50edo: Difference between revisions
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| Line 14: | Line 14: | ||
! | Degrees of 50edo | ! | Degrees of 50edo | ||
! | Cents value | ! | Cents value | ||
!7mus | !7mus | ||
! | Ratios* | ! | Ratios* | ||
! | Generator for* | ! | Generator for* | ||
|- | |- | ||
| | | 0 | ||
|0 | |||
|0 | |||
| | 1/1 | | | 1/1 | ||
| | | | | | ||
| Line 25: | Line 26: | ||
| | 1 | | | 1 | ||
| | 24 | | | 24 | ||
|30.72 (1E.B8<sub>16</sub>) | |30.72 (1E.B8<sub>16</sub>) | ||
| | 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 | ||
| Line 32: | Line 32: | ||
| | 2 | | | 2 | ||
| | 48 | | | 48 | ||
|61.44 (3D.71<sub>16</sub>) | |61.44 (3D.71<sub>16</sub>) | ||
| | 33/32, 36/35, 50/49, 55/54, 64/63 | | | 33/32, 36/35, 50/49, 55/54, 64/63 | ||
| Line 39: | Line 38: | ||
| | 3 | | | 3 | ||
| | 72 | | | 72 | ||
|92.16 (5C.29<sub>16</sub>) | |92.16 (5C.29<sub>16</sub>) | ||
| | 21/20, 25/24, 26/25, 27/26, 28/27 | | | 21/20, 25/24, 26/25, 27/26, 28/27 | ||
| Line 46: | Line 44: | ||
| | 4 | | | 4 | ||
| | 96 | | | 96 | ||
|122.88 (7A.E1<sub>16</sub>) | |122.88 (7A.E1<sub>16</sub>) | ||
| | 22/21 | | | 22/21 | ||
| Line 53: | Line 50: | ||
| | 5 | | | 5 | ||
| | 120 | | | 120 | ||
|153.6 (99.9A<sub>16</sub>) | |153.6 (99.9A<sub>16</sub>) | ||
| | 16/15, 15/14, 14/13 | | | 16/15, 15/14, 14/13 | ||
| Line 60: | Line 56: | ||
| | 6 | | | 6 | ||
| | 144 | | | 144 | ||
|184.32 (B8.52<sub>16</sub>) | |184.32 (B8.52<sub>16</sub>) | ||
| | 13/12, 12/11 | | | 13/12, 12/11 | ||
| Line 67: | Line 62: | ||
| | 7 | | | 7 | ||
| | 168 | | | 168 | ||
|215.04 (D7.0A<sub>16</sub>) | |215.04 (D7.0A<sub>16</sub>) | ||
| | 11/10 | | | 11/10 | ||
| Line 74: | Line 68: | ||
| | 8 | | | 8 | ||
| | 192 | | | 192 | ||
|245.76 (F5.C3<sub>16</sub>) | |245.76 (F5.C3<sub>16</sub>) | ||
| | 9/8, 10/9 | | | 9/8, 10/9 | ||
| Line 81: | Line 74: | ||
| | 9 | | | 9 | ||
| | 216 | | | 216 | ||
|276.48 (114.7B<sub>16</sub>) | |276.48 (114.7B<sub>16</sub>) | ||
| | 25/22 | | | 25/22 | ||
| Line 88: | Line 80: | ||
| | 10 | | | 10 | ||
| | 240 | | | 240 | ||
|307.2 (133.33<sub>16</sub>) | |307.2 (133.33<sub>16</sub>) | ||
| | 8/7, 15/13 | | | 8/7, 15/13 | ||
| Line 95: | Line 86: | ||
| | 11 | | | 11 | ||
| | 264 | | | 264 | ||
|337.92 (151.EB8<sub>16</sub>) | |337.92 (151.EB8<sub>16</sub>) | ||
| | 7/6 | | | 7/6 | ||
| Line 102: | Line 92: | ||
| | 12 | | | 12 | ||
| | 288 | | | 288 | ||
|368.64 (170.A4<sub>16</sub>) | |368.64 (170.A4<sub>16</sub>) | ||
| | 13/11 | | | 13/11 | ||
| Line 109: | Line 98: | ||
| | 13 | | | 13 | ||
| | 312 | | | 312 | ||
|399.36 (18F.5C<sub>16</sub>) | |399.36 (18F.5C<sub>16</sub>) | ||
| | 6/5 | | | 6/5 | ||
| Line 116: | Line 104: | ||
| | 14 | | | 14 | ||
| | 336 | | | 336 | ||
|430.08 (1AE.148<sub>16</sub>) | |430.08 (1AE.148<sub>16</sub>) | ||
| | 27/22, 39/32, 40/33, 49/40 | | | 27/22, 39/32, 40/33, 49/40 | ||
| Line 123: | Line 110: | ||
| | 15 | | | 15 | ||
| | 360 | | | 360 | ||
|460.8 (1CC.CD<sub>16</sub>) | |460.8 (1CC.CD<sub>16</sub>) | ||
| | 16/13, 11/9 | | | 16/13, 11/9 | ||
| Line 130: | Line 116: | ||
| | 16 | | | 16 | ||
| | 384 | | | 384 | ||
|491.52 (1EB.85<sub>16</sub>) | |491.52 (1EB.85<sub>16</sub>) | ||
| | 5/4 | | | 5/4 | ||
| Line 137: | Line 122: | ||
| | 17 | | | 17 | ||
| | 408 | | | 408 | ||
|522.24 (20A.4<sub>16</sub>) | |522.24 (20A.4<sub>16</sub>) | ||
| | 14/11 | | | 14/11 | ||
| Line 144: | Line 128: | ||
| | 18 | | | 18 | ||
| | 432 | | | 432 | ||
|552.96 (228.F6<sub>16</sub>) | |552.96 (228.F6<sub>16</sub>) | ||
| | 9/7 | | | 9/7 | ||
| Line 151: | Line 134: | ||
| | 19 | | | 19 | ||
| | 456 | | | 456 | ||
|583.68 (247.AE<sub>16</sub>) | |583.68 (247.AE<sub>16</sub>) | ||
| | 13/10 | | | 13/10 | ||
| Line 158: | Line 140: | ||
| | 20 | | | 20 | ||
| | 480 | | | 480 | ||
|614.4 (266.66<sub>16</sub>) | |614.4 (266.66<sub>16</sub>) | ||
| | 33/25, 55/42, 64/49 | | | 33/25, 55/42, 64/49 | ||
| Line 165: | Line 146: | ||
| | 21 | | | 21 | ||
| | 504 | | | 504 | ||
|645.12 (285.1F<sub>16</sub>) | |645.12 (285.1F<sub>16</sub>) | ||
| | 4/3 | | | 4/3 | ||
| Line 172: | Line 152: | ||
| | 22 | | | 22 | ||
| | 528 | | | 528 | ||
|675.84 (2A3.D7<sub>16</sub>) | |675.84 (2A3.D7<sub>16</sub>) | ||
| | 15/11 | | | 15/11 | ||
| Line 179: | Line 158: | ||
| | 23 | | | 23 | ||
| | 552 | | | 552 | ||
|706.56 (2C2.8F<sub>16</sub>) | |706.56 (2C2.8F<sub>16</sub>) | ||
| | 11/8, 18/13 | | | 11/8, 18/13 | ||
| Line 186: | Line 164: | ||
| | 24 | | | 24 | ||
| | 576 | | | 576 | ||
|737.28 (2E1.48<sub>16</sub>) | |737.28 (2E1.48<sub>16</sub>) | ||
| | 7/5 | | | 7/5 | ||
| Line 193: | Line 170: | ||
| | 25 | | | 25 | ||
| | 600 | | | 600 | ||
|768 (300<sub>16</sub>) | |768 (300<sub>16</sub>) | ||
| | 63/44, 88/63, 78/55, 55/39 | | | 63/44, 88/63, 78/55, 55/39 | ||
| Line 200: | Line 176: | ||
| | 26 | | | 26 | ||
| | 624 | | | 624 | ||
|798.72 (31E.B8<sub>16</sub>) | |798.72 (31E.B8<sub>16</sub>) | ||
| | 10/7 | | | 10/7 | ||
| Line 207: | Line 182: | ||
| | 27 | | | 27 | ||
| | 648 | | | 648 | ||
|829.44 (33D.71<sub>16</sub>) | |829.44 (33D.71<sub>16</sub>) | ||
| | 16/11, 13/9 | | | 16/11, 13/9 | ||
| Line 214: | Line 188: | ||
| | 28 | | | 28 | ||
| | 672 | | | 672 | ||
|860.16 (35C.29<sub>16</sub>) | |860.16 (35C.29<sub>16</sub>) | ||
| | 22/15 | | | 22/15 | ||
| Line 221: | Line 194: | ||
| | 29 | | | 29 | ||
| | 696 | | | 696 | ||
|900.88 (37A.E1<sub>16</sub>) | |900.88 (37A.E1<sub>16</sub>) | ||
| | 3/2 | | | 3/2 | ||
| Line 228: | Line 200: | ||
| | 30 | | | 30 | ||
| | 720 | | | 720 | ||
|921.6 (399.9A<sub>16</sub>) | |921.6 (399.9A<sub>16</sub>) | ||
| | 50/33, 84/55, 49/32 | | | 50/33, 84/55, 49/32 | ||
| Line 235: | Line 206: | ||
| | 31 | | | 31 | ||
| | 744 | | | 744 | ||
|952.32 (3B8.52<sub>16</sub>) | |952.32 (3B8.52<sub>16</sub>) | ||
| | 20/13 | | | 20/13 | ||
| Line 242: | Line 212: | ||
| | 32 | | | 32 | ||
| | 768 | | | 768 | ||
|983.04 (3D7.0A<sub>16</sub>) | |983.04 (3D7.0A<sub>16</sub>) | ||
| | 14/9 | | | 14/9 | ||
| Line 249: | Line 218: | ||
| | 33 | | | 33 | ||
| | 792 | | | 792 | ||
|1013.76 (3F5.C3<sub>16</sub>) | |1013.76 (3F5.C3<sub>16</sub>) | ||
| | 11/7 | | | 11/7 | ||
| Line 256: | Line 224: | ||
| | 34 | | | 34 | ||
| | 816 | | | 816 | ||
|1044.48 (414.7B<sub>16</sub>) | |1044.48 (414.7B<sub>16</sub>) | ||
| | 8/5 | | | 8/5 | ||
| Line 263: | Line 230: | ||
| | 35 | | | 35 | ||
| | 840 | | | 840 | ||
|1095.2 (433.33<sub>16</sub>) | |1095.2 (433.33<sub>16</sub>) | ||
| | 13/8, 18/11 | | | 13/8, 18/11 | ||
| Line 270: | Line 236: | ||
| | 36 | | | 36 | ||
| | 864 | | | 864 | ||
|1105.92 (451.EB8<sub>16</sub>) | |1105.92 (451.EB8<sub>16</sub>) | ||
| | 44/27, 64/39, 33/20, 80/49 | | | 44/27, 64/39, 33/20, 80/49 | ||
| Line 277: | Line 242: | ||
| | 37 | | | 37 | ||
| | 888 | | | 888 | ||
|1136.64 (470.A4<sub>16</sub> | |1136.64 (470.A4<sub>16</sub> | ||
| | 5/3 | | | 5/3 | ||
| Line 284: | Line 248: | ||
| | 38 | | | 38 | ||
| | 912 | | | 912 | ||
|1167.36 (48F.5C<sub>16</sub>) | |1167.36 (48F.5C<sub>16</sub>) | ||
| | 22/13 | | | 22/13 | ||
| Line 291: | Line 254: | ||
| | 39 | | | 39 | ||
| | 936 | | | 936 | ||
|1198.08 (4AE.148<sub>16</sub>) | |1198.08 (4AE.148<sub>16</sub>) | ||
| | 12/7 | | | 12/7 | ||
| Line 298: | Line 260: | ||
| | 40 | | | 40 | ||
| | 960 | | | 960 | ||
|1228.8 (4CC.CD<sub>16</sub>) | |1228.8 (4CC.CD<sub>16</sub>) | ||
| | 7/4 | | | 7/4 | ||
| Line 305: | Line 266: | ||
| | 41 | | | 41 | ||
| | 984 | | | 984 | ||
|1261.52 (4EB.85<sub>16</sub>) | |1261.52 (4EB.85<sub>16</sub>) | ||
| | 44/25 | | | 44/25 | ||
| Line 312: | Line 272: | ||
| | 42 | | | 42 | ||
| | 1008 | | | 1008 | ||
|1290.24 (50A.4<sub>16</sub>) | |1290.24 (50A.4<sub>16</sub>) | ||
| | 16/9, 9/5 | | | 16/9, 9/5 | ||
| Line 319: | Line 278: | ||
| | 43 | | | 43 | ||
| | 1032 | | | 1032 | ||
|1320.96 (528.F6<sub>16</sub>) | |1320.96 (528.F6<sub>16</sub>) | ||
| | 20/11 | | | 20/11 | ||
| Line 326: | Line 284: | ||
| | 44 | | | 44 | ||
| | 1056 | | | 1056 | ||
|1351.68 (547.AE<sub>16</sub>) | |1351.68 (547.AE<sub>16</sub>) | ||
| | 24/13, 11/6 | | | 24/13, 11/6 | ||
| Line 333: | Line 290: | ||
| | 45 | | | 45 | ||
| | 1080 | | | 1080 | ||
|1382.4 (566.66<sub>16</sub>) | |1382.4 (566.66<sub>16</sub>) | ||
| | 15/8, 28/15, 13/7 | | | 15/8, 28/15, 13/7 | ||
| Line 340: | Line 296: | ||
| | 46 | | | 46 | ||
| | 1104 | | | 1104 | ||
|1413.12 (585.1F<sub>16</sub>) | |1413.12 (585.1F<sub>16</sub>) | ||
| | 21/11 | | | 21/11 | ||
| Line 347: | Line 302: | ||
| | 47 | | | 47 | ||
| | 1128 | | | 1128 | ||
|1443.84 (5A3.D7<sub>16</sub>) | |1443.84 (5A3.D7<sub>16</sub>) | ||
| | 40/21, 48/25, 25/13, 52/27, 27/14 | | | 40/21, 48/25, 25/13, 52/27, 27/14 | ||
| Line 354: | Line 308: | ||
| | 48 | | | 48 | ||
| | 1152 | | | 1152 | ||
|1474.56 (5C2.8F<sub>16</sub>) | |1474.56 (5C2.8F<sub>16</sub>) | ||
| | 64/33, 35/18, 49/25, 108/55, 63/32 | | | 64/33, 35/18, 49/25, 108/55, 63/32 | ||
| Line 361: | Line 314: | ||
| | 49 | | | 49 | ||
| | 1176 | | | 1176 | ||
|1505.28 (5E1.48<sub>16</sub>) | |1505.28 (5E1.48<sub>16</sub>) | ||
| | 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 | ||
| Line 368: | Line 320: | ||
|50 | |50 | ||
|1200 | |1200 | ||
|1536 (600<sub>16</sub>) | |1536 (600<sub>16</sub>) | ||
|2/1 | |2/1 | ||
Revision as of 13:27, 12 December 2019
50edo divides the octave into 50 equal parts of precisely 24 cents each. In the 5-limit, it tempers out 81/80, making it a meantone system, and in that capacity has historically has drawn some notice. In "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 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.
50 tempers out 126/125, 225/224 and 3136/3125 in the 7-limit, indicating it supports 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 15&50 temperament (Coblack), and provides the optimal patent val for 11 and 13 limit bimeantone. It is also the unique equal temperament tempering out both 81/80 and the 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
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 "A Theory of Evolving Tonality").
Intervals
| Degrees of 50edo | Cents value | 7mus | Ratios* | Generator for* |
|---|---|---|---|---|
| 0 | 0 | 0 | 1/1 | |
| 1 | 24 | 30.72 (1E.B816) | 45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168 | Sengagen |
| 2 | 48 | 61.44 (3D.7116) | 33/32, 36/35, 50/49, 55/54, 64/63 | |
| 3 | 72 | 92.16 (5C.2916) | 21/20, 25/24, 26/25, 27/26, 28/27 | Vishnu (2/oct), Coblack (5/oct) |
| 4 | 96 | 122.88 (7A.E116) | 22/21 | Injera (50d val, 2/oct) |
| 5 | 120 | 153.6 (99.9A16) | 16/15, 15/14, 14/13 | |
| 6 | 144 | 184.32 (B8.5216) | 13/12, 12/11 | |
| 7 | 168 | 215.04 (D7.0A16) | 11/10 | |
| 8 | 192 | 245.76 (F5.C316) | 9/8, 10/9 | |
| 9 | 216 | 276.48 (114.7B16) | 25/22 | Tremka, Machine (50b val) |
| 10 | 240 | 307.2 (133.3316) | 8/7, 15/13 | |
| 11 | 264 | 337.92 (151.EB816) | 7/6 | Septimin (13-limit) |
| 12 | 288 | 368.64 (170.A416) | 13/11 | |
| 13 | 312 | 399.36 (18F.5C16) | 6/5 | |
| 14 | 336 | 430.08 (1AE.14816) | 27/22, 39/32, 40/33, 49/40 | |
| 15 | 360 | 460.8 (1CC.CD16) | 16/13, 11/9 | |
| 16 | 384 | 491.52 (1EB.8516) | 5/4 | Wizard (2/oct) |
| 17 | 408 | 522.24 (20A.416) | 14/11 | Ditonic |
| 18 | 432 | 552.96 (228.F616) | 9/7 | Hedgehog (50cc val, 2/oct) |
| 19 | 456 | 583.68 (247.AE16) | 13/10 | Bisemidim (2/oct) |
| 20 | 480 | 614.4 (266.6616) | 33/25, 55/42, 64/49 | |
| 21 | 504 | 645.12 (285.1F16) | 4/3 | Meantone/Meanpop |
| 22 | 528 | 675.84 (2A3.D716) | 15/11 | |
| 23 | 552 | 706.56 (2C2.8F16) | 11/8, 18/13 | Barton, Emka |
| 24 | 576 | 737.28 (2E1.4816) | 7/5 | |
| 25 | 600 | 768 (30016) | 63/44, 88/63, 78/55, 55/39 | |
| 26 | 624 | 798.72 (31E.B816) | 10/7 | |
| 27 | 648 | 829.44 (33D.7116) | 16/11, 13/9 | |
| 28 | 672 | 860.16 (35C.2916) | 22/15 | |
| 29 | 696 | 900.88 (37A.E116) | 3/2 | |
| 30 | 720 | 921.6 (399.9A16) | 50/33, 84/55, 49/32 | |
| 31 | 744 | 952.32 (3B8.5216) | 20/13 | |
| 32 | 768 | 983.04 (3D7.0A16) | 14/9 | |
| 33 | 792 | 1013.76 (3F5.C316) | 11/7 | |
| 34 | 816 | 1044.48 (414.7B16) | 8/5 | |
| 35 | 840 | 1095.2 (433.3316) | 13/8, 18/11 | |
| 36 | 864 | 1105.92 (451.EB816) | 44/27, 64/39, 33/20, 80/49 | |
| 37 | 888 | 1136.64 (470.A416 | 5/3 | |
| 38 | 912 | 1167.36 (48F.5C16) | 22/13 | |
| 39 | 936 | 1198.08 (4AE.14816) | 12/7 | |
| 40 | 960 | 1228.8 (4CC.CD16) | 7/4 | |
| 41 | 984 | 1261.52 (4EB.8516) | 44/25 | |
| 42 | 1008 | 1290.24 (50A.416) | 16/9, 9/5 | |
| 43 | 1032 | 1320.96 (528.F616) | 20/11 | |
| 44 | 1056 | 1351.68 (547.AE16) | 24/13, 11/6 | |
| 45 | 1080 | 1382.4 (566.6616) | 15/8, 28/15, 13/7 | |
| 46 | 1104 | 1413.12 (585.1F16) | 21/11 | |
| 47 | 1128 | 1443.84 (5A3.D716) | 40/21, 48/25, 25/13, 52/27, 27/14 | |
| 48 | 1152 | 1474.56 (5C2.8F16) | 64/33, 35/18, 49/25, 108/55, 63/32 | |
| 49 | 1176 | 1505.28 (5E1.4816) | 88/45, 96/49, 55/28, 128/65, 65/33, 77/39, 180/91, 196/99, 99/50, 240/121, 336/169 | |
| 50 | 1200 | 1536 (60016) | 2/1 |
- Using the 13-limit patent val, except as noted.
Selected just intervals by error
The following table shows how some prominent just intervals are represented in 50edo (ordered by absolute error).
Best direct mapping, even if inconsistent
| Interval, complement | Error (abs., in cents) |
| 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 |
| 11/9, 18/11 | 11.408 |
| 9/8, 16/9 | 11.910 |
Patent val mapping
| Interval, complement | Error (abs., in cents) |
| 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 |
Commas
50 EDO tempers out the following commas. (Note: This assumes the 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.
| Monzo | Cents | Ratio | Name 1 | Name 2 | |
|---|---|---|---|---|---|
| | -4 4 -1 > | 21.51 | 81/80 | Syntonic comma | Didymus comma | |
| | -27 -2 13 > | 18.17 | Ditonma | |||
| | 23 6 -14 > | 3.34 | Vishnu comma | |||
| | 1 2 -3 1 > | 13.79 | 126/125 | Starling comma | Small septimal comma | |
| | -5 2 2 -1 > | 7.71 | 225/224 | Septimal kleisma | Marvel comma | |
| | 6 0 -5 2 > | 6.08 | 3136/3125 | Hemimean | Middle second comma | |
| | -6 -8 2 5 > | 1.12 | Wizma | |||
| |-11 2 7 -3 > | 1.63 | Meter | |||
| | 11 -10 -10 10 > | 5.57 | Linus | |||
| |-13 10 0 -1 > | 50.72 | 59049/57344 | Harrison's comma | ||
| | 2 3 1 -2 -1 > | 3.21 | 540/539 | Swets' comma | Swetisma | |
| | -3 4 -2 -2 2 > | 0.18 | 9801/9800 | Kalisma | Gauss' comma | |
| | 5 -1 3 0 -3 > | 3.03 | 4000/3993 | Wizardharry | Undecimal schisma | |
| | -7 -1 1 1 1 > | 4.50 | 385/384 | Keenanisma | Undecimal kleisma | |
| | -1 0 1 2 -2 > | 21.33 | 245/242 | Cassacot | ||
| | 2 -1 0 1 -2 1 > | 4.76 | 364/363 | Gentle comma | ||
| | 2 -1 -1 2 0 -1 > | 8.86 | 196/195 | Mynucuma | ||
| | 2 3 0 -1 1 -2 > | 7.30 | 1188/1183 | Kestrel Comma | ||
| | 3 0 2 0 1 -3 > | 2.36 | 2200/2197 | Petrma | Parizek comma | |
| | -3 1 1 1 0 -1 > | 16.57 | 105/104 | Animist comma | Small tridecimal comma | |
| | 4 2 0 0 -1 -1 > | 12.06 | 144/143 | Grossma | ||
| | 3 -2 0 1 -1 -1 0 0 1 > | 1.34 | 1288/1287 | Triaphonisma |
Music
Twinkle canon – 50 edo by Claudi Meneghin
Fantasia Catalana by Claudi Meneghin
Fugue on the Dragnet theme by Claudi Meneghin
the late little xmas album by Cam Taylor
Harpsichord meantone improvisation 1 in 50EDO by Cam Taylor
Long improvisation 2 in 50EDO by Cam Taylor
Chord sequence for Difference tones in 50EDO by Cam Taylor
Enharmonic Modulations in 50EDO by Cam Taylor
Harmonic Clusters on 50EDO Harpsichord by Cam Taylor
Fragment in Fifty by Cam Taylor
Additional reading
More information about Robert Smith's temperament
50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor
iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor