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44edo: Difference between revisions

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MisterShafXen (talk | contribs)
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removed ratios of 7 (for now); checked consistency
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MisterShafXen (talk | contribs)
1,074 edits
added some ratios of 7, can't finish rn bc I'm running low on battery
Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit
Line 18: Line 18:


== Intervals ==
== Intervals ==
{{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.}}
{{Todo|complete table|inline=1|text = Recommend dual ratios for the 7th harmonic which has a lot of relative error; might need some additional ratios.}}


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 27: Line 27:
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
!Ratios of 7 (patent val)
!Ratios of 7 (44d val)
! colspan="3" | [[Ups and downs notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
Line 32: Line 34:
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
|
|
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 39: Line 43:
| 27.3
| 27.3
| [[65/64]]
| [[65/64]]
|
|[[64/63]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 46: Line 52:
| 54.5
| 54.5
| [[32/31]], [[33/32]]
| [[32/31]], [[33/32]]
|51/49
|
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 53: Line 61:
| 81.8
| 81.8
| [[23/22]]
| [[23/22]]
|
|[[22/21]]
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 60: Line 70:
| 109.1
| 109.1
| [[16/15]]
| [[16/15]]
|
|147/136
| Dupminor 2nd, Downmid 2nd
| Dupminor 2nd, Downmid 2nd
| ^^m2, v~2
| ^^m2, v~2
Line 67: Line 79:
| 136.4
| 136.4
| [[13/12]]
| [[13/12]]
|[[14/13]]
|
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 74: Line 88:
| 163.6
| 163.6
| [[11/10]], [[32/29]]
| [[11/10]], [[32/29]]
|31/28
|551/504
| Dudmajor 2nd, Upmid 2nd
| Dudmajor 2nd, Upmid 2nd
| vvM2, ^~2
| vvM2, ^~2
Line 81: Line 97:
| 190.9
| 190.9
| [[19/17]]
| [[19/17]]
|143/126
|352/315
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 88: Line 106:
| 218.2
| 218.2
| [[9/8]]
| [[9/8]]
|[[8/7]]
|143/126
| Major 2nd
| Major 2nd
| M2
| M2
Line 95: Line 115:
| 245.5
| 245.5
| 52/45
| 52/45
|65/56
|[[8/7]]
| Upmajor 2nd, Downminor 3rd
| Upmajor 2nd, Downminor 3rd
| ^M2, vm3
| ^M2, vm3
Line 102: Line 124:
| 272.7
| 272.7
| [[32/27]]
| [[32/27]]
|[[7/6]]
|221/189
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 109: Line 133:
| 300.0
| 300.0
| [[19/16]]
| [[19/16]]
|
|896/729
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 116: Line 142:
| 327.3
| 327.3
| [[11/9]], [[29/24]]
| [[11/9]], [[29/24]]
|896/729
|76/63
| Dupminor 3rd, Downmid 3rd
| Dupminor 3rd, Downmid 3rd
| ^^m3, v~3
| ^^m3, v~3
Line 123: Line 151:
| 354.5
| 354.5
| [[16/13]]
| [[16/13]]
|26/21
|
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 130: Line 160:
| 381.8
| 381.8
| [[5/4]]
| [[5/4]]
|
|26/21
| Dudmajor 3rd, Upmid 3rd
| Dudmajor 3rd, Upmid 3rd
| vvM3, ^~3
| vvM3, ^~3
Line 137: Line 169:
| 409.1
| 409.1
| 171/136
| 171/136
|
|[[80/63]]
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 144: Line 178:
| 436.4
| 436.4
| [[81/64]]
| [[81/64]]
|[[9/7]]
|
| Major 3rd
| Major 3rd
| M3
| M3
Line 151: Line 187:
| 463.6
| 463.6
| [[13/10]]
| [[13/10]]
|
|[[9/7]]
| Upmajor 3rd, Down 4th
| Upmajor 3rd, Down 4th
| ^M3, v4
| ^M3, v4
Line 158: Line 196:
| 490.9
| 490.9
| [[4/3]]
| [[4/3]]
|62/49
|
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 165: Line 205:
| 518.2
| 518.2
| 171/128
| 171/128
|189/143
|256/189
| Up 4th
| Up 4th
| ^4
| ^4
Line 172: Line 214:
| 545.5
| 545.5
| [[11/8]]
| [[11/8]]
|29/21
|
| Dup 4th, Downmid 4th, Dim 5th
| Dup 4th, Downmid 4th, Dim 5th
| ^^4, v~4, d5
| ^^4, v~4, d5
Line 179: Line 223:
| 572.7
| 572.7
| 46/33
| 46/33
|
|29/21
| Mid 4th, Updim 5th
| Mid 4th, Updim 5th
| ~4, ^d5
| ~4, ^d5
Line 186: Line 232:
| 600.0
| 600.0
| 44/31, 31/22
| 44/31, 31/22
|[[7/5]], [[10/7]]
|
| Upmid 4th, Downmid 5th
| Upmid 4th, Downmid 5th
| ^~4, v~5
| ^~4, v~5
Line 193: Line 241:
| 627.3
| 627.3
| 33/23
| 33/23
|
|[[10/7]]
| Downaug 4th, Mid 5th
| Downaug 4th, Mid 5th
| vA4, ~5
| vA4, ~5
Line 200: Line 250:
| 654.5
| 654.5
| [[16/11]]
| [[16/11]]
|
|
| Aug 4th, Upmid 5th, Dud 5th
| Aug 4th, Upmid 5th, Dud 5th
| A4, ^~5, vv5
| A4, ^~5, vv5
Line 207: Line 259:
| 681.8
| 681.8
| 256/171
| 256/171
|
|
| Down 5th
| Down 5th
| v5
| v5
Line 214: Line 268:
| 709.1
| 709.1
| [[3/2]]
| [[3/2]]
|
|
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 221: Line 277:
| 736.4
| 736.4
| 195/128
| 195/128
|
|
| Up 5th, Downminor 6th
| Up 5th, Downminor 6th
| ^5, vm6
| ^5, vm6
Line 228: Line 286:
| 763.6
| 763.6
| 99/64, [[128/81]]
| 99/64, [[128/81]]
|
|
| Minor 6th
| Minor 6th
| m6
| m6
Line 235: Line 295:
| 790.9
| 790.9
| 69/44
| 69/44
|
|
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 242: Line 304:
| 818.2
| 818.2
| [[8/5]]
| [[8/5]]
|
|
| Dupminor 6th, Downmid 6th
| Dupminor 6th, Downmid 6th
| ^^m6, v~6
| ^^m6, v~6
Line 249: Line 313:
| 845.5
| 845.5
| [[13/8]]
| [[13/8]]
|
|
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 256: Line 322:
| 872.7
| 872.7
| [[5/3]], [[48/29]]
| [[5/3]], [[48/29]]
|
|
| Dudmajor 6th, Upmid 6th
| Dudmajor 6th, Upmid 6th
| vvM6, ^~6
| vvM6, ^~6
Line 263: Line 331:
| 900.0
| 900.0
| [[32/19]]
| [[32/19]]
|
|
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 270: Line 340:
| 927.3
| 927.3
| [[27/16]]
| [[27/16]]
|
|
| Major 6th
| Major 6th
| M6
| M6
Line 277: Line 349:
| 954.5
| 954.5
| 45/26
| 45/26
|
|
| Upmajor 6th, Downminor 7th
| Upmajor 6th, Downminor 7th
| ^M6, vm7
| ^M6, vm7
Line 284: Line 358:
| 981.8
| 981.8
| [[16/9]]
| [[16/9]]
|
|
| Minor 7th
| Minor 7th
| m7
| m7
Line 291: Line 367:
| 1009.1
| 1009.1
| [[9/5]]
| [[9/5]]
|
|
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 298: Line 376:
| 1036.4
| 1036.4
| [[20/11]], [[29/16]]
| [[20/11]], [[29/16]]
|
|
| Dupminor 7th, Downmid 7th
| Dupminor 7th, Downmid 7th
| ^^m7, v~7
| ^^m7, v~7
Line 305: Line 385:
| 1063.6
| 1063.6
| [[24/13]]
| [[24/13]]
|
|
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 312: Line 394:
| 1090.9
| 1090.9
| [[15/8]]
| [[15/8]]
|
|
| Dudmajor 7th, Upmid 7th
| Dudmajor 7th, Upmid 7th
| vvM7, ^~7
| vvM7, ^~7
Line 319: Line 403:
| 1118.2
| 1118.2
| 44/23
| 44/23
|
|
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 326: Line 412:
| 1145.5
| 1145.5
| [[31/16]]
| [[31/16]]
|
|
| Major 7th
| Major 7th
| M7
| M7
Line 333: Line 421:
| 1172.7
| 1172.7
| 128/65
| 128/65
|
|
| Upmajor 7th, Down 8ve
| Upmajor 7th, Down 8ve
| ^M7, v8
| ^M7, v8
Line 340: Line 430:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
|
|
| Perfect 8ve
| Perfect 8ve
| P8
| P8
Retrieved from "https://en.xen.wiki/w/44edo"