Kite's ups and downs notation: Difference between revisions
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→Examples: EDOs 12-24: added a paragraph about edos 13 and 18 being notated as 13b and 18b |
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Sharp-1, flat-2, etc. refer to the number of EDOsteps made by seven 5ths minus four 8ves. All sharp-1 and flat-1 edos can be notated without ups and downs, because the up is exactly equivalent to a sharp or flat. | Sharp-1, flat-2, etc. refer to the number of EDOsteps made by seven 5ths minus four 8ves. All sharp-1 and flat-1 edos can be notated without ups and downs, because the up is exactly equivalent to a sharp or flat. | ||
A ring is a circle of 5ths. In multi-ring edos like 14, 15 and 24, a single ring doesn't contain all the edo's notes. In contrast, edos like 12, 19 and 22 are single-ring. It's possible to notate any single-ring edo with conventional notation if notes are permitted to be out of order (e.g. 22edo could have C Db B# C#). But multi-ring edos absolutely require ups and downs. | A ring is a circle of 5ths. In multi-ring (aka ringy) edos like 14, 15 and 24, a single ring doesn't contain all the edo's notes. In contrast, edos like 12, 19 and 22 are single-ring. It's possible to notate any single-ring edo with conventional notation if notes are permitted to be out of order (e.g. 22edo could have C Db B# C# D). But multi-ring edos absolutely require ups and downs. | ||
13-edo and 18-edo aren't compatible with heptatonic notation, because the minor 2nd is descending. Thus the minor 3rd is flatter than the major 2nd, the 4th is flatter than the major 3rd, etc. These edos are best notated using the 2nd best fifth, i.e. as 13b and 18b. | |||
12-edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: d2. | 12-edo is sharp-1, thus doesn't need ups and downs. Enharmonic interval: d2. | ||
| Line 334: | Line 336: | ||
| P8 | | P8 | ||
|} | |} | ||
17-edo is sharp-2 and has mid intervals. Enharmonic intervals: vvA1 and vm2. | 17-edo is sharp-2 and thus has mid intervals. Enharmonic intervals: vvA1 and vm2. | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
| rowspan="2" |'''[[17edo|17-edo]]''' | | rowspan="2" |'''[[17edo|17-edo]]''' | ||
| Line 829: | Line 831: | ||
! colspan="2" |C Eb Gb | ! colspan="2" |C Eb Gb | ||
|- | |- | ||
!nothing | |||
|C | |C | ||
|Cm | |Cm | ||
| Line 839: | Line 841: | ||
|Co | |Co | ||
|- | |- | ||
!3rd | |||
|Cv | |Cv | ||
|Cvm | |Cvm | ||
| Line 849: | Line 851: | ||
|Cvo | |Cvo | ||
|- | |- | ||
!5th | |||
|C(v5) | |C(v5) | ||
|Cm(v5) | |Cm(v5) | ||
| Line 859: | Line 861: | ||
|Co(v5) | |Co(v5) | ||
|- | |- | ||
!3rd, 5th | |||
|Cv(v5) | |Cv(v5) | ||
|Cvm(v5) | |Cvm(v5) | ||
| Line 906: | Line 908: | ||
!C Eb G A | !C Eb G A | ||
|- | |- | ||
!nothing | |||
|CM7 | |CM7 | ||
|C7 | |C7 | ||
| Line 918: | Line 920: | ||
|Cm6 | |Cm6 | ||
|- | |- | ||
!3rd | |||
|'''Cv,M7''' | |'''Cv,M7''' | ||
|'''Cv,7''' | |'''Cv,7''' | ||
| Line 930: | Line 932: | ||
|'''Cvm,6''' | |'''Cvm,6''' | ||
|- | |- | ||
!5th | |||
|CM7(v5) | |CM7(v5) | ||
|C7(v5) | |C7(v5) | ||
| Line 942: | Line 944: | ||
|Cm6(v5) | |Cm6(v5) | ||
|- | |- | ||
!7th | |||
|'''C,vM7''' | |'''C,vM7''' | ||
|'''C,v7''' | |'''C,v7''' | ||
| Line 954: | Line 956: | ||
|Cm,v6 | |Cm,v6 | ||
|- | |- | ||
!3rd, 5th | |||
|Cv(v5)M7 | |Cv(v5)M7 | ||
|Cv(v5)7 | |Cv(v5)7 | ||
| Line 966: | Line 968: | ||
|Cvm(v5)6 | |Cvm(v5)6 | ||
|- | |- | ||
!3rd, 7th | |||
|CvM7 | |CvM7 | ||
|Cv7 | |Cv7 | ||
| Line 978: | Line 980: | ||
|Cvm6 | |Cvm6 | ||
|- | |- | ||
!5th, 7th | |||
|C(v5)vM7 | |C(v5)vM7 | ||
|C(v5)v7 | |C(v5)v7 | ||
| Line 990: | Line 992: | ||
|Cm(v5)v6 | |Cm(v5)v6 | ||
|- | |- | ||
!3rd, 5th, 7th | |||
|CvM7(v5) | |CvM7(v5) | ||
|Cv7(v5) | |Cv7(v5) | ||
| Line 1,032: | Line 1,034: | ||
!C Eb G A D | !C Eb G A D | ||
|- | |- | ||
!nothing | |||
|'''C,9''' | |'''C,9''' | ||
|CM9 | |CM9 | ||
| Line 1,041: | Line 1,043: | ||
|Cm6,9 | |Cm6,9 | ||
|- | |- | ||
!3rd | |||
|'''Cv,9''' | |'''Cv,9''' | ||
|CM9(v3) | |CM9(v3) | ||
| Line 1,050: | Line 1,052: | ||
|'''Cvm,6,9 *''' | |'''Cvm,6,9 *''' | ||
|- | |- | ||
!5th | |||
|'''C,9(v5)''' | |'''C,9(v5)''' | ||
|CM9(v5) | |CM9(v5) | ||
| Line 1,059: | Line 1,061: | ||
|Cm6(v5)9 | |Cm6(v5)9 | ||
|- | |- | ||
!6th/7th | |||
| ------ | | ------ | ||
|CM9(v7) | |CM9(v7) | ||
| Line 1,068: | Line 1,070: | ||
|Cm,v6,9 | |Cm,v6,9 | ||
|- | |- | ||
!9th | |||
|'''C,v9''' | |'''C,v9''' | ||
|CM7,v9 | |CM7,v9 | ||
| Line 1,077: | Line 1,079: | ||
|Cm6,v9 | |Cm6,v9 | ||
|- | |- | ||
!3rd, 5th | |||
|Cv(v5)9 | |Cv(v5)9 | ||
|CM9(v3v5) | |CM9(v3v5) | ||
| Line 1,086: | Line 1,088: | ||
|Cvm(v5)6,9 | |Cvm(v5)6,9 | ||
|- | |- | ||
!3rd, 6th/7th | |||
| ------ | | ------ | ||
|CvM9 | |CvM9 | ||
| Line 1,095: | Line 1,097: | ||
|Cvm6,9 | |Cvm6,9 | ||
|- | |- | ||
!3rd, 9th | |||
|Cv,v9 | |Cv,v9 | ||
|'''Cv,M7v9''' or | |'''Cv,M7v9''' or | ||
| Line 1,111: | Line 1,113: | ||
Cm6(v3)v9 | Cm6(v3)v9 | ||
|- | |- | ||
!5th, 6th/7th | |||
| ------ | | ------ | ||
|CM9(v5v7) | |CM9(v5v7) | ||
| Line 1,120: | Line 1,122: | ||
|Cm(v5)v6,9 | |Cm(v5)v6,9 | ||
|- | |- | ||
!5th, 9th | |||
|C(v5)v9 | |C(v5)v9 | ||
|CM7(v5)v9 | |CM7(v5)v9 | ||
| Line 1,129: | Line 1,131: | ||
|Cm6(v5)v9 | |Cm6(v5)v9 | ||
|- | |- | ||
!6th/7th, 9th | |||
| ------ | | ------ | ||
|'''C,vM7v9''' | |'''C,vM7v9''' | ||
| Line 1,138: | Line 1,140: | ||
|Cm,v6v9 | |Cm,v6v9 | ||
|- | |- | ||
!3rd, 5th, 6th/7th | |||
| ------ | | ------ | ||
|CvM9(v5) | |CvM9(v5) | ||
| Line 1,147: | Line 1,149: | ||
|Cvm6(v5)9 | |Cvm6(v5)9 | ||
|- | |- | ||
!3rd, 5th, 9th | |||
|Cv(v5)v9 | |Cv(v5)v9 | ||
|Cv(v5)M7v9 or | |Cv(v5)M7v9 or | ||
| Line 1,162: | Line 1,164: | ||
Cm6(v3v5)v9 | Cm6(v3v5)v9 | ||
|- | |- | ||
!3rd, 6th/7th, 9th | |||
| ------ | | ------ | ||
|CvM7,v9 | |CvM7,v9 | ||
| Line 1,171: | Line 1,173: | ||
|Cvm6,v9 | |Cvm6,v9 | ||
|- | |- | ||
!5th, 6th/7th, 9th | |||
| ------ | | ------ | ||
|C(v5)vM7v9 | |C(v5)vM7v9 | ||
| Line 1,180: | Line 1,182: | ||
|Cm(v5)v6v9 | |Cm(v5)v6v9 | ||
|- | |- | ||
!3rd, 5th, 6th/7th, 9th | |||
| ------ | | ------ | ||
|CvM7(v5)v9 | |CvM7(v5)v9 | ||