Borcherdsma

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Interval information

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	1.078284e-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.