FloraC: FloraC moved page Meranisma to 3553/3552 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:21:53Z

FloraC moved page Meranisma to 3553/3552 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 = 3553/3552 | Name = meranisma | Color name = 37u19o17o1o1
thisunosolo unison | Comma = yes }} '''3553/3552''', the '''meranisma''', is a 37..."

2024-12-20T11:18:08Z

Created page with "{{Infobox Interval | Ratio = 3553/3552 | Name = meranisma | Color name = 37u19o17o1o1 <br> thisunosolo unison | Comma = yes }} '''3553/3552''', the '''meranisma''', is a 37..."

New page

{{Infobox Interval
| Ratio = 3553/3552
| Name = meranisma
| Color name = 37u19o17o1o1 <br> thisunosolo unison
| Comma = yes
}}

'''3553/3552''', the '''meranisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.49 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[209/208]] and [[222/221]]
* [[297/296]] and [[324/323]]
* [[741/740]] and [[936/935]]
* [[969/968]] and [[1332/1331]]
* [[1444/1443]] and [[2432/2431]]
* [[1666/1665]] and [[3136/3135]]

It can be factored into the following superparticular ratios:
* [[3565/3564]] and [[1055241/1055240]]
* [[3876/3875]] and [[42625/42624]]
* [[4256/4255]] and [[21505/21504]]
* [[5440/5439]] and [[10241/10240]]
* [[5797/5796]] and [[9177/9176]]
* [[7105/7104]] and [[7106/7105]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''meranismic'''. Using the 2.3.11.17.19.37 subgroup leads to the rank-5 temperament '''meranic'''.

=== Meranismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29

[[Comma list]]: 3553/3552

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 5 || ],
|-
| ⟨ || 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 || 0 || ],
|-
| ⟨ || 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 || 1 || ],
|-
| ⟨ || 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 = 701.971, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.242, ~13/8 = 840.528, ~17/16 = 104.849, ~19/16 = 297.398, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

=== Meranic ===

[[Subgroup]]: 2.3.11.17.19.37

[[Comma list]]: 3553/3552

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 3 || 4 || 4 || 5 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.971, ~11/8 = 551.242, ~17/16 = 104.849, ~19/16 = 297.398

{{Optimal ET sequence|legend=1| 5ll, 5g, 7ghll, 7g, 8, 9, 10, 10hl, 12el, 14l, 17l, 17g, 22l, 22h, 24, 89, 104, 113, 128, 137, 152, 157, 159, 169l, 181, 183, 205, 207, 231, 311, 335, 388, 400, 412, 436, 525, 581, 605, 629, 836, 860, 1465, 1489, 2325, 3390, 3814gh, 4226egh, 4250egh, 5715egh }}

== Etymology ==
This comma was named by [[Francium]] in 2024. It refers to {{W|3553 Mera}}, the asteroid, which in turn was named after Maera, a daughter of {{W|Praetus}}.

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

[[Category:Commas named after asteroids]]

3553/3552 - Revision history

FloraC: FloraC moved page Meranisma to 3553/3552 over redirect: 8-digit ratios are okay as page titles

Francium: Created page with "{{Infobox Interval | Ratio = 3553/3552 | Name = meranisma | Color name = 37u19o17o1o1 thisunosolo unison | Comma = yes }} '''3553/3552''', the '''meranisma''', is a 37..."

Francium: Created page with "{{Infobox Interval | Ratio = 3553/3552 | Name = meranisma | Color name = 37u19o17o1o1
thisunosolo unison | Comma = yes }} '''3553/3552''', the '''meranisma''', is a 37..."