53ed7
| ← 52ed7 | 53ed7 | 54ed7 → |
53 equal divisions of the 7th harmonic (abbreviated 53ed7) is a nonoctave tuning system that divides the interval of 7/1 into 53 equal parts of about 63.6 ¢ each. Each step represents a frequency ratio of 71/53, or the 53rd root of 7.
Theory
53ed7 is related to 19edo, 30edt, and Carlos Beta, but with the 7/1 rather than the 2/1 being just. The octave is about 7.6923 cents stretched. The patent val has a generally sharp tendency for harmonics up to 16, with exception for 11th harmonic.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.7 | +4.9 | +15.4 | +10.4 | +12.6 | +0.0 | +23.1 | +9.9 | +18.1 | -19.7 | +20.3 |
| Relative (%) | +12.1 | +7.8 | +24.2 | +16.4 | +19.9 | +0.0 | +36.3 | +15.5 | +28.5 | -31.1 | +32.0 | |
| Steps (reduced) |
19 (19) |
30 (30) |
38 (38) |
44 (44) |
49 (49) |
53 (0) |
57 (4) |
60 (7) |
63 (10) |
65 (12) |
68 (15) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.9 | +7.7 | +15.4 | +30.8 | -10.6 | +17.5 | -12.5 | +25.8 | +4.9 | -12.0 | -25.4 |
| Relative (%) | +13.9 | +12.1 | +24.2 | +48.4 | -16.7 | +27.6 | -19.7 | +40.6 | +7.8 | -19.0 | -40.0 | |
| Steps (reduced) |
70 (17) |
72 (19) |
74 (21) |
76 (23) |
77 (24) |
79 (26) |
80 (27) |
82 (29) |
83 (30) |
84 (31) |
85 (32) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 63.5628 | 28/27, 27/26 | |
| 2 | 127.1255 | 14/13 | |
| 3 | 190.6883 | 19/17 | |
| 4 | 254.2510 | 22/19 | |
| 5 | 317.8138 | 6/5, 77/64 | |
| 6 | 381.3765 | 96/77 | |
| 7 | 444.9393 | 22/17 | |
| 8 | 508.5020 | ||
| 9 | 572.0648 | 32/23 | |
| 10 | 635.6275 | 13/9 | |
| 11 | 699.1903 | 3/2 | |
| 12 | 762.7530 | 14/9 | |
| 13 | 826.3158 | ||
| 14 | 889.8785 | 77/46 | |
| 15 | 953.4413 | 26/15 | |
| 16 | 1017.0040 | 9/5 | |
| 17 | 1080.5668 | 28/15 | |
| 18 | 1144.1296 | 64/33 | |
| 19 | 1207.6923 | 161/80 | pseudo-octave |
| 20 | 1271.2551 | 25/12 | |
| 21 | 1334.8178 | 54/25 | |
| 22 | 1398.3806 | 56/25, 110/49 | |
| 23 | 1461.9433 | ||
| 24 | 1525.5061 | ||
| 25 | 1589.0688 | 5/2 | |
| 26 | 1652.6316 | 13/5 | |
| 27 | 1716.1943 | 35/13 | |
| 28 | 1779.7571 | 14/5 | |
| 29 | 1843.3198 | ||
| 30 | 1906.8826 | pseudo-3/1 | |
| 31 | 1970.4453 | 25/8 | |
| 32 | 2034.0081 | 68/21 | |
| 33 | 2097.5708 | 84/25 | |
| 34 | 2161.1336 | 80/23 | |
| 35 | 2224.6964 | 76/21 | |
| 36 | 2288.2591 | 15/4 | |
| 37 | 2351.8219 | 35/9 | |
| 38 | 2415.3846 | 105/26 | pseudo-4/1 |
| 39 | 2478.9474 | 46/11, 88/21 | |
| 40 | 2542.5101 | 100/23 | |
| 41 | 2606.0729 | 9/2 | |
| 42 | 2669.6356 | 14/3 | |
| 43 | 2733.1984 | 63/13 | |
| 44 | 2796.7611 | 161/32 | pseudo-5/1 |
| 45 | 2860.3239 | ||
| 46 | 2923.8866 | 119/22 | |
| 47 | 2987.4494 | ||
| 48 | 3051.0121 | 64/11, 35/6 | |
| 49 | 3114.5749 | 133/22 | pseudo-6/1 |
| 50 | 3178.1376 | 119/19 | |
| 51 | 3241.7004 | 13/2 | |
| 52 | 3305.2632 | 27/4 | |
| 53 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |