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44edo: Difference between revisions

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→Harmonics: second table
→Intervals: don't need the enormously complex ratios. + some missing simpler ratios
Line 21: Line 21:
{{Todo|complete table|inline=1|text = Continue adding dual ratios for the 7th harmonic which has a lot of relative error; might need some additional ratios; remove excessively complex ratios; finish consistency check (including putting inconsistently-mapped intervals in ''italics'').}}
{{Todo|complete table|inline=1|text = Continue adding dual ratios for the 7th harmonic which has a lot of relative error; might need some additional ratios; remove excessively complex ratios; finish consistency check (including putting inconsistently-mapped intervals in ''italics'').}}


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).  


{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-1 right-2 center-7 center-8"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
!Ratios of 7 tending<br>
! Ratios of 7 tending<br>sharp (patent val)
sharp (patent val)
! Ratios of 7 tending<br>flat (44d val)
!Ratios of 7 tending<br>
flat (44d val)
! colspan="3" | [[Ups and downs notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
Line 47: Line 45:
| [[65/64]]
| [[65/64]]
|
|
|[[64/63]]
| [[64/63]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 55: Line 53:
| 54.5
| 54.5
| [[32/31]], [[33/32]]
| [[32/31]], [[33/32]]
|51/49
| 51/49
|
|
| Minor 2nd
| Minor 2nd
Line 65: Line 63:
| [[23/22]]
| [[23/22]]
|
|
|[[22/21]]
| [[22/21]]
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 73: Line 71:
| 109.1
| 109.1
| [[16/15]]
| [[16/15]]
|
| [[15/14]]
|147/136
| [[14/13]]
| Dupminor 2nd, Downmid 2nd
| Dupminor 2nd, Downmid 2nd
| ^^m2, v~2
| ^^m2, v~2
Line 82: Line 80:
| 136.4
| 136.4
| [[13/12]]
| [[13/12]]
|[[14/13]]
| [[14/13]]
|
| [[15/14]]
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 90: Line 88:
| 6
| 6
| 163.6
| 163.6
| [[11/10]], [[32/29]]
| [[11/10]], [[12/11]], [[32/29]]
|31/28
| 31/28
|551/504
|  
| Dudmajor 2nd, Upmid 2nd
| Dudmajor 2nd, Upmid 2nd
| vvM2, ^~2
| vvM2, ^~2
Line 100: Line 98:
| 190.9
| 190.9
| [[19/17]]
| [[19/17]]
|143/126
|  
|352/315
|  
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 109: Line 107:
| 218.2
| 218.2
| [[9/8]]
| [[9/8]]
|[[8/7]]
| [[8/7]]
|143/126
|  
| Major 2nd
| Major 2nd
| M2
| M2
Line 117: Line 115:
| 9
| 9
| 245.5
| 245.5
| 52/45
| [[15/13]]
|65/56
|  
|[[8/7]]
| [[7/6]], [[8/7]]
| Upmajor 2nd, Downminor 3rd
| Upmajor 2nd, Downminor 3rd
| ^M2, vm3
| ^M2, vm3
Line 127: Line 125:
| 272.7
| 272.7
| [[32/27]]
| [[32/27]]
|[[7/6]]
| [[7/6]]
|221/189
|  
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 135: Line 133:
| 11
| 11
| 300.0
| 300.0
| [[19/16]]
| [[13/11]], [[19/16]]
|
|
|896/729
|  
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 144: Line 142:
| 12
| 12
| 327.3
| 327.3
| [[11/9]], [[29/24]]
| [[6/5]], [[11/9]], [[29/24]]
|896/729
|  
|76/63
|  
| Dupminor 3rd, Downmid 3rd
| Dupminor 3rd, Downmid 3rd
| ^^m3, v~3
| ^^m3, v~3
Line 154: Line 152:
| 354.5
| 354.5
| [[16/13]]
| [[16/13]]
|26/21
| [[26/21]]
|
|  
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 163: Line 161:
| 381.8
| 381.8
| [[5/4]]
| [[5/4]]
|
|  
|26/21
| [[26/21]]
| Dudmajor 3rd, Upmid 3rd
| Dudmajor 3rd, Upmid 3rd
| vvM3, ^~3
| vvM3, ^~3
Line 171: Line 169:
| 15
| 15
| 409.1
| 409.1
| [[19/15]], 171/136
| [[19/15]]
|
|
|[[80/63]]
| [[14/11]]
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 180: Line 178:
| 16
| 16
| 436.4
| 436.4
| [[81/64]]
| [[81/64]], [[128/99]]
|[[9/7]]
| [[9/7]], [[14/11]]
|
|
| Major 3rd
| Major 3rd
Line 191: Line 189:
| [[13/10]]
| [[13/10]]
|
|
|[[9/7]]
| [[9/7]]
| Upmajor 3rd, Down 4th
| Upmajor 3rd, Down 4th
| ^M3, v4
| ^M3, v4
Line 199: Line 197:
| 490.9
| 490.9
| [[4/3]]
| [[4/3]]
|62/49
|  
|
|
| Perfect 4th
| Perfect 4th
Line 208: Line 206:
| 518.2
| 518.2
| 171/128
| 171/128
|189/143
| 189/143
|256/189
| 256/189
| Up 4th
| Up 4th
| ^4
| ^4
Line 216: Line 214:
| 20
| 20
| 545.5
| 545.5
| [[11/8]]
| [[11/8]], [[15/11]]
|29/21
| [[29/21]]
|
|
| Dup 4th, Downmid 4th, Dim 5th
| Dup 4th, Downmid 4th, Dim 5th
Line 227: Line 225:
| 46/33
| 46/33
|
|
|29/21
| [[7/5]], [[29/21]]
| Mid 4th, Updim 5th
| Mid 4th, Updim 5th
| ~4, ^d5
| ~4, ^d5
Line 235: Line 233:
| 600.0
| 600.0
| 44/31, 31/22
| 44/31, 31/22
|[[7/5]], [[10/7]]
| [[7/5]], [[10/7]]
|
|
| Upmid 4th, Downmid 5th
| Upmid 4th, Downmid 5th
Line 245: Line 243:
| 33/23
| 33/23
|
|
|[[10/7]]
| [[10/7]], [[42/29]]
| Downaug 4th, Mid 5th
| Downaug 4th, Mid 5th
| vA4, ~5
| vA4, ~5
Line 252: Line 250:
| 24
| 24
| 654.5
| 654.5
| [[16/11]]
| [[16/11]], [[22/15]]
|
| [[42/29]]
|
|  
| Aug 4th, Upmid 5th, Dud 5th
| Aug 4th, Upmid 5th, Dud 5th
| A4, ^~5, vv5
| A4, ^~5, vv5
Line 280: Line 278:
| 736.4
| 736.4
| 195/128
| 195/128
|
|  
|
| [[14/9]]
| Up 5th, Downminor 6th
| Up 5th, Downminor 6th
| ^5, vm6
| ^5, vm6
Line 288: Line 286:
| 28
| 28
| 763.6
| 763.6
| 99/64, [[128/81]]
| [[99/64]], [[128/81]]
|
| [[11/7]], [[14/9]]
|
|  
| Minor 6th
| Minor 6th
| m6
| m6
Line 298: Line 296:
| 790.9
| 790.9
| 69/44
| 69/44
|
|  
|
| [[11/7]]
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 307: Line 305:
| 818.2
| 818.2
| [[8/5]]
| [[8/5]]
|
|  
|
| [[21/13]]
| Dupminor 6th, Downmid 6th
| Dupminor 6th, Downmid 6th
| ^^m6, v~6
| ^^m6, v~6
Line 316: Line 314:
| 845.5
| 845.5
| [[13/8]]
| [[13/8]]
|
| [[21/13]]
|
|
| Mid 6th
| Mid 6th
Line 324: Line 322:
| 32
| 32
| 872.7
| 872.7
| [[5/3]], [[48/29]]
| [[5/3]], [[18/11]], [[48/29]]
|
|
|
|
Line 333: Line 331:
| 33
| 33
| 900.0
| 900.0
| [[32/19]]
| [[22/13]], [[32/19]]
|
|
|
|
Line 351: Line 349:
| 35
| 35
| 954.5
| 954.5
| 45/26
| [[26/15]]
|
|
|
| [[7/4]], [[12/7]]
| Upmajor 6th, Downminor 7th
| Upmajor 6th, Downminor 7th
| ^M6, vm7
| ^M6, vm7
Line 378: Line 376:
| 38
| 38
| 1036.4
| 1036.4
| [[20/11]], [[29/16]]
| [[11/6]], [[20/11]], [[29/16]]
|
|  
|
|  
| Dupminor 7th, Downmid 7th
| Dupminor 7th, Downmid 7th
| ^^m7, v~7
| ^^m7, v~7
Line 388: Line 386:
| 1063.6
| 1063.6
| [[24/13]]
| [[24/13]]
|
| [[13/7]]
|
| [[28/15]]
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 397: Line 395:
| 1090.9
| 1090.9
| [[15/8]]
| [[15/8]]
|
| [[28/15]]
|
| [[13/7]]
| Dudmajor 7th, Upmid 7th
| Dudmajor 7th, Upmid 7th
| vvM7, ^~7
| vvM7, ^~7
Line 406: Line 404:
| 1118.2
| 1118.2
| 44/23
| 44/23
|
|  
|
| [[21/11]]
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 415: Line 413:
| 1145.5
| 1145.5
| [[31/16]]
| [[31/16]]
|
|  
|
|  
| Major 7th
| Major 7th
| M7
| M7
Line 424: Line 422:
| 1172.7
| 1172.7
| 128/65
| 128/65
|
|  
|
| [[63/32]]
| Upmajor 7th, Down 8ve
| Upmajor 7th, Down 8ve
| ^M7, v8
| ^M7, v8
Line 433: Line 431:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
|
|  
|
|  
| Perfect 8ve
| Perfect 8ve
| P8
| P8
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