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{{Infobox ET
{{Infobox ET}}
| Prime factorization = 2 x 5<sup>2</sup>
{{ED intro}}
| Step size = 24.000
| Fifth = 29\50 = 696¢
| Major 2nd = 8\50 = 192¢
| Semitones = 3:5 (72¢:120¢)
| Consistency = 9
| Monotonicity = 19
}}
 
'''50edo''' divides the [[octave]] into 50 equal parts of precisely 24 [[cent|cents]] each.


== Theory ==
== Theory ==
In the [[5-limit]], 50edo tempers out [[81/80]], making it a [[meantone]] system, and in that capacity has historically has drawn some notice. In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts &ndash; 50edo, in one word. Later, W.S.B. Woolhouse noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is the highest edo which maps [[9/8]] and [[10/9]] to the same interval in a [[consistent]] manner, with two stacked fifths falling almost precisely in the middle of the two.
As an equal temperament, 50et [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a [[meantone]] system, and in that capacity has historically drawn some notice; it is a somewhat sharp approximation of [[2/7-comma meantone]] (and is almost exactly 5/18-comma meantone). In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts &ndash; 50edo, in one word. Later, {{w|W. S. B. Woolhouse}} noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher-limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is also the highest edo for which the mapping of [[9/8]] and [[10/9]] to the same interval is [[consistent]], with two stacked fifths falling almost exactly 3/7-syntonic-comma sharp of 10/9 and 4/7-comma flat of 9/8. It is also almost consistent to the no-21s [[25-odd-limit]], only barely missing consistent mappings of [[11/9]] and [[18/11]].


50edo tempers out 126/125, 225/224 and 3136/3125 in the [[7-limit]], indicating it [[support]]s septimal meantone; 245/242, 385/384 and 540/539 in the [[11-limit]] and 105/104, 144/143 and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension meanpop, it can be used to advantage for the [[Starling temperaments #Coblack temperament|coblack (15&amp;50) temperament]], and provides the optimal patent val for 11 and 13 limit [[Meantone_family #Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo|23 6 -14}};, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.
50edo is also quite strong in the realm of tertian harmony for a meantone system, as the errors on [[7/6]], [[6/5]], [[5/4]], and [[9/7]] are all balanced to be roughly half as flat as the fifth, meaning that this set of thirds taken as a whole is minimally out-of-tune given the damage induced by meantone. Though it fails to approximate [[11/9]] well by virtue of not having a perfect hemififth, it inherits the excellent [[16/13]] from [[10edo]] and additionally has a 1.2{{c}} flat [[13/11]], providing even more qualities of roughly just thirds alongside their more complex [[fifth complement]]s.


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|50}}
{{Harmonics in equal|50|intervals=odd|columns=11}}
{{Harmonics in equal|50|intervals=odd|columns=12|start=12|collapsed=true|title=Approximation of odd harmonics in 50edo (continued)}}
 
=== As a tuning of other temperaments ===
50et tempers out [[126/125]], [[225/224]] and [[3136/3125]] in the [[7-limit]], indicating it [[support]]s septimal meantone; [[245/242]], [[385/384]] and [[540/539]] in the [[11-limit]] and [[105/104]], [[144/143]] and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension [[meanpop]], it can be used to advantage for the [[coblack]] temperament (15 &amp; 50), and provides the optimal patent val for 11- and 13-limit [[Meantone family #Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo| 23 6 -14 }}, so that in 50edo seven chromatic semitones stack to a perfect fourth. By comparison, this gives a perfect fifth in 12edo, a doubly diminished fifth in 31edo, and a diminished fourth in 19edo.


=== Relations ===
=== Relations ===
The 50edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "Golden Tone System" ([[Das Goldene Tonsystem]]) of [[Thorvald Kornerup]] (and similarly as the next step from 31edo in [[Joseph Yasser]]'s "[http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&redir_esc=y A Theory of Evolving Tonality]").
The 50edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "[[Golden meantone|Golden Tone System]]" ([[Das Goldene Tonsystem]]) of [[Thorvald Kornerup]] (and similarly as the next step from 31edo in [[Joseph Yasser]]'s "[https://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&redir_esc=y A Theory of Evolving Tonality]").


== Intervals ==
== Intervals ==
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2 left-3"
|-
|-
! #
! &#35;
! Cents
! Cents
! Ratios*
! Ratios<ref group="note">{{sg|50edo|limit=13-limit}}</ref>
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and vvd2)
|-
|-
| 0
| 0
| 0
| 0
| 1/1
| [[1/1]]
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 39: Line 35:
| 1
| 1
| 24
| 24
| 45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168
| ''[[45/44]]'', [[49/48]], [[56/55]], [[65/64]],<br> [[66/65]], [[78/77]], [[91/90]], [[99/98]],<br> [[100/99]], [[121/120]], ''[[169/168]]''
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 46: Line 42:
| 2
| 2
| 48
| 48
| 33/32, 36/35, 50/49, 55/54, 64/63
| ''[[27/26]]'', [[33/32]], [[36/35]],<br> ''[[50/49]]'', ''[[55/54]]'', ''[[64/63]]''
| Dim 2nd, Downaug 1sn
| Dim 2nd, Downaug 1sn
| d2, vA1
| d2, vA1
Line 53: Line 49:
| 3
| 3
| 72
| 72
| 21/20, 25/24, 26/25, 27/26, 28/27
| ''[[21/20]]'', [[25/24]], [[26/25]], [[28/27]]
| Aug 1sn, Updim 2nd
| Aug 1sn, Updim 2nd
| A1, ^d2
| A1, ^d2
Line 60: Line 56:
| 4
| 4
| 96
| 96
| 22/21
| ''[[22/21]]''
| Downminor 2nd
| Downminor 2nd
| vm2
| vm2
Line 67: Line 63:
| 5
| 5
| 120
| 120
| 16/15, 15/14, 14/13
| [[16/15]], [[15/14]], [[14/13]]
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 74: Line 70:
| 6
| 6
| 144
| 144
| 13/12, 12/11
| [[13/12]], [[12/11]]
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 81: Line 77:
| 7
| 7
| 168
| 168
| 11/10
| [[11/10]]
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 88: Line 84:
| 8
| 8
| 192
| 192
| 9/8, 10/9
| [[9/8]], [[10/9]]
| Major 2nd
| Major 2nd
| M2
| M2
Line 95: Line 91:
| 9
| 9
| 216
| 216
| 25/22
| [[25/22]]
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 102: Line 98:
| 10
| 10
| 240
| 240
| 8/7, 15/13
| [[8/7]], [[15/13]]
| Downaug 2nd, Dim 3rd
| Downaug 2nd, Dim 3rd
| vA2, d3
| vA2, d3
Line 109: Line 105:
| 11
| 11
| 264
| 264
| 7/6
| [[7/6]]
| Updim 3rd, Aug 2nd
| Updim 3rd, Aug 2nd
| ^d3, A2
| ^d3, A2
Line 116: Line 112:
| 12
| 12
| 288
| 288
| 13/11
| [[13/11]]
| Downminor 3rd
| Downminor 3rd
| vm3
| vm3
Line 123: Line 119:
| 13
| 13
| 312
| 312
| 6/5
| [[6/5]]
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 130: Line 126:
| 14
| 14
| 336
| 336
| 27/22, 39/32, 40/33, 49/40
| ''[[27/22]]'', [[39/32]], [[40/33]], ''[[49/40]]''
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 137: Line 133:
| 15
| 15
| 360
| 360
| 16/13, 11/9
| [[16/13]], ''[[11/9]]''
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 144: Line 140:
| 16
| 16
| 384
| 384
| 5/4
| [[5/4]]
| Major 3rd
| Major 3rd
| M3
| M3
Line 151: Line 147:
| 17
| 17
| 408
| 408
| 14/11
| [[14/11]]
| Upmajor 3rd
| Upmajor 3rd
| ^M3
| ^M3
Line 158: Line 154:
| 18
| 18
| 432
| 432
| 9/7
| [[9/7]]
| Downaug 3rd, Dim 4th
| Downaug 3rd, Dim 4th
| vA3, d4
| vA3, d4
Line 165: Line 161:
| 19
| 19
| 456
| 456
| 13/10
| [[13/10]]
| Updim 4th, Aug 3rd
| Updim 4th, Aug 3rd
| A3, ^d4
| A3, ^d4
Line 172: Line 168:
| 20
| 20
| 480
| 480
| 33/25, 55/42, 64/49
| [[33/25]], ''[[55/42]]'', ''[[64/49]]''
| Down 4th
| Down 4th
| v4
| v4
Line 179: Line 175:
| 21
| 21
| 504
| 504
| 4/3
| [[4/3]]
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 186: Line 182:
| 22
| 22
| 528
| 528
| 15/11
| [[15/11]]
| Up 4th
| Up 4th
| ^4
| ^4
Line 193: Line 189:
| 23
| 23
| 552
| 552
| 11/8, 18/13
| [[11/8]], [[18/13]]
| Downaug 4th
| Downaug 4th
| vA4
| vA4
Line 200: Line 196:
| 24
| 24
| 576
| 576
| 7/5
| [[7/5]]
| Aug 4th
| Aug 4th
| A4
| A4
Line 207: Line 203:
| 25
| 25
| 600
| 600
| 63/44, 88/63, 78/55, 55/39
| ''[[63/44]]'', ''[[88/63]]'', [[78/55]], [[55/39]]
| Upaug 4th, Downdim 5th
| Upaug 4th, Downdim 5th
| ^A4, vd5
| ^A4, vd5
Line 214: Line 210:
| 26
| 26
| 624
| 624
| 10/7
| [[10/7]]
| Dim 5th
| Dim 5th
| d5
| d5
Line 221: Line 217:
| 27
| 27
| 648
| 648
| 16/11, 13/9
| [[16/11]], [[13/9]]
| Updim 5th
| Updim 5th
| ^d5
| ^d5
Line 228: Line 224:
| 28
| 28
| 672
| 672
| 22/15
| [[22/15]]
| Down 5th
| Down 5th
| v5
| v5
Line 235: Line 231:
| 29
| 29
| 696
| 696
| 3/2
| [[3/2]]
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 242: Line 238:
| 30
| 30
| 720
| 720
| 50/33, 84/55, 49/32
| [[50/33]], ''[[84/55]]'', ''[[49/32]]''
| Up 5th
| Up 5th
| ^5
| ^5
Line 249: Line 245:
| 31
| 31
| 744
| 744
| 20/13
| [[20/13]]
| Downaug 5th, Dim 6th
| Downaug 5th, Dim 6th
| vA5, d6
| vA5, d6
Line 256: Line 252:
| 32
| 32
| 768
| 768
| 14/9
| [[14/9]]
| Updim 6th, Aug 5th
| Updim 6th, Aug 5th
| ^d6, A5
| ^d6, A5
Line 263: Line 259:
| 33
| 33
| 792
| 792
| 11/7
| [[11/7]]
| Downminor 6th
| Downminor 6th
| vm6
| vm6
Line 270: Line 266:
| 34
| 34
| 816
| 816
| 8/5
| [[8/5]]
| Minor 6th
| Minor 6th
| m6
| m6
Line 277: Line 273:
| 35
| 35
| 840
| 840
| 13/8, 18/11
| [[13/8]], ''[[18/11]]''
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 284: Line 280:
| 36
| 36
| 864
| 864
| 44/27, 64/39, 33/20, 80/49
| ''[[44/27]]'', [[64/39]], [[33/20]], ''[[80/49]]''
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 291: Line 287:
| 37
| 37
| 888
| 888
| 5/3
| [[5/3]]
| Major 6th
| Major 6th
| M6
| M6
Line 298: Line 294:
| 38
| 38
| 912
| 912
| 22/13
| [[22/13]]
| Upmajor 6th
| Upmajor 6th
| ^M6
| ^M6
Line 305: Line 301:
| 39
| 39
| 936
| 936
| 12/7
| [[12/7]]
| Downaug 6th, Dim 7th
| Downaug 6th, Dim 7th
| vA6, d7
| vA6, d7
Line 312: Line 308:
| 40
| 40
| 960
| 960
| 7/4
| [[7/4]]
| Updim 7th, Aug 6th
| Updim 7th, Aug 6th
| ^d7, A6
| ^d7, A6
Line 319: Line 315:
| 41
| 41
| 984
| 984
| 44/25
| [[44/25]]
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 326: Line 322:
| 42
| 42
| 1008
| 1008
| 16/9, 9/5
| [[16/9]], [[9/5]]
| Minor 7th
| Minor 7th
| m7
| m7
Line 333: Line 329:
| 43
| 43
| 1032
| 1032
| 20/11
| [[20/11]]
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 340: Line 336:
| 44
| 44
| 1056
| 1056
| 24/13, 11/6
| [[24/13]], [[11/6]]
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 347: Line 343:
| 45
| 45
| 1080
| 1080
| 15/8, 28/15, 13/7
| [[15/8]], [[28/15]], [[13/7]]
| Major 7th
| Major 7th
| M7
| M7
Line 354: Line 350:
| 46
| 46
| 1104
| 1104
| 21/11
| ''[[21/11]]''
| Upmajor 7th
| Upmajor 7th
| ^M7
| ^M7
Line 361: Line 357:
| 47
| 47
| 1128
| 1128
| 40/21, 48/25, 25/13, 52/27, 27/14
| ''[[40/21]]'', [[48/25]], [[25/13]], [[27/14]]
| Downaug 7th, Dim 8ve
| Downaug 7th, Dim 8ve
| vA7, d8
| vA7, d8
Line 368: Line 364:
| 48
| 48
| 1152
| 1152
| 64/33, 35/18, 49/25, 108/55, 63/32
| ''[[52/27]]'', [[64/33]], [[35/18]],<br> ''[[49/25]]'', ''[[108/55]]'', ''[[63/32]]''
| Updim 8ve, Aug 7th
| Updim 8ve, Aug 7th
| ^d8, A7
| ^d8, A7
Line 375: Line 371:
| 49
| 49
| 1176
| 1176
| 88/45, 96/49, 55/28, 128/65, 65/33, 77/39, 180/91, 196/99, 99/50, 240/121, 336/169
| ''[[88/45]]'', [[96/49]], [[55/28]], [[128/65]],<br> [[65/33]], [[77/39]], [[180/91]], [[196/99]],<br> [[99/50]], [[240/121]], ''[[336/169]]''
| Down 8ve
| Down 8ve
| v8
| v8
Line 382: Line 378:
| 50
| 50
| 1200
| 1200
| 2/1
| [[2/1]]
| Perfect 8ve
| Perfect 8ve
| P8
| P8
| D
| D
|}
|}
<nowiki>*</nowiki> using the patent val
<references group="note" />
 
== Notation ==
=== Stein–Zimmermann–Gould notation ===
50edo can be notated with [[Stein–Zimmermann–Gould notation]]:
{{Sharpness-sharp3-szg}}


== JI approximation ==
Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.
=== 15-odd-limit mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 50edo (ordered by absolute error). Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.  


{| class="wikitable center-all mw-collapsible mw-collapsed"
=== Kite's ups and downs notation ===
|+style=white-space:nowrap| Direct approximation (even if inconsistent)
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
|-
{{Ups and downs sharpness}}
! Interval, complement
 
! Error (abs, [[cent|¢]])
=== Sagittal notation ===
|-
This notation uses the same sagittal sequence as edos [[57edo #Sagittal notation|57]], [[64edo #Sagittal notation|64]], and [[71edo #Second-best fifth notation|71b]].
| '''[[16/13]], [[13/8]]'''
 
| '''0.528'''
==== Evo flavor ====
|-
<imagemap>
| [[15/14]], [[28/15]]
File:50-EDO_Evo_Sagittal.svg
| 0.557
desc none
|-
rect 80 0 300 50 [[Sagittal_notation]]
| '''[[11/8]], [[16/11]]'''
rect 300 0 599 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
| '''0.682'''
rect 20 80 160 106 [[1053/1024]]
|-
default [[File:50-EDO_Evo_Sagittal.svg]]
| [[13/11]], [[22/13]]
</imagemap>
| 1.210
 
|-
==== Revo flavor ====
| [[13/10]], [[20/13]]
<imagemap>
| 1.786
File:50-EDO_Revo_Sagittal.svg
|-
desc none
| '''[[5/4]], [[8/5]]'''
rect 80 0 300 50 [[Sagittal_notation]]
| '''2.314'''
rect 300 0 583 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
|-
rect 20 80 160 106 [[1053/1024]]
| [[7/6]], [[12/7]]
default [[File:50-EDO_Revo_Sagittal.svg]]
| 2.871
</imagemap>
|-
 
| [[11/10]], [[20/11]]
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.
| 2.996
 
|-
== Approximation to JI ==
| [[9/7]], [[14/9]]
[[File:50ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 29-limit intervals approximated in 50edo]]
| 3.084
|-
| [[6/5]], [[5/3]]
| 3.641
|-
| [[13/12]], [[24/13]]
| 5.427
|-
| '''[[4/3]], [[3/2]]'''
| '''5.955'''
|-
| [[7/5]], [[10/7]]
| 6.512
|-
| [[12/11]], [[11/6]]
| 6.637
|-
| [[15/13]], [[26/15]]
| 7.741
|-
| [[16/15]], [[15/8]]
| 8.269
|-
| [[14/13]], [[13/7]]
| 8.298
|-
| '''[[8/7]], [[7/4]]'''
| '''8.826'''
|-
| [[15/11]], [[22/15]]
| 8.951
|-
| [[14/11]], [[11/7]]
| 9.508
|-
| [[10/9]], [[9/5]]
| 9.596
|-
| [[18/13]], [[13/9]]
| 11.382
|-
| ''[[11/9]], [[18/11]]''
| ''11.408''
|-
| [[9/8]], [[16/9]]
| 11.910
|}


{| class="wikitable center-all mw-collapsible mw-collapsed"
=== 15-odd-limit interval mappings ===
|+style=white-space:nowrap| Patent val mapping
{{Q-odd-limit intervals|50|15}}
|-
! Interval, complement
! Error (abs, [[cent|¢]])
|-
| '''[[16/13]], [[13/8]]'''
| '''0.528'''
|-
| [[15/14]], [[28/15]]
| 0.557
|-
| '''[[11/8]], [[16/11]]'''
| '''0.682'''
|-
| [[13/11]], [[22/13]]
| 1.210
|-
| [[13/10]], [[20/13]]
| 1.786
|-
| '''[[5/4]], [[8/5]]'''
| '''2.314'''
|-
| [[7/6]], [[12/7]]
| 2.871
|-
| [[11/10]], [[20/11]]
| 2.996
|-
| [[9/7]], [[14/9]]
| 3.084
|-
| [[6/5]], [[5/3]]
| 3.641
|-
| [[13/12]], [[24/13]]
| 5.427
|-
| '''[[4/3]], [[3/2]]'''
| '''5.955'''
|-
| [[7/5]], [[10/7]]
| 6.512
|-
| [[12/11]], [[11/6]]
| 6.637
|-
| [[15/13]], [[26/15]]
| 7.741
|-
| [[16/15]], [[15/8]]
| 8.269
|-
| [[14/13]], [[13/7]]
| 8.298
|-
| '''[[8/7]], [[7/4]]'''
| '''8.826'''
|-
| [[15/11]], [[22/15]]
| 8.951
|-
| [[14/11]], [[11/7]]
| 9.508
|-
| [[10/9]], [[9/5]]
| 9.596
|-
| [[18/13]], [[13/9]]
| 11.382
|-
| [[9/8]], [[16/9]]
| 11.910
|-
| ''[[11/9]], [[18/11]]''
| ''12.592''
|}


== Regular temperament properties ==
== Regular temperament properties ==
=== Temperament measures ===
=== Temperament measures ===
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
Line 565: Line 442:
| 2.3
| 2.3
| {{monzo| -79 50 }}
| {{monzo| -79 50 }}
| [{{val| 50 79 }}]
| {{mapping| 50 79 }}
| +1.88
| +1.88
| 1.88
| 1.88
Line 572: Line 449:
| 2.3.5
| 2.3.5
| 81/80, {{monzo| -27 -2 13 }}
| 81/80, {{monzo| -27 -2 13 }}
| [{{val| 50 79 116 }}]
| {{mapping| 50 79 116 }}
| +1.58
| +1.58
| 1.59
| 1.59
Line 579: Line 456:
| 2.3.5.7
| 2.3.5.7
| 81/80, 126/125, 84035/82944
| 81/80, 126/125, 84035/82944
| [{{val| 50 79 116 140 }}]
| {{mapping| 50 79 116 140 }}
| +1.98
| +1.98
| 1.54
| 1.54
Line 586: Line 463:
| 2.3.5.7.11
| 2.3.5.7.11
| 81/80, 126/125, 245/242, 385/384
| 81/80, 126/125, 245/242, 385/384
| [{{val| 50 79 116 140 173 }}]
| {{mapping| 50 79 116 140 173 }}
| +1.54
| +1.54
| 1.63
| 1.63
Line 593: Line 470:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 81/80, 105/104, 126/125, 144/143, 245/242
| 81/80, 105/104, 126/125, 144/143, 245/242
| [{{val| 50 79 116 140 173 185 }}]
| {{mapping| 50 79 116 140 173 185 }}
| +1.31
| +1.31
| 1.57
| 1.57
Line 600: Line 477:


=== Commas ===
=== Commas ===
50edo [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val|50 79 116 140 173 185 204 212 226}}, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.
50et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 50 79 116 140 173 185 204 212 226 }}, comma values in cents rounded to 2 decimal places. This list is not all-inclusive, and is based on the interval table from Scala version 2.2.


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-5"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cent]]s
! [[Cent]]s
! Name(s)
! Name
|-
| 3
| <abbr title="717897987691852588770249/604462909807314587353088">(20 digits)</abbr>
| {{monzo| -79 50 }}
| 297.75
| 50-comma
|-
|-
| 5
| 5
Line 614: Line 497:
| {{monzo| -4 4 -1 }}
| {{monzo| -4 4 -1 }}
| 21.51
| 21.51
| Syntonic comma, Didymus comma
| Syntonic comma
|-
|-
| 5
| 5
Line 626: Line 509:
| {{monzo| 23 6 -14 }}
| {{monzo| 23 6 -14 }}
| 3.34
| 3.34
| [[Vishnuzma]], Vishnu comma
| [[Vishnuzma]]
|-
|-
| 7
| 7
Line 633: Line 516:
| 50.72
| 50.72
| Harrison's comma
| Harrison's comma
|-
| 7
| [[16807/16384]]
| {{monzo| -14 0 0 5}}
| 44.13
| Cloudy comma
|-
| 7
| [[3645/3584]]
| {{monzo| -9 6 1 -1 }}
| 29.22
| Schismean comma
|-
|-
| 7
| 7
Line 638: Line 533:
| {{monzo| 1 2 -3 1 }}
| {{monzo| 1 2 -3 1 }}
| 13.79
| 13.79
| Starling comma, Small septimal comma
| Starling comma
|-
|-
| 7
| 7
Line 644: Line 539:
| {{monzo| -5 2 2 -1 }}
| {{monzo| -5 2 2 -1 }}
| 7.71
| 7.71
| Septimal kleisma, Marvel comma
| Marvel comma
|-
|-
| 7
| 7
Line 650: Line 545:
| {{monzo| 6 0 -5 2 }}
| {{monzo| 6 0 -5 2 }}
| 6.08
| 6.08
| Hemimean, Middle second comma
| Hemimean comma
|-
|-
| 7
| 7
Line 656: Line 551:
| {{monzo| 11 -10 -10 10 }}
| {{monzo| 11 -10 -10 10 }}
| 5.57
| 5.57
| [[Linus]]
| [[Linus comma]]
|-
|-
| 7
| 7
Line 674: Line 569:
| {{monzo| -1 0 1 2 -2 }}
| {{monzo| -1 0 1 2 -2 }}
| 21.33
| 21.33
| Cassacot
| Frostma
|-
|-
| 11
| 11
Line 680: Line 575:
| {{monzo| -7 -1 1 1 1 }}
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| 4.50
| Keenanisma, undecimal kleisma
| Keenanisma
|-
|-
| 11
| 11
Line 686: Line 581:
| {{monzo| 2 3 1 -2 -1 }}
| {{monzo| 2 3 1 -2 -1 }}
| 3.21
| 3.21
| Swets' comma, Swetisma
| Swetisma
|-
|-
| 11
| 11
Line 692: Line 587:
| {{monzo| 5 -1 3 0 -3 }}
| {{monzo| 5 -1 3 0 -3 }}
| 3.03
| 3.03
| Wizardharry, undecimal schisma
| Wizardharry comma
|-
|-
| 11
| 11
Line 698: Line 593:
| {{monzo| -3 4 -2 -2 2 }}
| {{monzo| -3 4 -2 -2 2 }}
| 0.18
| 0.18
| Kalisma, Gauss' comma
| Kalisma
|-
|-
| 13
| 13
Line 704: Line 599:
| {{monzo| -3 1 1 1 0 -1 }}
| {{monzo| -3 1 1 1 0 -1 }}
| 16.57
| 16.57
| Animist comma, small tridecimal comma
| Animist comma
|-
|-
| 13
| 13
Line 722: Line 617:
| {{monzo| 2 3 0 -1 1 -2 }}
| {{monzo| 2 3 0 -1 1 -2 }}
| 7.30
| 7.30
| Kestrel Comma
| Kestrel comma
|-
| 13
| [[31213/31104]]
| {{monzo| -7 -5 0 4 0 1 }}
| 6.06
| Praveensma
|-
|-
| 13
| 13
Line 728: Line 629:
| {{monzo| 2 -1 0 1 -2 1 }}
| {{monzo| 2 -1 0 1 -2 1 }}
| 4.76
| 4.76
| Gentle comma
| Minor minthma
|-
|-
| 13
| 13
Line 734: Line 635:
| {{monzo| 3 0 2 0 1 -3 }}
| {{monzo| 3 0 2 0 1 -3 }}
| 2.36
| 2.36
| Petrma, Parizek comma
| Petrma
|-
|-
| 17
| 17
Line 740: Line 641:
| {{monzo| 1 0 1 0 0 -2 1 }}
| {{monzo| 1 0 1 0 0 -2 1 }}
| 10.21
| 10.21
|  
| Major naiadma
|-
|-
| 17
| 17
Line 746: Line 647:
| {{monzo| -2 0 -1 0 -1 1 1 }}
| {{monzo| -2 0 -1 0 -1 1 1 }}
| 7.85
| 7.85
|  
| Minor naiadma
|-
|-
| 17
| 17
Line 752: Line 653:
| {{monzo| -5 -2 0 0 0 0 2 }}
| {{monzo| -5 -2 0 0 0 0 2 }}
| 6.00
| 6.00
| minor seconds comma
| Semitonisma
|-
|-
| 17
| 17
Line 758: Line 659:
| {{monzo| -1 1 3 0 -1 0 -1 }}
| {{monzo| -1 1 3 0 -1 0 -1 }}
| 4.62
| 4.62
|  
| Ursulisma
|-
|-
| 19
| 19
Line 764: Line 665:
| {{monzo| -3 2 0 0 0 0 1 -1 }}
| {{monzo| -3 2 0 0 0 0 1 -1 }}
| 11.35
| 11.35
| ganassisma
| Ganassisma
|-
|-
| 19
| 19
Line 770: Line 671:
| {{monzo| -1 2 -1 0 0 0 -1 1}}
| {{monzo| -1 2 -1 0 0 0 -1 1}}
| 10.15
| 10.15
|  
| Malcolmisma
|-
|-
| 19
| 19
Line 776: Line 677:
| {{monzo| 1 1 1 1 -1 0 0 1}}
| {{monzo| 1 1 1 1 -1 0 0 1}}
| 8.26
| 8.26
|  
| Spleen comma
|-
|-
| 19
| 19
Line 782: Line 683:
| {{monzo| 2 4 0 0 0 0 -1 -1 }}
| {{monzo| 2 4 0 0 0 0 -1 -1 }}
| 5.35
| 5.35
|  
| Photisma
|-
|-
| 19
| 19
Line 788: Line 689:
| {{monzo| -3 -2 -1 0 0 0 0 2 }}
| {{monzo| -3 -2 -1 0 0 0 0 2 }}
| 4.80
| 4.80
|  
| Go comma
|-
|-
| 19
| 19
Line 794: Line 695:
| {{monzo| -1 2 1 0 1 -1 0 -1 }}
| {{monzo| -1 2 1 0 1 -1 0 -1 }}
| 3.50
| 3.50
|  
| Eulalisma
|-
| 23
| [[507/506]]
| 2.3.11.13.23 {{monzo| -1 1 -1 2 -1 }}
| 3.42
| Laodicisma
|-
| 23
| [[529/528]]
| 2.3.11.23 {{monzo| -4 -1 -1 2 }}
| 3.28
| Preziosisma
|-
| 23
| [[576/575]]
| 2.3.5.23 {{monzo| 6 2 -2 -1 }}
| 3.01
| Worcester comma
|-
|-
| 23
| 23
Line 802: Line 721:
| Triaphonisma
| Triaphonisma
|}
|}
<references/>
<references group="note" />


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+ Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br> per Octave
! Periods<br>per 8ve
! Generator
! Generator*
! Cents
! Cents*
! Associated<br>Ratio
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
| 1
| 1
| 1\50
| 1\50
| 24.00
| 24.0
| 686/675
| 686/675
| [[Sengagen]]
| [[Sengagen]]
Line 822: Line 741:
| 1
| 1
| 9\50
| 9\50
| 216.00
| 216.0
| 17/15
| 17/15
| [[Tremka]]
| [[Tremka]]
Line 828: Line 747:
| 1
| 1
| 11\50
| 11\50
| 264.00
| 264.0
| 7/6
| 7/6
| [[Septimin]]
| [[Septimin]]
Line 834: Line 753:
| 1
| 1
| 13\50
| 13\50
| 312.00
| 312.0
| 6/5
| 6/5
| [[Oolong]]
| [[Oolong]]
Line 840: Line 759:
| 1
| 1
| 17\50
| 17\50
| 408.00
| 408.0
| 15625/12288
| 325/256
| [[Ditonic]] / [[coditone]]
| [[Coditone]]
|-
|-
| 1
| 1
| 19\50
| 19\50
| 456.00
| 456.0
| 125/96
| 125/96
| [[Qak]]
| [[Qak]]
Line 852: Line 771:
| 1
| 1
| 21\50
| 21\50
| 504.00
| 504.0
| 4/3
| 4/3
| [[Meantone]] / [[meanpop]]
| [[Meantone]] / [[meanpop]]
Line 858: Line 777:
| 1
| 1
| 23\50
| 23\50
| 552.00
| 552.0
| 11/8
| 11/8
| [[Emka]]
| [[Emka]]
Line 864: Line 783:
| 2
| 2
| 2\50
| 2\50
| 48.00
| 48.0
| 36/35
| 36/35
| [[Pombe]]
| [[Pombe]]
Line 870: Line 789:
| 2
| 2
| 3\50
| 3\50
| 72.00
| 72.0
| 25/24
| 25/24
| [[Vishnu]] / [[vishnean]]
| [[Vishnu]] / [[vishnean]]
|-
| 2
| 4\50
| 96.00
| 35/33
| [[Bimeantone]]
|-
|-
| 2
| 2
| 6\50
| 6\50
| 144.00
| 144.0
| 12/11
| 12/11
| [[Bisemidim]]
| [[Bisemidim]]
Line 888: Line 801:
| 2
| 2
| 9\50
| 9\50
| 216.00
| 216.0
| 17/15
| 17/15
| [[Wizard]] / [[lizard]] / [[gizzard]]
| [[Wizard]] / [[lizard]] / [[gizzard]]
Line 894: Line 807:
| 2
| 2
| 12\50
| 12\50
| 288.00
| 288.0
| 13/11
| 13/11
| [[Vines]]
| [[Vines]]
|-
| 2
| 21\50<br>(4\50)
| 504.0<br>(96.0)
| 4/3<br>(35/33)
| [[Bimeantone]]
|-
|-
| 5
| 5
| 21\50 <br>(1\50)
| 21\50<br>(1\50)
| 504.00 <br>(24.00)
| 504.0<br>(24.0)
| 4/3 <br>&nbsp;
| 4/3<br>(49/48)
| [[Cloudtone]]
| [[Cloudtone]]
|-
|-
| 5
| 5
| 3\50
| 23\50<br>(3\50)
| 72.00
| 552.0<br>(72.0)
| 21/20, 25/24
| 11/8<br>(21/20)
| [[Coblack]]
| [[Coblack]]
|-
|-
| 10
| 10
| 21\50 <br>(1\50)
| 7\50<br>(3\50)
| 504.00 <br>(24.00)
| 168.0<br>(72.0)
| 4/3 <br>&nbsp;
| 54/49<br>(25/24)
| [[Decic]]
| [[Decavish]]
|-
|-
| 10
| 10
| 2\50 <br>(3\50)
| 21\50<br>(1\50)
| 48.00 <br>(72.00)
| 504.0<br>(24.0)
| 36/35 <br>(25/24)
| 4/3<br>(78/77)
| [[Decavish]]
| [[Decic]]
|}
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
== Octave stretch or compression ==
50edo's [[prime]]s 3, 5, 7, 17, 19, and 23 are all tuned flat and its 11 and 13 have close to no error, so 50edo can benefit from slight [[octave stretching]]. Some slightly stretched-octave tunings of 50edo include (least to most stretch): [[equal tuning|166ed10]], [[ed5|116ed5]], [[zpi|238zpi]] and [[ed12|179ed12]].
== Instruments ==
; Lumatone
See [[Lumatone mapping for 50edo]].
; Piano
A [[:Category:Piano|piano]] playing with a 50edo ensemble may wish to use the tuning [[116ed5]]. This tuning is almost exactly the same as 50edo, but with octaves [[octave stretch|stretched]] by 1 cent. Because pianos usually use stretched octaves, this tuning will sit better with the [[timbre]] of the piano, while still being close enough that it sounds perfectly in-tune with the other instruments tuned to 50edo.


== Music ==
== Music ==
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin]
=== Modern renderings ===
* [http://soonlabel.com/xenharmonic/archives/1118 Fantasia Catalana by Claudi Meneghin]
; {{W|Johann Sebastian Bach}}
* [http://soonlabel.com/xenharmonic/archives/1929 Fugue on the Dragnet theme by Claudi Meneghin]
* [https://www.youtube.com/watch?v=RnYqc0NKMLM "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2024)
* [https://soundcloud.com/camtaylor-1/sets/the-late-little-xmas-album the late little xmas album by Cam Taylor]
* [https://www.youtube.com/watch?v=e6fMO-sue4Y "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) &ndash; rendered by Claudi Meneghin (2024)
* [https://soundcloud.com/cam-taylor-2-1/harpsichord-meantone Harpsichord meantone improvisation 1 in 50EDO by Cam Taylor]
* [https://www.youtube.com/watch?v=M3wQu4UF1pg "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) &ndash; rendered by Claudi Meneghin (2024, organ sound rendering)
* [https://soundcloud.com/cam-taylor-2-1/long-improvisation-2-in-50edo Long improvisation 2 in 50EDO by Cam Taylor]
* [https://www.youtube.com/watch?v=qjb9DDM32Ic "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742-1749) &mdash; rendered by Claudi Meneghin (2025, harpsichord sound rendering)
* [https://soundcloud.com/camtaylor-1/chord-sequence-for-difference Chord sequence for Difference tones in 50EDO by Cam Taylor]
 
* [https://soundcloud.com/camtaylor-1/enharmonic-modulations-in Enharmonic Modulations in 50EDO by Cam Taylor]
; {{W|David Belasco}}
* [https://soundcloud.com/cam-taylor-2-1/harmonic-clusters-on-50edo-harpsichord-bosanquet-axis-through-pianoteq Harmonic Clusters on 50EDO Harpsichord by Cam Taylor]
* [https://www.youtube.com/shorts/WcExL9W2Gyc ''The Prettiest Little Song Of All''] (1908) - microtonal cover in 50edo by [[Bryan Deister]] (2025)
* [https://soundcloud.com/camtaylor-1/fragment-in-fifty Fragment in Fifty] by Cam Taylor
 
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=yrM50pvmD5c ''Prelude in E Minor "The Great"''] &ndash; rendered by Claudi Meneghin (2023)
 
; {{W|John Bull (composer)|John Bull}}
* [https://www.youtube.com/watch?v=6RewllRJ5rU ''Fantasia «Ut Re Mi Fa Sol La»''] (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – rendered by Claudi Meneghin (2026)
 
; {{w|Frédéric Chopin}}
* [https://www.youtube.com/shorts/7Bisk0I2H4o ''Prelude Op. 28, No. 7 in A major''] (1839), arranged for fortepiano, tuned into 50-edo – rendered by [[Claudi Meneghin]] (2025)
 
; {{W|Louis Couperin}}
* [https://www.youtube.com/shorts/NSzakO66Roc ''«La Piémontoise»''] (1658?) &ndash; rendered by Claudi Meneghin (2026)
 
; {{W|Gabriel Fauré}}
* [https://www.youtube.com/watch?v=7djfrUlw2ck  ''Pavane'', op. 50] (1887) &ndash; arranged for harpsichord and rendered by Claudi Meneghin (2020)
 
; {{W|Toby Fox}}
* [https://www.youtube.com/shorts/ynz5XvJOHiE ''Piano that may not be played that well''] via ''{{W|Deltarune}} Chapters 3 + 4'' (2025) (microtonal cover in 50edo) by [[Bryan Deister]] (2025)
 
; {{W|Iyowa}}
* [https://www.youtube.com/shorts/L6jF5_HEGkM ''Heat Abnormal''] (2024) - microtonal cover in 50edo by [[Bryan Deister]] (2025)
 
; {{W|Akira Kamiya}}
* [https://www.youtube.com/watch?v=5UnPAhRqmb4 ''funfunfun ta yo''] (2007) &ndash; rendered by MortisTheneRd (2024)
 
; {{W|Laufey_(singer)|Laufey}}
* [https://www.youtube.com/shorts/J34qt45jZW4 ''Snow White''] (2025) - microtonal cover in 50edo by [[Bryan Deister]] (2025)
 
; {{W|Wolfgang Amadeus Mozart}}
* [https://www.youtube.com/watch?v=YK_kFs4PL2g&list=WL&index=347 ''Gigue KV 574 («Leipziger Gigue»)''] (1789) – rendered by Claudi Meneghin (2026)
 
; {{W|Akiko Shikata}}
* [https://www.youtube.com/shorts/eXGcC52YMh8 ''Mother''] via ''{{W|Umineko_When_They_Cry|Umineko no Naku Koro ni}}'' (2007) - microtonal cover in 50edo by [[Bryan Deister]] (2026)
 
=== 21st century===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/zCsc5n6dr_I ''microtonal improv in 50edo''] (2024)
* [https://www.youtube.com/shorts/dAyMY-14yZo ''50edo improv''] (2025-10-13)
* [https://www.youtube.com/shorts/DIiLORDPfUI ''50edo improv''] (2026-05-25)
* [https://www.youtube.com/watch?v=LqzPpl01WXc ''Fantasy in 50edo''] (2026)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=pH6E35hwUnM ''On My Way To Somewhere''] (2023)
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=Zh2jWoIXAf8 ''La Petite Poule Grise - Fugue''] (2014, uploaded 2019)
* [https://www.youtube.com/shorts/IhKVro5YEcA ''Canon on «Twinkle Twinkle Little Star» in 50-edo, for Organ''] (≤2014, restored and re-hosted 2025)
* [https://www.youtube.com/watch?v=TRXy0FJOKIA ''Fugue on the Dragnet theme''] (2014)
* [https://www.youtube.com/watch?v=wcTVED9zFrU ''Blue Fugue for Organ''] (2018)
* [https://www.youtube.com/watch?v=28x3vqw9kDI ''Happy Birthday Canon'', 6-in-1 Canon in 50edo] (2019)
* [https://www.youtube.com/watch?v=szUpO3FAOes ''Fantasia Catalana''] (2020)
* [https://www.youtube.com/watch?v=38UMa3oWSIE ''Preludi Nocturn i Fuga sobre la Lluna la Pruna''] (2020)
* [https://www.youtube.com/watch?v=C4EkNEu4EeU ''Canon at the Semitone on The Mother's Malison Theme'', for Organ] (2022)
* [https://www.youtube.com/watch?v=FyDKSjS9Qtg ''Fugue on an Original Theme'', for Baroque Ensemble] (2023) ([https://www.youtube.com/watch?v=TXwlLV2TCsw for Organ])
* [https://www.youtube.com/watch?v=2nD_7Ot8-0A ''Catalan Fugue (La Santa Espina)''] (2023)
* [https://www.youtube.com/watch?v=TBxDmpM9Xa8 ''Canon in C='' for Baroque Wind Ensemble] (2023)
* [https://www.youtube.com/watch?v=sIr394fGEEg ''Fantasia Catalana'', for Baroque Ensemble] (2023)
* ''Chord Progression: The Octave Divided into Five Parts in 50 edo'' (intended for demonstrating chord progressions, as the title indicates, but actually works as a short composition)
** [https://www.youtube.com/shorts/7_kROtWc4Sw <nowiki>organ rendition</nowiki>] (2023)
** [https://www.youtube.com/shorts/qsuM1sA2-A0 <nowiki>harpsichord rendition</nowiki>] (2024)
* [https://www.youtube.com/shorts/2x5atFuN6WA ''Baroque Blues - 4-Part Fugue for Baroque Consort''] (2026)
* ''Fugue on the French Lullaby «La Petite Poule Grise»'' (2026)
** [https://www.youtube.com/watch?v=RrsZ-bzf1mE Baroque ensemble rendition]
** [https://www.youtube.com/watch?v=wgsWzn_vfIM organ rendition]
 
; [[Cam Taylor]]
* [https://soundcloud.com/camtaylor-1/sets/the-late-little-xmas-album ''the late little xmas album''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/harpsichord-meantone ''Harpsichord meantone improvisation 1 in 50EDO''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/long-improvisation-2-in-50edo ''Long improvisation 2 in 50EDO''] (2014)
* [https://soundcloud.com/camtaylor-1/chord-sequence-for-difference ''Chord sequence for Difference tones in 50EDO''] (2014)
* [https://soundcloud.com/camtaylor-1/enharmonic-modulations-in ''Enharmonic Modulations in 50EDO''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/harmonic-clusters-on-50edo-harpsichord-bosanquet-axis-through-pianoteq ''Harmonic Clusters on 50EDO Harpsichord''] (2014)
* [https://soundcloud.com/camtaylor-1/fragment-in-fifty ''Fragment in Fifty''] (2014)


== Additional reading ==
== Additional reading ==
Line 939: Line 943:
* [http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html More information about Robert Smith's temperament]{{Dead link}}
* [http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html More information about Robert Smith's temperament]{{Dead link}}
* [https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh 50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor]{{Dead link}}
* [https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh 50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor]{{Dead link}}
* [http://iamcamtaylor.wordpress.com/ iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]    
* [http://iamcamtaylor.wordpress.com/ iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]    


[[Category:50edo]]
[[Category:50edo]]
[[Category:Equal divisions of the octave]]
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[[Category:Golden]]
[[Category:Golden meantone]]
[[Category:Historical]]
[[Category:Listen]]
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Meanpop]]
[[Category:Meanpop]]
[[Category:Theory]]
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