Francium: typo

2024-11-22T16:17:34Z

typo

← Older revision		Revision as of 16:17, 22 November 2024
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	'''10693/10692''', the '''zangarisma''', is a [[37-limit]] [[superparticular interval\|superparticular comma}} of about 0.16 [[cent]]s.		'''10693/10692''', the '''zangarisma''', is a [[37-limit]] [[superparticular interval\|superparticular comma]] of about 0.16 [[cent]]s.

	== Commatic relationships ==		== Commatic relationships ==

Francium: Created page with "{{Infobox Interval | Ratio = 10693/10692 | Name = Zangarisma | Color name = 37o17oo1u3
thisososolu 3rd | Comma = yes }} '''10693/10692''', the '''zangarisma''', is a 3..."

2024-11-22T16:15:17Z

Created page with "{{Infobox Interval | Ratio = 10693/10692 | Name = Zangarisma | Color name = 37o17oo1u3 <br> thisososolu 3rd | Comma = yes }} '''10693/10692''', the '''zangarisma''', is a 3..."

New page

{{Infobox Interval
| Ratio = 10693/10692
| Name = Zangarisma
| Color name = 37o17oo1u3 <br> thisososolu 3rd
| Comma = yes
}}

'''10693/10692''', the '''zangarisma''', is a [[37-limit]] [[superparticular interval|superparticular comma}} of about 0.16 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular ratios:
* [[289/288]] and [[297/296]]
* [[1156/1155]] and [[1296/1295]]
* [[3367/3366]] and [[4914/4913]]
* [[3774/3773]] and [[5832/5831]]

It can be factored into following superparticular commas:
* [[11271/11270]] and [[208495/208494]]
* [[11914/11913]] and [[104329/104328]]
* [[12376/12375]] and [[78625/78624]]
* [[18241/18240]] and [[25840/25839]]
* [[19684/19683]] and [[23409/23408]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''zangarismic'''. Using the 2.3.11.17.37 subgroup leads to the rank-4 temperament '''zangaric'''.

=== Zangarismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]: 10693/10692

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 2 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 5 || ],
|-
| ⟨ || 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 || -2 || ],
|-
| ⟨ || 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 = 701.967, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.329, ~13/8 = 840.528, ~17/16 = 104.923, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

=== Zangaric ===

[[Subgroup]]: 2.3.11.17.37

[[Comma list]]: 10693/10692

[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 1 || 3 || 4 || 2 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 5 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || -2 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.967, ~11/8 = 551.329, ~17/16 = 104.923

{{Optimal ET sequence|legend=1| 5eg, 8ll, 9g, 10e, 10l, 12el, 14l, 21eg, 22, 24, 111, 135, 159, 183, 207, 253, 277, 328, 352, 376, 535, 559, 583, 605, 629, 764, 788, 812, 1648, 2000, 2024, 2812, 2836, 3672, 6508 }}

== Etymology ==
This comma was named by [[Francium]] in 2024. It refers to {{W|10693 Zangari}}, the asteroid, which in turn was named after a postdoctoral researcher.

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

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

Zangarisma - Revision history

Francium: typo

Francium: Created page with "{{Infobox Interval | Ratio = 10693/10692 | Name = Zangarisma | Color name = 37o17oo1u3 thisososolu 3rd | Comma = yes }} '''10693/10692''', the '''zangarisma''', is a 3..."

Francium: Created page with "{{Infobox Interval | Ratio = 10693/10692 | Name = Zangarisma | Color name = 37o17oo1u3
thisososolu 3rd | Comma = yes }} '''10693/10692''', the '''zangarisma''', is a 3..."