BudjarnLambeth at 10:05, 3 November 2024

2024-11-03T10:05:49Z

← Older revision		Revision as of 10:05, 3 November 2024
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Commas named after ~~postal codes~~]]		[[Category:Commas named after place names]]

BudjarnLambeth at 08:39, 3 November 2024

2024-11-03T08:39:57Z

← Older revision		Revision as of 08:39, 3 November 2024
Line 96:		Line 96:
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			[[Category:Commas named after postal codes]]

Francium: Created page with "{{Infobox Interval | Ratio = 9361/9360 | Name = friesachisma | Color name = 37o23o3u1og2
thisotwethothulogu 2nd | Comma = yes }} '''9361/9360''', the '''friesachisma''',..."

2024-10-18T13:42:21Z

Created page with "{{Infobox Interval | Ratio = 9361/9360 | Name = friesachisma | Color name = 37o23o3u1og2 <br> thisotwethothulogu 2nd | Comma = yes }} '''9361/9360''', the '''friesachisma''',..."

New page

{{Infobox Interval
| Ratio = 9361/9360
| Name = friesachisma
| Color name = 37o23o3u1og2 <br> thisotwethothulogu 2nd
| Comma = yes
}}

'''9361/9360''', the '''friesachisma''', is a [[37-limit]] [[superparticular ratio|superparticular comma]] of about 0.18 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[253/252]] and [[260/259]]
* [[391/390]] and [[408/407]]
* [[3381/3380]] and [[5292/5291]]

It can be factored into the following superparticular intervals:
* [[9801/9800]] and [[208495/208494]]
* [[10241/10240]] and [[108928/108927]]
* [[10557/10556]] and [[82621/82620]]
* [[10626/10625]] and [[78625/78624]]
* [[10648/10647]] and [[77441/77440]]
* [[10693/10692]] and [[75141/75140]]
* [[11914/11913]] and [[43681/43680]]
* [[12673/12672]] and [[35816/35815]]
* [[14652/14651]] and [[25921/25920]]
* [[16576/16575]] and [[21505/21504]]
* [[18241/18240]] and [[19228/19227]]

== Temperaments ==
Tempering out this comma leads to the rank-11 temperament '''friesachismic'''. Using the 2.3.5.11.13.23.37 subgroup leads to the rank-6 temperament '''friesachic'''.

=== Friesachismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37

[[Comma list]]: 9361/9360

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 4 || ],
|-
| ⟨ || 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 || -1 || ],
|-
| ⟨ || 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 || -1 || ],
|-
| ⟨ || 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 = 701.965, ~5/4 = 386.325, ~7/4 = 968.826, ~11/8 = 551.293, ~13/8 = 840.556, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.232, ~29/16 = 1029.577, ~31/16 = 1145.036

{{Optimal ET sequence|legend=1| 5cfik, 5egj, 5eghj, 6fhijl, 7dfghijjk, 8di, 9gijk, 10jk, 10k, 10, 10h, 12l, 12fk, 12fjk, 14cfjjkkl, 14cfjjl, 15gkl, 16j, 17cgk, 17cghk, 19egh, 21, 22i, 22fh, 24, 26ik, 29gjk, 29gk, 31fghjk, 31l, 34dhk, 38dfij, 39dfgijkl, 46, 50jk, 50k, 53, 53j, 58hik, 62, 65d, 68jl, 72hijk, 72ijk, 80, 80k, 94, 99efk, 103hl, 125f, 130j, 145jkl, 149, 152fgj, 159k, 181, 183k, 183, 198gl, 212ghj, 212gh, 217, 224, 239, 243e, 248h, 270, 311k, 311, 422l, 487, 525, 566gjl, 571, 597ik, 631, 639hj, 692ik, 718, 764j, 764hj, 814k, 814, 863efgjk, 882, 908, 1012, 1106, 1164fi, … }}

=== Friesachic ===

[[Subgroup]]: 2.3.5.11.13.23.37

[[Comma list]]: 9361/9360

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

[[Optimal tuning]] ([[CTE]]): ~2=1\1, ~3/2 = 701.965, ~5/4 = 386.325, ~11/8 = 551.293, ~13/8 = 840.556, ~23/16 = 628.232

{{Optimal ET sequence|legend=1| 5e, 7fi, 7, 8i, 10, 12l, 12f, 14cfl, 15l, 19e, 22i, 22f, 24, 29, 34, 46, 50, 53, 65, 79l, 80, 87, 96, 118, 125f, 130, 152f, 159, 183, 224, 277, 357, 407, 684, 764, 988, 1012, 1171, 1448, 1696, 1855l, 2000, 2277, 2684, 5144, 6132, 7828l, 8816il, 9828il, 10512eil }}

== Etymology ==
The friesachisma was named by [[Francium]] in 2024, referencing the postal code of {{W|Friesach}}, Austria.

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

Friesachisma - Revision history

BudjarnLambeth at 10:05, 3 November 2024

BudjarnLambeth at 08:39, 3 November 2024

Francium: Created page with "{{Infobox Interval | Ratio = 9361/9360 | Name = friesachisma | Color name = 37o23o3u1og2 thisotwethothulogu 2nd | Comma = yes }} '''9361/9360''', the '''friesachisma''',..."

Francium: Created page with "{{Infobox Interval | Ratio = 9361/9360 | Name = friesachisma | Color name = 37o23o3u1og2
thisotwethothulogu 2nd | Comma = yes }} '''9361/9360''', the '''friesachisma''',..."