398edo - 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"

2026-03-13T13:31:50Z

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 87:		Line 87:
	\| [[Bisupermajor]]		\| [[Bisupermajor]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T06:28:15Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:28, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|398~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:07, 15 January 2025

2025-01-15T18:07:05Z

← Older revision		Revision as of 18:07, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 398 factors into ~~2 × 199~~, 398edo has [[2edo]] and [[199edo]] as its subsets.		Since 398 factors into {{factorisation\|398}}, 398edo has [[2edo]] and [[199edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| {{monzo\| 631 -398 }}		\| {{monzo\| 631 -398 }}
	\| {{mapping\| 398 631 }}		\| {{mapping\| 398 631 }}
	\| ~~−0~~.1759		\| −0.1759
	\| 0.1759		\| 0.1759
	\| 5.83		\| 5.83
Line 33:		Line 33:
	\| 390625000/387420489, {{monzo\| -53 10 16 }}		\| 390625000/387420489, {{monzo\| -53 10 16 }}
	\| {{mapping\| 398 631 924 }}		\| {{mapping\| 398 631 924 }}
	\| ~~−0~~.0622		\| −0.0622
	\| 0.2157		\| 0.2157
	\| 7.15		\| 7.15
Line 54:		Line 54:
	\| 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935		\| 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935
	\| {{mapping\| 398 631 924 1117 1377 1473 }}		\| {{mapping\| 398 631 924 1117 1377 1473 }}
	\| ~~−0~~.0243		\| −0.0243
	\| 0.2313		\| 0.2313
	\| 7.67		\| 7.67
Line 87:		Line 87:
	\| [[Bisupermajor]]		\| [[Bisupermajor]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294: Partial undo

2024-11-16T13:00:59Z

Partial undo

← Older revision		Revision as of 13:00, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 631 -398 }}		\| {{monzo\| 631 -398 }}
	\| {{mapping\| 398 631 }}		\| {{mapping\| 398 631 }}
	\| -0.1759		\| −0.1759
	\| 0.1759		\| 0.1759
	\| 5.83		\| 5.83
Line 24:		Line 33:
	\| 390625000/387420489, {{monzo\| -53 10 16 }}		\| 390625000/387420489, {{monzo\| -53 10 16 }}
	\| {{mapping\| 398 631 924 }}		\| {{mapping\| 398 631 924 }}
	\| -0.0622		\| −0.0622
	\| 0.2157		\| 0.2157
	\| 7.15		\| 7.15
Line 45:		Line 54:
	\| 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935		\| 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935
	\| {{mapping\| 398 631 924 1117 1377 1473 }}		\| {{mapping\| 398 631 924 1117 1377 1473 }}
	\| -0.0243		\| −0.0243
	\| 0.2313		\| 0.2313
	\| 7.67		\| 7.67
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 70:		Line 86:
	\| 11/10		\| 11/10
	\| [[Bisupermajor]]		\| [[Bisupermajor]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 02:55, 16 November 2024

2024-11-16T02:55:15Z

← Older revision		Revision as of 02:55, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! 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		\| 2.3
Line 56:		Line 48:
	\| 0.2313		\| 0.2313
	\| 7.67		\| 7.67
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 84:		Line 70:
	\| 11/10		\| 11/10
	\| [[Bisupermajor]]		\| [[Bisupermajor]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

FloraC: Review

2024-01-16T15:03:52Z

Review

← Older revision		Revision as of 15:03, 16 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~398et~~ is only consistent to the [[5-odd-limit]]~~. Using~~ the patent val, it tempers out ~~1220703125~~/~~1219784832, 1280000000/1275989841~~, [[65625/65536]], 102760448/102515625 and 200120949/200000000 in the 7-limit; ~~1073741824~~/~~1071794405~~, ~~100663296~~/~~100656875, 161280/161051, 35156250/35153041, 2097152/2096325~~, [[~~4000~~/~~3993~~]], ~~2734375~~/~~2725888~~, ~~496125~~/~~495616~~, [[131072/130977]], [[~~6250~~/~~6237~~]], ~~9765625~~/~~9732096~~, ~~4302592~~/~~4296875~~, ~~352947~~/~~352000, 422576/421875, 184877/184320~~, [[~~3025~~/~~3024~~]], ~~9453125/9437184~~ and ~~456533~~/~~455625~~ in the 11-limit. It [[support]]s ~~[[quartonic]],~~ [[yarman]], [[bisupermajor]] and [[semiquindromeda]].		398edo is only [[consistent]] to the [[5-odd-limit]], though it has a reasonable approximation to the full 13-limit using the [[patent val]], which [[tempering out\|tempers out]] [[10976/10935]], [[65625/65536]], 1500625/1492992, 102760448/102515625, 102942875/102036672, and 200120949/200000000 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 59290/59049, 117649/117128, and [[131072/130977]] in the 11-limit; and [[625/624]], [[1575/1573]], [[2080/2079]], [[2200/2197]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It [[support]]s [[yarman I]], [[bisupermajor]] and [[semiquindromeda]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	398 factors into 2 × 199, ~~with~~ [[2edo]] and [[199edo]] as its ~~subset edos~~.		Since 398 factors into 2 × 199, 398edo has [[2edo]] and [[199edo]] as its subsets.

	== 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" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|631 -398}}		\| {{monzo\| 631 -398 }}
	\|{{mapping\|398 631}}		\| {{mapping\| 398 631 }}
	\| -0.1759		\| -0.1759
	\| 0.1759		\| 0.1759
	\| 5.83		\| 5.83
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|390625000/387420489, {{monzo\|-53 10 16}}		\| 390625000/387420489, {{monzo\| -53 10 16 }}
	\|{{mapping\|398 631 924}}		\| {{mapping\| 398 631 924 }}
	\| -0.0622		\| -0.0622
	\| 0.2157		\| 0.2157
	\| 7.15		\| 7.15
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|10976/10935, 65625/65536, ~~1280000000~~/~~1275989841~~		\| 10976/10935, 65625/65536, 200120949/200000000
	\|{{mapping\|398 631 924 1117}}		\| {{mapping\| 398 631 924 1117 }}
	\| +0.0412		\| +0.0412
	\| 0.2588		\| 0.2588
	\| 8.58		\| 8.58
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024, ~~6250~~/~~6237~~, 10976/10935, ~~496125~~/~~495616~~		\| 3025/3024, 4000/3993, 10976/10935, 65625/65536
	\|{{mapping\|398 631 924 1117 1377}}		\| {{mapping\| 398 631 924 1117 1377 }}
	\| +0.0075		\| +0.0075
	\| 0.2411		\| 0.2411
	\| 8.00		\| 8.00
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|~~2080~~/~~2079~~, ~~625~~/~~624~~, ~~3025~~/~~3024~~, ~~4096~~/~~4095~~, 10976/10935		\| 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935
	\|{{mapping\|398 631 924 1117 1377 1473}}		\| {{mapping\| 398 631 924 1117 1377 1473 }}
	\| -0.0243		\| -0.0243
	\| 0.2313		\| 0.2313
Line 67:		Line 67:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|5\398		\| 5\398
	\|15.08		\| 15.08
	\|126/125		\| 126/125
	\|[[Yarman]]		\| [[Yarman I]]
	\|-		\|-
	\|1		\| 1
	\|183\398		\| 183\398
	\|551.76		\| 551.76
	\|11/8		\| 11/8
	\|~~[[Emka]] /~~ [[Emkay]]		\| [[Emkay]]
	\|-		\|-
	\|2		\| 2
	\|54\398		\| 54\398
	\|162.81		\| 162.81
	\|11/10		\| 11/10
	\|~~[[Kwazy]] /~~ [[Bisupermajor]]		\| [[Bisupermajor]]
	\|}		\|}

	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|398}} == Theory == 398et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 1280000000/12759898..."

2024-01-10T20:19:08Z

Created page with "{{Infobox ET}} {{EDO intro|398}} == Theory == 398et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 1280000000/12759898..."

New page

{{Infobox ET}}
{{EDO intro|398}}

== Theory ==
398et is only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out 1220703125/1219784832, 1280000000/1275989841, [[65625/65536]], 102760448/102515625 and 200120949/200000000 in the 7-limit; 1073741824/1071794405, 100663296/100656875, 161280/161051, 35156250/35153041, 2097152/2096325, [[4000/3993]], 2734375/2725888, 496125/495616, [[131072/130977]], [[6250/6237]], 9765625/9732096, 4302592/4296875, 352947/352000, 422576/421875, 184877/184320, [[3025/3024]], 9453125/9437184 and 456533/455625 in the 11-limit. It [[support]]s [[quartonic]], [[yarman]], [[bisupermajor]] and [[semiquindromeda]].

=== Prime harmonics ===
{{Harmonics in equal|398}}

=== Subsets and supersets ===
398 factors into 2 × 199, with [[2edo]] and [[199edo]] as its subset edos.

== 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|631 -398}}
|{{mapping|398 631}}
| -0.1759
| 0.1759
| 5.83
|-
|2.3.5
|390625000/387420489, {{monzo|-53 10 16}}
|{{mapping|398 631 924}}
| -0.0622
| 0.2157
| 7.15
|-
|2.3.5.7
|10976/10935, 65625/65536, 1280000000/1275989841
|{{mapping|398 631 924 1117}}
| +0.0412
| 0.2588
| 8.58
|-
|2.3.5.7.11
|3025/3024, 6250/6237, 10976/10935, 496125/495616
|{{mapping|398 631 924 1117 1377}}
| +0.0075
| 0.2411
| 8.00
|-
|2.3.5.7.11.13
|2080/2079, 625/624, 3025/3024, 4096/4095, 10976/10935
|{{mapping|398 631 924 1117 1377 1473}}
| -0.0243
| 0.2313
| 7.67
|}

=== 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
|5\398
|15.08
|126/125
|[[Yarman]]
|-
|1
|183\398
|551.76
|11/8
|[[Emka]] / [[Emkay]]
|-
|2
|54\398
|162.81
|11/10
|[[Kwazy]] / [[Bisupermajor]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct