35th-octave temperaments - Revision history

ArrowHead294 at 03:42, 14 February 2025

2025-02-14T03:42:58Z

← Older revision		Revision as of 03:42, 14 February 2025
Line 1:		Line 1:
	{{~~Fractional~~-octave ~~navigation~~\|35}}		{{Infobox fractional-octave\|35}}
	[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.		[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.

	== Insanobromismic ==		== Insanobromismic ==
	{{Main\|Insanobromisma}}		{{Main\|Insanobromisma}}

BudjarnLambeth: navbox

2024-12-05T07:27:31Z

navbox

← Older revision		Revision as of 07:27, 5 December 2024
Line 131:		Line 131:

	Optimal tuning (CTE): ~5/4 = 386.174		Optimal tuning (CTE): ~5/4 = 386.174

			{{Navbox fractional-octave}}

	[[Category:35edo]]		[[Category:35edo]]
	~~[[Category:Temperament collections]]~~

Eliora: /* Insanobromismic */

2023-08-02T14:15:49Z

Insanobromismic

← Older revision		Revision as of 14:15, 2 August 2023
Line 2:		Line 2:
	[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.		[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.
	== Insanobromismic ==		== Insanobromismic ==
			{{Main\|Insanobromisma}}

			This is the comma that identifies [[51/50]] with 1 step of 35edo.

	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

Eliora: /* Insanobromismic */

2023-08-02T14:15:24Z

Insanobromismic

@@ Line 5: / Line 5: @@
 Subgroup: 2.3.5.7.11.13.17
-Comma list: [36 -35 70 0 0 0 -35⟩
+Comma list: {{monzo|36 -35 70 0 0 0 -35}}
 == Bromine ==
 Bromine is named after the 35th chemical element.

Eliora at 14:08, 2 August 2023

2023-08-02T14:08:39Z

← Older revision		Revision as of 14:08, 2 August 2023
Line 1:		Line 1:
	{{Fractional-octave navigation\|35}}		{{Fractional-octave navigation\|35}}
	[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.		[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.
			== Insanobromismic ==

			Subgroup: 2.3.5.7.11.13.17

			Comma list: [36 -35 70 0 0 0 -35⟩

			{{#switch: 1 \| 1 = [[Mapping]]:  \| 2 = [[Sval]] [[mapping]]:  \| 3 = [[Gencom]] [[mapping]]:  }}<span class="left-delim">[</span>{{bra\| 35 0 0 0 0 0 36 }}{{#if: 0 1 0 0 0 0 -1\|, {{bra\| 0 1 0 0 0 0 -1 }} }}{{#if: 0 0 1 0 0 0 2\|, {{bra\| 0 0 1 0 0 0 2 }} }}{{#if: 0 0 0 1 0 0 0\|, {{bra\| 0 0 0 1 0 0 0 }} }}<span class="right-delim">]</span>
	== Bromine ==		== Bromine ==
	Bromine is named after the 35th chemical element.		Bromine is named after the 35th chemical element.

Eliora at 22:37, 14 July 2023

2023-07-14T22:37:19Z

← Older revision		Revision as of 22:37, 14 July 2023
Line 1:		Line 1:
			{{Fractional-octave navigation\|35}}
	[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.		[[35edo]] is a tuning system that's not remarkable in its own right from a regular temperament theory perspective, but some of its multiples are either [[zeta]] edos like [[3395edo]], have an exceptionally precise perfect fifth like [[665edo]], or have high consistency limits like [[525edo]]. In addition, one step of 35edo is close to [[50/49]] in low limits and [[51/50]] in the higher limits.

Eliora: /* 11-limit */ left only the optimal et sequence

2023-05-28T00:05:31Z

11-limit: left only the optimal et sequence

← Older revision		Revision as of 00:05, 28 May 2023
Line 32:		Line 32:
	Optimal tuning (CTE): ~3/2 = 701.975		Optimal tuning (CTE): ~3/2 = 701.975

	~~Supporting ETs:~~ {{~~EDOs~~\|665, 2730, 3395, 6125~~, 6790, 8855~~, 9520}}		{{Optimal ET sequence\|legend=1\|665, 2730, 3395, 6125, 9520}}

	=== 13-limit ===		=== 13-limit ===

Eliora: /* 11-limit */

2023-05-19T12:39:15Z

11-limit

← Older revision		Revision as of 12:39, 19 May 2023
Line 19:		Line 19:

	While 665edo still tunes bromine in the 11-limit, it is not recommended due to error on the 11th harmonic. [[2730edo]] or [[3395edo]] are better tunings. Alternately, considering bromine as a no-11s temperament keeps it within the realm of [[very high accuracy temperaments]], having [[TE error]] of less than 0.005 cents per octave.		While 665edo still tunes bromine in the 11-limit, it is not recommended due to error on the 11th harmonic. [[2730edo]] or [[3395edo]] are better tunings. Alternately, considering bromine as a no-11s temperament keeps it within the realm of [[very high accuracy temperaments]], having [[TE error]] of less than 0.005 cents per octave.

			If a strong 11th harmonic is needed, [[6125edo]] is the tuning for that.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Eliora: /* 11-limit */

2023-05-19T12:37:44Z

11-limit

← Older revision		Revision as of 12:37, 19 May 2023
Line 29:		Line 29:

	Optimal tuning (CTE): ~3/2 = 701.975		Optimal tuning (CTE): ~3/2 = 701.975

			Supporting ETs: {{EDOs\|665, 2730, 3395, 6125, 6790, 8855, 9520}}

	=== 13-limit ===		=== 13-limit ===

Eliora: /* Bromine */ expand to 11-limit and 19-limit via 2730edo's consistency, also can't keep the "normal" matrix due to limitations of the sintel's finder so 152 and -7 for 19-limit in the mapping

2023-05-19T12:32:25Z

Bromine: expand to 11-limit and 19-limit via 2730edo's consistency, also can't keep the "normal" matrix due to limitations of the sintel's finder so 152 and -7 for 19-limit in the mapping

← Older revision		Revision as of 12:32, 19 May 2023
Line 4:		Line 4:
	Bromine is named after the 35th chemical element.		Bromine is named after the 35th chemical element.

	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	Comma list: {{monzo\|47 -7 -7 -7}}, {{monzo\|6 -37 13 8}}		[[Comma list]]: {{monzo\|47 -7 -7 -7}}, {{monzo\|6 -37 13 8}}

	Mapping: [{{val\|35 0 -418 653}}, {{val\|0 1 9 -10}}]		[[Mapping]]: [{{val\|35 0 -418 653}}, {{val\|0 1 9 -10}}]

	Mapping generators: ~38263752/37515625 = 1\35, ~3		Mapping generators: ~38263752/37515625 = 1\35, ~3

	Optimal tuning (CTE): ~3/2 = 701.973		[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.973

	{{~~Optimal ET sequence\|legend=1~~\|665, 2065, 2730, 3395, 4060, 7455}}		[[Support]]ing [[ET]]s: {{EDOs\|665, 2065, 2730, 3395, 4060, 7455}}

	=== ~~2.3.5.7.13 subgroup~~ ===		=== 11-limit ===

	~~Subgroup: 2~~.3.5.7.13		While 665edo still tunes bromine in the 11-limit, it is not recommended due to error on the 11th harmonic. [[2730edo]] or [[3395edo]] are better tunings. Alternately, considering bromine as a no-11s temperament keeps it within the realm of [[very high accuracy temperaments]], having [[TE error]] of less than 0.005 cents per octave.

	~~Comma list~~: ~~1990656/1990625, 1686616064/1686498489, 44302336000/44295075909~~		Subgroup: 2.3.5.7.11

	~~Sval mapping~~: ~~[{{val\|35 0 -418 653 1239}}~~, ~~{{val\|0 1 9 -10 -20}}]~~		Comma list: 151263/151250, 115091701760/115063885233, 45137758519296/45135986328125

	~~Sval mapping generators~~: ~~~38263752/37515625 = 1\~~35, ~3		Mapping: [{{val\|35 0 -418 653 2451}}, {{val\|0 1 9 -10 -42}}]

	Optimal tuning (CTE): ~3/2 = 701.~~973~~		Mapping generators: ~1203125/1179648 = 1\35, ~3

			Optimal tuning (CTE): ~3/2 = 701.975

			=== 13-limit ===

			Subgroup: 2.3.5.7.11.13

			Comma list: 123201/123200, 151263/151250, 1990656/1990625, 8683257856/8681088735

			Mapping: [{{val\|35 0 -418 653 2451 1239}}, {{val\|0 1 9 -10 -42 -20}}]

			Mapping generators: ~1485/1456 = 1\35, ~3

			Optimal tuning (CTE): ~3/2 = 701.975

	Supporting ETs: 665, 3395, ...		Supporting ETs: 665, 3395, ...

	=== ~~2.3.5.7.13.~~17 ~~subgroup~~ ===		=== 17-limit ===

	The period is mapped to ~51/50.		The period is mapped to ~51/50.

	Subgroup: 2.3.5.7.13.17		Subgroup: 2.3.5.7.11.13.17

	Comma list: ~~426496~~/~~426465~~, ~~1990656~~/~~1990625~~, ~~6251648~~/~~6251175~~, ~~51200000~~/~~51195483~~		Comma list: 12376/12375, 123201/123200, 194481/194480, 1713660/1713481, 24635975/24634368

	~~Sval mapping~~: [{{val\|35 0 -418 653 1239 -800}}, {{val\|0 1 9 -10 -20 17}}]		Mapping: [{{val\|35 0 -418 653 2451 1239 -800}}, {{val\|0 1 9 -10 -42 -20 17}}]

	~~Sval mapping~~ generators: ~51/50 = 1\35, ~3		Mapping generators: ~51/50 = 1\35, ~3

	Optimal tuning (CTE): ~3/2 = 701.~~973~~		Optimal tuning (CTE): ~3/2 = 701.97...

	Supporting ETs: {{EDOs\|665, 2730, 3395, 6125, 7455, 10185}}...		Supporting ETs: {{EDOs\|665, 2730, 3395, 6125, 7455, 10185}}...

			=== 19-limit ===

			[[Subgroup]]: 2.3.5.7.11.13.17.19

			[[Comma list]]: 12376/12375, 12636/12635, 13377/13376, 14080/14079, 14365/14364, 486400/486387

			[[Mapping]]: [{{val\|35 0 -418 653 2451 1239 -800 152}}, {{val\|0 1 9 -10 -42 -20 17 -7}}]

			[[Mapping]] [[generator]]s: ~51/50 = 1\35, ~3

			[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.97...

			[[Support]]ing [[ET]]s: {{EDOs\|665, 2730, 3395, 6125, 6790h, 7455eh}}...

	== Tritonopodismic (rank-3) ==		== Tritonopodismic (rank-3) ==