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Kite's ups and downs notation: Difference between revisions

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→Examples: edos 12-24: more updating
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===Enharmonic equivalents===
===Enharmonic equivalents===
Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22edo, Db can be spelled ^C or vB# or even ^^B (double-up B, or '''dup''' B for short, rhymes with "cup"). Respelling is done by adding or subtracting an [[Enharmonic unisons in ups and downs notation|enharmonic unison]], EU for short.  
Conventionally, in C you use D# instead of Eb when you have a Gaug chord. You have the freedom to spell your notes how you like, to make your chords look right. Likewise, in 22edo, Db can be spelled ^C or vB# or even ^^B (double-up B, or '''dup''' B for short, rhymes with "cup"). Respelling is done by adding or subtracting an [[Enharmonic unisons in ups and downs notation|enharmonic unison]], '''EU''' for short.  


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 unisons are like vanishing 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 EUs needed always equals the difference between the notation's rank and the tuning's rank."  
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 unisons are like vanishing 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 EUs needed always equals the difference between the notation's rank and the tuning's rank."  
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There are four flat-N edos on this list. 16edo and 23edo are flat-1, 18b is flat-2 and 13b is flat-3. There are two ways to notate such edos: with sharp lowering the pitch, and major/aug narrower than minor/dim, or with sharp raising the pitch, and major/aug wider than minor/dim. Both notations are shown. In the 2nd notation, note that a fifth above B is Fb, not F#.   
There are four flat-N edos on this list. 16edo and 23edo are flat-1, 18b is flat-2 and 13b is flat-3. There are two ways to notate such edos: with sharp lowering the pitch, and major/aug narrower than minor/dim, or with sharp raising the pitch, and major/aug wider than minor/dim. Both notations are shown. In the 2nd notation, note that a fifth above B is Fb, not F#.   


12edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: d2.  
12edo is sharp-1, thus doesn't need ups and downs. Enharmonic unison: d2.  
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |[[12-edo|'''12edo''']]
| rowspan="2" |[[12-edo|'''12edo''']]
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|P8
|P8
|}
|}
There are two ways to notate 13b-edo. The enharmonic intervals for the 1st notation are ^<sup>3</sup>A1 and vM2. For the 2nd they are v<sup>3</sup>A1 and vm2.
There are two ways to notate 13b-edo. The enharmonic unisons for the 1st notation are ^<sup>3</sup>A1 and vM2. For the 2nd they are v<sup>3</sup>A1 and vm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[13-edo|13b-edo]]'''
| rowspan="4" |'''[[13-edo|13b-edo]]'''
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|}
|}


Because every 14edo interval is perfect, the quality can be omitted. Sharps and flats can also be omitted. 14edo contains 2 rings of 7edo: an up/down-ring and a plain-ring. Enharmonic intervals: A1 and vvm2.
Because every 14edo interval is perfect, the quality can be omitted. Sharps and flats can also be omitted. 14edo contains 2 rings of 7edo: an up/down-ring and a plain-ring. Enharmonic unisons: A1 and vvm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[14-edo|14edo]]'''
| rowspan="2" |'''[[14-edo|14edo]]'''
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|8
|8
|}
|}
15edo contains 3 rings of 5edo: an up-ring, a down-ring, and a plain-ring. Enharmonic intervals: v<sup>3</sup>A1 and m2.
15edo contains 3 rings of 5edo: an up-ring, a down-ring, and a plain-ring. Enharmonic unisons: v<sup>3</sup>A1 and m2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[15-edo|15edo]]'''
| rowspan="2" |'''[[15-edo|15edo]]'''
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| P8
| P8
|}
|}
16edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic interval: either AA2 or dd2.  
16edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic unison: either AA2 or dd2.  
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[16-edo|16edo]]'''
| rowspan="4" |'''[[16-edo|16edo]]'''
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| P8
| P8
|}
|}
17edo is sharp-2 and thus has mid intervals. Enharmonic intervals: vvA1 and vm2.
17edo is sharp-2 and thus has mid intervals. Enharmonic unisons: vvA1 and vm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[17edo]]'''
| rowspan="2" |'''[[17edo]]'''
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|P8
|P8
|}
|}
18b-edo contains 2 rings of 9edo: an up/down-ring and a plain-ring. There are two ways to notate it. Enharmonic intervals: either ^^A1 and vvM2, or vvA1 and vvm2.
18b-edo contains 2 rings of 9edo: an up/down-ring and a plain-ring. There are two ways to notate it. Enharmonic unisons: either ^^A1 and vvM2, or vvA1 and vvm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[18-edo|18b-edo]]'''
| rowspan="4" |'''[[18-edo|18b-edo]]'''
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| P8
| P8
|}
|}
19edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: dd2.
19edo is sharp-1, thus doesn't need ups and downs. Enharmonic unison: dd2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[19-edo|19edo]]'''
| rowspan="2" |'''[[19-edo|19edo]]'''
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|P8
|P8
|}
|}
20edo contains 4 rings of 5edo: an up-ring, a down-ring, a dup/dud-ring, and a plain-ring. Enharmonic intervals: v<sup>4</sup>A1 and m2.
20edo contains 4 rings of 5edo: an up-ring, a down-ring, a dup/dud-ring, and a plain-ring. Enharmonic unisons: v<sup>4</sup>A1 and m2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[20-edo|20edo]]'''
| rowspan="2" |'''[[20-edo|20edo]]'''
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|P8
|P8
|}
|}
Because every 21edo interval is perfect, the quality can be omitted. 21edo contains 3 rings of 7edo: an up-ring, a down-ring and a plain-ring. Enharmonic intervals: A1 and v<sup>3</sup>m2.
Because every 21edo interval is perfect, the quality can be omitted. 21edo contains 3 rings of 7edo: an up-ring, a down-ring and a plain-ring. Enharmonic unisons: A1 and v<sup>3</sup>m2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[21-edo|21edo]]'''
| rowspan="2" |'''[[21-edo|21edo]]'''
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|8
|8
|}
|}
22edo is sharp-3. Enharmonic intervals: v<sup>3</sup>A1 and vm2.
22edo is sharp-3. Enharmonic unisons: v<sup>3</sup>A1 and vm2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[22-edo|22edo]]'''
| rowspan="2" |'''[[22-edo|22edo]]'''
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|etc.
|etc.
|}
|}
23edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic interval: either A<sup>3</sup>2 or d<sup>3</sup>2.
23edo is flat-1, thus doesn't need ups and downs. There are two ways to notate it. Enharmonic unison: either A<sup>3</sup>2 or d<sup>3</sup>2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="4" |'''[[23-edo|23edo]]'''
| rowspan="4" |'''[[23-edo|23edo]]'''
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|P8
|P8
|}
|}
24edo contains 2 rings of 12edo: an up/down-ring and a plain-ring. Enharmonic intervals: vvA1 and d2.
24edo contains 2 rings of 12edo: an up/down-ring and a plain-ring. Enharmonic unisons: vvA1 and d2.
{| class="wikitable" style="text-align:center;"  
{| class="wikitable" style="text-align:center;"  
| rowspan="2" |'''[[24-edo|24edo]]'''
| rowspan="2" |'''[[24-edo|24edo]]'''
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