Borcherdsma - Revision history

Overthink: proving this

2026-01-27T04:36:11Z

proving this

← Older revision		Revision as of 04:36, 27 January 2026
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	(The last two edos are taken from the list of [[minimal consistent edos]].)		(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 by patent val is not known, although it is known to be above 6.61 × 10<sup>11</sup>. It is also known to be below 9.46 × 10<sup>11</sup>, as beyond that, a prime would need to have 50% or more relative error in order to map the comma to 0 steps. This is because the sum of the absolute values of the monzo entries for primes greater than 2 is 17, so there must be some prime with an absolute error at least 1/17th this commas size, or around 6.343 × 10<sup>-10</sup>{{C}}, and the largest EDO where this is less than half the step size is around 9.459 × 10<sup>11</sup>.

	[[Category: Superparticular ratios]]		[[Category: Superparticular ratios]]
	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]

Godtone: silly wording, also idk what "distinct odd-consistency-limit" is but it appears to be an idiosyncratic term made up on the fly

2025-02-10T21:14:42Z

silly wording, also idk what "distinct odd-consistency-limit" is but it appears to be an idiosyncratic term made up on the fly

← Older revision		Revision as of 21:14, 10 February 2025
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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~~. 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~~.		[[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 ~~with~~ [[distinctly consistent~~\|distinct~~ odd~~-consistency~~-limit~~]] 79~~ (and also all the way to 131)		[[2901533edo]] - the minimal edo [[distinctly consistent]] in the 79-odd-limit (and also all the way to 131-odd-limit).

	[[70910024edo]] - the minimal edo ~~with distinct~~ odd~~-consistency~~-limit ~~133~~ (~~and also 135~~)		[[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>.

BudjarnLambeth at 02:22, 4 November 2024

2024-11-04T02:22:33Z

← Older revision		Revision as of 02:22, 4 November 2024
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	[[Category: Superparticular ratios]]		[[Category: Superparticular ratios]]
	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after mathematicians]]

BudjarnLambeth at 09:05, 3 November 2024

2024-11-03T09:05:49Z

← Older revision		Revision as of 09:05, 3 November 2024
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	[[Category: Superparticular ratios]]		[[Category: Superparticular ratios]]
			[[Category:Commas named after individuals]]

Akselai: 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 = 71u59u³47o31o29o19o3u1uury<..."

2024-03-29T16:53:12Z

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 = 71u59u347o31o29o19o3u1uury<..."

New page

{{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 = 71u59u347o31o29o19o3u1uury5-2
}}

'''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 {{w|Supersingular prime (moonshine theory)|supersingular prime}}s - primes dividing the order of the {{w|monster group}}.

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:

[[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 [[distinctly consistent|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.

[[Category: Superparticular ratios]]

Borcherdsma - Revision history

Overthink: proving this

Godtone: silly wording, also idk what "distinct odd-consistency-limit" is but it appears to be an idiosyncratic term made up on the fly

BudjarnLambeth at 02:22, 4 November 2024

BudjarnLambeth at 09:05, 3 November 2024

Akselai: 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 = 71u59u347o31o29o19o3u1uury<..."

Akselai: 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 = 71u59u³47o31o29o19o3u1uury<..."