241200edo
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Prime factorization
24 × 32 × 52 × 67
Step size
0.00497512¢
Fifth
141093\241200 (701.955¢) (→15677\26800)
Semitones (A1:m2)
22851:18135 (113.7¢ : 90.22¢)
Consistency limit
39
Distinct consistency limit
39
Special properties
| ← 241199edo | 241200edo | 241201edo → |
241200 equal divisions of the octave (abbreviated 241200edo or 241200ed2), also called 241200-tone equal temperament (241200tet) or 241200 equal temperament (241200et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 241200 equal parts of about 0.00498 ¢ each. Each step represents a frequency ratio of 21/241200, or the 241200th root of 2.
241200edo is the 60th zeta peak edo and the first one that 1200 divides, making it compatible with cents. It is also a zeta peak integer edo. It is a strong 37-limit system, distinctly consistent in the 39-odd-limit, with a lower 37-limit relative error than any previous equal temperaments.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00022 | -0.00028 | -0.00004 | +0.00047 | -0.00030 | -0.00019 | -0.00058 | -0.00072 | -0.00008 | -0.00075 | -0.00076 | +0.00227 | -0.00029 | +0.00084 |
| Relative (%) | +0.0 | +4.5 | -5.6 | -0.7 | +9.4 | -6.0 | -3.7 | -11.6 | -14.4 | -1.6 | -15.0 | -15.2 | +45.6 | -5.9 | +16.9 | |
| Steps (reduced) |
241200 (0) |
382293 (141093) |
560049 (77649) |
677134 (194734) |
834415 (110815) |
892546 (168946) |
985896 (21096) |
1024600 (59800) |
1091083 (126283) |
1171745 (206945) |
1194952 (230152) |
1256520 (50520) |
1292242 (86242) |
1308815 (102815) |
1339767 (133767) | |
| Harmonic | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.00206 | +0.00247 | +0.00077 | +0.00143 | -0.00003 | +0.00157 | +0.00042 | +0.00243 | +0.00048 | +0.00011 | +0.00194 | +0.00036 | +0.00081 | -0.00029 | -0.00082 |
| Relative (%) | -41.4 | +49.6 | +15.4 | +28.7 | -0.5 | +31.6 | +8.4 | +48.9 | +9.6 | +2.2 | +39.0 | +7.3 | +16.3 | -5.9 | -16.6 | |
| Steps (reduced) |
1381574 (175574) |
1418894 (212894) |
1430494 (224494) |
1463141 (15941) |
1483319 (36119) |
1492986 (45786) |
1520472 (73272) |
1537660 (90460) |
1561947 (114747) |
1591899 (144699) |
1605961 (158761) |
1612784 (165584) |
1626042 (178842) |
1632486 (185286) |
1645027 (197827) | |