238edo
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Prime factorization
2 × 7 × 17
Step size
5.04202¢
Fifth
139\238 (700.84¢)
Semitones (A1:m2)
21:19 (105.9¢ : 95.8¢)
Consistency limit
3
Distinct consistency limit
3
| ← 237edo | 238edo | 239edo → |
238 equal divisions of the octave (abbreviated 238edo or 238ed2), also called 238-tone equal temperament (238tet) or 238 equal temperament (238et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 238 equal parts of about 5.04 ¢ each. Each step represents a frequency ratio of 21/238, or the 238th root of 2.
It is part of the optimal ET sequence for the apotropaia, enodia, fantastic, gizzard, gracecordial, hecate, marvel, marvell, vines and wizard temperaments.
Theory
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.11 | +1.92 | -0.76 | -1.74 | +1.49 | +0.93 | -0.03 | +1.98 | -1.01 | -0.50 |
| Relative (%) | +0.0 | -22.1 | +38.1 | -15.0 | -34.5 | +29.5 | +18.4 | -0.7 | +39.2 | -19.9 | -9.9 | |
| Steps (reduced) |
238 (0) |
377 (139) |
553 (77) |
668 (192) |
823 (109) |
881 (167) |
973 (21) |
1011 (59) |
1077 (125) |
1156 (204) |
1179 (227) | |
Intervals
See Table of 238edo intervals.
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