155edo: Difference between revisions
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[[ | 155edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 42 -25 -1 }} in the 5-limit; [[245/243]], [[3136/3125]], and 823543/819200 in the 7-limit, supporting [[clyde]]. 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 === | |||
{{Harmonics in equal|155}} | |||
=== Subsets and supersets === | |||
Since 155 factors into {{factorization|155}}, 155edo contains [[5edo]] and [[31edo]] as subsets. | |||
Latest revision as of 15:32, 18 March 2025
| ← 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, supporting clyde. 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.