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44edo: Difference between revisions

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m →Music: Bryan Deister's ''Buried Treasure - 44edo'' (2026): Add Orpheum release
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Line 19: Line 19:


== Intervals ==
== Intervals ==
{{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-1 right-2 center-7 center-8"
{| class="wikitable center-1 right-2 center-5 center-6"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
! Ratios of 7 tending<br>sharp (patent val)
! Ratios of 7 tending<br>flat (44d val)
! colspan="3" | [[Ups and downs notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
Line 35: Line 31:
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
|
|
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 44: Line 38:
| 27.3
| 27.3
| [[65/64]]
| [[65/64]]
|
| [[64/63]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 52: Line 44:
| 2
| 2
| 54.5
| 54.5
| [[32/31]], [[33/32]]
| [[28/27]], [[32/31]], [[33/32]], [[34/33]], [[36/35]]
| 51/49
|
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 61: Line 51:
| 3
| 3
| 81.8
| 81.8
| [[23/22]]
| [[19/18]], [[20/19]], [[23/22]], [[24/23]]
|
| [[22/21]]
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 70: Line 58:
| 4
| 4
| 109.1
| 109.1
| [[16/15]]
| [[15/14]], [[16/15]], [[17/16]], [[18/17]]
| [[15/14]]
| Dupminor 2nd, downmid 2nd
| [[14/13]]
| Dupminor 2nd, Downmid 2nd
| ^^m2, v~2
| ^^m2, v~2
| ^^Eb
| ^^Eb
Line 79: Line 65:
| 5
| 5
| 136.4
| 136.4
| [[13/12]]
| [[13/12]], [[14/13]]
| [[14/13]]
| [[15/14]]
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 88: Line 72:
| 6
| 6
| 163.6
| 163.6
| [[11/10]], [[12/11]], [[32/29]]
| ''[[10/9]]'', [[11/10]], [[12/11]], [[32/29]]
| 31/28
| Dudmajor 2nd, upmid 2nd
|
| Dudmajor 2nd, Upmid 2nd
| vvM2, ^~2
| vvM2, ^~2
| vvE
| vvE
Line 98: Line 80:
| 190.9
| 190.9
| [[19/17]]
| [[19/17]]
|
|
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 106: Line 86:
| 8
| 8
| 218.2
| 218.2
| [[9/8]]
| [[8/7]], ''[[9/8]]'', [[17/15]]
| [[8/7]]
|
| Major 2nd
| Major 2nd
| M2
| M2
Line 115: Line 93:
| 9
| 9
| 245.5
| 245.5
| [[15/13]]
| [[15/13]], [[22/19]]
|
| Upmajor 2nd, downminor 3rd
| [[7/6]], [[8/7]]
| Upmajor 2nd, Downminor 3rd
| ^M2, vm3
| ^M2, vm3
| ^E, vF
| ^E, vF
Line 124: Line 100:
| 10
| 10
| 272.7
| 272.7
| [[32/27]]
| [[7/6]], [[20/17]]
| [[7/6]]
|
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 134: Line 108:
| 300.0
| 300.0
| [[13/11]], [[19/16]]
| [[13/11]], [[19/16]]
|
|
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 142: Line 114:
| 12
| 12
| 327.3
| 327.3
| [[6/5]], [[11/9]], [[29/24]]
| [[6/5]], ''[[11/9]]'', [[17/14]], [[29/24]]
|
| Dupminor 3rd, downmid 3rd
|
| Dupminor 3rd, Downmid 3rd
| ^^m3, v~3
| ^^m3, v~3
| ^^F
| ^^F
Line 151: Line 121:
| 13
| 13
| 354.5
| 354.5
| [[16/13]]
| [[16/13]], [[26/21]], [[39/32]]
| [[26/21]]
|
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 161: Line 129:
| 381.8
| 381.8
| [[5/4]]
| [[5/4]]
|
| Dudmajor 3rd, upmid 3rd
| [[26/21]]
| Dudmajor 3rd, Upmid 3rd
| vvM3, ^~3
| vvM3, ^~3
| vvF#
| vvF#
Line 169: Line 135:
| 15
| 15
| 409.1
| 409.1
| [[19/15]]
| [[19/15]], [[24/19]]
|
| [[14/11]]
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 178: Line 142:
| 16
| 16
| 436.4
| 436.4
| [[81/64]], [[128/99]]
| [[9/7]], ''[[14/11]]'', [[22/17]]
| [[9/7]], [[14/11]]
|
| Major 3rd
| Major 3rd
| M3
| M3
Line 187: Line 149:
| 17
| 17
| 463.6
| 463.6
| [[13/10]]
| [[13/10]], [[17/13]]
|
| Upmajor 3rd, down 4th
| [[9/7]]
| Upmajor 3rd, Down 4th
| ^M3, v4
| ^M3, v4
| ^F#, vG
| ^F#, vG
Line 197: Line 157:
| 490.9
| 490.9
| [[4/3]]
| [[4/3]]
|
|
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 205: Line 163:
| 19
| 19
| 518.2
| 518.2
| 171/128
| [[19/14]]
| 189/143
| 256/189
| Up 4th
| Up 4th
| ^4
| ^4
Line 214: Line 170:
| 20
| 20
| 545.5
| 545.5
| [[11/8]], [[15/11]]
| [[11/8]], [[15/11]], [[26/19]]
| [[29/21]]
| Dup 4th, downmid 4th, dim 5th
|
| Dup 4th, Downmid 4th, Dim 5th
| ^^4, v~4, d5
| ^^4, v~4, d5
| Ab, ^^G
| Ab, ^^G
Line 223: Line 177:
| 21
| 21
| 572.7
| 572.7
| 46/33
| [[18/13]], [[32/23]]
|
| [[7/5]], [[29/21]]
| Mid 4th, Updim 5th
| Mid 4th, Updim 5th
| ~4, ^d5
| ~4, ^d5
Line 232: Line 184:
| 22
| 22
| 600.0
| 600.0
| 44/31, 31/22
| [[17/12]], [[24/17]], ''[[7/5]]'', ''[[10/7]]''
| [[7/5]], [[10/7]]
| Upmid 4th, downmid 5th
|
| Upmid 4th, Downmid 5th
| ^~4, v~5
| ^~4, v~5
| vvG#, ^^Ab
| vvG#, ^^Ab
Line 241: Line 191:
| 23
| 23
| 627.3
| 627.3
| 33/23
| [[13/9]], [[23/16]]
|
| Downaug 4th, mid 5th
| [[10/7]], [[42/29]]
| Downaug 4th, Mid 5th
| vA4, ~5
| vA4, ~5
| vvvA, ^^^Ab
| vvvA, ^^^Ab
Line 250: Line 198:
| 24
| 24
| 654.5
| 654.5
| [[16/11]], [[22/15]]
| [[16/11]], [[19/13]], [[22/15]]
| [[42/29]]
| Aug 4th, upmid 5th, dud 5th
|
| Aug 4th, Upmid 5th, Dud 5th
| A4, ^~5, vv5
| A4, ^~5, vv5
| G#, vvA
| G#, vvA
Line 259: Line 205:
| 25
| 25
| 681.8
| 681.8
| 256/171
| [[28/19]]
|
|
| Down 5th
| Down 5th
| v5
| v5
Line 269: Line 213:
| 709.1
| 709.1
| [[3/2]]
| [[3/2]]
|
|
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 277: Line 219:
| 27
| 27
| 736.4
| 736.4
| 195/128
| [[20/13]], [[26/17]]
|
| Up 5th, downminor 6th
| [[14/9]]
| Up 5th, Downminor 6th
| ^5, vm6
| ^5, vm6
| ^A, vBb
| ^A, vBb
Line 286: Line 226:
| 28
| 28
| 763.6
| 763.6
| [[99/64]], [[128/81]]
| [[14/9]], ''[[11/7]]'', [[17/11]]
| [[11/7]], [[14/9]]
|
| Minor 6th
| Minor 6th
| m6
| m6
Line 295: Line 233:
| 29
| 29
| 790.9
| 790.9
| 69/44
| [[19/12]], [[30/19]]
|
| [[11/7]]
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 305: Line 241:
| 818.2
| 818.2
| [[8/5]]
| [[8/5]]
|
| Dupminor 6th, downmid 6th
| [[21/13]]
| Dupminor 6th, Downmid 6th
| ^^m6, v~6
| ^^m6, v~6
| ^^Bb
| ^^Bb
Line 313: Line 247:
| 31
| 31
| 845.5
| 845.5
| [[13/8]]
| [[13/8]], [[21/13]]
| [[21/13]]
|
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 322: Line 254:
| 32
| 32
| 872.7
| 872.7
| [[5/3]], [[18/11]], [[48/29]]
| [[5/3]], ''[[18/11]]'', [[28/17]], [[48/29]]
|
| Dudmajor 6th, upmid 6th
|
| Dudmajor 6th, Upmid 6th
| vvM6, ^~6
| vvM6, ^~6
| vvB
| vvB
Line 332: Line 262:
| 900.0
| 900.0
| [[22/13]], [[32/19]]
| [[22/13]], [[32/19]]
|
|
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 340: Line 268:
| 34
| 34
| 927.3
| 927.3
| [[27/16]]
| [[12/7]], [[17/10]]
|
|
| Major 6th
| Major 6th
| M6
| M6
Line 349: Line 275:
| 35
| 35
| 954.5
| 954.5
| [[26/15]]
| [[19/11]], [[26/15]]
|
| Upmajor 6th, downminor 7th
| [[7/4]], [[12/7]]
| Upmajor 6th, Downminor 7th
| ^M6, vm7
| ^M6, vm7
| ^B, vC
| ^B, vC
Line 358: Line 282:
| 36
| 36
| 981.8
| 981.8
| [[16/9]]
| [[7/4]], ''[[16/9]]'', [[30/17]]
|
|
| Minor 7th
| Minor 7th
| m7
| m7
Line 367: Line 289:
| 37
| 37
| 1009.1
| 1009.1
| [[9/5]]
| [[34/19]]
|
|
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 376: Line 296:
| 38
| 38
| 1036.4
| 1036.4
| [[11/6]], [[20/11]], [[29/16]]
| ''[[9/5]]'', [[11/6]], [[20/11]], [[29/16]]
|
| Dupminor 7th, downmid 7th
|
| Dupminor 7th, Downmid 7th
| ^^m7, v~7
| ^^m7, v~7
| ^^C
| ^^C
Line 385: Line 303:
| 39
| 39
| 1063.6
| 1063.6
| [[24/13]]
| [[13/7]], [[24/13]]
| [[13/7]]
| [[28/15]]
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 394: Line 310:
| 40
| 40
| 1090.9
| 1090.9
| [[15/8]]
| [[15/8]], [[17/9]], [[28/15]], [[32/17]]
| [[28/15]]
| Dudmajor 7th, upmid 7th
| [[13/7]]
| Dudmajor 7th, Upmid 7th
| vvM7, ^~7
| vvM7, ^~7
| vvC#
| vvC#
Line 403: Line 317:
| 41
| 41
| 1118.2
| 1118.2
| 44/23
| [[19/10]], [[36/19]], [[44/23]], [[23/12]]
|
| [[21/11]]
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 412: Line 324:
| 42
| 42
| 1145.5
| 1145.5
| [[31/16]]
| [[27/14]], [[31/16]], [[33/17]], [[35/18]], [[64/33]]
|
|
| Major 7th
| Major 7th
| M7
| M7
Line 421: Line 331:
| 43
| 43
| 1172.7
| 1172.7
| 128/65
| [[128/65]]
|
| Upmajor 7th, down 8ve
| [[63/32]]
| Upmajor 7th, Down 8ve
| ^M7, v8
| ^M7, v8
| ^C#, vD
| ^C#, vD
Line 431: Line 339:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
|
|
| Perfect 8ve
| Perfect 8ve
| P8
| P8
| D
| D
|}
|}
<nowiki/>* As a 2.3.5.11.13.17.19.23.29.31-subgroup temperament
<nowiki/>* As a 19-limit temperament, with additional ratios of 23, 29, and 31
 
== Approximation to JI ==
=== Interval mappings ===
{{Q-odd-limit intervals|44}}


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
44edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.  
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp6-szg}}
 
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt-szg}}
 
=== Kite's ups and downs notation ===
44edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.  
{{Sharpness-sharp6a}}
{{Sharpness-sharp6a}}


Half-sharps and half-flats can be used to avoid triple arrows:
Half-sharps and half-flats can be used to avoid triple arrows:
{{Sharpness-sharp6b}}
{{Sharpness-sharp6b}}
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp6}}
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt}}


=== Sagittal notation ===
=== Sagittal notation ===
Line 510: Line 421:
| 22/21
| 22/21
| [[Nautilus]] (44d)
| [[Nautilus]] (44d)
|-
| 1
| 5\44
| 136.36
| 14/13
| [[Doublethink]]
|-
|-
| 1
| 1
Line 533: Line 450:
| 409.09
| 409.09
| 5/4
| 5/4
| [[Hocus]] (44)
| [[Hocus]]
|-
| 1
| 17\44
| 463.64
| 72/55
| [[Borwell]] (44e)
|-
| 1
| 19\44
| 518.18
| 88/65
| [[Undecimation]]
|-
|-
| 2
| 2
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