12348edo
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Prime factorization
22 × 32 × 73
Step size
0.0971817¢
Fifth
7223\12348 (701.944¢)
Semitones (A1:m2)
1169:929 (113.6¢ : 90.28¢)
Consistency limit
41
Distinct consistency limit
41
| ← 12347edo | 12348edo | 12349edo → |
12348 equal divisions of the octave (abbreviated 12348edo or 12348ed2), also called 12348-tone equal temperament (12348tet) or 12348 equal temperament (12348et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 12348 equal parts of about 0.0972 ¢ each. Each step represents a frequency ratio of 21/12348, or the 12348th root of 2.. It is a remarkable very high-limit equal temperament, consistent through the 41-odd-limit distinctly, tempering out 17205/17204, 25025/25024, 28861/28860, 44955/44954, 47125/47124, 52326/52325, 83657/83655, 89376/89375, 866133/866125, 1183455/1183424, 1843155/1843072, and 4629625/4629474.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0114 | -0.0163 | -0.0212 | -0.0060 | -0.0029 | +0.0009 | -0.0397 | +0.0055 | -0.0339 | -0.0404 |
| Relative (%) | +0.0 | -11.7 | -16.8 | -21.9 | -6.2 | -3.0 | +0.9 | -40.9 | +5.7 | -34.9 | -41.6 | |
| Steps (reduced) |
12348 (0) |
19571 (7223) |
28671 (3975) |
34665 (9969) |
42717 (5673) |
45693 (8649) |
50472 (1080) |
52453 (3061) |
55857 (6465) |
59986 (10594) |
61174 (11782) | |