BudjarnLambeth at 01:42, 4 November 2024

2024-11-04T01:42:40Z

← Older revision		Revision as of 01:42, 4 November 2024
Line 83:		Line 83:

	== Etymology ==		== Etymology ==
	The name ''girardisma'' was named by [[Francium]] in 2024. It refers to [[Wikipedia:10450 Girard\|10450 Girard]], the asteroid.		The name ''girardisma'' was named by [[Francium]] in 2024. It refers to [[Wikipedia:10450 Girard\|10450 Girard]], the asteroid. Which was in turn named after an American astronomer.

	== See also ==		== See also ==
Line 90:		Line 90:

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

BudjarnLambeth at 08:38, 3 November 2024

2024-11-03T08:38:32Z

← Older revision		Revision as of 08:38, 3 November 2024
Line 88:		Line 88:
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			[[Category:Commas named after asteroids]]

Francium: /* Commatic relationships */ found a commatic relationship

2024-10-31T17:35:12Z

Commatic relationships: found a commatic relationship

← Older revision		Revision as of 17:35, 31 October 2024
Line 9:		Line 9:

	== Commatic relationships ==		== Commatic relationships ==
	This comma can be factored into the following superparticular commas:		This comma is the difference between the superparticular pair [[1936/1935]] and [[2376/2375]].

			It can be factored into the following superparticular commas:
	* [[10648/10647]] and [[561925/561924]]		* [[10648/10647]] and [[561925/561924]]
	* [[10880/10879]] and [[264385/264384]]		* [[10880/10879]] and [[264385/264384]]

Francium: Created page with "{{Infobox Interval | Ratio = 10450/10449 | Name = girardisma | Color name = 43u19o1oyy1
fothunoloyoyo unison | Comma = yes }} '''10450/10449''', the '''girardisma''', is..."

2024-10-15T10:14:54Z

Created page with "{{Infobox Interval | Ratio = 10450/10449 | Name = girardisma | Color name = 43u19o1oyy1 <br> fothunoloyoyo unison | Comma = yes }} '''10450/10449''', the '''girardisma''', is..."

New page

{{Infobox Interval
| Ratio = 10450/10449
| Name = girardisma
| Color name = 43u19o1oyy1 <br> fothunoloyoyo unison
| Comma = yes
}}

'''10450/10449''', the '''girardisma''', is a [[43-limit]] [[superparticular ratio|superparticular comma]] of about 0.17 [[cent]]s.

== Commatic relationships ==
This comma can be factored into the following superparticular commas:
* [[10648/10647]] and [[561925/561924]]
* [[10880/10879]] and [[264385/264384]]
* [[14535/14534]] and [[37180/37179]]
* [[17545/17544]] and [[25840/25839]]
* [[20125/20124]] and [[21736/21735]]

== Temperaments ==
Tempering out this comma in the full 43-limit leads to the rank-13 temperament '''girardismic'''. Using the 2.3.5.11.19.43 subgroup leads to the rank-5 temperament '''girardic'''.

=== Girardismic ===

[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37.41.43

[[Comma list]]: 10450/10449

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 5 || 5 || 7 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -5 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 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 || 0 || 0 || 1 || 0 || 0 || 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 || 0 || 0 || 1 || 0 || 0 || 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 || 0 || 0 || 1 || 0 || 0 || 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 || 0 || 0 || 1 || 0 || ]]
|}
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.969, ~5/4 = 386.301, ~7/4 = 968.826, ~11/8 = 551.304, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.492, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036, ~37/32 = 251.344, ~41/32 = 429.062

{{Optimal ET sequence|legend=1| 5fi, 5f, 5, 5g, 7dfghijjkllmmmn, 7dfghijjkllmn, 7dfghijjkmn, 7l, 8dhhimmn, 8dhhijjmmn, 10h, 12del, 12el, 12fijkmn, 14cfjjkklmmn, 14cfjjlmmn, 17cgn, 17cgkn, 19eghijjkklmnn, 19eghikklmnn, 22h, 24dn, 26eiknn, 26ik, 27egj, 27egij, 31fghjk, 34dhkn, 34dhjkmn, 34dhjklmn, 38dfijlm, 39dfgijkl, 39dfgijklmm, 45efghhijkmmnn, 46kln, 46ln, 53gikn, 53gkn, 53kn, 53ej, 58, 60eln, 72hijkllmn, 72hijkmn, 77m, 80, 80k, 87, 99efkmn, 111jln, 113l, 113, 118fikl, 121hhiklm, 125fm, 137n, 140kn, 144ghj, 145jkl, 152fjm, 152fgjm, 171, 183k, 183, 193, 217n, 217ln, 236dghin, 243eklmn, 270m, 270, 270i, 296, 311n, 373g, 388, 422, 422l, 525, 540, 566gjl, 639hjmn, 653, 711, 718, 764hj, 836, 863efgjk, 882, 908m, 954hjln, 1065, 1164fimn, 1178j, 1178, … }}

=== Girardic ===

[[Subgroup]]: 2.3.5.11.19.43

[[Comma list]]: 10450/10449

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 3 || 4 || 7 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || -5 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.969, ~5/4 = 386.301, ~11/8 = 551.304, ~19/16 = 297.492

{{Optimal ET sequence|legend=1| 5, 7hn, 7, 12e, 14cn, 15, 19ehnn, 19h, 22h, 24n, 26, 27e, 31h, 34hn, 38, 41, 53n, 65, 118, 152, 217n, 270, 335, 460, 487, 566, 612, 677, 718, 836, 988, 1053, 1323, 1513, 1783, 2501, 2836, 4284, 4349, 4501, 6284, 7120, 8785, 9120 }}

== Etymology ==
The name ''girardisma'' was named by [[Francium]] in 2024. It refers to [[Wikipedia:10450 Girard|10450 Girard]], the asteroid.

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

Girardisma - Revision history

BudjarnLambeth at 01:42, 4 November 2024

BudjarnLambeth at 08:38, 3 November 2024

Francium: /* Commatic relationships */ found a commatic relationship

Francium: Created page with "{{Infobox Interval | Ratio = 10450/10449 | Name = girardisma | Color name = 43u19o1oyy1 fothunoloyoyo unison | Comma = yes }} '''10450/10449''', the '''girardisma''', is..."

Francium: Created page with "{{Infobox Interval | Ratio = 10450/10449 | Name = girardisma | Color name = 43u19o1oyy1
fothunoloyoyo unison | Comma = yes }} '''10450/10449''', the '''girardisma''', is..."