393edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:40Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
Line 62:		Line 62:
	\| [[Würschmidt]]		\| [[Würschmidt]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

ArrowHead294 at 12:24, 21 February 2025

2025-02-21T12:24:49Z

← Older revision		Revision as of 12:24, 21 February 2025
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	~~! rowspan="2" \|[[Subgroup]]~~
	~~! rowspan="2" \|[[Comma list\|Comma List]]~~
	~~! rowspan="2" \|[[Mapping]]~~
	~~! rowspan="2" \|Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \|Tuning Error~~
	\|-
	~~![[TE error\|Absolute]] (¢)~~
	~~![[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\|2.3		! rowspan="2" \| [[Subgroup]]
	\|{{monzo\|623 -393}}		! rowspan="2" \| [[Comma list]]
	\|{{mapping\|393 623}}		! rowspan="2" \| [[Mapping]]
	\| -0.1057		! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
			\|-
			\| 2.3
			\| {{monzo\|623 -393}}
			\| {{mapping\|393 623}}
			\| −0.1057
	\| 0.1057		\| 0.1057
	\| 3.43		\| 3.43
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|393216/390625, {{monzo\|-46 51 -15}}		\| 393216/390625, {{monzo\|-46 51 -15}}
	\| -0.2819		\| −0.2819
	\| 0.2636		\| 0.2636
	\| 8.63		\| 8.63
Line 47:		Line 48:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|127\393		\| 127\393
	\|387.79		\| 387.79
	\|5/4		\| 5/4
	\|[[Würschmidt]]		\| [[Würschmidt]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Francium: changed EDO intro to ED intro

2025-02-21T06:19:12Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:19, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|393~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: Created page with "{{Infobox ET}} {{EDO intro|393}} == Theory == 393et is only consistent to the 5-limit, with three mappings possible for the 7-limit: * {{val|393 623 913 1103}} (patent val),..."

2023-12-06T13:44:42Z

Created page with "{{Infobox ET}} {{EDO intro|393}} == Theory == 393et is only consistent to the 5-limit, with three mappings possible for the 7-limit: * {{val|393 623 913 1103}} (patent val),..."

New page

{{Infobox ET}}
{{EDO intro|393}}

== Theory ==
393et is only consistent to the 5-limit, with three mappings possible for the 7-limit:
* {{val|393 623 913 1103}} (patent val),
* {{val|393 623 '''912''' 1103}} (393c),
* {{val|393 623 913 '''1104'''}} (393d).

Using the patent val, it tempers out [[393216/390625]] and {{monzo|-46 51 -15}} in the 5-limit; [[10976/10935]], [[393216/390625]] and 5250987/5242880 in the 7-limit.

Using the 393c val, it tempers out [[2109375/2097152]] and {{monzo|32 -48 19}} in the 5-limit; [[2401/2400]], 1071875/1062882 and [[2109375/2097152]] in the 7-limit.

Using the 393d val, it tempers out [[393216/390625]] and {{monzo|-46 51 -15}} in the 5-limit; [[250047/250000]], 2460375/2458624 and [[2097152/2083725]] in the 7-limit.

=== Odd harmonics ===
{{Harmonics in equal|393}}

=== Subsets and supersets ===
393 factors into 3 × 131, with [[3edo]] and [[131edo]] as its subset edos. [[786edo]], which doubles it, gives a good correction to the harmonic 7.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|623 -393}}
|{{mapping|393 623}}
| -0.1057
| 0.1057
| 3.43
|-
|2.3.5
|393216/390625, {{monzo|-46 51 -15}}
| -0.2819
| 0.2636
| 8.63
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|1
|127\393
|387.79
|5/4
|[[Würschmidt]]
|}