31867edo: Difference between revisions
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{{Infobox ET}} | {{novelty}}{{stub}}{{Infobox ET}} | ||
{{EDO intro|31867}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed. | {{EDO intro|31867}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed. | ||
Revision as of 04:09, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
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(convergent)
Template:EDO intro It is the denominator of the next convergent for log23 past 15601, before 79335, and has a fifth which is about 0.00000039 cents compressed.
31867edo is consistent through the 21-odd-limit, tempering out [305 -106 -59⟩ and [-122 285 -142⟩ in the 5-limit; [-7 30 -9 -7⟩, [51 -13 -1 -10⟩, and [-8 2 -62 53⟩ in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; 123201/123200, 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0000 | +0.0044 | +0.0008 | +0.0110 | +0.0033 | -0.0067 | +0.0111 | -0.0131 | -0.0106 | -0.0141 |
| Relative (%) | +0.0 | -0.0 | +11.7 | +2.1 | +29.3 | +8.8 | -17.8 | +29.4 | -34.9 | -28.0 | -37.4 | |
| Steps (reduced) |
31867 (0) |
50508 (18641) |
73993 (10259) |
89462 (25728) |
110242 (14641) |
117922 (22321) |
130255 (2787) |
135369 (7901) |
144152 (16684) |
154809 (27341) |
157875 (30407) | |