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44edo: Difference between revisions

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=== Harmonics ===
=== Harmonics ===
{{Harmonics in equal|44}}
{{Harmonics in equal|44|columns=11}}
{{Harmonics in equal|44|columns=11|start=12|collapsed=1|title=Approximation of odd harmonics in 44edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
Line 18: 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-5 center-6"
 
{| class="wikitable center-all right-2 left-3"
|-
|-
! #
! #
! 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 36: Line 31:
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
|
|
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 45: Line 38:
| 27.3
| 27.3
| [[65/64]]
| [[65/64]]
|
|[[64/63]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 53: 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 62: 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 71: Line 58:
| 4
| 4
| 109.1
| 109.1
| [[16/15]]
| [[15/14]], [[16/15]], [[17/16]], [[18/17]]
|
| Dupminor 2nd, downmid 2nd
|147/136
| Dupminor 2nd, Downmid 2nd
| ^^m2, v~2
| ^^m2, v~2
| ^^Eb
| ^^Eb
Line 80: Line 65:
| 5
| 5
| 136.4
| 136.4
| [[13/12]]
| [[13/12]], [[14/13]]
|[[14/13]]
|
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 89: Line 72:
| 6
| 6
| 163.6
| 163.6
| [[11/10]], [[32/29]]
| ''[[10/9]]'', [[11/10]], [[12/11]], [[32/29]]
|31/28
| Dudmajor 2nd, upmid 2nd
|551/504
| Dudmajor 2nd, Upmid 2nd
| vvM2, ^~2
| vvM2, ^~2
| vvE
| vvE
Line 99: Line 80:
| 190.9
| 190.9
| [[19/17]]
| [[19/17]]
|143/126
|352/315
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 107: Line 86:
| 8
| 8
| 218.2
| 218.2
| [[9/8]]
| [[8/7]], ''[[9/8]]'', [[17/15]]
|[[8/7]]
|143/126
| Major 2nd
| Major 2nd
| M2
| M2
Line 116: Line 93:
| 9
| 9
| 245.5
| 245.5
| 52/45
| [[15/13]], [[22/19]]
|65/56
| Upmajor 2nd, downminor 3rd
|[[8/7]]
| Upmajor 2nd, Downminor 3rd
| ^M2, vm3
| ^M2, vm3
| ^E, vF
| ^E, vF
Line 125: Line 100:
| 10
| 10
| 272.7
| 272.7
| [[32/27]]
| [[7/6]], [[20/17]]
|[[7/6]]
|221/189
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 134: Line 107:
| 11
| 11
| 300.0
| 300.0
| [[19/16]]
| [[13/11]], [[19/16]]
|
|896/729
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 143: Line 114:
| 12
| 12
| 327.3
| 327.3
| [[11/9]], [[29/24]]
| [[6/5]], ''[[11/9]]'', [[17/14]], [[29/24]]
|896/729
| Dupminor 3rd, downmid 3rd
|76/63
| Dupminor 3rd, Downmid 3rd
| ^^m3, v~3
| ^^m3, v~3
| ^^F
| ^^F
Line 152: 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 162: 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 170: Line 135:
| 15
| 15
| 409.1
| 409.1
| [[19/15]], 171/136
| [[19/15]], [[24/19]]
|
|[[80/63]]
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 179: Line 142:
| 16
| 16
| 436.4
| 436.4
| [[81/64]]
| [[9/7]], ''[[14/11]]'', [[22/17]]
|[[9/7]]
|
| Major 3rd
| Major 3rd
| M3
| M3
Line 188: 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 198: Line 157:
| 490.9
| 490.9
| [[4/3]]
| [[4/3]]
|62/49
|
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 206: Line 163:
| 19
| 19
| 518.2
| 518.2
| 171/128
| [[19/14]]
|189/143
|256/189
| Up 4th
| Up 4th
| ^4
| ^4
Line 215: Line 170:
| 20
| 20
| 545.5
| 545.5
| [[11/8]]
| [[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 224: Line 177:
| 21
| 21
| 572.7
| 572.7
| 46/33
| [[18/13]], [[32/23]]
|
|29/21
| Mid 4th, Updim 5th
| Mid 4th, Updim 5th
| ~4, ^d5
| ~4, ^d5
Line 233: 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 242: Line 191:
| 23
| 23
| 627.3
| 627.3
| 33/23
| [[13/9]], [[23/16]]
|
| Downaug 4th, mid 5th
|[[10/7]]
| Downaug 4th, Mid 5th
| vA4, ~5
| vA4, ~5
| vvvA, ^^^Ab
| vvvA, ^^^Ab
Line 251: Line 198:
| 24
| 24
| 654.5
| 654.5
| [[16/11]]
| [[16/11]], [[19/13]], [[22/15]]
|
| Aug 4th, upmid 5th, dud 5th
|
| Aug 4th, Upmid 5th, Dud 5th
| A4, ^~5, vv5
| A4, ^~5, vv5
| G#, vvA
| G#, vvA
Line 260: Line 205:
| 25
| 25
| 681.8
| 681.8
| 256/171
| [[28/19]]
|
|
| Down 5th
| Down 5th
| v5
| v5
Line 270: Line 213:
| 709.1
| 709.1
| [[3/2]]
| [[3/2]]
|
|
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 278: Line 219:
| 27
| 27
| 736.4
| 736.4
| 195/128
| [[20/13]], [[26/17]]
|
| Up 5th, downminor 6th
|
| Up 5th, Downminor 6th
| ^5, vm6
| ^5, vm6
| ^A, vBb
| ^A, vBb
Line 287: Line 226:
| 28
| 28
| 763.6
| 763.6
| 99/64, [[128/81]]
| [[14/9]], ''[[11/7]]'', [[17/11]]
|
|
| Minor 6th
| Minor 6th
| m6
| m6
Line 296: Line 233:
| 29
| 29
| 790.9
| 790.9
| 69/44
| [[19/12]], [[30/19]]
|
|
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 306: Line 241:
| 818.2
| 818.2
| [[8/5]]
| [[8/5]]
|
| Dupminor 6th, downmid 6th
|
| Dupminor 6th, Downmid 6th
| ^^m6, v~6
| ^^m6, v~6
| ^^Bb
| ^^Bb
Line 314: Line 247:
| 31
| 31
| 845.5
| 845.5
| [[13/8]]
| [[13/8]], [[21/13]]
|
|
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 323: Line 254:
| 32
| 32
| 872.7
| 872.7
| [[5/3]], [[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 261:
| 33
| 33
| 900.0
| 900.0
| [[32/19]]
| [[22/13]], [[32/19]]
|
|
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 341: Line 268:
| 34
| 34
| 927.3
| 927.3
| [[27/16]]
| [[12/7]], [[17/10]]
|
|
| Major 6th
| Major 6th
| M6
| M6
Line 350: Line 275:
| 35
| 35
| 954.5
| 954.5
| 45/26
| [[19/11]], [[26/15]]
|
| Upmajor 6th, downminor 7th
|
| Upmajor 6th, Downminor 7th
| ^M6, vm7
| ^M6, vm7
| ^B, vC
| ^B, vC
Line 359: Line 282:
| 36
| 36
| 981.8
| 981.8
| [[16/9]]
| [[7/4]], ''[[16/9]]'', [[30/17]]
|
|
| Minor 7th
| Minor 7th
| m7
| m7
Line 368: Line 289:
| 37
| 37
| 1009.1
| 1009.1
| [[9/5]]
| [[34/19]]
|
|
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 377: Line 296:
| 38
| 38
| 1036.4
| 1036.4
| [[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 386: Line 303:
| 39
| 39
| 1063.6
| 1063.6
| [[24/13]]
| [[13/7]], [[24/13]]
|
|
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 395: Line 310:
| 40
| 40
| 1090.9
| 1090.9
| [[15/8]]
| [[15/8]], [[17/9]], [[28/15]], [[32/17]]
|
| Dudmajor 7th, upmid 7th
|
| Dudmajor 7th, Upmid 7th
| vvM7, ^~7
| vvM7, ^~7
| vvC#
| vvC#
Line 404: Line 317:
| 41
| 41
| 1118.2
| 1118.2
| 44/23
| [[19/10]], [[36/19]], [[44/23]], [[23/12]]
|
|
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 413: 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 422: Line 331:
| 43
| 43
| 1172.7
| 1172.7
| 128/65
| [[128/65]]
|
| Upmajor 7th, down 8ve
|
| Upmajor 7th, Down 8ve
| ^M7, v8
| ^M7, v8
| ^C#, vD
| ^C#, vD
Line 432: 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 511: Line 421:
| 22/21
| 22/21
| [[Nautilus]] (44d)
| [[Nautilus]] (44d)
|-
| 1
| 5\44
| 136.36
| 14/13
| [[Doublethink]]
|-
|-
| 1
| 1
Line 534: 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
Line 570: Line 498:
** [https://www.youtube.com/shorts/Oi3v0c7jbjM ''<nowiki>[short clip]</nowiki>'']
** [https://www.youtube.com/shorts/Oi3v0c7jbjM ''<nowiki>[short clip]</nowiki>'']
** [https://www.youtube.com/shorts/ZOoiGuUA-9Y ''<nowiki>[short 2]</nowiki>'']
** [https://www.youtube.com/shorts/ZOoiGuUA-9Y ''<nowiki>[short 2]</nowiki>'']
** [https://www.youtube.com/watch?v=lclipVgCvf4 ''<nowiki>[complete song]</nowiki>'']
** [https://www.youtube.com/watch?v=lclipVgCvf4 ''<nowiki>[complete song original release]</nowiki>'']
** [https://www.youtube.com/watch?v=JUVotVQwpiY ''<nowiki>[complete song Orpheum release]</nowiki>'']


[[Category:44edo| ]] <!-- main article -->
[[Category:44edo| ]] <!-- main article -->
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