Xenharmonic Wiki

44edo: Difference between revisions

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- intervals of 7
Reduce cent values to one decimal place
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== 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 = 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.}}
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-all right-2 left-3"
|-
|-
! Degrees
! #
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
Line 29: Line 30:
|-
|-
| 0
| 0
| 0.000
| 0.0
| [[1/1]]
| [[1/1]]
| Perfect 1sn
| Perfect 1sn
Line 36: Line 37:
|-
|-
| 1
| 1
| 27.273
| 27.3
|  
|  
| Up 1sn
| Up 1sn
Line 43: Line 44:
|-
|-
| 2
| 2
| 54.545
| 54.5
| [[32/31]], [[33/32]]
| [[32/31]], [[33/32]]
| Minor 2nd
| Minor 2nd
Line 50: Line 51:
|-
|-
| 3
| 3
| 81.818
| 81.8
| [[23/22]]
| [[23/22]]
| Upminor 2nd
| Upminor 2nd
Line 57: Line 58:
|-
|-
| 4
| 4
| 109.091
| 109.1
| [[16/15]]
| [[16/15]]
| Dupminor 2nd, Downmid 2nd
| Dupminor 2nd, Downmid 2nd
Line 64: Line 65:
|-
|-
| 5
| 5
| 136.364
| 136.4
| [[13/12]]
| [[13/12]]
| Mid 2nd
| Mid 2nd
Line 71: Line 72:
|-
|-
| 6
| 6
| 163.636
| 163.6
| [[11/10]], [[32/29]]
| [[11/10]], [[32/29]]
| Dudmajor 2nd, Upmid 2nd
| Dudmajor 2nd, Upmid 2nd
Line 78: Line 79:
|-
|-
| 7
| 7
| 190.909
| 190.9
| [[28/25]]
| [[28/25]]
| Downmajor 2nd
| Downmajor 2nd
Line 85: Line 86:
|-
|-
| 8
| 8
| 218.182
| 218.2
| [[9/8]]
| [[9/8]]
| Major 2nd
| Major 2nd
Line 92: Line 93:
|-
|-
| 9
| 9
| 245.455
| 245.5
|  
|  
| Upmajor 2nd, Downminor 3rd
| Upmajor 2nd, Downminor 3rd
Line 99: Line 100:
|-
|-
| 10
| 10
| 272.727
| 272.7
| [[32/27]]
| [[32/27]]
| Minor 3rd
| Minor 3rd
Line 106: Line 107:
|-
|-
| 11
| 11
| 300.000
| 300.0
| [[19/16]]
| [[19/16]]
| Upminor 3rd
| Upminor 3rd
Line 113: Line 114:
|-
|-
| 12
| 12
| 327.273
| 327.3
| [[11/9]], [[29/24]]
| [[11/9]], [[29/24]]
| Dupminor 3rd, Downmid 3rd
| Dupminor 3rd, Downmid 3rd
Line 120: Line 121:
|-
|-
| 13
| 13
| 354.545
| 354.5
| [[16/13]]
| [[16/13]]
| Mid 3rd
| Mid 3rd
Line 127: Line 128:
|-
|-
| 14
| 14
| 381.818
| 381.8
| [[5/4]]
| [[5/4]]
| Dudmajor 3rd, Upmid 3rd
| Dudmajor 3rd, Upmid 3rd
Line 134: Line 135:
|-
|-
| 15
| 15
| 409.091
| 409.1
|  
|  
| Downmajor 3rd
| Downmajor 3rd
Line 141: Line 142:
|-
|-
| 16
| 16
| 436.364
| 436.4
| [[81/64]]
| [[81/64]]
| Major 3rd
| Major 3rd
Line 148: Line 149:
|-
|-
| 17
| 17
| 463.636
| 463.6
|  
|  
| Upmajor 3rd, Down 4th
| Upmajor 3rd, Down 4th
Line 155: Line 156:
|-
|-
| 18
| 18
| 490.909
| 490.9
| [[4/3]]
| [[4/3]]
| Perfect 4th
| Perfect 4th
Line 162: Line 163:
|-
|-
| 19
| 19
| 518.182
| 518.2
|  
|  
| Up 4th
| Up 4th
Line 169: Line 170:
|-
|-
| 20
| 20
| 545.455
| 545.5
| [[11/8]]
| [[11/8]]
| Dup 4th, Downmid 4th, Dim 5th
| Dup 4th, Downmid 4th, Dim 5th
Line 176: Line 177:
|-
|-
| 21
| 21
| 572.727
| 572.7
|  
|  
| Mid 4th, Updim 5th
| Mid 4th, Updim 5th
Line 183: Line 184:
|-
|-
| 22
| 22
| 600.000
| 600.0
|  
|  
| Upmid 4th, Downmid 5th
| Upmid 4th, Downmid 5th
Line 190: Line 191:
|-
|-
| 23
| 23
| 627.273
| 627.3
|  
|  
| Downaug 4th, Mid 5th
| Downaug 4th, Mid 5th
Line 197: Line 198:
|-
|-
| 24
| 24
| 654.545
| 654.5
| [[16/11]]
| [[16/11]]
| Aug 4th, Upmid 5th, Dud 5th
| Aug 4th, Upmid 5th, Dud 5th
Line 204: Line 205:
|-
|-
| 25
| 25
| 681.818
| 681.8
|  
|  
| Down 5th
| Down 5th
Line 211: Line 212:
|-
|-
| 26
| 26
| 709.091
| 709.1
| [[3/2]]
| [[3/2]]
| Perfect 5th
| Perfect 5th
Line 218: Line 219:
|-
|-
| 27
| 27
| 736.364
| 736.4
|  
|  
| Up 5th, Downminor 6th
| Up 5th, Downminor 6th
Line 225: Line 226:
|-
|-
| 28
| 28
| 763.636
| 763.6
|  
|  
| Minor 6th
| Minor 6th
Line 232: Line 233:
|-
|-
| 29
| 29
| 790.909
| 790.9
| [[128/81]]
| [[128/81]]
| Upminor 6th
| Upminor 6th
Line 239: Line 240:
|-
|-
| 30
| 30
| 818.182
| 818.2
| [[8/5]]
| [[8/5]]
| Dupminor 6th, Downmid 6th
| Dupminor 6th, Downmid 6th
Line 246: Line 247:
|-
|-
| 31
| 31
| 845.455
| 845.5
| [[13/8]]
| [[13/8]]
| Mid 6th
| Mid 6th
Line 253: Line 254:
|-
|-
| 32
| 32
| 872.727
| 872.7
| [[5/3]], [[48/29]]
| [[5/3]], [[48/29]]
| Dudmajor 6th, Upmid 6th
| Dudmajor 6th, Upmid 6th
Line 260: Line 261:
|-
|-
| 33
| 33
| 900.000
| 900.0
| [[27/16]]
| [[27/16]]
| Downmajor 6th
| Downmajor 6th
Line 267: Line 268:
|-
|-
| 34
| 34
| 927.273
| 927.3
|  
|  
| Major 6th
| Major 6th
Line 274: Line 275:
|-
|-
| 35
| 35
| 954.545
| 954.5
|  
|  
| Upmajor 6th, Downminor 7th
| Upmajor 6th, Downminor 7th
Line 281: Line 282:
|-
|-
| 36
| 36
| 981.818
| 981.8
| [[16/9]]
| [[16/9]]
| Minor 7th
| Minor 7th
Line 288: Line 289:
|-
|-
| 37
| 37
| 1009.091
| 1009.1
| [[9/5]]
| [[9/5]]
| Upminor 7th
| Upminor 7th
Line 295: Line 296:
|-
|-
| 38
| 38
| 1036.364
| 1036.4
| [[20/11]], [[29/16]]
| [[20/11]], [[29/16]]
| Dupminor 7th, Downmid 7th
| Dupminor 7th, Downmid 7th
Line 302: Line 303:
|-
|-
| 39
| 39
| 1063.636
| 1063.6
| [[24/13]]
| [[24/13]]
| Mid 7th
| Mid 7th
Line 309: Line 310:
|-
|-
| 40
| 40
| 1090.909
| 1090.9
| [[15/8]]
| [[15/8]]
| Dudmajor 7th, Upmid 7th
| Dudmajor 7th, Upmid 7th
Line 316: Line 317:
|-
|-
| 41
| 41
| 1118.182
| 1118.2
| [[40/21]]
| [[40/21]]
| Downmajor 7th
| Downmajor 7th
Line 323: Line 324:
|-
|-
| 42
| 42
| 1145.455
| 1145.5
| [[31/16]]
| [[31/16]]
| Major 7th
| Major 7th
Line 330: Line 331:
|-
|-
| 43
| 43
| 1172.727
| 1172.7
|  
|  
| Upmajor 7th, Down 8ve
| Upmajor 7th, Down 8ve
Line 337: Line 338:
|-
|-
| 44
| 44
| 1200.000
| 1200.0
| [[2/1]]
| [[2/1]]
| Perfect 8ve
| Perfect 8ve
Retrieved from "https://en.xen.wiki/w/44edo"