Borcherdsma: Difference between revisions
Created page with "{{Novelty}} {{Infobox Interval | Name = borcherdsma | Monzo = 6 0 5 -1 -2 -1 0 1 0 1 1 0 0 0 1 0 -3 0 0 -1 | Comma = yes | Color name = 71u59u<sup>3</sup>47o31o29o19o3u1uury<..." |
m silly wording, also idk what "distinct odd-consistency-limit" is but it appears to be an idiosyncratic term made up on the fly |
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It is named after the Fields medalist mathematician {{w|Richard Borcherds}}, in reference to his contributions in the theory of the {{w|monstrous moonshine}}. | It is named after the Fields medalist mathematician {{w|Richard Borcherds}}, in reference to his contributions in the theory of the {{w|monstrous moonshine}}. | ||
Notable [[edo]]s that temper it out include: | Notable [[edo]]s that temper it out by [[patent val]] include: | ||
[[6edo]] - the smallest edo that does so | [[6edo]] - the smallest edo that does so. | ||
[[7edo]] - the second smallest edo that does so. 7edo is a [[strict zeta edo]], but that's not a lot of progress from 6edo yet. | [[7edo]] - the second smallest edo that does so. 7edo is a [[strict zeta edo]], but that's not a lot of progress from 6edo yet. | ||
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[[8539edo]] - the third strict zeta edo that does so. | [[8539edo]] - the third strict zeta edo that does so. | ||
[[2901533edo]] - the minimal edo | [[2901533edo]] - the minimal edo [[distinctly consistent]] in the 79-odd-limit (and also all the way to 131-odd-limit). | ||
[[70910024edo]] - the minimal edo | [[70910024edo]] - the minimal edo [[distinctly consistent]] in the 133- and 135-odd-limit. | ||
(The last two edos are taken from the list of [[minimal consistent edos]].) | |||
The largest edo to temper out the borcherdsma is not known, although it is known to be above 6.61 × 10<sup>11</sup> and conjectured to be below 10<sup>12</sup>. | The largest edo to temper out the borcherdsma is not known, although it is known to be above 6.61 × 10<sup>11</sup> and conjectured to be below 10<sup>12</sup>. | ||
[[Category: Superparticular ratios]] | [[Category: Superparticular ratios]] | ||
[[Category:Commas named after mathematicians]] | |||
Latest revision as of 21:14, 10 February 2025
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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. |
| Interval information |
160561400000/160561399999, the borcherdsma, is a 71-limit superparticular comma, measuring 1.078 × 10-8 cents. It is the smallest superparticular interval in the 2.3.5.7.11.13.17.19.23.29.31.41.47.59.71 subgroup, which consists of all the supersingular primes - primes dividing the order of the monster group.
It is named after the Fields medalist mathematician Richard Borcherds, in reference to his contributions in the theory of the monstrous moonshine.
Notable edos that temper it out by patent val include:
6edo - the smallest edo that does so.
7edo - the second smallest edo that does so. 7edo is a strict zeta edo, but that's not a lot of progress from 6edo yet.
1578edo - the second strict zeta edo that does so, after 7edo.
8539edo - the third strict zeta edo that does so.
2901533edo - the minimal edo distinctly consistent in the 79-odd-limit (and also all the way to 131-odd-limit).
70910024edo - the minimal edo distinctly consistent in the 133- and 135-odd-limit.
(The last two edos are taken from the list of minimal consistent edos.)
The largest edo to temper out the borcherdsma is not known, although it is known to be above 6.61 × 1011 and conjectured to be below 1012.