50ed11/5
Jump to navigation
Jump to search
Prime factorization
2 × 52
Step size
27.3001¢
Octave
44\50ed11/5 (1201.2¢) (→22\25ed11/5)
Twelfth
70\50ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit
6
Distinct consistency limit
4
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 49ed11/5 | 50ed11/5 | 51ed11/5 → |
50 equal divisions of 11/5 (abbreviated 50ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 50 equal parts of about 27.3 ¢ each. Each step represents a frequency ratio of (11/5)1/50, or the 50th root of 11/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 27.3 | |
| 2 | 54.6 | 30/29, 31/30, 32/31 |
| 3 | 81.9 | 21/20, 22/21, 23/22 |
| 4 | 109.2 | 16/15, 17/16 |
| 5 | 136.5 | 13/12 |
| 6 | 163.8 | 11/10 |
| 7 | 191.1 | 19/17, 28/25, 29/26 |
| 8 | 218.4 | 17/15, 25/22 |
| 9 | 245.7 | 15/13, 23/20 |
| 10 | 273 | |
| 11 | 300.3 | 19/16, 25/21, 31/26 |
| 12 | 327.6 | 23/19, 29/24 |
| 13 | 354.9 | 16/13 |
| 14 | 382.2 | 5/4 |
| 15 | 409.5 | 19/15, 24/19 |
| 16 | 436.8 | |
| 17 | 464.1 | 17/13, 30/23 |
| 18 | 491.4 | |
| 19 | 518.7 | 23/17, 31/23 |
| 20 | 546 | 11/8, 26/19 |
| 21 | 573.3 | 32/23 |
| 22 | 600.6 | 17/12, 24/17 |
| 23 | 627.9 | 23/16 |
| 24 | 655.2 | 19/13 |
| 25 | 682.5 | |
| 26 | 709.8 | |
| 27 | 737.1 | 23/15, 26/17, 29/19 |
| 28 | 764.4 | |
| 29 | 791.7 | 19/12, 30/19 |
| 30 | 819 | 8/5 |
| 31 | 846.3 | 31/19 |
| 32 | 873.6 | |
| 33 | 900.9 | 32/19 |
| 34 | 928.2 | 29/17 |
| 35 | 955.5 | 26/15 |
| 36 | 982.8 | 23/13, 30/17 |
| 37 | 1010.1 | |
| 38 | 1037.4 | 20/11, 31/17 |
| 39 | 1064.7 | 24/13 |
| 40 | 1092 | 15/8, 32/17 |
| 41 | 1119.3 | 21/11 |
| 42 | 1146.6 | 29/15, 31/16 |
| 43 | 1173.9 | |
| 44 | 1201.2 | 2/1 |
| 45 | 1228.5 | |
| 46 | 1255.8 | 31/15 |
| 47 | 1283.1 | 21/10 |
| 48 | 1310.4 | 17/8, 32/15 |
| 49 | 1337.7 | 13/6 |
| 50 | 1365 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +9.1 | -1.7 | -10.9 | -1.7 | +9.4 | +9.1 | +7.6 | +4.4 | +12.6 | +6.4 |
| Relative (%) | +4.4 | +33.2 | -6.2 | -40.0 | -6.2 | +34.4 | +33.2 | +27.8 | +16.3 | +46.3 | +23.4 | |
| Steps (reduced) |
44 (44) |
70 (20) |
102 (2) |
123 (23) |
152 (2) |
163 (13) |
180 (30) |
187 (37) |
199 (49) |
214 (14) |
218 (18) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.4 | -13.5 | +13.2 | -4.3 | +6.1 | +11.6 | +8.4 | +9.8 | -8.7 | -2.2 | -2.4 |
| Relative (%) | +1.4 | -49.6 | +48.4 | -15.7 | +22.4 | +42.3 | +30.9 | +36.0 | -31.8 | -7.9 | -8.8 | |
| Steps (reduced) |
229 (29) |
235 (35) |
239 (39) |
244 (44) |
252 (2) |
259 (9) |
261 (11) |
267 (17) |
270 (20) |
272 (22) |
277 (27) | |