Kite's color notation: Difference between revisions
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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 general term, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha. | 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 general term, not used in actual subgroup names, that indicates the absence of 5 and the presence of higher primes, e.g. zala, latha and zalatha. | ||
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 3oA♭, but 13/8 is only 3o6. <u>This is the rationale for using large/small rather than major/minor</u>. Intervals names and chord names become unambiguous for la and tha intervals. Also, commonly used intervals and chords get concise names: gu 3rd not gu minor 3rd, | 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 3oA♭, but 13/8 is only 3o6. <u>This is the rationale for using large/small 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. Also, commonly used intervals and chords are all central, and get concise names: gu 3rd not gu minor 3rd, A gu not A gu minor, etc. (see chord names below). | ||
'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Sova''' is an alternate form of so, to distinguish it from the solfege syllable Sol. | '''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''' and '''17u'''. '''Sova''' is an alternate form of so, to distinguish it from the solfege syllable Sol. | ||
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Triads are named after their 3rd, e.g. Cy. "Yo C" is a note, "C yo" is a chord. The four main yaza triads:[[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]] | Triads are named after their 3rd, e.g. Cy. "Yo C" is a note, "C yo" is a chord. The four main yaza triads:[[File:lattice62.png|alt=lattice62.png|640x138px|lattice62.png]] | ||
If the root isn't wa, the root color is added to the interval color: yo A gu = yAg = yA + (w1 g3 w5) = yA + wC + yE. | If the root isn't wa, the root color is added to the interval color: "yo A gu" = yAg = yA + (w1 g3 w5) = yA + wC + yE. | ||
Tetrads are named Cy6, Dg7, etc. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated: | Tetrads are named Cy6 ("C yo six"), Dg7, etc. The 11 main yaza tetrads, with chord homonyms (same shape, different root) equated: | ||
[[File:Lattice63.png|639x639px]] | [[File:Lattice63.png|639x639px]] | ||
The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. There are h9 chords, s11 chords, etc. | The y,z7 chord is also called the h7 chord ("aitch-seven"), because it's part of the harmonic series. The s7 ("sub-seven") chord is part of the subharmonic series. It's the first 7 subharmonics, with the 3rd subharmonic becoming the root. Note that s7 has no 7th. There are h9 chords, s11 chords, etc. The number must be odd, Ch8 is invalid. Ch9,13 = w1 y3 w5 z7 w9 3o13 has an added 13th harmonic. | ||
A 9th chord contains a 3rd, 5th and 7th. An 11th chord contains all these plus a 9th. A 13th chord contains all these plus an 11th. The 5th, 9th and/or 13th default to wa. The 6th, 7th, and/or 11th default to the color of the 3rd. Thus Cy13 = w1 y3 w5 y7 w9 y11 w13, and Cy9 and Cy11 are subsets of this chord. However, an add-11 chord defaults to a wa 11: Cz7,11 = w1 z3 w5 z7 w11. Added 9ths default to wa: Cy,9 = w1 y3 w5 w9. | |||
An | <u>Alterations are always in parentheses</u>, additions never are, e.g. z7(zg5). An alteration's degree must match a note in the chord, e.g. z7(y6) is invalid. But an exception is made for sus chords, where degree 2 or 4 alter the 3rd: C(z4) = w1 z4 w5. The sus note defaults to wa: Cz7(4) = w1 w4 w5 z7. | ||
Omissions are indicated by "no", the Hendrix chord might be Ch7z10no5. <u>Enharmonic substitutions aren't allowed</u>, 7/3 is a m10, not an A9. A no3 chord can also be written as a 5 chord with an added note: C5z7 = w1 w5 z7, and C(zg5)z7 = w1 zg5 z7. Omissions in harmonic and subharmonic chords refer to degree not harmonic. Ch11no3 omits y3, not the 3rd harmonic w5. However, numbers ≥ 15 always refer to (sub)harmonics, as in Ch15 or Cs15. | |||
== Staff notation == | == Staff notation == | ||
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[[File:Notation example 2.png|786x786px]] | [[File:Notation example 2.png|786x786px]] | ||
Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, p and q (long forms po and qu = "ku"), to indicate raising/lowering by a pythagorean comma. For example, yF# = ypG♭, and zE♭= zqD#. This allows trills to always be written as a 2nd.[[File:Notation example 5a.png|992x992px]] | Color notation can optionally be made more similar to Sagittal notation by including two more accidentals, p and q (long forms po and qu = "ku"), to indicate raising/lowering by a pythagorean comma. For example, yF# = ypG♭, and zE♭= zqD#. This allows trills to always be written as a 2nd, less cluttered.[[File:Notation example 5a.png|992x992px]] | ||
== Chord Progressions, Keys and Modulations == | == Chord Progressions, Keys and Modulations == | ||
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Rank-2 temperaments can be notated with ups and downs as well. Some require another accidental pair, lifts and drops (/ and \). See the [[Pergen|pergens]] page. | Rank-2 temperaments can be notated with ups and downs as well. Some require another accidental pair, lifts and drops (/ and \). See the [[Pergen|pergens]] page. | ||
'''(OBSOLETE LINKS, IGNORE THEM):''' | |||
[[7-limit_interval_names|7-limit interval names]] | |||
[[Note_names|Note names]] | |||
[[Chord_names|Chord names]] | |||
[[Chord_progressions,_scales,_keys_and_modulations|Chord progressions, scales, keys and modulations]] | |||
[[Staff_notation|Staff notation]] | |||
[[Paradoxical_intervals|Paradoxical intervals]] | |||
[[Higher_primes|Higher primes]] | |||
[[Category:color_notation]] | [[Category:color_notation]] | ||
[[Category:ji]] | [[Category:ji]] | ||
[[Category:notation]] | [[Category:notation]] | ||
[[Category:todo:add_examples]] | [[Category:todo:add_examples]] | ||