FloraC: FloraC moved page Polishookisma to 8464/8463 over redirect: 8-digit ratios are okay as page titles

2025-01-07T14:22:25Z

FloraC moved page Polishookisma to 8464/8463 over redirect: 8-digit ratios are okay as page titles

← Older revision	Revision as of 14:22, 7 January 2025
(No difference)

Francium: Created page with "{{Infobox Interval | Ratio = 8464/8463 | Name = Polishookisma | Color name = 31u23oo3ur2
thiwubitwetho-athuru 2nd | Comma = yes }} '''8464/8463''', the '''polishookisma'..."

2024-12-18T17:10:05Z

Created page with "{{Infobox Interval | Ratio = 8464/8463 | Name = Polishookisma | Color name = 31u23oo3ur2 <br> thiwubitwetho-athuru 2nd | Comma = yes }} '''8464/8463''', the '''polishookisma'..."

New page

{{Infobox Interval
| Ratio = 8464/8463
| Name = Polishookisma
| Color name = 31u23oo3ur2 <br> thiwubitwetho-athuru 2nd
| Comma = yes
}}

'''8464/8463''', the '''polishookisma''', is a [[31-limit]] [[superparticular interval|superparticular comma]] of about 0.20 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[92/91]] and [[93/92]]
* [[736/735]] and [[806/805]]
* [[1288/1287]] and [[1519/1518]]
* [[2016/2015]] and [[2646/2645]]
* [[2185/2184]] and [[2945/2944]]
* [[4096/4095]] and [[7936/7935]]
* [[4186/4185]] and [[8281/8280]]

It can be factored into the following superparticular ratios:
* [[8625/8624]] and [[453376/453375]]
* [[8960/8959]] and [[152881/152880]]
* [[10557/10556]] and [[42688/42687]]
* [[10648/10647]] and [[41262/41261]]
* [[13300/13299]] and [[23276/23275]]

== Temperaments ==
Tempering out this comma in the full 31-limit leads to the rank-10 temperament '''polishookismic'''. Using the 2.3.7.13.23.31 subgroup leads to the rank-5 temperament '''polishookic'''.

=== Polishookismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.23.29.31

[[Comma list]]: 8464/8463

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.959, ~5/4 = 386.314, ~7/4 = 968.838, ~11/8 = 551.318, ~13/8 = 840.549, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.210, ~29/16 = 1029.577

=== Polishookic ===

[[Subgroup]]: 2.3.7.13.23.31

[[Comma list]]: 8464/8463

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.959, ~7/4 = 968.838, ~13/8 = 840.549, ~23/16 = 628.210

{{Optimal ET sequence|legend=1| 5fik, 5, 7, 9ik, 10k, 12, 12fik, 14, 17, 29, 31k, 36k, 45fi, 46, 53, 63, 77, 113, 130, 311, 436, 441, 571, 1335, 1470, 1525, 1600, 1776, 1853, 1983, 2424, 2554, 3125, 5679, 6884, 7455, 10009 }}

== Etymology ==
This comma was named by [[Francium]] in 2024. It refers to {{W|8464 Polishook}}, the asteroid, which in turn was named after {{W|David Polishook}}, an Israeli astronomer.

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

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

8464/8463 - Revision history

FloraC: FloraC moved page Polishookisma to 8464/8463 over redirect: 8-digit ratios are okay as page titles

Francium: Created page with "{{Infobox Interval | Ratio = 8464/8463 | Name = Polishookisma | Color name = 31u23oo3ur2 thiwubitwetho-athuru 2nd | Comma = yes }} '''8464/8463''', the '''polishookisma'..."

Francium: Created page with "{{Infobox Interval | Ratio = 8464/8463 | Name = Polishookisma | Color name = 31u23oo3ur2
thiwubitwetho-athuru 2nd | Comma = yes }} '''8464/8463''', the '''polishookisma'..."