Kite's ups and downs notation: Difference between revisions

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From the [[Pergen|pergens]] article: "Conventional notation is generated by the octave and the 5th, and the notation (not the tuning itself) is rank-2. Each additional pair of accidentals increases the notation's rank by one, analogous to adding primes to a JI subgroup. Enharmonic intervals are like commas in that each one reduces the notation's rank by one (assuming they are linearly independent). Obviously, the notation's rank must match the actual tuning's rank. Therefore the minimum number of enharmonics needed always equals the difference between the notation's rank and the tuning's rank."

Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v3A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v3A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v4M2.

Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v3A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v3A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v4M2. Thus ^^F = vvG.

=== Staff Notation ===

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The issue arises because while English normally places the adjective before the noun, it doesn't do so with sharps and flats. A flattened B should logically be called "flat B" not "B flat", and be written bB not Bb. If it were, then it would seem very natural to have the up come first, as in ^bB. This would be the typical English adjective-adjective-noun construction. Instead we must use ^Bb, an unnatural adjective-noun-adjective construction. This issue fortunately arises only for note names. On the staff, the flat comes before the note, so naturally the up comes before the flat. In relative notation, the quality comes before the interval, as in minor 3rd and augmented 4th, or in jazz terms flat 3rd and sharp 4th. So terms like upminor 3rd and downsharp 4th have a natural adjective-adjective-noun construction.

=== Further notes ===

EDO intervals are often written as 7\22. This can also be written as vM3\22. This is useful when comparing EDOs, e.g. vM3\22 vs. vM3\15.

==Examples: EDOs 12-24==

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All 7th chords follow this same pattern. Likewise, if a 6th is not a P4 or A4 above the 3rd, it's an "add-6" chord. Permitting add-7 chords has the added benefit that the wordy "minor-7 flat-5" and the illogical "half-dim" can be replaced with "dim add-7", written Cd,7.

In the table below, if a chord is '''bolded''', the comma must be spoken as "add".

In the table below, if a chord is '''bolded''', the comma (the actual punctuation mark, not the interval) must be spoken as "add".

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'''Ninth chords:'''

In '''bolded''' chords, the comma is spoken as "add". Double alterations need only a single pair of parentheses, e.g. C vE vG B D is named CM9(v3v5). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In these chords, marked with an asterisk '''*''', only the first comma is spoken as "add".

In '''bolded''' chords, the comma punctuation is spoken as "add". Double alterations need only a single pair of parentheses, e.g. C vE vG B D is named CM9(v3v5). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In these chords, marked with an asterisk '''*''', only the first comma is spoken as "add".

{| class="wikitable" style="text-align:center;"

|+

@@ Line 59: / Line 59: @@
 From the [[Pergen|pergens]] article: "Conventional notation is generated by the octave and the 5th, and the notation (not the tuning itself) is rank-2. Each additional pair of accidentals increases the notation's rank by one, analogous to adding primes to a JI subgroup. Enharmonic intervals are like commas in that each one reduces the notation's rank by one (assuming they are linearly independent). Obviously, the notation's rank must match the actual tuning's rank. Therefore the minimum number of enharmonics needed always equals the difference between the notation's rank and the tuning's rank."
-Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v<sup>3</sup>A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v<sup>3</sup>A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v<sup>4</sup>M2.
+Since 22edo is rank-1, and conventional notation plus ups and downs is rank-3, two enharmonic intervals are needed to define the notation: v<sup>3</sup>A1 and vm2. Either interval can be added to or subtracted from any note to respell the note. For example, ^C + vm2 = Db and ^^Eb + v<sup>3</sup>A1 = vE. Any combination of these two enharmonic intervals is also an enharmonic interval, for example their sum v<sup>4</sup>M2. Thus ^^F = vvG.
 === Staff Notation ===
@@ Line 68: / Line 68: @@
 The issue arises because while English normally places the adjective before the noun, it doesn't do so with sharps and flats. A flattened B should logically be called "flat B" not "B flat", and be written bB not Bb. If it were, then it would seem very natural to have the up come first, as in ^bB. This would be the typical English adjective-adjective-noun construction. Instead we must use ^Bb, an unnatural adjective-noun-adjective construction. This issue fortunately arises only for note names. On the staff, the flat comes before the note, so naturally the up comes before the flat. In relative notation, the quality comes before the interval, as in minor 3rd and augmented 4th, or in jazz terms flat 3rd and sharp 4th. So terms like upminor 3rd and downsharp 4th have a natural adjective-adjective-noun construction.
+=== Further notes ===
+EDO intervals are often written as 7\22. This can also be written as vM3\22. This is useful when comparing EDOs, e.g. vM3\22 vs. vM3\15.
 ==Examples: EDOs 12-24==
@@ Line 886: / Line 889: @@
 All 7th chords follow this same pattern. Likewise, if a 6th is not a P4 or A4 above the 3rd, it's an "add-6" chord. Permitting add-7 chords has the added benefit that the wordy "minor-7 flat-5" and the illogical "half-dim" can be replaced with "dim add-7", written Cd,7.
-In the table below, if a chord is '''bolded''', the comma must be spoken as "add".
+In the table below, if a chord is '''bolded''', the comma (the actual punctuation mark, not the interval) must be spoken as "add".
 {| class="wikitable" style="text-align:center;"
 |+
@@ Line 1,012: / Line 1,015: @@
 <u>'''Ninth chords:'''</u>
-In '''bolded''' chords, the comma is spoken as "add". Double alterations need only a single pair of parentheses, e.g. C vE vG B D is named CM9(v3v5). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In these chords, marked with an asterisk '''*''', only the first comma is spoken as "add".
+In '''bolded''' chords, the comma punctuation is spoken as "add". Double alterations need only a single pair of parentheses, e.g. C vE vG B D is named CM9(v3v5). Double additions mostly need only a single comma, e.g. C E G vBb vD is named C,v7v9. But certain 6/9 chords require two commas. In these chords, marked with an asterisk '''*''', only the first comma is spoken as "add".
 {| class="wikitable" style="text-align:center;"
 |+