Kite's color notation: Difference between revisions

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'''Color notation''' is a [[musical notation]] system for [[just intonation~~]] that was primarily developed by [[Kite Giedraitis~~]].

'''Color notation''' is a [[musical notation]] system for [[just intonation]]. Color notation has many features that other just intonation notations lack:

Color notation has many features that other ~~microtonal~~ notations lack:

* No new symbols: all new accidentals are familiar characters; hence they are immediately speed-readable.

* Furthermore, they are all on the QWERTY keyboard, making the notation easily typeable.

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

Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o, and under colors end with -u. The color for 3-limit ends in -a for '''all''', which includes over (3/2,~~ ~~9/8), under (4/3,~~ ~~16/9) and neither (1/1,~~ ~~2/1).

Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o and under colors end with -u. The color for [[3-limit]] ends in -a for '''all''', which includes over (3/2, 9/8), under (4/3, 16/9) and neither (1/1, 2/1).

{| class="right-1"

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A color and a degree indicate a ratio, and vice versa. Every ratio has a spoken name and a written name. For 3/2, they are wa 5th and w5. Colors and degrees always add up predictably: {{nowrap|z3 + g3 {{=}} zg5}} {{nowrap|{{=}} zogu 5th}}. Zogu, not guzo; higher primes always come first. Opposite colors cancel: {{nowrap|y3 + g3 {{=}} w5}}.

The JI lattice consists of many '''rows''', each one a chain of 5ths. Each row has its own color, and each color has its own row.

The JI lattice consists of many '''rows''', each one a [[Chain of fifths|chain of 5ths]]. Each row has its own color, and each color has its own row.

File:Lattice32.png | 694x694px

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desc none

</imagemap>

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⟩.

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

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|-

! Ratio

!Monzo

! Cents

! colspan="2" | Color & degree

|-

| 1/1

|[0 0⟩

| 0{{c}}

| wa unison

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|-

| 21/20

|[-2 1 -1 1⟩

| 84{{c}}

| zogu 2nd

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|-

| 16/15

|[-4 1 1⟩

| 112{{c}}

| gu 2nd

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|-

| 15/14

|[-1 1 1 -1⟩

| 119{{c}}

| ruyo unison

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|-

| 10/9

|[1 -2 1⟩

| 182{{c}}

| yo 2nd

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|-

| 9/8

|[-3 2⟩

| 204{{c}}

| wa 2nd

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|-

| 8/7

|[3 0 0 -1⟩

| 231{{c}}

| ru 2nd

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|-

| 7/6

|[-1 -1 0 1⟩

| 267{{c}}

| zo 3rd

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|-

| 6/5

|[1 1 -1⟩

| 316{{c}}

| gu 3rd

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|-

| 5/4

|[-2 0 1⟩

| 386{{c}}

| yo 3rd

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|-

| 9/7

|[0 2 0 -1⟩

| 435{{c}}

| ru 3rd

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|-

| 21/16

|[-4 1 0 1⟩

| 471{{c}}

| zo 4th

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|-

| 4/3

|[2 -1⟩

| 498{{c}}

| wa 4th

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|-

| 7/5

|[0 0 -1 1⟩

| 583{{c}}

| zogu 5th

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|-

| 10/7

|[1 0 1 -1⟩

| 617{{c}}

| ruyo 4th

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|-

| 3/2

|[-1 1⟩

| 702{{c}}

| wa 5th

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|-

| 32/21

|[5 -1 0 -1⟩

| 729{{c}}

| ru 5th

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|-

| 14/9

|[1 -2 0 1⟩

| 765{{c}}

| zo 6th

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|-

| 8/5

|[3 0 -1⟩

| 814{{c}}

| gu 6th

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|-

| 5/3

|[0 -1 1⟩

| 884{{c}}

| yo 6th

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|-

| 12/7

|[2 1 0 -1⟩

| 933{{c}}

| ru 6th

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|-

| 7/4

|[-2 0 0 1⟩

| 969{{c}}

| zo 7th

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|-

| 16/9

|[4 -2⟩

| 996{{c}}

| wa 7th

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|-

| 9/5

|[0 2 -1⟩

| 1018{{c}}

| gu 7th

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|-

| 28/15

|[2 -1 -1 1⟩

| 1081{{c}}

| zogu octave

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|-

| 15/8

|[-3 1 1⟩

| 1088{{c}}

| yo 7th

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|-

| 40/21

|[3 -1 1 -1⟩

| 1116{{c}}

| ruyo 7th

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|-

| 2/1

|[1 0⟩

| 1200{{c}}

| wa octave

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|}

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:

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). Intervals on the lattice's far right and 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:

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

The general term for large/small/central is '''magnitude'''. Only intervals have a magnitude, notes never do, and L and s never appear on the staff. A ratio's magnitude is the sum of all the [[monzo]] exponents except the first one, divided by 7, and rounded off. {{nowrap|0 {{=}} central|1 {{=}} large|2 {{=}} double large}}, etc. {{nowrap|81/64 {{=}} {{vector| -6 4 }}}}, and 4/7 rounds to 1, so ~~{{nowrap|~~81/64 {{=}} Lw3}}. Similarly, {{nowrap|135/128 {{=}} {{vector| -7 3 1 }}}} =~~ ~~Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees: {{nowrap|w2 + w2 {{=}} Lw3}}.

The general term for large/small/central is '''magnitude'''. Only intervals have a magnitude, notes never do, and L and s never appear on the staff. A ratio's magnitude is the sum of all the [[monzo]] exponents except the first one, divided by 7, and rounded off. {{nowrap|0 {{=}} central|1 {{=}} large|2 {{=}} double large}}, etc. {{nowrap|81/64 {{=}} {{vector| -6 4 }}}}, and 4/7 rounds to 1, so 81/64 is a lawa 3rd = Lw3. Similarly, {{nowrap|135/128 {{=}} {{vector| -7 3 1 }}}} is a layo unison = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees: {{nowrap|w2 + w2 {{=}} Lw3}}.

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

Colors can be doubled or tripled, which are abbreviated '''bi-''' ("bee") and '''tri-''' ("tree"): 49/25 is a bizogu 9th = zzgg9, and 128/125 is a trigu 2nd = ggg2. Bi- is only used if it shortens the name: 25/16 is a yoyo 5th, not a biyo 5th. Likewise with magnitudes: double-large is lala and triple-large is trila. 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.

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 {{nowrap|121/64 {{=}} 1102{{c}}}}. Going from a {{nowrap|yo M7 {{=}} 1088{{c}}}} up to this m7 raises the pitch, and 121/120 is a dim unison.

Degrees can be '''[[Negative interval|negative]]''': 50/49 = 35¢ is a biruyo negative 2nd = rryy-2. It's negative 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.

'''Compound''', abbreviated '''co-''' or '''c''', is a [[wikipedia:Interval_(music)#Compound_intervals|conventional music theory term]] that means widened by an octave. 15/4 is a compound {{nowrap|yo 7th {{=}} coyo 7th}} =~~ ~~cy7. 5/1 is a double-compound {{nowrap|yo 3rd {{=}} cocoyo 3rd}} = ccy3~~. 9/1 is a {{nowrap|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.

'''Compound''', abbreviated '''co-''' or '''c''', is a [[wikipedia:Interval_(music)#Compound_intervals|conventional music theory term]] that means widened by an octave. 15/4 is a compound {{nowrap|yo 7th {{=}} coyo 7th}} = cy7. 5/1 is a double-compound {{nowrap|yo 3rd {{=}} cocoyo 3rd}} = ccy3. 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.

== Note names ==

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== Prime subgroup names ==

Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. ~~{{nowrap|~~Ya ~~{{=}}~~ the 2.3.5 prime subgroup}} =~~ ~~5-limit. {{nowrap|'''Za''' {{=}} 7-all}} ~~= ~~2.3.7 {{nowrap|{{=}} no-fives 7-limit}}. ~~{{nowrap|~~Yaza ~~{{=}}~~ 2.3.5.7}} {{nowrap|{{=}} the full 7-limit}}. '''Nowa''' means without wa, and {{nowrap|yaza nowa {{=}} 2.5.7}}.

Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya refers to the 2.3.5 prime subgroup = 5-limit. {{nowrap|'''Za''' {{=}} 7-all}} refers to 2.3.7 {{nowrap|{{=}} no-fives 7-limit}}. Yaza refers to 2.3.5.7 {{nowrap|{{=}} the full 7-limit}}. '''Nowa''' means without wa, and {{nowrap|yaza nowa {{=}} 2.5.7}}.

Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and {{nowrap|yaza '''noca''' {{=}} 3.5.7}} =~~ ~~[[Bohlen–Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca, and in certain theoretical discussions. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.

Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and {{nowrap|yaza '''noca''' {{=}} 3.5.7}} = [[Bohlen–Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca, and in certain theoretical discussions. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.

More on prime subgroups in the next section.

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Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed:

{{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 ~~words~~, 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 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{{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.

{{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.

(One might be tempted to write 11o instead of 1o. This would work on a score, but would be confusing in chord names. The triad C11o would look like a diminished 11th chord. In general, color notation avoids naming primes with the numbers found in chord names, which are 2 4 5 6 7 9 11 and 13.)

'''Tho''' ~~/θ/~~ = 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 = 3o6 ~~= tho 6th,~~ 14/13 = 3uz2 ~~= thuzo 2nd~~. (See the preceding paragraph for why ~~it's~~ 3o and not 13o.)

'''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 subgroups: yala = 2.3.5.11, zalatha nowa = 2.7.11.13, and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a descriptive adjective, not used in actual prime subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''', '''noyaza''', etc.

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On the score and in note names, the 1o accidental either raises by 33/32 or lowers by 729/704. The meaning will usually be clear from context, however it's safer to write at the top of the page either "1o4 = P4" or "1o4 = A4". Likewise, 3o6 should be noted as either m6 or M6. While the note 11/8 above C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. Likewise, 13/8 above C is either 3oA or 3oAb, but 13/8 is only 3o6. This is the primary rationale for using large/small/central rather than major/minor. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale is that commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, E gu not E gu minor, etc. (see [[#Chord Names]] below).

'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa. (See the 3rd paragraph in this section for why ~~it's~~ 17o and not 7o.)

'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa. (See the 3rd paragraph in this section for why iso is 17o and not 7o.)

'''No''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. '''Ino''' is an alternate form of no, because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu chord" from "the new chord". (See the 3rd paragraph in this section for why ~~it's~~ 19o and not 9o.)

'''No''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. '''Ino''' is an alternate form of no, because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu chord" from "the new chord". (See the 3rd paragraph in this section for why ino is 19o and not 9o.)

The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th not inogu 4th.

'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a ~~= yazatwetha~~. 23/16 = 23o5 ~~= twetho 5th~~, and 23/22 = 23o1u2 ~~= twetholu 2nd~~. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over).

'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yazatwetha = yaza23a. 23/16 is a twetho 5th = 23o5, and 23/22 is a twetholu 2nd = 23o1u2. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over).

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".

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|-

! word

| ya

| yo

| za

| zo

| (i)la

| (i)lo

| ~~tha~~

| tho

| (i)sa

| (i)so

| (i)na

| (i)no

| ~~twetha~~

| twetho

| ~~twena~~

| tweno

| ~~thiwa~~

| thiwo

| ~~thisa~~

| thiso

| ~~fowa~~

| fowo

| ~~fotha~~

| fotho

| ~~fosa~~

| foso

| ~~fitha~~

| fitho

| ~~fina~~

| fino

| ~~siwa~~

| siwo

| ~~sisa~~

| siso

|-

! on the

! on the score

score

| M3

| m7

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| P5

| M6

| ~~m7 or~~

| M7

M7

| M7

| m2

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''Yaza latha sana twetha twena thiwa thisa / Fowa fotha fosa fitha fina siwa sisa''

Unfortunately seventy can't become se- because that already means 17-~~exponent~~ (see [[#Exponents]] below). Setho means 13~~17~~-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:

Unfortunately seventy can't become se- because that already means 17-fold (see [[#Exponents]] below). Setho means 17-fold 13-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:

{| class="wikitable"

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|-

! word

| ~~fitwewa~~

| fitwewo

| ~~fitwetha~~

| fitwetho

| ~~fitwena~~

| fitweno

| ~~fithitha~~

| fithitho

| ~~fithina~~

| fithino

| ~~fifosa~~

| fifoso

| ~~fifiwa~~

| fifiwo

| ~~fifitha~~

| fifitho

| ~~fifisa~~

| fifiso

| ~~fifina~~

| fifino

| ~~fisitha~~

| fisitho

| ~~sisisa~~

| sisiso

|}

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== Exponents ==

Exponent syllables aka multiplier syllables provide a way to shorten names that have repeated syllables. For example, 250/243 = ~~2~~1~~ * 3~~-5~~ * 5~~3~~~~ is a yoyoyo unison which shortens to triyo ~~1sn~~. Exponents can also apply to magnitudes (Wa-~~22 = sasasawa 4th --> trisawa 4th~~) and octaves (13/1 ~~= cococotho 6th~~ --~~> tricotho 6th)~~.

Exponent syllables aka multiplier syllables provide a way to shorten names that have repeated syllables. For example, 250/243 = {{vector| 1 -5 3 }} is a yoyoyo unison which shortens to triyo unison. Exponents can also apply to magnitudes (triple-small is trisa) and octaves (triple-compound is trico).

The triyo unison can be written as y31 for, but it's more convenient (as well as closer to the spoken form) to write 3y1. Trilo is written 3(1o) to distinguish it from 31o, thirty-one-over.

We've seen bi- for double and tri- for triple. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. Colorspeak syllables usually end in one of the five basic vowels. Quad and quin are both exceptions, so quad may optionally be spoken as "kwah", and quin as "kwee".

Except for quad, all exponent syllables are prime numbers. Septuple is '''sep-'''. Above 7, all exponent syllables are the root color word plus -e. Eleven-fold is '''le-''' = "e'''l'''even '''e'''xponent", pronounced as in "lens". Thirteen-fold is '''the-''' as in "thesaurus". Note that sep- means seven-fold and '''se-''' means seventeen-fold.

Except for quad, all exponent syllables are prime numbers. Septuple is '''sep-'''. Above 7, all exponent syllables are the root color word plus -e for exponent. Eleven-fold is '''le-''' = "e'''l'''even '''e'''xponent", pronounced as in "lens". Thirteen-fold is '''the-''' as in "thesaurus". Note that sep- means seven-fold and '''se-''' means seventeen-fold.

Exponents can be combined: sextuple = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. The component syllables are simply the number's prime factors in descending order, except that quad replaces bibi and comes before tri.

Exponents affect all subsequent syllables until the '''-a-''' delimiter occurs: trizogu = ~~z3g3~~, but trizo-agu = ~~z3g~~. The "a" in la- and sa- also acts as a delimiter: trilayo = ~~L3y, not L3y3, which~~ would be trila-triyo.

Exponents affect all subsequent syllables until the '''-a-''' delimiter occurs: trizogu = 3zg is triple-zo triple-gu, but trizo-agu = 3zag is triple-zo single-gu. The "a" in la- and sa- also acts as a delimiter: trilayo = 3Ly is triple-large single-yo. (Triple-large triple-yo would be trila-triyo = 3L3y.)

Long color names use hyphens to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity.

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The hyphen is generally omitted if it would create a subunit of 1 syllable. Thus despite the 2nd rule, layo, lalagu and sagugu are all unhyphenated. And despite the 3rd rule, coyo, cozogu and cocowa are unhyphenated. However, the last rule always holds, e.g. 284/243 = 22 * 3-5 * 71 is a sa-seventy-wo 3rd.

==Converting a ratio to/from a color name ==

Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. 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 not 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.

Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. But is it y4 or Ly4? The magnitude is not summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 = {{vector|-5 2 1}}, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.

For more complex ratios, a more direct method is needed:

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[[File:Notation example 1.png|frameless|781x781px]]

L and s never appear on the staff. Tripled colors are written as y3 not ~~y3 or~~ yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. A fingering can be copied from one note and pasted to another note. The font used here is Arial Black.

L and s never appear on the staff. Tripled colors are written as 3y not yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. A fingering can be copied from one note and pasted to another note. The font used here is Arial Black.

This 10-page score uses the free open-source font Petaluma Script. The letters are 9pt, except that a "z" between two staff lines is 8pt. [[File:Evening Rondo colors.pdf]]

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Subtracting po lowers the degree. Thus ruyopo Db = ruyo C#.

Po and qu can be used with intervals as well. A ruyo ~~1sn~~ becomes a ruyopo 2nd. Neither the color nor the magnitude changes.

Po and qu can be used with intervals as well. A ruyo unison becomes a ruyopo 2nd. Neither the color nor the magnitude changes.

One reason to change the degree is for ease of naming chords. See the Hendrix chord in the next section. Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]]

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Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''' (e.g. s6(zg5) or h7,zg9), etc.

==Chord progressions, keys, scales and modulations==

A conventional chord name like IIm7 names the chord root relative to the tonic and the chord notes relative to the chord root. The "m7" is shorthand for (P1, m3, P5, m7). Adding each of these intervals to the M2 root gives us the four notes of the chord: M2, P4, M6 and P8. In the key of E, it would be F#m7 = F# + (P1, m3, P5, m7) = F#, A, C# and E.

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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{{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.

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 & 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.

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 = gT+z, and [[Blackwood]] is Sawa + ya = swT+y.

MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[~~Naming Rank-2 Scales using Mode Numbers~~]].

MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Genchain mode numbering]].

==Ups and downs, lifts and drops, plain and mid==

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| colspan="2" | -a-

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

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

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

|-

|co-

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

|add an untempered prime to the temperament

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

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

|-

|and

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|mid

|~

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

|for 2nds, 3rd, 6ths and 7ths, exactly halfway between major and minor a mid 4th is halfway-augmented, and a mid 5th is halfway-diminished

a mid 4th is halfway-augmented, and a mid 5th is halfway-diminished

|}

==Translations==

For translations of color notation terms into other languages, see [[Color notation/Translations]]. Translating avoids using sounds not in one's native language. For example, in many European languages, "th-" for prime 13 becomes "tr-".

== Origins ==

Color notation was primarily developed by [[Kite Giedraitis]], with much assistance from [[User:AthiTrydhen|Praveen Venkataramana]].

==See also==

@@ Line 1: / Line 1: @@
-'''Color notation''' is a [[musical notation]] system for [[just intonation]] that was primarily developed by [[Kite Giedraitis]].
+'''Color notation''' is a [[musical notation]] system for [[just intonation]]. Color notation has many features that other just intonation notations lack:
-Color notation has many features that other microtonal notations lack:
 * No new symbols: all new accidentals are familiar characters; hence they are immediately speed-readable.
 * Furthermore, they are all on the QWERTY keyboard, making the notation easily typeable.
@@ Line 10: / Line 8: @@
 == Color names for primes 3, 5, and 7 ==
-Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o, and under colors end with -u. The color for 3-limit ends in -a for '''all''', which includes over (3/2,&nbsp;9/8), under (4/3,&nbsp;16/9) and neither (1/1,&nbsp;2/1).
+Every prime above 3 has two colors, an '''over''' color (prime in the numerator) and an '''under''' color (prime in the denominator). Over colors end with -o and under colors end with -u. The color for [[3-limit]] ends in -a for '''all''', which includes over (3/2, 9/8), under (4/3, 16/9) and neither (1/1, 2/1).
 {| class="right-1"
@@ Line 35: / Line 33: @@
 A color and a degree indicate a ratio, and vice versa. Every ratio has a spoken name and a written name. For 3/2, they are wa 5th and w5. Colors and degrees always add up predictably: {{nowrap|z3 + g3 {{=}} zg5}} {{nowrap|{{=}} zogu 5th}}. Zogu, not guzo; higher primes always come first. Opposite colors cancel: {{nowrap|y3 + g3 {{=}} w5}}.
-The JI lattice consists of many '''rows''', each one a chain of 5ths. Each row has its own color, and each color has its own row.
+The JI lattice consists of many '''rows''', each one a [[Chain of fifths|chain of 5ths]]. Each row has its own color, and each color has its own row.
 <imagemap>
 File:Lattice32.png | 694x694px
@@ Line 75: / Line 73: @@
 desc none
 </imagemap>
+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⟩.
 The following table lists all the intervals in this lattice. See the [[gallery of just intervals]] for many more examples.
@@ Line 81: / Line 81: @@
 |-
 ! Ratio
+!Monzo
 ! Cents
 ! colspan="2" | Color &amp; degree
 |-
 | 1/1
+|[0 0⟩
 | 0{{c}}
 | wa unison
@@ Line 90: / Line 92: @@
 |-
 | 21/20
+|[-2 1 -1 1⟩
 | 84{{c}}
 | zogu 2nd
@@ Line 95: / Line 98: @@
 |-
 | 16/15
+|[-4 1 1⟩
 | 112{{c}}
 | gu 2nd
@@ Line 100: / Line 104: @@
 |-
 | 15/14
+|[-1 1 1 -1⟩
 | 119{{c}}
 | ruyo unison
@@ Line 105: / Line 110: @@
 |-
 | 10/9
+|[1 -2 1⟩
 | 182{{c}}
 | yo 2nd
@@ Line 110: / Line 116: @@
 |-
 | 9/8
+|[-3 2⟩
 | 204{{c}}
 | wa 2nd
@@ Line 115: / Line 122: @@
 |-
 | 8/7
+|[3 0 0 -1⟩
 | 231{{c}}
 | ru 2nd
@@ Line 120: / Line 128: @@
 |-
 | 7/6
+|[-1 -1 0 1⟩
 | 267{{c}}
 | zo 3rd
@@ Line 125: / Line 134: @@
 |-
 | 6/5
+|[1 1 -1⟩
 | 316{{c}}
 | gu 3rd
@@ Line 130: / Line 140: @@
 |-
 | 5/4
+|[-2 0 1⟩
 | 386{{c}}
 | yo 3rd
@@ Line 135: / Line 146: @@
 |-
 | 9/7
+|[0 2 0 -1⟩
 | 435{{c}}
 | ru 3rd
@@ Line 140: / Line 152: @@
 |-
 | 21/16
+|[-4 1 0 1⟩
 | 471{{c}}
 | zo 4th
@@ Line 145: / Line 158: @@
 |-
 | 4/3
+|[2 -1⟩
 | 498{{c}}
 | wa 4th
@@ Line 150: / Line 164: @@
 |-
 | 7/5
+|[0 0 -1 1⟩
 | 583{{c}}
 | zogu 5th
@@ Line 155: / Line 170: @@
 |-
 | 10/7
+|[1 0 1 -1⟩
 | 617{{c}}
 | ruyo 4th
@@ Line 160: / Line 176: @@
 |-
 | 3/2
+|[-1 1⟩
 | 702{{c}}
 | wa 5th
@@ Line 165: / Line 182: @@
 |-
 | 32/21
+|[5 -1 0 -1⟩
 | 729{{c}}
 | ru 5th
@@ Line 170: / Line 188: @@
 |-
 | 14/9
+|[1 -2 0 1⟩
 | 765{{c}}
 | zo 6th
@@ Line 175: / Line 194: @@
 |-
 | 8/5
+|[3 0 -1⟩
 | 814{{c}}
 | gu 6th
@@ Line 180: / Line 200: @@
 |-
 | 5/3
+|[0 -1 1⟩
 | 884{{c}}
 | yo 6th
@@ Line 185: / Line 206: @@
 |-
 | 12/7
+|[2 1 0 -1⟩
 | 933{{c}}
 | ru 6th
@@ Line 190: / Line 212: @@
 |-
 | 7/4
+|[-2 0 0 1⟩
 | 969{{c}}
 | zo 7th
@@ Line 195: / Line 218: @@
 |-
 | 16/9
+|[4 -2⟩
 | 996{{c}}
 | wa 7th
@@ Line 200: / Line 224: @@
 |-
 | 9/5
+|[0 2 -1⟩
 | 1018{{c}}
 | gu 7th
@@ Line 205: / Line 230: @@
 |-
 | 28/15
+|[2 -1 -1 1⟩
 | 1081{{c}}
 | zogu octave
@@ Line 210: / Line 236: @@
 |-
 | 15/8
+|[-3 1 1⟩
 | 1088{{c}}
 | yo 7th
@@ Line 215: / Line 242: @@
 |-
 | 40/21
+|[3 -1 1 -1⟩
 | 1116{{c}}
 | ruyo 7th
@@ Line 220: / Line 248: @@
 |-
 | 2/1
+|[1 0⟩
 | 1200{{c}}
 | wa octave
@@ Line 225: / Line 254: @@
 |}
-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:
+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). Intervals on the lattice's far right and 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:
 [[File:Lattice41a.png|833x833px]]
-The general term for large/small/central is '''magnitude'''. Only intervals have a magnitude, notes never do, and L and s never appear on the staff. A ratio's magnitude is the sum of all the [[monzo]] exponents except the first one, divided by 7, and rounded off. {{nowrap|0 {{=}} central|1 {{=}} large|2 {{=}} double large}}, etc. {{nowrap|81/64 {{=}} {{vector| -6 4 }}}}, and 4/7 rounds to 1, so {{nowrap|81/64 {{=}} Lw3}}. Similarly, {{nowrap|135/128 {{=}} {{vector| -7 3 1 }}}} =&nbsp;Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees: {{nowrap|w2 + w2 {{=}} Lw3}}.
+The general term for large/small/central is '''magnitude'''. Only intervals have a magnitude, notes never do, and L and s never appear on the staff. A ratio's magnitude is the sum of all the [[monzo]] exponents except the first one, divided by 7, and rounded off. {{nowrap|0 {{=}} central|1 {{=}} large|2 {{=}} double large}}, etc. {{nowrap|81/64 {{=}} {{vector| -6 4 }}}}, and 4/7 rounds to 1, so 81/64 is a lawa 3rd = Lw3. Similarly, {{nowrap|135/128 {{=}} {{vector| -7 3 1 }}}} is a layo unison = Ly1. Unfortunately, magnitudes do not add up predictably like colors and degrees: {{nowrap|w2 + w2 {{=}} Lw3}}.
-Colors can be doubled or tripled, which are abbreviated '''bi-''' ("bee") and '''tri-''' ("tree"): {{nowrap|49/25 {{=}} bizogu 9th}} =&nbsp;zzgg9 and {{nowrap|128/125 {{=}} trigu 2nd}} =&nbsp;g<sup>3</sup>2. Bi- is only used if it shortens the name: {{nowrap|25/16 {{=}} yoyo 5th}}, not biyo 5th. Likewise with magnitudes: double-large is lala and triple-large is trila. For quadruple, etc., see [[#Exponents]].
+Colors can be doubled or tripled, which are abbreviated '''bi-''' ("bee") and '''tri-''' ("tree"): 49/25 is a bizogu 9th = zzgg9, and 128/125 is a trigu 2nd = ggg2. Bi- is only used if it shortens the name: 25/16 is a yoyo 5th, not a biyo 5th. Likewise with magnitudes: double-large is lala and triple-large is trila. 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.
-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 {{nowrap|121/64 {{=}} 1102{{c}}}}. Going from a {{nowrap|yo M7 {{=}} 1088{{c}}}} up to this m7 raises the pitch, and 121/120 is a dim unison.
+Degrees can be '''[[Negative interval|negative]]''': 50/49 = 35¢ is a biruyo negative 2nd = rryy-2. It's negative 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.
-'''Compound''', abbreviated '''co-''' or '''c''', is a [[wikipedia:Interval_(music)#Compound_intervals|conventional music theory term]] that means widened by an octave. 15/4 is a compound {{nowrap|yo 7th {{=}} coyo 7th}} =&nbsp;cy7. 5/1 is a double-compound {{nowrap|yo 3rd {{=}} cocoyo 3rd}} =&nbsp;ccy3. 9/1 is a {{nowrap|tricowa 2nd {{=}} c<sup>3</sup>w2}}. 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.
+'''Compound''', abbreviated '''co-''' or '''c''', is a [[wikipedia:Interval_(music)#Compound_intervals|conventional music theory term]] that means widened by an octave. 15/4 is a compound {{nowrap|yo 7th {{=}} coyo 7th}} = cy7. 5/1 is a double-compound {{nowrap|yo 3rd {{=}} cocoyo 3rd}} =&nbsp;ccy3. 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.
 == Note names ==
@@ Line 245: / Line 274: @@
 == Prime subgroup names ==
-Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. {{nowrap|Ya {{=}} the 2.3.5 prime subgroup}} =&nbsp;5-limit. {{nowrap|'''Za''' {{=}} 7-all}} =&nbsp;2.3.7 {{nowrap|{{=}} no-fives 7-limit}}. {{nowrap|Yaza {{=}} 2.3.5.7}} {{nowrap|{{=}} the full 7-limit}}. '''Nowa''' means without wa, and {{nowrap|yaza nowa {{=}} 2.5.7}}.
+Just as wa means 3-all or 3-limit, '''ya''' means 5-all and includes wa, yo, gu, yoyo, gugu, etc. Ya refers to the 2.3.5 prime subgroup = 5-limit. {{nowrap|'''Za''' {{=}} 7-all}} refers to 2.3.7 {{nowrap|{{=}} no-fives 7-limit}}. Yaza refers to 2.3.5.7 {{nowrap|{{=}} the full 7-limit}}. '''Nowa''' means without wa, and {{nowrap|yaza nowa {{=}} 2.5.7}}.
-Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and {{nowrap|yaza '''noca''' {{=}} 3.5.7}} =&nbsp;[[Bohlen–Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca, and in certain theoretical discussions. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.
+Prime 2 (even more colorless than wa) is '''clear''', abbreviated '''ca''', and {{nowrap|yaza '''noca''' {{=}} 3.5.7}} = [[Bohlen–Pierce]]. 2-limit intervals like 2/1 are called wa not clear, for simplicity. '''Nowaca''' means without 2 or 3, thus 5.7.11 is yazala nowaca. Clear/ca is only ever used in the terms noca and nowaca, and in certain theoretical discussions. However, an additional mnemonic for "co-" (compound, widened by an octave) is "clear-over", in the sense that the ratio's numerator is multiplied by 2.
 More on prime subgroups in the next section.
@@ Line 254: / Line 283: @@
 Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed:
-{{nowrap|'''Lo''' {{=}} 11-over|'''lu''' {{=}} 11-under}}, and {{nowrap|'''la''' {{=}} 11-all}} =&nbsp;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 {{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 1oo, trilu is 1u<sup>3</sup>, 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{{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.
+{{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.
 (One might be tempted to write 11o instead of 1o. This would work on a score, but would be confusing in chord names. The triad C11o would look like a diminished 11th chord. In general, color notation avoids naming primes with the numbers found in chord names, which are 2 4 5 6 7 9 11 and 13.)
-'''Tho''' /θ/ = 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 = 3o6 = tho 6th, 14/13 = 3uz2 = thuzo 2nd. (See the preceding paragraph for why it's 3o and not 13o.)
+'''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.)
 <u>Prime subgroups:</u> yala = 2.3.5.11, zalatha nowa = 2.7.11.13, and yazalatha = 2.3.5.7.11.13 = the full 13-limit. '''Noya''' is a descriptive adjective, not used in actual prime subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha are all noya. Likewise, there's '''noza''', '''noyaza''', etc.
@@ Line 264: / Line 293: @@
 On the score and in note names, the 1o accidental either raises by 33/32 or lowers by 729/704. The meaning will usually be clear from context, however it's safer to write at the top of the page either "1o4 = P4" or "1o4 = A4". Likewise, 3o6 should be noted as either m6 or M6. While the note 11/8 above C can be written two ways, either as 1oF or as 1oF#, the interval 11/8 can only be written one way, as 1o4. Likewise, 13/8 above C is either 3oA or 3oAb, but 13/8 is only 3o6. <u>This is the primary rationale for using large/small/central rather than major/minor</u>. 11/9 is ambiguously major or minor, but unambiguously central. Intervals names and chord names become unambiguous for la and tha intervals. Another rationale is that commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, E gu not E gu minor, etc. (see [[#Chord Names]] below).
-'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa. (See the 3rd paragraph in this section for why it's 17o and not 7o.)
+'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa. (See the 3rd paragraph in this section for why iso is 17o and not 7o.)
-'''No''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. '''Ino''' is an alternate form of no, because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu chord" from "the new chord". (See the 3rd paragraph in this section for why it's 19o and not 9o.)
+'''No''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. '''Ino''' is an alternate form of no, because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu chord" from "the new chord". (See the 3rd paragraph in this section for why ino is 19o and not 9o.)
 The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th not inogu 4th.
-'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over).
+'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yazatwetha = yaza23a. 23/16 is a twetho 5th = 23o5, and 23/22 is a twetholu 2nd = 23o1u2. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over).
 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".
@@ Line 314: / Line 343: @@
 |-
 ! word
-| ya
+| yo
-| za
+| zo
-| (i)la
+| (i)lo
-| tha
+| tho
-| (i)sa
+| (i)so
-| (i)na
+| (i)no
-| twetha
+| twetho
-| twena
+| tweno
-| thiwa
+| thiwo
-| thisa
+| thiso
-| fowa
+| fowo
-| fotha
+| fotho
-| fosa
+| foso
-| fitha
+| fitho
-| fina
+| fino
-| siwa
+| siwo
-| sisa
+| siso
 |-
-! on the
+! on the<br>score
-score
 | M3
 | m7
@@ Line 348: / Line 376: @@
 | P5
 | M6
-| m7 or
+| M7
-M7
 | M7
 | m2
@@ Line 357: / Line 384: @@
 ''Yaza latha sana twetha twena thiwa thisa / Fowa fotha fosa fitha fina siwa sisa''
-Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Exponents]] below). Setho means 13<sup>17</sup>-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:
+Unfortunately seventy can't become se- because that already means 17-fold (see [[#Exponents]] below). Setho means 17-fold 13-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:
 {| class="wikitable"
@@ Line 389: / Line 416: @@
 |-
 ! word
-| fitwewa
+| fitwewo
-| fitwetha
+| fitwetho
-| fitwena
+| fitweno
-| fithitha
+| fithitho
-| fithina
+| fithino
-| fifosa
+| fifoso
-| fifiwa
+| fifiwo
-| fifitha
+| fifitho
-| fifisa
+| fifiso
-| fifina
+| fifino
-| fisitha
+| fisitho
-| sisisa
+| sisiso
 |}
@@ Line 428: / Line 455: @@
 == Exponents ==
-Exponent syllables aka multiplier syllables provide a way to shorten names that have repeated syllables. For example, 250/243 = 2<sup>1</sup> * 3<sup>-5</sup> * 5<sup>3</sup> is a yoyoyo unison which shortens to triyo 1sn. Exponents can also apply to magnitudes (Wa-22 = sasasawa 4th --> trisawa 4th) and octaves (13/1 = cococotho 6th --> tricotho 6th).
+Exponent syllables aka multiplier syllables provide a way to shorten names that have repeated syllables. For example, 250/243 = {{vector| 1 -5 3 }} is a yoyoyo unison which shortens to triyo unison. Exponents can also apply to magnitudes (triple-small is trisa) and octaves (triple-compound is trico).
+The triyo unison can be written as y<sup>3</sup>1 for, but it's more convenient (as well as closer to the spoken form) to write 3y1. Trilo is written 3(1o) to distinguish it from 31o, thirty-one-over.
 We've seen bi- for double and tri- for triple. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. Colorspeak syllables usually end in one of the five basic vowels. Quad and quin are both exceptions, so quad may optionally be spoken as "kwah", and quin as "kwee".
-Except for quad, all exponent syllables are prime numbers. Septuple is '''sep-'''. Above 7, all exponent syllables are the root color word plus -e. Eleven-fold is '''le-''' = "e'''<u>l</u>'''even '''<u>e</u>'''xponent", pronounced as in "<u>le</u>ns". Thirteen-fold is '''the-''' as in "<u>the</u>saurus". Note that sep- means seven-fold and '''se-''' means seven<u>teen</u>-fold.
+Except for quad, all exponent syllables are prime numbers. Septuple is '''sep-'''. Above 7, all exponent syllables are the root color word plus -e for exponent. Eleven-fold is '''le-''' = "e'''<u>l</u>'''even '''<u>e</u>'''xponent", pronounced as in "<u>le</u>ns". Thirteen-fold is '''the-''' as in "<u>the</u>saurus". Note that sep- means seven-fold and '''se-''' means seven<u>teen</u>-fold.
 Exponents can be combined: sextuple = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. The component syllables are simply the number's prime factors in descending order, except that quad replaces bibi and comes before tri.
-Exponents affect all subsequent syllables until the '''-a-''' delimiter occurs: trizogu = z<sup>3</sup>g<sup>3</sup>, but trizo-agu = z<sup>3</sup>g. The "a" in la- and sa- also acts as a delimiter: trilayo = L<sup>3</sup>y, not L<sup>3</sup>y<sup>3</sup>, which would be trila-triyo.
+Exponents affect all subsequent syllables until the '''-a-''' delimiter occurs: trizogu = 3zg is triple-zo triple-gu, but trizo-agu = 3zag is triple-zo single-gu. The "a" in la- and sa- also acts as a delimiter: trilayo = 3Ly is triple-large single-yo. (Triple-large triple-yo would be trila-triyo = 3L3y.)
 Long color names use hyphens to make the name easier to parse. There are strict rules for hyphenation, to ensure uniformity.
@@ Line 445: / Line 474: @@
 The hyphen is generally omitted if it would create a subunit of 1 syllable. Thus despite the 2nd rule, layo, lalagu and sagugu are all unhyphenated. And despite the 3rd rule, coyo, cozogu and cocowa are unhyphenated. However, the last rule always holds, e.g. 284/243 =  2<sup>2</sup> * 3<sup>-5</sup> * 71 is a sa-seventy-wo 3rd.
 ==Converting a ratio to/from a color name ==
-Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. 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.
+Often a ratio can be converted by breaking it down into simpler ratios with familiar color names, then adding. For example, 45/32 is 5/4 times 9/8, which is y3 plus w2. The colors and degrees are summed, making y4. But is it y4 or Ly4? The magnitude is <u>not</u> summed, and must be found either visually from the lattices above, or from the monzo directly. 45/32 =  {{vector|-5 2 1}}, and (2+1)/7 rounds to 0, so it's central, and 45/32 = y4.
 For more complex ratios, a more direct method is needed:
@@ Line 476: / Line 505: @@
 [[File:Notation example 1.png|frameless|781x781px]]
-L and s never appear on the staff. Tripled colors are written as y3 not y<sup>3</sup> or yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. A fingering can be copied from one note and pasted to another note. The font used here is Arial Black.
+L and s never appear on the staff. Tripled colors are written as 3y not yyy. In MuseScore, color accidentals are made by adding fingerings to the notes, then editing the fingering text. A fingering can be copied from one note and pasted to another note. The font used here is Arial Black.
 This 10-page score uses the free open-source font Petaluma Script. The letters are 9pt, except that a "z" between two staff lines is 8pt. [[File:Evening Rondo colors.pdf]]
@@ Line 492: / Line 521: @@
 <u>Subtracting po lowers the degree</u>. Thus ruyopo Db = ruyo C#.
-Po and qu can be used with intervals as well. A ruyo 1sn becomes a ruyopo 2nd. Neither the color nor the magnitude changes.
+Po and qu can be used with intervals as well. A ruyo unison becomes a ruyopo 2nd. Neither the color nor the magnitude changes.
 One reason to change the degree is for ease of naming chords. See the Hendrix chord in the next section. Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]]
@@ Line 524: / Line 553: @@
 Chords can be classified as '''bicolored''' (e.g. g7 or r6), '''tricolored''' (e.g. z7(zg5) or z,y6), '''quadricolored''' (e.g. s6(zg5) or h7,zg9), etc.
 ==Chord progressions, keys, scales and modulations==
 A conventional chord name like IIm7 names the chord root relative to the tonic and the chord notes relative to the chord root. The "m7" is shorthand for (P1, m3, P5, m7). Adding each of these intervals to the M2 root gives us the four notes of the chord: M2, P4, M6 and P8. In the key of E, it would be F#m7 = F# + (P1, m3, P5, m7) = F#, A, C# and E.
@@ Line 548: / Line 575: @@
 {{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 y<sup>3</sup>T. 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.
+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.
+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.
-MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Naming Rank-2 Scales using Mode Numbers]].
+MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Genchain mode numbering]].
 ==Ups and downs, lifts and drops, plain and mid==
@@ Line 702: / Line 729: @@
 | colspan="2" | -a-
 |delimits an exponent such as bi-, tri-, etc.
-|Trizogu = z<sup>3</sup>g<sup>3</sup> = 1029/1000, but Trizo-agu = z<sup>3</sup>g = 343/320
+|Trizogu = 3zg = 1029/1000, but Trizo-agu = 3zag = 343/320
 |-
 |co-
@@ Line 759: / Line 786: @@
 | style="text-align: center;" | +
 |add an untempered prime to the temperament
-|Blackwood = 2.3.5 with 256/243 tempered out = Sawa + ya
+|Blackwood = 2.3.5 with 256/243 tempered out = Sawati + ya
 |-
 |and
@@ Line 816: / Line 843: @@
 |mid
 |~
-|for 2nds, 3rd, 6ths and 7ths, exactly halfway between major and minor
+|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
-a mid 4th is halfway-augmented, and a mid 5th is halfway-diminished
 |}
 ==Translations==
 For translations of color notation terms into other languages, see [[Color notation/Translations]]. Translating avoids using sounds not in one's native language. For example, in many European languages, "th-" for prime 13 becomes "tr-".
+== Origins ==
+Color notation was primarily developed by [[Kite Giedraitis]], with much assistance from [[User:AthiTrydhen|Praveen Venkataramana]].
 ==See also==