14th-octave temperaments - Revision history

FloraC: Text replacement - "{{Technical data page}}

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	{{Infobox fractional-octave\|14}}		{{Infobox fractional-octave\|14}}
	While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.		While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.

BudjarnLambeth: {{Technical data page}}

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{{Technical data page}}<br><br>

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	While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.		While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.

ArrowHead294 at 03:54, 14 February 2025

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	While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.		While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.

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	[[Badness]]: 0.196		[[Badness]]: 0.196
	===11-limit===
			=== 11-limit ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	Badness: 0.0450		Badness: 0.0450
	===13-limit===
			=== 13-limit ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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			{{Navbox fractional-octave}}

	[[Category:14edo]]		[[Category:14edo]]
	~~[[Category:Temperament collections]]~~

Eliora at 15:18, 7 July 2023

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			{{Fractional-octave navigation\|14}}
	While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.		While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.

Eliora at 19:42, 3 July 2023

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			[[Category:14edo]]
			[[Category:Temperament collections]]

Eliora: silicon to 14th octave temperaments per new system of organizing fractional-octave temperaments

2023-07-03T19:41:32Z

silicon to 14th octave temperaments per new system of organizing fractional-octave temperaments

New page

While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list.

== Silicon ==
The name of silicon temperament comes from the 14th element. Defined upwards to the 13-limit. When tuned in 742edo, it is generated by a [[53edo]] fifth intermingled with [[14edo]] periods.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 14348907/14336000, 56358560858112/56296884765625

[[Mapping]]: [{{val| 14 0 -145 239 }}, {{val| 0 1 8 -9 }}]

Mapping generators: ~6125/5832, ~3

[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.870

{{Optimal ET sequence|legend=1| 224, 518, 742, 966, 1708, 2674 }}

[[Badness]]: 0.196
===11-limit===
Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 1240029/1239040, 2359296/2358125

Mapping: [{{val| 14 0 -145 239 115 }}, {{val| 0 1 8 -9 -3 }}]

Optimal tuning (CTE): ~3/2 = 701.872

{{Optimal ET sequence|legend=1| 224, 518, 742, 966, 1708, 4382e }}

Badness: 0.0450
===13-limit===
Subgroup: 2.3.5.7.11.13

Comma list: 4096/4095, 6656/6655, 9801/9800, 24192/24167

Mapping: [{{val| 14 0 -145 239 115 74 }}, {{val| 0 1 8 -9 -3 -1 }}]

Optimal tuning (CTE): ~3/2 = 701.8733

{{Optimal ET sequence|legend=1| 224, 518, 742, 966, 1708f }}

Badness: 0.0269