Kite's color notation: Difference between revisions
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'''Color notation''' is a [[musical notation]] system for [[just intonation]]. | {{Redirect|Color notation|Dolores Catherino's polychromatic notation system|Polychromatic system}} | ||
* No new symbols: all | '''Color notation''' is a [[musical notation]] system for [[just intonation]]. Features: | ||
* No new symbols: all microtonal [[Inflections and alterations|inflections]] are familiar characters; hence they are immediately speed-readable. | |||
* Furthermore, they are all on the QWERTY keyboard, making the notation easily typeable. | * Furthermore, they are all on the QWERTY keyboard, making the notation easily typeable. | ||
* Every | * Every microtonal inflection has a spoken name (colorspeak), making the notation speakable. | ||
* Most importantly, one can name not only notes but also intervals. As a result, color notation can name scales, chords, chord progressions, and even prime subgroups and temperaments. | * Most importantly, one can name not only notes but also intervals. As a result, color notation can name scales, chords, chord progressions, and even prime subgroups and temperaments. Thus it's not merely a notation but a complete nomenclature. | ||
'''Colorspeak''' is the term for spoken color notation. It's designed to be easily pronounced no matter what one's native language is and also to be very concise; almost every element of colorspeak is only one short syllable ending with a vowel. The five basic vowels are pronounced {{w|open central unrounded vowel|/a/}}, {{w|open-mid front unrounded vowel|/ɛ/}}, {{w|close front unrounded vowel|/i/}}, {{w|mid back rounded vowel|/o/}} and {{w|close back rounded vowel|/u/}} (as in m'''a''', m'''e'''t, m'''e''', m'''ow''', and m'''oo''') by an English speaker, but perhaps differently by others (e.g. perhaps {{w|close-mid front unrounded vowel|/e/}} instead of {{nowrap|/ɛ/}}). | '''Colorspeak''' is the term for spoken color notation. It's designed to be easily pronounced no matter what one's native language is and also to be very concise; almost every element of colorspeak is only one short syllable ending with a vowel. The five basic vowels are pronounced {{w|open central unrounded vowel|/a/}}, {{w|open-mid front unrounded vowel|/ɛ/}}, {{w|close front unrounded vowel|/i/}}, {{w|mid back rounded vowel|/o/}} and {{w|close back rounded vowel|/u/}} (as in m'''a''', m'''e'''t, m'''e''', m'''ow''', and m'''oo''') by an English speaker, but perhaps differently by others (e.g. perhaps {{w|close-mid front unrounded vowel|/e/}} instead of {{nowrap|/ɛ/}}). | ||
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</imagemap> | </imagemap> | ||
If two ratios have the same color, their [[Monzo|monzos]] differ only in the first two numbers. For example, | If two ratios have the same color, their [[Monzo|prime-counts aka monzos]] differ only in the first two numbers. For example, all zogu ratios have a prime-count of the form {{monzo| a b -1 1 }}. | ||
The following table lists all the intervals in this lattice. See the [[gallery of just intervals]] for many more examples. | 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 | ! Ratio | ||
! | ! Prime-count | ||
! Cents | ! Cents | ||
! colspan="2" | Color & degree | ! colspan="2" | Color & degree | ||
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[[File:Lattice41a.png|833x833px]] | [[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]] | 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|prime-counts]] 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-''' ("b{{w|close front unrounded vowel|ee}}", /bi/) and '''tri-''' ("tr{{w|close front unrounded vowel|ee}}", /tɹi/): 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 can be doubled or tripled, which are abbreviated '''bi-''' ("b{{w|close front unrounded vowel|ee}}", /bi/) and '''tri-''' ("tr{{w|close front unrounded vowel|ee}}", /tɹi/): 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]]. | ||
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== Note names == | == Note names == | ||
Notes are named zEb, yyG#, etc. spoken as "zo E flat" and "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. The relative-notation lattice above can be mentally superimposed on this absolute-notation lattice to name every note and interval. For example, {{nowrap|D + y3 {{=}} yF#}}, and from yE to {{nowrap|ryF# {{=}} r2}}. | Notes are named zEb, yyG#, etc. spoken as "zo E flat" and "yoyo G sharp". Notes are never large or small, only intervals are. Uncolored notes default to wa. | ||
Adding gu raises a note by [[81/80]], and adding yo lowers it. Adding ru raises it by [[64/63]], and adding zo lowers it. Mnemonic: g'''<u>u</u>''' and r'''<u>u</u>''' go '''<u>u</u>'''p, and y'''<u>o</u>''' and z'''<u>o</u>''' go d'''<u>o</u>'''wn. But beware, this '''<u>u</u>'''nder/'''<u>u</u>'''p correlation is just a coincidence. (A [[mapping comma]] is always up, and the first two mapping commas happen to be -under commas, but half of the time they will be -over commas.) | |||
The relative-notation lattice above can be mentally superimposed on this absolute-notation lattice to name every note and interval. For example, {{nowrap|D + y3 {{=}} yF#}}, and from yE to {{nowrap|ryF# {{=}} r2}}. | |||
[[File:Lattice51.png|frameless|962x962px]] | [[File:Lattice51.png|frameless|962x962px]] | ||
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Colors for primes greater than 7 are named after the number itself, using the prefix '''i-''' for disambiguation as needed: | 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" (/ilo/). 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. | {{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" (/ilo/). 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. Sans serif fonts like the one you're reading right now conflate upper-case-i with lower-case-L, so ilo and ila are capitalized as iLo and iLa rather than Ilo and Ila. iLo and lu are abbreviated to '''1o''' and '''1u''' both 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. 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. iLo notes could be called lovender, and lu notes could be called luvender. Both are "shades" of lavender. | ||
( | '''Tho''' ([[wikipedia:Voiceless_dental_fricative|/θ/]] 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. | ||
<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. | |||
On the score and in note names, the 1o [[Inflections and alterations|inflection]] either raises by 33/32 or lowers by 729/704, i.e. 11's [[mapping comma]] can vary. 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. | |||
''' | '''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". | ||
One might be tempted to write ilo as 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. Color notation avoids naming primes with the numbers found in chord names, which are 2 4 5 6 7 9 11 and 13. Thus tho is 3o not 13o, iso is 17o not 7o, and ino is 19o not 9o. | |||
The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th not inogu 4th. | The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th not inogu 4th. | ||
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== Converting a ratio to/from a color name == | == 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. 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 | 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|prime-count vector]] or '''PCV''' 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: | For more complex ratios, a more direct method is needed: | ||
'''<u>Converting a ratio</u>:''' Find the | '''<u>Converting a ratio</u>:''' Find the PCV 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 PCV 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 prime counts 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{{c}}, 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]]. | ||
Example: ratio = 63/40 | Example: ratio = 63/40 | ||
* | * PCV = {{vector| -3 2 -1 1 }} | ||
* Color = zogu | * Color = zogu | ||
* Stepspan = {{vmp| 7 11 16 20 | -3 2 -1 1 }} = -21 + 22 - 16 + 20 = 5 steps | * Stepspan = {{vmp| 7 11 16 20 | -3 2 -1 1 }} = -21 + 22 - 16 + 20 = 5 steps | ||
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* Interval = zogu 6th or zg6 (63/20 would be zg13 = czg6) | * Interval = zogu 6th or zg6 (63/20 would be zg13 = czg6) | ||
<u>'''Converting a color name'''</u>: Let S be the stepspan of the interval, {{nowrap|S {{=}} degree − sign (degree)}}. Let M be the magnitude of the color name, with {{nowrap|L {{=}} 1|LL {{=}} 2}}, etc. Small is negative and central is zero. Let C be the number of "co-" prefixes. Let the | <u>'''Converting a color name'''</u>: Let S be the stepspan of the interval, {{nowrap|S {{=}} degree − sign (degree)}}. Let M be the magnitude of the color name, with {{nowrap|L {{=}} 1|LL {{=}} 2}}, etc. Small is negative and central is zero. Let C be the number of "co-" prefixes. Let the PCV be {{vector| a b c d e … }}. The colors directly give you all the prime counts except for a and b. Let S' be the dot product of {{vector| 0 0 c d e … }} with the pseudo-edomapping. Let {{nowrap|M' {{=}} round((2(S − S') + c + d + e + ...) / 7)}}. Then {{nowrap|a {{=}} −3 (S – S') – 11 (M – M') + C}} and {{nowrap|b {{=}} 2 (S − S') + 7 (M − M')}}. (Derivation [https://gist.github.com/m-yac/2236a03dd9fe89a992477fbcbc63746c here]) Convert the PCV to a ratio. | ||
Example: interval = sgg2 = sagugu 2nd | Example: interval = sgg2 = sagugu 2nd | ||
* S = 2 - 1 = 1 step, M = small = -1, C = 0. | * S = 2 - 1 = 1 step, M = small = -1, C = 0. PCV = {{vector| a b -2 }} | ||
* S' = {{vmp| 7 11 16 | 0 0 -2 }} = -32. S - S' = 1 - (-32) = 33. | * S' = {{vmp| 7 11 16 | 0 0 -2 }} = -32. S - S' = 1 - (-32) = 33. | ||
* M' = round ((2·33 + (-2)) / 7) = round (64 / 7) = 9. M - M' = -1 - 9 = -10. | * M' = round ((2·33 + (-2)) / 7) = round (64 / 7) = 9. M - M' = -1 - 9 = -10. | ||
* a = -3 (S - S') - 11 (M - M') + C = -3·33 - 11·(-10) + 0 = -99 + 110 = 11. | * a = -3 (S - S') - 11 (M - M') + C = -3·33 - 11·(-10) + 0 = -99 + 110 = 11. | ||
* b = 2 (S - S') + 7 (M - M') = 2·33 + 7·(-10) = 66 - 70 = -4 | * b = 2 (S - S') + 7 (M - M') = 2·33 + 7·(-10) = 66 - 70 = -4 | ||
* | * PCV = {{vector| 11 -4 -2 }}, ratio = 2048/2025. | ||
== Chord names == | == Chord names == | ||
Triads are named after their 3rd, e.g. a [[4:5:6|yo chord]] has a yo 3rd. A yo chord rooted on C is a Cy chord {{nowrap|{{=}} "C yo"}} {{nowrap|{{=}} {{dash|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 {{nowrap|C5 {{=}} w1 w5}} or {{nowrap|C(zg5) {{=}} w1 zg5}}. The four main yaza triads: | Triads are named after their 3rd, e.g. a [[4:5:6|yo chord]] has a yo 3rd. A yo chord rooted on C is a Cy chord {{nowrap|{{=}} "C yo"}} {{nowrap|{{=}} {{dash|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 {{nowrap|C5 {{=}} w1 w5}} or {{nowrap|C(zg5) {{=}} w1 zg5}}. The four main yaza triads: | ||
[[File: | [[File:lattice62.png|640x138px|lattice62.png]] | ||
Tetrads are named e.g. {{nowrap|"C yo-six" {{=}} [[12:15:18:20|Cy6]]}} {{nowrap|{{=}} C yE G yA}}. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated: | Tetrads are named e.g. {{nowrap|"C yo-six" {{=}} [[12:15:18:20|Cy6]]}} {{nowrap|{{=}} C yE G yA}}. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated: | ||
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*w1 z4 w5 z7 = Cz7(z4) or C(z4)z7 = "C zo-seven zo-four" or "C zo-four zo-seven" | *w1 z4 w5 z7 = Cz7(z4) or C(z4)z7 = "C zo-seven zo-four" or "C zo-four zo-seven" | ||
Omissions are indicated by "no". The za [[Hendrix chord]] is Ch7z10no5. (To write it as a sharp-9 chord, | Omissions are indicated by "no". The za [[Hendrix chord]] is Ch7z10no5. (To write it as a sharp-9 chord, see [[Color notation#Po and qu|po and qu]] below.) A no3 tetrad can also be written as a 5 chord with an added 6th or 7th: Cy6no3 = C5y6, and Cz7(zg5)no3 = C(zg5)z7. | ||
The [[4:5:6:7|y,z7 chord]] is called the h7 chord ("har-seven"), because it's part of the harmonic series. {{nowrap|[[4:5:6:7:9|Ch9]] {{=}} Cy,z7,9}} and {{nowrap|[[4:5:6:7:9:11|Ch11]] {{=}} Cy,z7,w9,1o11}}. The [[60:70:84:105|s7 ("sub-seven") chord]] is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. {{nowrap|[[140:180:210:252:315|Cs9]] {{=}} Cr,g7,9}} and {{nowrap|Cs11 {{=}} C1o11(1or5,1og9)}}. Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ''ascends'' from the root, but in a sub9 chord it ''descends'' from the top note, and becomes the new root. Thus the s7 chord is contained in the ''upper'' four notes of the s9 chord, not the lower four. | The [[4:5:6:7|y,z7 chord]] is called the h7 chord ("har-seven"), because it's part of the harmonic series. {{nowrap|[[4:5:6:7:9|Ch9]] {{=}} Cy,z7,9}} and {{nowrap|[[4:5:6:7:9:11|Ch11]] {{=}} Cy,z7,w9,1o11}}. The [[60:70:84:105|s7 ("sub-seven") chord]] is part of the subharmonic series. It's the first 7 subharmonics, with the 7th subharmonic becoming the root. {{nowrap|[[140:180:210:252:315|Cs9]] {{=}} Cr,g7,9}} and {{nowrap|Cs11 {{=}} C1o11(1or5,1og9)}}. Note that s9 is not s7 plus a 9th, but a completely different chord. Usually the 9th ''ascends'' from the root, but in a sub9 chord it ''descends'' from the top note, and becomes the new root. Thus the s7 chord is contained in the ''upper'' four notes of the s9 chord, not the lower four. | ||
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In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets roughly halfway through the pump: Cy - yAg - [y=w]Dg - Gy - Cy. The pattern is [''old''=''new'']: the previous chord implies yDg and the following chord implies wDg. See [[Comma pump examples]]. | In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets roughly halfway through the pump: Cy - yAg - [y=w]Dg - Gy - Cy. The pattern is [''old''=''new'']: the previous chord implies yDg and the following chord implies wDg. See [[Comma pump examples]]. | ||
Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key of A minor is A gu and the scale is the gu scale. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb | Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key of A minor is A gu and the scale is the gu scale. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo-zo. The [[centaur]] scale is yo-zo-zogu. Like chords, scales can be classified as bicolored (A gu), tricolored (Bb yo-zo), quadricolored (centaur), etc. | ||
Scales can be named more precisely analogous to how chords are named. The tonic, 2nd, 4th and 5th default to wa. Thus a yo scale is w1 w2 y3 w4 w5 y6 y7 w8. If the 2nd were instead yo, it would be a yo yo-2 scale, written y(y2). If the 2nd is sometimes yo, sometimes wa, the scale is yo plus yo-2, written y+y2. (A hexatonic scale might use "minus".) The 5-limit harmonic minor scale is gu yo-7. The Bbh7 - Ebh7 - Bbh7 - Fh9 scale is Bb yo plus zo-3-4-7, written Bb y+z347. | Scales can be named more precisely analogous to how chords are named. The tonic, 2nd, 4th and 5th default to wa. Thus a yo scale is w1 w2 y3 w4 w5 y6 y7 w8. If the 2nd were instead yo, it would be a yo yo-2 scale, written y(y2). If the 2nd is sometimes yo, sometimes wa, the scale is yo plus yo-2, written y+y2. (A hexatonic scale might use "minus".) The 5-limit harmonic minor scale is gu yo-7. The Bbh7 - Ebh7 - Bbh7 - Fh9 scale is Bb yo plus zo-3-4-7, written Bb y+z347. | ||
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Just as there is a har7 chord, there is a har15 scale: w1 w2 y3 1o4 w5 3o6 z7 y7 w8. A har-N scale (where N is odd) is harmonics (N+1)/2 to N+1. The tonic of the scale is always a power of 2. Thus the har9 scale is not 5:6:7:8:9:10 but 8:9:10:12:14:16 = w1 w2 y3 w5 z7 w8. The 5:6:7:8:9:10 scale is the over-5 mode of this scale, written "har9 /5". Since there are no gaps in the harmonic series fragment, 5:6:7:8:9:10 can be abbreviated as 5::10. Likewise there are subharmonic scales and modes. The sub15 scale is 16:15:14:13:12:11:10:9:8 or 16::8. The notes are w1 g2 r2 3u3 w4 1u5 g5 w7 w8. | Just as there is a har7 chord, there is a har15 scale: w1 w2 y3 1o4 w5 3o6 z7 y7 w8. A har-N scale (where N is odd) is harmonics (N+1)/2 to N+1. The tonic of the scale is always a power of 2. Thus the har9 scale is not 5:6:7:8:9:10 but 8:9:10:12:14:16 = w1 w2 y3 w5 z7 w8. The 5:6:7:8:9:10 scale is the over-5 mode of this scale, written "har9 /5". Since there are no gaps in the harmonic series fragment, 5:6:7:8:9:10 can be abbreviated as 5::10. Likewise there are subharmonic scales and modes. The sub15 scale is 16:15:14:13:12:11:10:9:8 or 16::8. The notes are w1 g2 r2 3u3 w4 1u5 g5 w7 w8. | ||
A pentatonic scale is assumed to be a major or minor pentatonic scale with an altered 3rd, 6th or 7th. Yo and ru imply a major pentatonic scale, and zo and gu imply minor. Thus zo pentatonic = w1 z3 w4 w5 z7 w8. Wa, ila or tha pentatonic scales need to specify major or minor, e.g. ilo major pentatonic = w1 w2 1o3 w5 1o6 w8 and ilo minor pentatonic = w1 1o3 w4 w5 1o7 w8. [[wikipedia:Anhemitonic_scale|Hemitonic]] scales can be named e.g. yo minor pentatonic = w1 y3 w4 w5 y7 w8 or zo major pentatonic = w1 w2 z3 w5 z6 w8. | |||
Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating in either direction is modulating '''waward'''. Modulating from a yo key to the relative gu, and perhaps from there to the parallel yo is modulating '''yoward'''. A root movement by a yo interval (e.g. Iy - yVIg) is a yoward move. Likewise, there's '''guward''', and '''y<u>a</u>ward''' includes both. Likewise, there's '''zoward''', '''ruward''', '''zaward''', '''iloward''', etc. | Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating in either direction is modulating '''waward'''. Modulating from a yo key to the relative gu, and perhaps from there to the parallel yo is modulating '''yoward'''. A root movement by a yo interval (e.g. Iy - yVIg) is a yoward move. Likewise, there's '''guward''', and '''y<u>a</u>ward''' includes both. Likewise, there's '''zoward''', '''ruward''', '''zaward''', '''iloward''', etc. | ||
== Staff notation == | |||
Notes on the staff default to wa. Non-wa notes have a color [[Inflections and alterations|inflection]] 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 inflections only apply to one specific "version" of that note (e.g. A flat or A natural). For example, the yo inflection in the first chord applies to all the D-naturals in that measure, but not to the D-flats. | |||
[[File:Notation example 1.png|frameless|781x781px]] | |||
L and s never appear on the staff. Tripled colors are written as 3y not yyy. In MuseScore, color inflections 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 of "Evening Rondo" 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]] | |||
=== Color signatures === | |||
Key signatures are generally standardized, so as to be extremely speed-readable. Thus a piece that uses the D harmonic minor scale won't have a key signature of Bb and C#, but rather just Bb, and every C in the score will be individually sharpened. | |||
Color signatures are likewise standardized using the same rule for naming chords and scales. The tonic, 2nd, 4th and 5th are all one color, and the 3rd, 6th and 7th are all another color. The color signature is written on the staff next to the conventional key signature using a triple stack and/or a quadruple stack of color inflections, similar to the [[How to read 41-equal scores#Scales and key signatures|arrow stacks]] of ups and downs notation. For example, the "Evening Rondo" score linked above uses a key signature of one sharp and a color signature of a triple stack of zo's to indicate an E zo scale. Another example, a triple stack of yo's would make color notation more similar to Johnston notation. | |||
The tonic always starts off wa, but a piece can modulate to a non-wa tonic. For example, one might start in C yo (triple yo-stack) but modulate yowards to yo A gu (quadruple yo-stack) and then to yo A yo (quadruple yo-stack and triple yoyo-stack). Every triple stack always has the same shape, so that it can be parsed as a single object. Likewise for quadruple stacks. | |||
A color signature can instead be written out explicitly above the staff. This method is less readable but more powerful. Here D and Db have different colors, which wouldn't be possible using color stacks. | |||
[[File:Notation example 2.png|786x786px]] | |||
=== Po and qu === | |||
'''Po''' and '''qu''' (/ku/) (short forms '''p''' and '''q''') are two optional inflections 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]). | |||
For example, F# minus a pythagorean comma is Gb. And Gb plus a pythagorean comma is po Gb. Thus an alternate name for F# is po Gb. <u>Adding po raises the degree by one</u>. The new note name is always a 12edo equivalent of the old note name. Adding qu lowers the degree: {{nowrap|Gb {{=}} qu F#}}. If one is resolving from 31oGb to G, one can rename 31oGb as 31oqF# = thiwoqu F sharp. | |||
<u>Subtracting po lowers the degree</u>. Thus ruyopo Db = ruyo C#. | |||
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. For example, the za [[Hendrix chord]] is Ch7z10no5. To write it as a sharp-9 chord, use qu: Ch7zq9no5. | |||
Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]] | |||
== Temperament names and comma names == | == Temperament names and comma names == | ||
| Line 585: | Line 600: | ||
==Ups and downs, lifts and drops, plain and mid== | ==Ups and downs, lifts and drops, plain and mid== | ||
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 | 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", inflections that always map to exactly one edostep. Ups and downs are used on the score just like color inflections are. Notes are named e.g. up C sharp = ^C#. [[Sharpness | Sharp-1 and flat-1]] edos don't require ups and downs. | ||
Unlike actual colors, virtual colors generally add up to something simpler, e.g. three of 22edo's ups adds up to an A1. Unlike actual colors, virtual colors combine with major, minor, etc. Intervals are named upmajor 3rd = ^M3, up 4th = ^4, downaug 5th = vA5, etc. | Unlike actual colors, virtual colors generally add up to something simpler, e.g. three of 22edo's ups adds up to an A1. Unlike actual colors, virtual colors combine with major, minor, etc. Intervals are named upmajor 3rd = ^M3, up 4th = ^4, downaug 5th = vA5, etc. | ||
| Line 864: | Line 879: | ||
==See also== | ==See also== | ||
* [[xen-calc]] – A web app that converts to/from ratios, | * [[xen-calc]] – A web app that converts to/from ratios, prime-count vectors and color notation, and also supports ups and downs notation. | ||
* [[ledzo notation]] – A similar competing notation system. | * [[ledzo notation]] – A similar competing notation system. | ||