Kite's color notation: Difference between revisions

If two ratios have the same color, their [[Monzo|monzos]] differ only in the first two numbers. For example, the zogu 5th 7/5 is [0 0 -1 1⟩ and the zogu 2nd 21/20 is [-2 1 -1 1⟩. Thus all zogu ratios have a monzo of the form [a b -1 1⟩.

!Monzo

|[0 0⟩

|[-2 1 -1 1⟩

|[-4 1 1⟩

|[-1 1 1 -1⟩

|[1 -2 1⟩

|[-3 2⟩

|[3 0 0 -1⟩

|[-1 -1 0 1⟩

|[1 1 -1⟩

|[-2 0 1⟩

|[0 2 0 -1⟩

|[-4 1 0 1⟩

|[2 -1⟩

|[0 0 -1 1⟩

|[1 0 1 -1⟩

|[-1 1⟩

|[5 -1 0 -1⟩

|[1 -2 0 1⟩

|[3 0 -1⟩

|[0 -1 1⟩

|[2 1 0 -1⟩

|[-2 0 0 1⟩

|[4 -2⟩

|[0 2 -1⟩

|[2 -1 -1 1⟩

|[-3 1 1⟩

|[3 -1 1 -1⟩

|[1 0⟩

{{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. 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 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. IIo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender.   

'''Tho''' ([[wikipedia:Voiceless_dental_fricative|unvoiced th]] as in "'''th'''irteen") = 13-over, '''thu''' = 13-under, and '''tha''' = 13-all. Tho and thu are abbreviated as '''3o''' and '''3u''' on the score and in interval names, e.g. 13/8 is a tho 6th = 3o6 and 14/13 is a thuzo 2nd = 3uz2. Thuthu is written 3uu. (See the preceding paragraph for why tho is written 3o and not 13o.)  

!prime

|2

|(clear)

|—

|bi ("bee")

|double

|3

|wa (white)

|—

|tri ("tree")

|triple

|quad

|quadruple

|5

|yo (yellow)

|y

|gu (green)

|g

|ya

|—

|quin

|quintuple

|7

|zo (azul)

|z

|ru (red)

|r

|za

|—

|sep

|septuple

|11

|(i)lo

|1o

|lu

|1u

|(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

|23a

|twethe

|23-fold

!Meaning

!Example

|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-

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

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

|sa-

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

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

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

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

|disambiguation prefix

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

|delimits an exponent such as bi-, tri-, etc.

|Trizogu = 3zg = 1029/1000, but Trizo-agu = 3zag = 343/320

|co-

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

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

|har

|refers to a harmonic series (otonal) chord

|[[4:5:6:7]] = C har-seven = Ch7

|sub

|refers to a subharmonic series (utonal) chord

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

|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

| -ti

|T

|changes a comma name to a temperament name

|Gu = 81/80, Guti = meantone

| -bi

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

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

|Wa-

|w-

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

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

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

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

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

|3.5.7 = yaza noca, 3.5.7 &amp; 245/243 = Zozoyoti noca

|remove both 2 and 3 from the prime subgroup

|5.7.11 = yazala nowaca

|plus

|add an untempered prime to the temperament

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

|and

|joins commas that are tempered out

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

| -ward

|refers to the direction of chord root movement

|Iy - IVy = 4thwd, Iy - Vy = 5thwd, Iy - yIIIy = yoward, Ig - gIIIg = guward

!Meaning

|up

|^

|raised by some comma

|down

|v

|lowered by some comma

|refers collectively to both ups and downs

|lift

|/

|raised by some other comma

|drop

|\

|lowered by some other comma

|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<br>a mid 4th is halfway-augmented, and a mid 5th is halfway-diminished

==Translations==

*[[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.

==Further reading==

*Giedraitis, Kite. [http://www.tallkite.com/AlternativeTunings.html ''Alternative Tunings: Theory, Notation and Practice''].