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did my best to add ratios
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→Intervals: sed -E "s#([0-9]+)/([0-9]+)#\[\[\1/\2\]\]#g" 44EDOintervals.txt > 44EDOintervals.new.txt # also adjust ToDo because consistency check and additional column for ratios of 7 are still needed; add subgroup specification; replaced some ratios, but needs further checking
Line 18: Line 18:


== Intervals ==
== Intervals ==
{{Todo|complete table|inline=1|text = Add a column of approximated JI ratios to the following table; recommend dual ratios for the 7th harmonic which has a lot of relative error.}}
{{Todo|complete table|inline=1|text = Consistency check in column of approximated JI ratios in the following table; recommend dual ratios for the 7th harmonic which has a lot of relative error; might need some additional ratios; 29th harmonic is not terrible, so either add ratios of 29 or remove ratios of 31.}}
In 44edo, sharps and flats alter pitch by 6 edosteps. This means intervals can be notated with half sharps and half flats equal to 3 EDOsteps, in addition to ups and downs. The table below uses only sharps, flats, and ups and downs. When translating music from 22edo to 44edo, single ups and downs simply become double ups and downs (vEb in 22edo would be vvEb in 44edo).  
In 44edo, sharps and flats alter pitch by 6 edosteps. This means intervals can be notated with half sharps and half flats equal to 3 EDOsteps, in addition to ups and downs. The table below uses only sharps, flats, and ups and downs. When translating music from 22edo to 44edo, single ups and downs simply become double ups and downs (vEb in 22edo would be vvEb in 44edo).  


Line 25: Line 25:
! Degrees
! Degrees
! Cents
! Cents
!Approximate JI ratios
!Approximate JI ratios*
! colspan="3" | [[Ups and downs notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
| 0
| 0
| 0.000
| 0.000
|1/1
| [[1/1]]
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 37: Line 37:
| 1
| 1
| 27.273
| 27.273
|64/63
| [[64/63]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 44: Line 44:
| 2
| 2
| 54.545
| 54.545
|33/32
| [[33/32]], [[32/31]]
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 51: Line 51:
| 3
| 3
| 81.818
| 81.818
|23/22
| [[23/22]]
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 58: Line 58:
| 4
| 4
| 109.091
| 109.091
|16/15
| [[16/15]]
| Dupminor 2nd, Downmid 2nd
| Dupminor 2nd, Downmid 2nd
| ^^m2, v~2
| ^^m2, v~2
Line 65: Line 65:
| 5
| 5
| 136.364
| 136.364
|69/64
| [[13/12]]
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 72: Line 72:
| 6
| 6
| 163.636
| 163.636
|11/10
| [[11/10]], [[32/29]]
| Dudmajor 2nd, Upmid 2nd
| Dudmajor 2nd, Upmid 2nd
| vvM2, ^~2
| vvM2, ^~2
Line 79: Line 79:
| 7
| 7
| 190.909
| 190.909
|28/25
| [[28/25]]
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 86: Line 86:
| 8
| 8
| 218.182
| 218.182
|9/8
| [[9/8]]
| Major 2nd
| Major 2nd
| M2
| M2
Line 93: Line 93:
| 9
| 9
| 245.455
| 245.455
|8/7
| [[8/7]]
| Upmajor 2nd, Downminor 3rd
| Upmajor 2nd, Downminor 3rd
| ^M2, vm3
| ^M2, vm3
Line 100: Line 100:
| 10
| 10
| 272.727
| 272.727
|7/6, 32/27
| [[7/6]], [[32/27]]
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 107: Line 107:
| 11
| 11
| 300.000
| 300.000
|19/16
| [[19/16]]
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 114: Line 114:
| 12
| 12
| 327.273
| 327.273
|11/9, 76/63
| [[11/9]], [[29/24]]
| Dupminor 3rd, Downmid 3rd
| Dupminor 3rd, Downmid 3rd
| ^^m3, v~3
| ^^m3, v~3
Line 121: Line 121:
| 13
| 13
| 354.545
| 354.545
|16/13
| [[16/13]]
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 128: Line 128:
| 14
| 14
| 381.818
| 381.818
|5/4
| [[5/4]]
| Dudmajor 3rd, Upmid 3rd
| Dudmajor 3rd, Upmid 3rd
| vvM3, ^~3
| vvM3, ^~3
Line 135: Line 135:
| 15
| 15
| 409.091
| 409.091
|80/63
| [[80/63]]
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 142: Line 142:
| 16
| 16
| 436.364
| 436.364
|81/64, 9/7
| [[81/64]], [[9/7]]
| Major 3rd
| Major 3rd
| M3
| M3
Line 149: Line 149:
| 17
| 17
| 463.636
| 463.636
|21/16
| [[21/16]]
| Upmajor 3rd, Down 4th
| Upmajor 3rd, Down 4th
| ^M3, v4
| ^M3, v4
Line 156: Line 156:
| 18
| 18
| 490.909
| 490.909
|4/3
| [[4/3]]
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 163: Line 163:
| 19
| 19
| 518.182
| 518.182
|4/3?
| [[19/14]]
| Up 4th
| Up 4th
| ^4
| ^4
Line 170: Line 170:
| 20
| 20
| 545.455
| 545.455
|11/8
| [[11/8]]
| Dup 4th, Downmid 4th, Dim 5th
| Dup 4th, Downmid 4th, Dim 5th
| ^^4, v~4, d5
| ^^4, v~4, d5
Line 177: Line 177:
| 21
| 21
| 572.727
| 572.727
|7/5
| [[7/5]]
| Mid 4th, Updim 5th
| Mid 4th, Updim 5th
| ~4, ^d5
| ~4, ^d5
Line 184: Line 184:
| 22
| 22
| 600.000
| 600.000
|99/70, 140/99
| [[99/70]], [[140/99]]
| Upmid 4th, Downmid 5th
| Upmid 4th, Downmid 5th
| ^~4, v~5
| ^~4, v~5
Line 191: Line 191:
| 23
| 23
| 627.273
| 627.273
|10/7
| [[10/7]]
| Downaug 4th, Mid 5th
| Downaug 4th, Mid 5th
| vA4, ~5
| vA4, ~5
Line 198: Line 198:
| 24
| 24
| 654.545
| 654.545
|16/11
| [[16/11]]
| Aug 4th, Upmid 5th, Dud 5th
| Aug 4th, Upmid 5th, Dud 5th
| A4, ^~5, vv5
| A4, ^~5, vv5
Line 205: Line 205:
| 25
| 25
| 681.818
| 681.818
|3/2?
| [[28/19]]
| Down 5th
| Down 5th
| v5
| v5
Line 212: Line 212:
| 26
| 26
| 709.091
| 709.091
|3/2
| [[3/2]]
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 219: Line 219:
| 27
| 27
| 736.364
| 736.364
|32/21
| [[32/21]]
| Up 5th, Downminor 6th
| Up 5th, Downminor 6th
| ^5, vm6
| ^5, vm6
Line 226: Line 226:
| 28
| 28
| 763.636
| 763.636
|14/9
| [[14/9]]
| Minor 6th
| Minor 6th
| m6
| m6
Line 233: Line 233:
| 29
| 29
| 790.909
| 790.909
|128/81
| [[128/81]]
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 240: Line 240:
| 30
| 30
| 818.182
| 818.182
|8/5
| [[8/5]]
| Dupminor 6th, Downmid 6th
| Dupminor 6th, Downmid 6th
| ^^m6, v~6
| ^^m6, v~6
Line 247: Line 247:
| 31
| 31
| 845.455
| 845.455
|13/8
| [[13/8]]
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 254: Line 254:
| 32
| 32
| 872.727
| 872.727
|5/3
| [[5/3]], [[48/29]]
| Dudmajor 6th, Upmid 6th
| Dudmajor 6th, Upmid 6th
| vvM6, ^~6
| vvM6, ^~6
Line 261: Line 261:
| 33
| 33
| 900.000
| 900.000
|27/16
| [[27/16]]
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 268: Line 268:
| 34
| 34
| 927.273
| 927.273
|12/7
| [[12/7]]
| Major 6th
| Major 6th
| M6
| M6
Line 275: Line 275:
| 35
| 35
| 954.545
| 954.545
|7/4?
| [[7/4]]?
| Upmajor 6th, Downminor 7th
| Upmajor 6th, Downminor 7th
| ^M6, vm7
| ^M6, vm7
Line 282: Line 282:
| 36
| 36
| 981.818
| 981.818
|7/4, 16/9
| [[7/4]], [[16/9]]
| Minor 7th
| Minor 7th
| m7
| m7
Line 289: Line 289:
| 37
| 37
| 1009.091
| 1009.091
|9/5
| [[9/5]]
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 296: Line 296:
| 38
| 38
| 1036.364
| 1036.364
|20/11
| [[20/11]], [[29/16]]
| Dupminor 7th, Downmid 7th
| Dupminor 7th, Downmid 7th
| ^^m7, v~7
| ^^m7, v~7
Line 303: Line 303:
| 39
| 39
| 1063.636
| 1063.636
|37/20
| [[24/13]]
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 310: Line 310:
| 40
| 40
| 1090.909
| 1090.909
|15/8
| [[15/8]]
| Dudmajor 7th, Upmid 7th
| Dudmajor 7th, Upmid 7th
| vvM7, ^~7
| vvM7, ^~7
Line 317: Line 317:
| 41
| 41
| 1118.182
| 1118.182
|40/21
| [[40/21]]
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 324: Line 324:
| 42
| 42
| 1145.455
| 1145.455
|27/14, 31/16
| [[27/14]], [[31/16]]
| Major 7th
| Major 7th
| M7
| M7
Line 331: Line 331:
| 43
| 43
| 1172.727
| 1172.727
|63/32
| [[63/32]]
| Upmajor 7th, Down 8ve
| Upmajor 7th, Down 8ve
| ^M7, v8
| ^M7, v8
Line 338: Line 338:
| 44
| 44
| 1200.000
| 1200.000
|2/1
| [[2/1]]
| Perfect 8ve
| Perfect 8ve
| P8
| P8
| D
| D
|}
|}
<nowiki>* In 2.3.5.7.11.13.17.19.23.29.31 subgroup</nowiki>


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/44edo"