50edo: Difference between revisions
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 |
m Added EDO info box and notation |
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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 | |||
| | | | ||
|} | |} |