155edo
| ← 154edo | 155edo | 156edo → |
155 equal divisions of the octave (abbreviated 155edo or 155ed2), also called 155-tone equal temperament (155tet) or 155 equal temperament (155et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 155 equal parts of about 7.74 ¢ each. Each step represents a frequency ratio of 21/155, or the 155th root of 2.
155edo is closely related to 31edo, but the patent vals differ on the mapping for 3. The equal temperament tempers out 15625/15552 (kleisma) and [42 -25 -1⟩ in the 5-limit; 245/243, 3136/3125, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 385/384, 896/891, 1331/1323, and 3773/3750 in the 11-limit; 196/195, 325/324, 625/624, and 1001/1000 in the 13-limit.
155edo is additionally notable for having an extremely precise (about 0.0006 cents sharp) approximation of 15/13, being the denominator of a convergent to its logarithm, the last one before 8743edo, having 28-strong telicity for this interval.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.56 | +0.78 | -1.08 | -2.62 | -1.64 | +3.34 | +3.34 | +3.43 | -3.32 | +1.48 | -1.18 |
| Relative (%) | +33.1 | +10.1 | -14.0 | -33.8 | -21.2 | +43.2 | +43.2 | +44.3 | -42.9 | +19.1 | -15.2 | |
| Steps (reduced) |
246 (91) |
360 (50) |
435 (125) |
491 (26) |
536 (71) |
574 (109) |
606 (141) |
634 (14) |
658 (38) |
681 (61) |
701 (81) | |
Subsets and supersets
Since 155 factors into 5 × 31, 155edo contains 5edo and 31edo as subsets.