FloraC: FloraC moved page Gabisma to 1665/1664 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:19:48Z

FloraC moved page Gabisma to 1665/1664 over redirect: 8-digit ratios are okay as page titles

← Older revision	Revision as of 14:19, 7 January 2025
(No difference)

Francium: Created page with "{{Infobox Interval | Ratio = 1665/1664 | Name = gabisma | Color name = 37o3uy1
thisothuyo unison | Comma = yes }} '''1665/1664''', the '''gabisma''', is a 37-limit [..."

2025-01-02T21:03:16Z

Created page with "{{Infobox Interval | Ratio = 1665/1664 | Name = gabisma | Color name = 37o3uy1 <br> thisothuyo unison | Comma = yes }} '''1665/1664''', the '''gabisma''', is a 37-limit [..."

New page

{{Infobox Interval
| Ratio = 1665/1664
| Name = gabisma
| Color name = 37o3uy1 <br> thisothuyo unison
| Comma = yes
}}

'''1665/1664''', the '''gabisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 1.0 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[105/104]] and [[112/111]]
* [[225/224]] and [[260/259]]
* [[481/480]] and [[676/675]]
* [[495/494]] and [[704/703]]
* [[729/728]] and [[1296/1295]]

It can be factored into the following superparticular intervals:
* [[1683/1682]] and [[155585/155584]]
* [[1701/1700]] and [[78625/78624]]
* [[1702/1701]] and [[76545/76544]]
* [[1729/1728]] and [[44955/44954]]
* [[1860/1859]] and [[15873/15872]]
* [[1925/1924]] and [[12321/12320]]
* [[2025/2024]] and [[9361/9360]]
* [[2109/2108]] and [[7905/7904]]
* [[2146/2145]] and [[7425/7424]]
* [[2185/2184]] and [[6993/6992]]
* [[2553/2552]] and [[4785/4784]]
* [[2601/2600]] and [[4625/4624]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''gabismic'''. Using the 2.3.5.13.37 subgroup leads to the rank-4 temperament '''gabic'''.

=== Gabismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]. 1665/1664

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 6 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -2 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 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 || 1 || ],
|-
| ⟨ || 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 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.862, ~5/4 = 386.214, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.781, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

=== Gabic ===

[[Subgroup]]: 2.3.5.13.37

[[Comma list]]: 1665/1664

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 3 || 6 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || -2 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.862, ~5/4 = 386.214, ~13/8 = 840.781

{{Optimal ET sequence|legend=1| 5, 7f, 7l, 9, 10, 12l, 12f, 15, 19, 34, 53, 171, 224, 277, 354, 407, 631, 684, 1038, 1091l, 1532l, 1756l, 1809l, 2163ll, 2216ll }}

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|1665 Gaby}}, the asteroid, which in turn was named after Gaby Reinmuth, the daughter-in-law of discoverer {{W|Karl Wilhelm Reinmuth}}.

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

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

1665/1664 - Revision history

FloraC: FloraC moved page Gabisma to 1665/1664 over redirect: 8-digit ratios are okay as page titles

Francium: Created page with "{{Infobox Interval | Ratio = 1665/1664 | Name = gabisma | Color name = 37o3uy1 thisothuyo unison | Comma = yes }} '''1665/1664''', the '''gabisma''', is a 37-limit [..."

Francium: Created page with "{{Infobox Interval | Ratio = 1665/1664 | Name = gabisma | Color name = 37o3uy1
thisothuyo unison | Comma = yes }} '''1665/1664''', the '''gabisma''', is a 37-limit [..."