FloraC: FloraC moved page Megumisma to 3774/3773 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:21:26Z

FloraC moved page Megumisma to 3774/3773 over redirect: 8-digit ratios are okay as page titles

← Older revision	Revision as of 14:21, 7 January 2025
(No difference)

Francium: Created page with "{{Infobox Interval | Ratio = 3774/3773 | Name = megumisma | Color name = 37o17o1ur³1
thisosolutriru unison | Comma = yes }} '''3774/3773''', the '''megumisma'..."

2025-01-01T19:15:59Z

Created page with "{{Infobox Interval | Ratio = 3774/3773 | Name = megumisma | Color name = 37o17o1ur31 thisosolutriru unison | Comma = yes }} '''3774/3773''', the '''megumisma'..."

New page

{{Infobox Interval
| Ratio = 3774/3773
| Name = megumisma
| Color name = 37o17o1ur31 thisosolutriru unison
| Comma = yes
}}

'''3774/3773''', the '''megumisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.46 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[148/147]] and [[154/153]]
* [[925/924]] and [[1225/1224]]
* [[1275/1274]] and [[1925/1924]]
* [[1332/1331]] and [[2058/2057]]

It can be factored into the following superparticular ratios:
* [[3876/3875]] and [[143375/143374]]
* [[5083/5082]] and [[14652/14651]]
* [[5832/5831]] and [[10693/10692]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''megumismic'''. Using the 2.3.7.11.17.37 subgroup leads to the rank-5 temperament '''megumic'''.

=== Megumismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]: 3774/3773

[[Mapping]]: 
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 3 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 3 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ],
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.946, ~5/4 = 386.314, ~7/4 = 968.910, ~11/8 = 551.360, ~13/8 = 840.528, ~17/16 = 104.896, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

=== Megumic ===

[[Subgroup]]: 2.3.7.11.17.37

[[Comma list]]: 3774/3773

[[Mapping]]: 
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 3 || 4 || 3 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 3 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || -1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.946, ~7/4 = 968.910, ~11/8 = 551.360, ~17/16 = 104.896

{{Optimal ET sequence|legend=1| 5, 9g, 10, 14l, 17g, 22, 31, 32, 36el, 46l, 53, 55gl, 58l, 63, 72, 121l, 135, 193l, 207, 328, 400, 535, 607, 629, 764, 836, 1371, 2000, 2207, 2607, 3443, 5650 }}

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|3774 Megumi}}, the asteroid, which in turn was named after Megumi, the wife of Japanese astronomer {{W|Takuo Kojima}} who discovered the asteroid.

== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]

[[Category:Commas named after asteroids]]
[[Category:Commas named after individuals]]

3774/3773 - Revision history

FloraC: FloraC moved page Megumisma to 3774/3773 over redirect: 8-digit ratios are okay as page titles

Francium: Created page with "{{Infobox Interval | Ratio = 3774/3773 | Name = megumisma | Color name = 37o17o1ur31 thisosolutriru unison | Comma = yes }} '''3774/3773''', the '''megumisma'..."

Francium: Created page with "{{Infobox Interval | Ratio = 3774/3773 | Name = megumisma | Color name = 37o17o1ur³1
thisosolutriru unison | Comma = yes }} '''3774/3773''', the '''megumisma'..."