50edo: Difference between revisions

Godtone (talk | contribs)
m Selected just intervals: 50 EDO is essentially 23-limit meantone because all the primes tend flat and thus a lot of error cancellation opportunities arise, furthermore, the prime 3 being almost perfectly 25% off justifies extra precision
Eli5121 (talk | contribs)
m Added EDO info box and notation
Line 1: Line 1:
{{Infobox ET
| Prime factorization = 2 x 5<sup>2</sup>
| Step size = 24.000
| Fifth = 29\50 = 696¢
| Major 2nd = 8\50 = 192¢
| Minor 2nd = 5\50 = 120¢
| Augmented 1sn = 3\50 = 72¢
}}
'''50edo''' divides the [[octave]] into 50 equal parts of precisely 24 [[cent|cents]] each.  
'''50edo''' divides the [[octave]] into 50 equal parts of precisely 24 [[cent|cents]] each.  


Line 17: Line 26:
! Cents
! Cents
! Ratios*
! Ratios*
! colspan="3" | [[Ups and Downs Notation]]
! Generator for*
! Generator for*
|-
|-
Line 22: Line 32:
| 0
| 0
| 1/1
| 1/1
| Perfect 1sn
| P1
| D
|  
|  
|-
|-
Line 27: Line 40:
| 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
| Up 1sn, Dim 2nd
| ^1, d2
| ^D, Ebb
| [[Hemimean_clan#Sengagen|Sengagen]]
| [[Hemimean_clan#Sengagen|Sengagen]]
|-
|-
Line 32: Line 48:
| 48
| 48
| 33/32, 36/35, 50/49, 55/54, 64/63
| 33/32, 36/35, 50/49, 55/54, 64/63
|  
| Downaug 1sn, Updim 2nd
| vA1, ^d2
| vD#, ^Ebb
|-
|-
| 3
| 3
| 72
| 72
| 21/20, 25/24, 26/25, 27/26, 28/27
| 21/20, 25/24, 26/25, 27/26, 28/27
| Aug 1sn
| A1
| D#
| [[Vishnuzmic_family#Vishnu|Vishnu]] (2/oct), [[Starling temperaments #Coblack temperament|Coblack]] (5/oct)
| [[Vishnuzmic_family#Vishnu|Vishnu]] (2/oct), [[Starling temperaments #Coblack temperament|Coblack]] (5/oct)
|-
|-
Line 42: Line 63:
| 96
| 96
| 22/21
| 22/21
| Downminor 2nd
| vm2
| vEb
| [[Meantone_family#Injera|Injera]] (50d val, 2/oct)
| [[Meantone_family#Injera|Injera]] (50d val, 2/oct)
|-
|-
Line 47: Line 71:
| 120
| 120
| 16/15, 15/14, 14/13
| 16/15, 15/14, 14/13
| Minor 2nd
| m2
| Eb
|  
|  
|-
|-
Line 52: Line 79:
| 144
| 144
| 13/12, 12/11
| 13/12, 12/11
| Upminor 2nd
| ^m2
| ^Eb
|  
|  
|-
|-
Line 57: Line 87:
| 168
| 168
| 11/10
| 11/10
| Downmajor 2nd
| vM2
| vE
|  
|  
|-
|-
Line 62: Line 95:
| 192
| 192
| 9/8, 10/9
| 9/8, 10/9
| Major 2nd
| M2
| E
|  
|  
|-
|-
Line 67: Line 103:
| 216
| 216
| 25/22
| 25/22
| Upmajor 2nd
| ^M2
| ^E
| [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)
|-
|-
Line 72: Line 111:
| 240
| 240
| 8/7, 15/13
| 8/7, 15/13
| Downaug 2nd, Dim 3rd
| vA2, d3
| vE#, Fb
|  
|  
|-
|-
Line 77: Line 119:
| 264
| 264
| 7/6
| 7/6
| Updim 3rd, Aug 2nd
| ^d3, A2
| ^Fb, E#
| [[Marvel_temperaments#Septimin-13-limit|Septimin (13-limit)]]
| [[Marvel_temperaments#Septimin-13-limit|Septimin (13-limit)]]
|-
|-
Line 82: Line 127:
| 288
| 288
| 13/11
| 13/11
| Downminor 3rd
| vm3
| vF
|  
|  
|-
|-
Line 87: Line 135:
| 312
| 312
| 6/5
| 6/5
| Minor 3rd
| m3
| F
| [[Oolong]]
| [[Oolong]]
|-
|-
Line 92: Line 143:
| 336
| 336
| 27/22, 39/32, 40/33, 49/40
| 27/22, 39/32, 40/33, 49/40
| Upminor 3rd
| ^m3
| ^F
|  
|  
|-
|-
Line 97: Line 151:
| 360
| 360
| 16/13, 11/9
| 16/13, 11/9
| Downmajor 3rd
| vM3
| vF#
|  
|  
|-
|-
Line 102: Line 159:
| 384
| 384
| 5/4
| 5/4
| Major 3rd
| M3
| F#
| [[Marvel_temperaments#Wizard-11-limit|Wizard]] (2/oct)
| [[Marvel_temperaments#Wizard-11-limit|Wizard]] (2/oct)
|-
|-
Line 107: Line 167:
| 408
| 408
| 14/11
| 14/11
| Upmajor 3rd
| ^M3
| ^F#
| [[Ditonmic_family|Ditonic]]
| [[Ditonmic_family|Ditonic]]
|-
|-
Line 112: Line 175:
| 432
| 432
| 9/7
| 9/7
| Downaug 3rd, Dim 4th
| vA3, d4
| vFx, Gb
| [[Porcupine_family#Hedgehog|Hedgehog]] (50cc val, 2/oct)
| [[Porcupine_family#Hedgehog|Hedgehog]] (50cc val, 2/oct)
|-
|-
Line 117: Line 183:
| 456
| 456
| 13/10
| 13/10
| Updim 4th, Aug 3rd
| A3, ^d4
| ^Gb, Fx
| [[Starling_temperaments#Bisemidim|Bisemidim]] (2/oct)
| [[Starling_temperaments#Bisemidim|Bisemidim]] (2/oct)
|-
|-
Line 122: Line 191:
| 480
| 480
| 33/25, 55/42, 64/49
| 33/25, 55/42, 64/49
| Down 4th
| v4
| vG
|  
|  
|-
|-
Line 127: Line 199:
| 504
| 504
| 4/3
| 4/3
| Perfect 4th
| P4
| G
| [[Meantone|Meantone]]/[[Meanpop|Meanpop]]
| [[Meantone|Meantone]]/[[Meanpop|Meanpop]]
|-
|-
Line 132: Line 207:
| 528
| 528
| 15/11
| 15/11
| Up 4th
| ^4
| ^G
|  
|  
|-
|-
Line 137: Line 215:
| 552
| 552
| 11/8, 18/13
| 11/8, 18/13
| Downaug 4th
| vA4
| vG#
| [[Chromatic_pairs#Barton|Barton]], [[Hemimean_clan#Emka|Emka]]
| [[Chromatic_pairs#Barton|Barton]], [[Hemimean_clan#Emka|Emka]]
|
|-
|-
| 24
| 24
| 576
| 576
| 7/5
| 7/5
| Aug 4th
| A4
| G#
|  
|  
|-
|-
Line 147: Line 232:
| 600
| 600
| 63/44, 88/63, 78/55, 55/39
| 63/44, 88/63, 78/55, 55/39
| Upaug 4th, Downdim 5th
| ^A4, vd5
| ^G#, vAb
|  
|  
|-
|-
Line 152: Line 240:
| 624
| 624
| 10/7
| 10/7
| Dim 5th
| d5
| Ab
|  
|  
|-
|-
Line 157: Line 248:
| 648
| 648
| 16/11, 13/9
| 16/11, 13/9
| Updim 5th
| ^d5
| ^Ab
|  
|  
|-
|-
Line 162: Line 256:
| 672
| 672
| 22/15
| 22/15
| Down 5th
| v5
| vA
|  
|  
|-
|-
Line 167: Line 264:
| 696
| 696
| 3/2
| 3/2
| Perfect 5th
| P5
| A
|  
|  
|-
|-
Line 172: Line 272:
| 720
| 720
| 50/33, 84/55, 49/32
| 50/33, 84/55, 49/32
| Up 5th
| ^5
| ^A
|  
|  
|-
|-
Line 177: Line 280:
| 744
| 744
| 20/13
| 20/13
|  
| Downaug 5th, Dim 6th
| vA5, d6
| vA#, Bbb
|-
|-
| 32
| 32
| 768
| 768
| 14/9
| 14/9
| Updim 6th, Aug 5th
| ^d6, A5
| ^Bbb, A#
|  
|  
|-
|-
Line 187: Line 295:
| 792
| 792
| 11/7
| 11/7
| Downminor 6th
| vm6
| vBb
|  
|  
|-
|-
Line 192: Line 303:
| 816
| 816
| 8/5
| 8/5
| Minor 6th
| m6
| Bb
|  
|  
|-
|-
Line 197: Line 311:
| 840
| 840
| 13/8, 18/11
| 13/8, 18/11
| Upminor 6th
| ^m6
| ^Bb
|  
|  
|-
|-
Line 202: Line 319:
| 864
| 864
| 44/27, 64/39, 33/20, 80/49
| 44/27, 64/39, 33/20, 80/49
| Downmajor 6th
| vM6
| vB
|  
|  
|-
|-
Line 207: Line 327:
| 888
| 888
| 5/3
| 5/3
| Major 6th
| M6
| B
|  
|  
|-
|-
Line 212: Line 335:
| 912
| 912
| 22/13
| 22/13
| Upmajor 6th
| ^M6
| ^B
|  
|  
|-
|-
Line 217: Line 343:
| 936
| 936
| 12/7
| 12/7
| Downaug 6th, Dim 7th
| vA6, d7
| vB#, Cb
|  
|  
|-
|-
Line 222: Line 351:
| 960
| 960
| 7/4
| 7/4
| Updim 7th, Aug 6th
| ^d7, A6
| ^Cb, B#
|  
|  
|-
|-
Line 227: Line 359:
| 984
| 984
| 44/25
| 44/25
| Downminor 7th
| vm7
| vC
|  
|  
|-
|-
Line 232: Line 367:
| 1008
| 1008
| 16/9, 9/5
| 16/9, 9/5
| Minor 7th
| m7
| C
|  
|  
|-
|-
Line 237: Line 375:
| 1032
| 1032
| 20/11
| 20/11
| Upminor 7th
| ^m7
| ^C
|  
|  
|-
|-
Line 242: Line 383:
| 1056
| 1056
| 24/13, 11/6
| 24/13, 11/6
| Downmajor 7th
| vM7
| vC#
|  
|  
|-
|-
Line 247: Line 391:
| 1080
| 1080
| 15/8, 28/15, 13/7
| 15/8, 28/15, 13/7
| Major 7th
| M7
| C#
|  
|  
|-
|-
Line 252: Line 399:
| 1104
| 1104
| 21/11
| 21/11
| Upmajor 7th
| ^M7
| ^C#
|  
|  
|-
|-
Line 257: Line 407:
| 1128
| 1128
| 40/21, 48/25, 25/13, 52/27, 27/14
| 40/21, 48/25, 25/13, 52/27, 27/14
| Downaug 7th, Dim 8ve
| vA7, d8
| vCx, Db
|  
|  
|-
|-
Line 262: Line 415:
| 1152
| 1152
| 64/33, 35/18, 49/25, 108/55, 63/32
| 64/33, 35/18, 49/25, 108/55, 63/32
| Updim 8ve, Aug 7th
| ^d8, A7
| ^Db, Cx
|  
|  
|-
|-
Line 267: Line 423:
| 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
| Down 8ve
| v8
| vD
|  
|  
|-
|-
Line 272: Line 431:
| 1200
| 1200
| 2/1
| 2/1
| Perfect 8ve
| P8
| D
|  
|  
|}
|}