302edo
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Prime factorization
2 × 151
Step size
3.97351¢
Fifth
177\302 (703.311¢)
Semitones (A1:m2)
31:21 (123.2¢ : 83.44¢)
Dual sharp fifth
177\302 (703.311¢)
Dual flat fifth
176\302 (699.338¢) (→88\151)
Dual major 2nd
51\302 (202.649¢)
Consistency limit
3
Distinct consistency limit
3
| ← 301edo | 302edo | 303edo → |
302 equal divisions of the octave (abbreviated 302edo or 302ed2), also called 302-tone equal temperament (302tet) or 302 equal temperament (302et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 302 equal parts of about 3.97 ¢ each. Each step represents a frequency ratio of 21/302, or the 302nd root of 2.
It is part of the optimal ET sequence for the quinticosiennic, semisept (23-lim), sensawer and shibboleth temperaments.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.36 | -0.88 | +0.71 | -1.26 | +1.00 | +1.86 | +0.47 | -1.64 | +0.50 | -1.91 | -0.46 |
| Relative (%) | +34.1 | -22.2 | +17.9 | -31.7 | +25.2 | +46.7 | +11.9 | -41.4 | +12.6 | -48.0 | -11.6 | |
| Steps (reduced) |
479 (177) |
701 (97) |
848 (244) |
957 (51) |
1045 (139) |
1118 (212) |
1180 (274) |
1234 (26) |
1283 (75) |
1326 (118) |
1366 (158) | |
Subsets and supersets
Since 302 factors into 2 × 151, 302edo has 2edo and 151edo as its subsets. 906edo, which triples it, gives a good correction to the harmonic 3.
Interval table
See Table of 302edo intervals.
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