18355edo: Difference between revisions
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{{Infobox ET}} | |||
{{ | {{ED intro}} It is an extremely strong 7-limit system, with a lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until [[84814edo|84814]], and a lower [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any besides [[171edo|171]] and [[3125edo|3125]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|18355|prec=4}} | {{Harmonics in equal|18355|prec=4}} | ||
Latest revision as of 14:08, 20 February 2025
| ← 18354edo | 18355edo | 18356edo → |
18355 equal divisions of the octave (abbreviated 18355edo or 18355ed2), also called 18355-tone equal temperament (18355tet) or 18355 equal temperament (18355et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 18355 equal parts of about 0.0654 ¢ each. Each step represents a frequency ratio of 21/18355, or the 18355th root of 2. It is an extremely strong 7-limit system, with a lower relative error than any division until 84814, and a lower TE logflat badness than any besides 171 and 3125.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0009 | +0.0006 | +0.0000 | +0.0087 | +0.0280 | -0.0249 | +0.0190 | +0.0013 | -0.0158 | -0.0179 |
| Relative (%) | +0.0 | +1.3 | +1.0 | +0.0 | +13.3 | +42.9 | -38.0 | +29.0 | +2.0 | -24.1 | -27.3 | |
| Steps (reduced) |
18355 (0) |
29092 (10737) |
42619 (5909) |
51529 (14819) |
63498 (8433) |
67922 (12857) |
75025 (1605) |
77971 (4551) |
83030 (9610) |
89168 (15748) |
90934 (17514) | |