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'''50edo''' divides the [[Octave|octave]] into 50 equal parts of precisely 24 [[cent|cent]]s each. In the [[5-limit|5-limit]], it tempers out 81/80, making it a [[Meantone|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 – 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|31edo]] extends meantone with a [[7/4|7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8|11/8]] and [[13/8|13/8]] are nearly pure. It is the highest edo that maps 9/8 and 10/9 to the same interval, with two stacked fifths falling almost precisely in the middle of the two.
'''50edo''' divides the [[Octave|octave]] into 50 equal parts of precisely 24 [[cent|cents]] each. In the [[5-limit|5-limit]], it tempers out 81/80, making it a [[Meantone|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 – 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|31edo]] extends meantone with a [[7/4|7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8|11/8]] and [[13/8|13/8]] are nearly pure. It is the highest edo that maps 9/8 and 10/9 to the same interval, with two stacked fifths falling almost precisely in the middle of the two.


50 tempers out 126/125, 225/224 and 3136/3125 in the [[7-limit|7-limit]], indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the [[11-limit|11-limit]] and 105/104, 144/143 and 196/195 in the [[13-limit|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 15&50 temperament ([http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11 Coblack]), and provides the optimal patent val for 11 and 13 limit [[Meantone_family#Septimal meantone-Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma|vishnuzma]], |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 tempers out 126/125, 225/224 and 3136/3125 in the [[7-limit|7-limit]], indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the [[11-limit|11-limit]] and 105/104, 144/143 and 196/195 in the [[13-limit|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 15&50 temperament ([http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11 Coblack]), and provides the optimal patent val for 11 and 13 limit [[Meantone_family#Septimal meantone-Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma|vishnuzma]], |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.


=Relations=
== Relations ==
The 50edo system is related to [[7edo|7edo]], [[12edo|12edo]], [[19edo|19edo]], [[31edo|31edo]] as the next approximation to the "Golden Tone System" ([[Das_Goldene_Tonsystem|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|7edo]], [[12edo|12edo]], [[19edo|19edo]], [[31edo|31edo]] as the next approximation to the "Golden Tone System" ([[Das_Goldene_Tonsystem|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]").


=Intervals=
== Intervals ==


{| class="wikitable"
{| class="wikitable center-all right-2 left-3"
|-
|-
! | Degrees of 50edo
! #
! | Cents value
! Cents
! | Ratios*
! Ratios*
! | Generator for*
! Generator for*
|-
|-
| 0
| 0
|0
| 0
| | 1/1
| 1/1
| |  
|  
|-
|-
| | 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, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168
| | [[Hemimean_clan#Sengagen|Sengagen]]
| [[Hemimean_clan#Sengagen|Sengagen]]
|-
|-
| | 2
| 2
| | 48
| 48
| | 33/32, 36/35, 50/49, 55/54, 64/63
| 33/32, 36/35, 50/49, 55/54, 64/63
| |  
|  
|-
|-
| | 3
| 3
| | 72
| 72
| | 21/20, 25/24, 26/25, 27/26, 28/27
| 21/20, 25/24, 26/25, 27/26, 28/27
| | [[Vishnuzmic_family#Vishnu|Vishnu]] (2/oct), [http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11 Coblack] (5/oct)
| [[Vishnuzmic_family#Vishnu|Vishnu]] (2/oct), [http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11 Coblack] (5/oct)
|-
|-
| | 4
| 4
| | 96
| 96
| | 22/21
| 22/21
| | [[Meantone_family#Injera|Injera]] (50d val, 2/oct)
| [[Meantone_family#Injera|Injera]] (50d val, 2/oct)
|-
|-
| | 5
| 5
| | 120
| 120
| | 16/15, 15/14, 14/13
| 16/15, 15/14, 14/13
| |  
|  
|-
|-
| | 6
| 6
| | 144
| 144
| | 13/12, 12/11
| 13/12, 12/11
| |  
|  
|-
|-
| | 7
| 7
| | 168
| 168
| | 11/10
| 11/10
| |  
|  
|-
|-
| | 8
| 8
| | 192
| 192
| | 9/8, 10/9
| 9/8, 10/9
| |  
|  
|-
|-
| | 9
| 9
| | 216
| 216
| | 25/22
| 25/22
| | [http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&limit=2.3.5.11.13 Tremka], [[Subgroup_temperaments#x2.9.7.11-Machine|Machine]] (50b val)
| [http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&limit=2.3.5.11.13 Tremka], [[Subgroup_temperaments#x2.9.7.11-Machine|Machine]] (50b val)
|-
|-
| | 10
| 10
| | 240
| 240
| | 8/7, 15/13
| 8/7, 15/13
| |  
|  
|-
|-
| | 11
| 11
| | 264
| 264
| | 7/6
| 7/6
| | [[Marvel_temperaments#Septimin-13-limit|Septimin (13-limit)]]
| [[Marvel_temperaments#Septimin-13-limit|Septimin (13-limit)]]
|-
|-
| | 12
| 12
| | 288
| 288
| | 13/11
| 13/11
| |  
|  
|-
|-
| | 13
| 13
| | 312
| 312
| | 6/5
| 6/5
| |  
|  
|-
|-
| | 14
| 14
| | 336
| 336
| | 27/22, 39/32, 40/33, 49/40
| 27/22, 39/32, 40/33, 49/40
| |  
|  
|-
|-
| | 15
| 15
| | 360
| 360
| | 16/13, 11/9
| 16/13, 11/9
| |  
|  
|-
|-
| | 16
| 16
| | 384
| 384
| | 5/4
| 5/4
| | [[Marvel_temperaments#Wizard-11-limit|Wizard]] (2/oct)
| [[Marvel_temperaments#Wizard-11-limit|Wizard]] (2/oct)
|-
|-
| | 17
| 17
| | 408
| 408
| | 14/11
| 14/11
| | [[Ditonmic_family|Ditonic]]
| [[Ditonmic_family|Ditonic]]
|-
|-
| | 18
| 18
| | 432
| 432
| | 9/7
| 9/7
| | [[Porcupine_family#Hedgehog|Hedgehog]] (50cc val, 2/oct)
| [[Porcupine_family#Hedgehog|Hedgehog]] (50cc val, 2/oct)
|-
|-
| | 19
| 19
| | 456
| 456
| | 13/10
| 13/10
| | [[Starling_temperaments#Bisemidim|Bisemidim]] (2/oct)
| [[Starling_temperaments#Bisemidim|Bisemidim]] (2/oct)
|-
|-
| | 20
| 20
| | 480
| 480
| | 33/25, 55/42, 64/49
| 33/25, 55/42, 64/49
| |  
|  
|-
|-
| | 21
| 21
| | 504
| 504
| | 4/3
| 4/3
| | [[Meantone|Meantone]]/[[Meanpop|Meanpop]]
| [[Meantone|Meantone]]/[[Meanpop|Meanpop]]
|-
|-
| | 22
| 22
| | 528
| 528
| | 15/11
| 15/11
| |  
|  
|-
|-
| | 23
| 23
| | 552
| 552
| | 11/8, 18/13
| 11/8, 18/13
| | [[Chromatic_pairs#Barton|Barton]], [[Hemimean_clan#Emka|Emka]]
| [[Chromatic_pairs#Barton|Barton]], [[Hemimean_clan#Emka|Emka]]
|-
|-
| | 24
| 24
| | 576
| 576
| | 7/5
| 7/5
| |  
|  
|-
|-
| | 25
| 25
| | 600
| 600
| | 63/44, 88/63, 78/55, 55/39
| 63/44, 88/63, 78/55, 55/39
| |  
|  
|-
|-
| | 26
| 26
| | 624
| 624
| | 10/7
| 10/7
| |  
|  
|-
|-
| | 27
| 27
| | 648
| 648
| | 16/11, 13/9
| 16/11, 13/9
| |  
|  
|-
|-
| | 28
| 28
| | 672
| 672
| | 22/15
| 22/15
| |  
|  
|-
|-
| | 29
| 29
| | 696
| 696
| | 3/2
| 3/2
| |  
|  
|-
|-
| | 30
| 30
| | 720
| 720
| | 50/33, 84/55, 49/32
| 50/33, 84/55, 49/32
| |  
|  
|-
|-
| | 31
| 31
| | 744
| 744
| | 20/13
| 20/13
| |  
|  
|-
|-
| | 32
| 32
| | 768
| 768
| | 14/9
| 14/9
| |  
|  
|-
|-
| | 33
| 33
| | 792
| 792
| | 11/7
| 11/7
| |  
|  
|-
|-
| | 34
| 34
| | 816
| 816
| | 8/5
| 8/5
| |  
|  
|-
|-
| | 35
| 35
| | 840
| 840
| | 13/8, 18/11
| 13/8, 18/11
| |  
|  
|-
|-
| | 36
| 36
| | 864
| 864
| | 44/27, 64/39, 33/20, 80/49
| 44/27, 64/39, 33/20, 80/49
| |  
|  
|-
|-
| | 37
| 37
| | 888
| 888
| | 5/3
| 5/3
| |  
|  
|-
|-
| | 38
| 38
| | 912
| 912
| | 22/13
| 22/13
| |  
|  
|-
|-
| | 39
| 39
| | 936
| 936
| | 12/7
| 12/7
| |  
|  
|-
|-
| | 40
| 40
| | 960
| 960
| | 7/4
| 7/4
| |  
|  
|-
|-
| | 41
| 41
| | 984
| 984
| | 44/25
| 44/25
| |  
|  
|-
|-
| | 42
| 42
| | 1008
| 1008
| | 16/9, 9/5
| 16/9, 9/5
| |  
|  
|-
|-
| | 43
| 43
| | 1032
| 1032
| | 20/11
| 20/11
| |  
|  
|-
|-
| | 44
| 44
| | 1056
| 1056
| | 24/13, 11/6
| 24/13, 11/6
| |  
|  
|-
|-
| | 45
| 45
| | 1080
| 1080
| | 15/8, 28/15, 13/7
| 15/8, 28/15, 13/7
| |  
|  
|-
|-
| | 46
| 46
| | 1104
| 1104
| | 21/11
| 21/11
| |  
|  
|-
|-
| | 47
| 47
| | 1128
| 1128
| | 40/21, 48/25, 25/13, 52/27, 27/14
| 40/21, 48/25, 25/13, 52/27, 27/14
| |  
|  
|-
|-
| | 48
| 48
| | 1152
| 1152
| | 64/33, 35/18, 49/25, 108/55, 63/32
| 64/33, 35/18, 49/25, 108/55, 63/32
| |  
|  
|-
|-
| | 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, 65/33, 77/39, 180/91, 196/99, 99/50, 240/121, 336/169
| |  
|  
|-
|-
|50
| 50
|1200
| 1200
|2/1
| 2/1
|
|  
|}
|}
*Using the 13-limit patent val, except as noted.
<nowiki/>* Using the 13-limit patent val, except as noted.
 
==Selected just intervals by error==
The following table shows how [[Just-24|some prominent just intervals]] are represented in 50edo (ordered by absolute error).


===Best direct mapping, even if inconsistent===
=== Selected just intervals by error ===
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"
{| class="wikitable center-all"
|+Direct mapping, even if inconsistent
|-
|-
| | '''Interval, complement'''
! Interval, complement
| | '''Error (abs., in [[cent|cents]])'''
! Error (abs, [[cent|¢]])
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| '''[[16/13|16/13]], [[13/8|13/8]]'''
| style="text-align:center;" | 0.528
| '''0.528'''
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| [[15/14|15/14]], [[28/15|28/15]]
| style="text-align:center;" | 0.557
| 0.557
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| '''[[11/8|11/8]], [[16/11|16/11]]'''
| style="text-align:center;" | 0.682
| '''0.682'''
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| [[13/11|13/11]], [[22/13|22/13]]
| style="text-align:center;" | 1.210
| 1.210
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | 1.786
| 1.786
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| '''[[5/4|5/4]], [[8/5|8/5]]'''
| style="text-align:center;" | 2.314
| '''2.314'''
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | 2.871
| 2.871
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| [[11/10|11/10]], [[20/11|20/11]]
| style="text-align:center;" | 2.996
| 2.996
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| [[9/7|9/7]], [[14/9|14/9]]
| style="text-align:center;" | 3.084
| 3.084
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | 3.641
| 3.641
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | 5.427
| 5.427
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | 5.955
| 5.955
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| [[7/5|7/5]], [[10/7|10/7]]
| style="text-align:center;" | 6.512
| 6.512
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | 6.637
| 6.637
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| [[15/13|15/13]], [[26/15|26/15]]
| style="text-align:center;" | 7.741
| 7.741
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | 8.269
| 8.269
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| [[14/13|14/13]], [[13/7|13/7]]
| style="text-align:center;" | 8.298
| 8.298
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| '''[[8/7|8/7]], [[7/4|7/4]]'''
| style="text-align:center;" | 8.826
| '''8.826'''
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | 8.951
| 8.951
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| [[14/11|14/11]], [[11/7|11/7]]
| style="text-align:center;" | 9.508
| 9.508
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| [[10/9|10/9]], [[9/5|9/5]]
| style="text-align:center;" | 9.596
| 9.596
|-
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | 11.382
| 11.382
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| ''[[11/9|11/9]], [[18/11|18/11]]''
| style="text-align:center;" | 11.408
| ''11.408''
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | 11.910
| 11.910
|}
|}


===Patent val mapping===
{| class="wikitable center-all"
 
|+Patent val mapping
{| class="wikitable"
|-
|-
| | '''Interval, complement'''
! Interval, complement
| | '''Error (abs., in [[cent|cents]])'''
! Error (abs, [[cent|¢]])
|-
|-
| style="text-align:center;" | [[16/13|16/13]], [[13/8|13/8]]
| '''[[16/13|16/13]], [[13/8|13/8]]'''
| style="text-align:center;" | 0.528
| '''0.528'''
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| [[15/14|15/14]], [[28/15|28/15]]
| style="text-align:center;" | 0.557
| 0.557
|-
|-
| style="text-align:center;" | [[11/8|11/8]], [[16/11|16/11]]
| '''[[11/8|11/8]], [[16/11|16/11]]'''
| style="text-align:center;" | 0.682
| '''0.682'''
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| [[13/11|13/11]], [[22/13|22/13]]
| style="text-align:center;" | 1.210
| 1.210
|-
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | 1.786
| 1.786
|-
|-
| style="text-align:center;" | [[5/4|5/4]], [[8/5|8/5]]
| '''[[5/4|5/4]], [[8/5|8/5]]'''
| style="text-align:center;" | 2.314
| '''2.314'''
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | 2.871
| 2.871
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| [[11/10|11/10]], [[20/11|20/11]]
| style="text-align:center;" | 2.996
| 2.996
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| [[9/7|9/7]], [[14/9|14/9]]
| style="text-align:center;" | 3.084
| 3.084
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | 3.641
| 3.641
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | 5.427
| 5.427
|-
|-
| style="text-align:center;" | [[4/3|4/3]], [[3/2|3/2]]
| [[4/3|4/3]], [[3/2|3/2]]
| style="text-align:center;" | 5.955
| 5.955
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| [[7/5|7/5]], [[10/7|10/7]]
| style="text-align:center;" | 6.512
| 6.512
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | 6.637
| 6.637
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| [[15/13|15/13]], [[26/15|26/15]]
| style="text-align:center;" | 7.741
| 7.741
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | 8.269
| 8.269
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| [[14/13|14/13]], [[13/7|13/7]]
| style="text-align:center;" | 8.298
| 8.298
|-
|-
| style="text-align:center;" | [[8/7|8/7]], [[7/4|7/4]]
| '''[[8/7|8/7]], [[7/4|7/4]]'''
| style="text-align:center;" | 8.826
| '''8.826'''
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | 8.951
| 8.951
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| [[14/11|14/11]], [[11/7|11/7]]
| style="text-align:center;" | 9.508
| 9.508
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| [[10/9|10/9]], [[9/5|9/5]]
| style="text-align:center;" | 9.596
| 9.596
|-
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | 11.382
| 11.382
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | 11.910
| 11.910
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| ''[[11/9|11/9]], [[18/11|18/11]]''
| style="text-align:center;" | 12.592
| ''12.592''
|}
|}


=Commas=
== Commas ==
50 EDO tempers out the following commas. (Note: This assumes the val &lt; 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.
50 EDO tempers out the following commas. (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.


{| class="wikitable"
{| class="wikitable center-all left-1 right-2"
|-
|-
! | Monzo
! Monzo
! | Cents
! Cents
! | Ratio
! Ratio
! | Name 1
! Name 1
! | Name 2
! Name 2
|-
|-
| |<nowiki> | -4 4 -1 </nowiki>&gt;
| |<nowiki> | -4 4 -1 </nowiki>&gt;
| style="text-align:right;" | 21.51
| 21.51
| style="text-align:center;" | 81/80
| 81/80
| | Syntonic comma
| Syntonic comma
| | Didymus comma
| Didymus comma
|-
|-
| |<nowiki> | -27 -2 13 </nowiki>&gt;
| |<nowiki> | -27 -2 13 </nowiki>&gt;
| style="text-align:right;" | 18.17
| 18.17
| style="text-align:center;" |  
|  
| | Ditonma
| Ditonma
| |  
|  
|-
|-
| |<nowiki> | 23 6 -14 </nowiki>&gt;
| |<nowiki> | 23 6 -14 </nowiki>&gt;
| style="text-align:right;" | 3.34
| 3.34
| style="text-align:center;" |  
|  
| | Vishnu comma
| Vishnu comma
| |  
|  
|-
|-
| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
| |<nowiki> | 1 2 -3 1 </nowiki>&gt;
| style="text-align:right;" | 13.79
| 13.79
| style="text-align:center;" | 126/125
| 126/125
| | Starling comma
| Starling comma
| | Small septimal comma
| Small septimal comma
|-
|-
| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
| style="text-align:right;" | 7.71
| 7.71
| style="text-align:center;" | 225/224
| 225/224
| | Septimal kleisma
| Septimal kleisma
| | Marvel comma
| Marvel comma
|-
|-
| |<nowiki> | 6 0 -5 2 </nowiki>&gt;
| |<nowiki> | 6 0 -5 2 </nowiki>&gt;
| style="text-align:right;" | 6.08
| 6.08
| style="text-align:center;" | 3136/3125
| 3136/3125
| | Hemimean
| Hemimean
| | Middle second comma
| Middle second comma
|-
|-
| |<nowiki> | -6 -8 2 5 </nowiki>&gt;
| |<nowiki> | -6 -8 2 5 </nowiki>&gt;
| style="text-align:right;" | 1.12
| 1.12
| style="text-align:center;" |  
|  
| | Wizma
| Wizma
| |  
|  
|-
|-
| |<nowiki> |-11 2 7 -3 </nowiki>&gt;
| |<nowiki> |-11 2 7 -3 </nowiki>&gt;
| style="text-align:right;" | 1.63
| 1.63
| style="text-align:center;" |  
|  
| | Meter
| Meter
| |  
|  
|-
|-
| |<nowiki> | 11 -10 -10 10 </nowiki>&gt;
| |<nowiki> | 11 -10 -10 10 </nowiki>&gt;
| style="text-align:right;" | 5.57
| 5.57
| style="text-align:center;" |  
|  
| | Linus
| Linus
| |  
|  
|-
|-
| |<nowiki> |-13 10 0 -1 </nowiki>&gt;
| |<nowiki> |-13 10 0 -1 </nowiki>&gt;
| style="text-align:right;" | 50.72
| 50.72
| style="text-align:center;" | 59049/57344
| 59049/57344
| | Harrison's comma
| Harrison's comma
| |  
|  
|-
|-
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| style="text-align:right;" | 3.21
| 3.21
| style="text-align:center;" | 540/539
| 540/539
| | Swets' comma
| Swets' comma
| | Swetisma
| Swetisma
|-
|-
| |<nowiki> | -3 4 -2 -2 2 </nowiki>&gt;
| |<nowiki> | -3 4 -2 -2 2 </nowiki>&gt;
| style="text-align:right;" | 0.18
| 0.18
| style="text-align:center;" | 9801/9800
| 9801/9800
| | Kalisma
| Kalisma
| | Gauss' comma
| Gauss' comma
|-
|-
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
| style="text-align:right;" | 3.03
| 3.03
| style="text-align:center;" | 4000/3993
| 4000/3993
| | Wizardharry
| Wizardharry
| | Undecimal schisma
| Undecimal schisma
|-
|-
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| style="text-align:right;" | 4.50
| 4.50
| style="text-align:center;" | 385/384
| 385/384
| | Keenanisma
| Keenanisma
| | Undecimal kleisma
| Undecimal kleisma
|-
|-
| |<nowiki> | -1 0 1 2 -2 </nowiki>&gt;
| |<nowiki> | -1 0 1 2 -2 </nowiki>&gt;
| style="text-align:right;" | 21.33
| 21.33
| style="text-align:center;" | 245/242
| 245/242
| | Cassacot
| Cassacot
| |  
|  
|-
|-
| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| style="text-align:right;" | 4.76
| 4.76
| style="text-align:center;" | 364/363
| 364/363
| | Gentle comma
| Gentle comma
| |  
|  
|-
|-
| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| style="text-align:right;" | 8.86
| 8.86
| style="text-align:center;" | 196/195
| 196/195
| | Mynucuma
| Mynucuma
| |  
|  
|-
|-
| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| style="text-align:right;" | 7.30
| 7.30
| style="text-align:center;" | 1188/1183
| 1188/1183
| | Kestrel Comma
| Kestrel Comma
| |  
|  
|-
|-
| |<nowiki> | 3 0 2 0 1 -3 </nowiki>&gt;
| |<nowiki> | 3 0 2 0 1 -3 </nowiki>&gt;
| style="text-align:right;" | 2.36
| 2.36
| style="text-align:center;" | 2200/2197
| 2200/2197
| | Petrma
| Petrma
| | Parizek comma
| Parizek comma
|-
|-
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| style="text-align:right;" | 16.57
| 16.57
| style="text-align:center;" | 105/104
| 105/104
| | Animist comma
| Animist comma
| | Small tridecimal comma
| Small tridecimal comma
| |
|-
|-
| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| style="text-align:right;" | 12.06
| 12.06
| style="text-align:center;" | 144/143
| 144/143
| | Grossma
| Grossma
| |  
|  
|-
|-
| |<nowiki> | 3 -2 0 1 -1 -1 0 0 1 </nowiki>&gt;
| |<nowiki> | 3 -2 0 1 -1 -1 0 0 1 </nowiki>&gt;
| style="text-align:right;" | 1.34
| 1.34
| style="text-align:center;" | 1288/1287
| 1288/1287
| | Triaphonisma
| Triaphonisma
| |  
|  
|}
|}


=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]
[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]


Line 603: Line 600:
[https://soundcloud.com/camtaylor-1/fragment-in-fifty Fragment in Fifty] by Cam Taylor
[https://soundcloud.com/camtaylor-1/fragment-in-fifty Fragment in Fifty] by Cam Taylor


=Additional reading=
== Additional reading ==
[http://www.archive.org/details/harmonicsorphilo00smit Robert Smith's book online]
[http://www.archive.org/details/harmonicsorphilo00smit Robert Smith's book online]


Line 611: Line 608:


[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:edo]]
[[Category:edo]]
Retrieved from "https://en.xen.wiki/w/50edo"