Borcherdsma
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| Factorization | 26 × 55 × 7-1 × 11-2 × 13-1 × 19 × 29 × 31 × 47 × 59-3 × 71-1 |
| Monzo | [6 0 5 -1 -2 -1 0 1 0 1 1 0 0 0 1 0 -3 0 0 -1⟩ |
| Size in cents | 1.0782841e-08¢ |
| Name | borcherdsma |
| Color name | 71u59u347o31o29o19o3u1uury5-2 |
| FJS name | [math]\text{d}{-2}^{5,5,5,5,5,19,29,31,47}_{7,11,11,13,59,59,59,71}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 74.4487 |
| Weil height (log2 max(n, d)) | 74.4487 |
| Wilson height (sopfr(nd)) | 453 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19982 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
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 include:
6edo - the smallest edo that does so. Although 6p does indeed temper the borcherdsma with its patent val, there's a lot of doubt whether one would seriously use it to tune the 71-limit.
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 with distinct odd-consistency-limit 79 (and also all the way to 131)
70910024edo - the minimal edo with distinct odd-consistency-limit 133 (and also 135)
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.