Kite's color notation: Difference between revisions

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'''Ru''' = red (alarming, inflamed) = 7-under = supermajor

The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z, etc. Use z (azure) not b (blue), because b ~~looks like a~~ flat ~~sign~~. Mnemonic: Z looks like 7 with an extra line on the bottom.

The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z, etc. Use z (azure) not b (blue), because b already means flat. Mnemonic: Z looks like 7 with an extra line on the bottom.

== Interval Names ==

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[[File:Lattice32.png|694x694px]]

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Degrees can be negative: 50/49 = double ruyo 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.

Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g32. Quadruple and quintuple are abbreviated '''quad''' and '''quint''', as in the quadgu comma. Degrees can be negative: 50/49 = double ruyo 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.

The next table lists all the intervals in the lattice above. See the [[Gallery of Just Intervals]] for many more examples.

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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 are all noya. Likewise, there's '''noza''' and '''noyaza'''.

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. This is the rationale for using large/small 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. 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).

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 rationale for using large/small 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. 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'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable Sol.

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The magnitude is part of the name: Schismic is LyT and shrutal is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios of that magnitude and color: Mavila is Ly1T and [[Father]] is g2T. The degree is never needed if the comma is ≤ 90¢.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are "plus" temperaments: Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7 and 81/80 is g+zT = gu plus za.

If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are "plus" temperaments: Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = g+z1aT = gu plus zala.

The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas. Both 12edo&ryyT and 5edo+yT are rank-2.

The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas, but plusses don't. Both 12edo&ryyT and 5edo+yT are rank-2.

There are two obvious ways to name multi-comma temperaments. The odd name minimizes the double odd limit of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y3&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma temperaments better. The question of which name to use is not yet fully resolved.

@@ Line 10: / Line 10: @@
 '''Ru''' = red (alarming, inflamed) = 7-under = supermajor
-The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z, etc. Use z (azure) not b (blue), because b looks like a flat sign. Mnemonic: Z looks like 7 with an extra line on the bottom.
+The colors come in a red-yellow-green-blue rainbow, with warm/cool colors indicating sharp/flat intervals. The rainbow of 3rds runs 9/7 - 5/4 - 6/5 - 7/6. Colors are abbreviated as w, y, z, etc. Use z (azure) not b (blue), because b already means flat. Mnemonic: Z looks like 7 with an extra line on the bottom.
 == Interval Names ==
@@ Line 19: / Line 19: @@
 [[File:Lattice32.png|694x694px]]
-Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Degrees can be negative: 50/49 = double ruyo 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.
+Colors can be doubled or tripled: 25/16 = yoyo 5th = yy5 and 128/125 = triple gu 2nd = g<sup>3</sup>2. Quadruple and quintuple are abbreviated '''quad''' and '''quint''', as in the quadgu comma. Degrees can be negative: 50/49 = double ruyo 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.
 The next table lists all the intervals in the lattice above. See the [[Gallery of Just Intervals]] for many more examples.
@@ Line 182: / Line 182: @@
 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 are all noya. Likewise, there's '''noza''' and '''noyaza'''.
-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).
+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 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'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable Sol.
@@ Line 245: / Line 245: @@
 The magnitude is part of the name: Schismic is LyT and shrutal is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios of that magnitude and color: Mavila is Ly1T and [[Father]] is g2T. The degree is never needed if the comma is ≤ 90¢.
-If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are "plus" temperaments: Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7 and 81/80 is g+zT = gu plus za.
+If the comma is wa, an edo is implied. The temperament is named after the edo, not the comma. 2.3.5.7 and the pyth comma and 225/224 is 12edo&ryyT. If the comma(s) don't include every prime in the subgroup, some primes are untempered. These are "plus" temperaments: Blackwood is 5edo+yT = 5-edo plus ya. 2.3.5.7.11 and 81/80 = g+z1aT = gu plus zala.
-The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas. Both 12edo&ryyT and 5edo+yT are rank-2.
+The temperament name indicates the prime subgroup and the rank of the temperament. For example, ryyT ([[Marvel]]) is rank-3 because it has 2 explicit colors ru and yo and 2 implicit colors wa and clear, and 4 colors minus 1 comma = rank-3. Edos count as commas, but plusses don't. Both 12edo&ryyT and 5edo+yT are rank-2.
 There are two obvious ways to name multi-comma temperaments. The odd name minimizes the double odd limit of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y<sup>3</sup>&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between single-comma temperaments better. The question of which name to use is not yet fully resolved.