Kite's color notation: Difference between revisions

== Color names for primes 3, 5, and 7 ==

File:Lattice32.png | 694x694px

The following table lists all the intervals in this lattice. See the [[gallery of just intervals]] for many more examples.

 

{| class="wikitable" style="text-align: center;"

! colspan="2" | '''color & degree'''

| 1/1

| 0¢

| wa unison

| w1

| 21/20

| 84¢

| zogu 2nd

| zg2

| 16/15

| 112¢

| gu 2nd

| g2

| 15/14

| 119¢

| ruyo unison

| ry1

| 10/9

| 182¢

| yo 2nd

| y2

| 9/8

| 204¢

| wa 2nd

| w2

| 8/7

| 231¢

| ru 2nd

| r2

| 7/6

| 267¢

| zo 3rd

| z3

| 6/5

| 316¢

| gu 3rd

| g3

| 5/4

| 386¢

| yo 3rd

| y3

| 9/7

| 435¢

| ru 3rd

| r3

| 21/16

| 471¢

| zo 4th

| z4

| 4/3

| 498¢

| wa 4th

| w4

| 7/5

| 583¢

| zogu 5th

| zg5

| 10/7

| 617¢

| ruyo 4th

| ry4

| 3/2

| 702¢

| wa 5th

| w5

| 32/21

| 729¢

| ru 5th

| r5

| 14/9

| 765¢

| zo 6th

| z6

| 8/5

| 814¢

| gu 6th

| g6

| 5/3

| 884¢

| yo 6th

| y6

| 12/7

| 933¢

| ru 6th

| r6

| 7/4

| 969¢

| zo 7th

| z7

| 16/9

| 996¢

| wa 7th

| w7

| 9/5

| 1018¢

| gu 7th

| g7

| 28/15

| 1081¢

| zogu octave

| zg8

| 15/8

| 1088¢

| yo 7th

| y7

| 2/1

| 1200¢

| wa octave

| w8

 

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 notation#Color%20Names%20for%20Higher%20Primes | #Color Names for Higher Primes]] below for why). Intervals on the lattice's far right or far left are called not augmented and diminished but '''large''' and '''small''', written as L and s, and abbreviated as '''la''' and '''sa'''. La and sa can always be distinguished from solfege's La and saregam's Sa by context. '''Central''', the default, means neither large nor small. This lattice shows the boundaries between the large, small and central zones:  

'''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 [[243/242 | 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.   

Similarly, '''tweno/-nu/-na''' = 29o/29u/29a, '''thiwo/-wu/-wa''' = 31o/31u/31a, etc. The abbreviations are '''twe-''', '''thi-''', '''fo-''', '''fi-''' and '''si-'''. Note that wa by itself means 3-limit, but -wa as a suffix means "-one-all".

 

! rowspan="2" | prime

| 5/4

| 7/4

| 11/8

| 13/8

| 17/16

| 19/16

| 23/16

| 29/16

| 31/16

| 37/32

| 41/32

| 43/32

| 47/32

| 53/32

| 59/32

| 61/32

| y3

| z7

| 1o4

| 3o6

| 17o2

| 19o3

| 23o5

| 29o7

| 31o7

| 37o3

| 41o3

| 43o4

| 47o5

| 53o6

| 59o7

| 61o7

| 67o2

! on the

| M3

| m7

| P4 or A4

| m6 or M6

| m2

| m3

| d5

| m7

| M7

| m3

| M3

| P4

| P5

| M6

| m7 or

| M7

| m2

Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Exponents]] 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. 103o is hundred-tho and 113o is one-ten-tho. Or one might use these terms:

 

| 71o2

| 73o2

| 79o3

| 83o4

| 89o4

| 97o5

| 101o6

| 103o6

| 107o6

| 109o6

| 113o7

| 127o8

| fitwewa

| fitwetha

| fitwena

| fithitha

| fithina

| fifosa

| fifiwa

| fifitha

| fifisa

| fifina

| fisitha

| sisisa

 

Note that 23/16 = 628¢ is a 5th, not a 4th (but see po & qu below). Furthermore, 31/16 = 1145¢ is a 7th not an 8ve, and 37/32 = 251¢ 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:

    

! unison

! 2nd

! 3rd

! 4th

! 5th

! 7th

! 8ve

| 250-450¢

| 450-600¢

| 950-1150¢

| 1150-1200¢

This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 37...]. An alternative method would use the actual 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here. Since negative intervals will arise no matter what, convenience is prioritized. For the first 26 primes, the 24edo-based degrees correspond to [[Val#Shorthand_notation | 7klmrs-edo]].

'''<u>Converting a ratio</u>:''' Find the [[Monzos | monzo]] 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 monzo 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 monzo exponents 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¢, 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]].     

'''Po''' and '''qu''' ("coo") (short forms '''p''' and '''q''') are two optional accidentals that indicate raising/lowering by a pythagorean comma. (Mnemonics: p stands for pythagorean, and q is the mirror image of p.) Why would one want to do that? Because by first subtracting that comma and then adding it on again, one can rename a note as another note. This is similar to [[Sagittal notation | Sagittal]] notation (see [http://tallkite.com/misc_files/Sagittal-JI-Translated-To-Colors.png Sagittal-JI-Translated-To-Colors.png]).

{{Main | Color notation/Temperament names}}

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 y³T. Certain commas over 90¢ 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 & Ruyoyo and [[Meantone family#Dominant | Dominant Meantone]] is Gu & 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.           

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", accidentals that always map to exactly one edostep. Ups and downs are used on the score just like color accidentals are. Notes are named e.g. up C sharp = ^C#. [[Sharpness | Sharp-1 and flat-1]] edos don't require ups and downs.                 

[[Tour of Regular Temperaments | Rank-2 temperaments]] can be notated with ups and downs as well. Plain and mid are also used in this context. Certain temperaments require an additional pair of virtual colors, '''lifts''' and '''drops''' (/ and \). Notes are named lift C = /C, downdrop F sharp = v\F#, etc. Intervals are named drop 4th = \4, uplift major 3rd = ^/M3, etc. Plain means neither up nor down nor lifted nor dropped. There may be upmid or liftmid intervals. Chords are named C-up add lift-seven = C^,/7 = C ^E G /Bb, C uplift-seven = C^/7 = C ^/E G ^/Bb, etc. See [[Pergen | pergens]].  

'''Over''' = prime in the numerator. '''Under''' = prime in the denominator. '''All''' = over, under or neither: wa = 3-limit, ya = 2.3.5, yaza = 2.3.5.7. '''Exponent''' = repeated syllable: triyo = yoyoyo = 125-over.  

{| class="wikitable" style="text-align: center;"

! colspan="2" | -o ("oh") for over

! colspan="2" | -u ("oo") for under

! colspan="2" | -a ("ah") for all

! colspan="2" | -e ("eh") for exponent

| 2

| colspan="2" | —

| colspan="2" | —

| (clear)

| —

| bi ("bee")

| double

| colspan="7" |  

| quad

| quadruple

| yo (yellow)

| y

| ya

| 7

| zo (azul)

| z

| ru (red)

| r

| sep

| septuple

| 11

| (i)lo

| 1o

| lu

| (i)la

| 1a

| le

| 11-fold

| 13

| tho

| 3o

| thu

| 3u

| tha

| 3a

| the

| 13-fold

| 17

| (i)so

| 17o

| su

| 17u

| (i)sa

| 17a

| se

| 17-fold

| 19

| (i)no

| 19o

| (i)nu

| 19u

| na

| 19a

| ne

| 19-fold

| 23

| twetho

| 23o

| twethu

| 23u

| twetha

| twethe

| 23-fold

| colspan="2" | central

| refers to a ratio centrally located in the lattice

| every ratio of odd limit < 81 is central (but only some > 81 are not central)

| la-

| style="text-align: center;" | L

| large, augmented by 2187/2048 from the central ratio

| 32/27 = wa 3rd = w3, 81/64 = lawa 3rd = Lw3

| style="text-align: center;" | s

| small, diminished by 2187/2048 from the central ratio

| 27/16 = wa 6th = w6, 128/81 = sawa 6th = sw6

| colspan="2" | magnitude

| refers to central, la, sa, lala, trisa, quadla, etc.

| the sum of all prime exponents except the 1st, divided by 7 and rounded off

| colspan="2" | i-

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

| colspan="2" | -a-

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

| co-

| style="text-align: center;" | c

| compound (conventional term for widened by an 8ve)

| 7/4 = zo 7th = z7, 7/2 = compound zo 7th = cozo 7th = cz7

| har

| style="text-align: center;" | h

| refers to a harmonic series (otonal) chord

| sub

| style="text-align: center;" | s

| [[60:70:84:105|7:6:5:4]] = C sub-seven = Cs7

| po

| style="text-align: center;" | p

| adds a pythagorean comma, to change the degree

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

| qu

| style="text-align: center;" | q

| subtracts a pythagorean comma

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

| -ti

| T

| changes a comma name to a temperament name

| Gu = 81/80, Guti = meantone

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

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

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

| w-

| alternate interval format, only used for 3-limit commas

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

| colspan="2" | nowa

| remove 3 (wa) from the prime subgroup, i.e. no-threes

| 2.5.7 = yaza nowa, 2.5.7 & 50/49 = Biruyoti nowa

| colspan="2" | noca

| remove 2 (clear) from the prime subgroup, i.e. non-8ve

| colspan="2" | nowaca

| remove both 2 and 3 from the prime subgroup

| 5.7.11 = yazala nowaca

| plus

| style="text-align: center;" | +

| add an untempered prime to the temperament

| Blackwood = 2.3.5 with 256/243 tempered out = Sawa + ya

| and

| style="text-align: center;" | &

| joins commas that are tempered out

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

| -ward

| style="text-align: center;" | -wd

| refers to the direction of chord root movement

| up

| down

| v

| lowered by some comma

| colspan="2" | arrow

| refers collectively to both ups and downs

| lift

| /

| raised by some other comma

| drop

| \

| lowered by some other comma

| colspan="2" | slash

| refers collectively to both lifts and drops

| plain

| ♢

| neither up nor down nor lifted nor dropped

| mid

| ~

| for 2nds, 3rd, 6ths and 7ths, exactly halfway between major and minor

* [[xen-calc]] – A web app that converts to/from ratios, monzos and color notation, and also supports ups and downs notation.

* [[ledzo notation]] – A similar competing notation system.

{{Navbox notation}}