 = 6 - 10 = -4, a = (1 - (-32) - 11·(-4)) / 7 = 77/7 = 11, monzo = |11 -4 -2>, ratio = 2048/2025.     

Notes on the staff default to wa. Non-wa notes have a color accidental like g, ry, etc. Like conventional sharp/flat accidentals, they apply to every such note in the measure and in the same octave. Unlike conventional accidentals which apply to a note (e.g. A), color accidentals only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo accidental in the first chord applies to all the D naturals in that measure, but not to the D flats.

L and s never appear on the staff. Tripled colors are written as y³ not yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. The font used here is Arial Black.

Triads are named after their 3rd, e.g. a yo chord has a yo 3rd. A yo chord rooted on C is a Cy chord = "C yo" = C yE G. Qualities such as major and minor aren't used, because a chord with an 11/9 3rd is hard to classify. Thirdless dyads are written C5 = w1 w5 or C(zg5) = w1 zg5. The four main yaza triads:

The color name of a rank-2 temperament can be used to name MOS and MODMOS scales, as in Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. This notation is discussed here: [[Naming Rank-2 Scales using Mode Numbers]].  

|+

!prime

! colspan="2" |-a for all

!multiplier

|-

|2

|(clear)

|bi

|-

|3

|wa (white)

|tri

|-

|5

|g

|ya

|quin

|-

|7

|r

|za

|sep

|-

|11

|1a

|le

|-

|13

|3a

|the

|-

|17

|17a

|se

|-

|19

|19a

|ne

|-

|23

|23a

|twenty-the

|}

29o = twenty-no, 31o = thirty-wo, 37o = thirty-so, etc. In the multiplier words for primes 11 and above, -e stands for exponent.

!example

|-

|quadruple, multiplier of 4

|-

| -bi

|as a suffix, 2nd smallest comma in the row segment

|Meantone = 81/80 = Gu = gT, Father = 16/15 = Gubi = g#2T

|-

|large

|augmented by 2187/2048 from the central ratio

|32/27 = (central) wa 3rd = w3, 81/64 = large wa 3rd = Lw3

|-

|small

|diminished by 2187/2048 from the central ratio

|27/16 = (central) wa 6th = w6, 128/81 = small wa 6th = sw6

|-

|la

|large, used in temperament & comma names

|Schismatic = (-15 8 1) = Layo = LyT

|-

|sa

|small, used in temperament & comma names

|Srutal = 2048/2025 = Sagugu = sggT

|-

|plus

|add an untempered prime to the temperament

|Blackwood = 2.3.5 with 256/243 tempered out = 5-edo + ya

|-

|-

|-

|remove both 2 and 3 from the subgroup

|5.7.11 = yazala nowaca

|-

|and

|joins commas that are tempered out

|7-limit Porcupine = 2.3.5.7 with 250/243 & 64/63 = Triyo & Ru

|-

|disambiguation prefix

|no 3rd = omit the 3rd, ino 3rd = 19/16

|-

|delimits a multiplier

|1029/1000 = Trizogu = z³g³, 343/320 = Trizo-agu = z³g

|-

|refers to the direction of chord root movement

|I - IV = 4thwd, I - V = 5thwd, I - III = yoward, i - iii = guward

|-

|po

|adds a pythagorean comma, to change the degree

|15/14 = ruyo unison = ry1 = ruyopo 2nd = ryp2

|-

|qu

|subtracts a pythagorean comma

|49/48 = zozo 2nd = zz2 = zozoqu unison = zzq1

==Translations==