402edo - 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"

2026-03-13T13:32:27Z

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 13:32, 13 March 2026
Line 81:		Line 81:
	\| [[Bischismic]] (402c, 7-limit)		\| [[Bischismic]] (402c, 7-limit)
	\|}		\|}
	<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

2025-02-21T06:24:05Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:24, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|402~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:51, 15 January 2025

2025-01-15T16:51:34Z

← Older revision		Revision as of 16:51, 15 January 2025
Line 8:		Line 8:
	* {{val\| 402 637 '''934''' 1129 }} (402c)		* {{val\| 402 637 '''934''' 1129 }} (402c)

	Using the patent val, it tempers out the [[semicomma]] in the 5-limit; [[4375/4374]], 7381125/7340032 and 3200000/3176523 in the 7-limit~~. It~~ [[support]]s [[~~abigail~~]].		Using the patent val, it tempers out the [[semicomma]] in the 5-limit and [[4375/4374]], 7381125/7340032, and 3200000/3176523 in the 7-limit, [[support]]ing [[Abigail]].

	Using the 402d val, it tempers out [[250047/250000]], 1500625/1492992 and 2460375/2458624 in the 7-limit.		Using the 402d val, it tempers out [[250047/250000]], and 1500625/1492992 and 2460375/2458624 in the 7-limit.

	Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000 and 13060694016/12867859375 in the 7-limit~~. It supports~~ [[bischismic]].		Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000, and 13060694016/12867859375 in the 7-limit, supporting [[bischismic]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 402 factors into 2 × 3 × 67, 402edo has subset edos {{EDOs\| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.		Since 402 factors into {{nowrap\|2 × 3 × 67}}, 402edo has subset edos {{EDOs\| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 81:		Line 81:
	\| [[Bischismic]] (402c, 7-limit)		\| [[Bischismic]] (402c, 7-limit)
	\|}		\|}
	<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

2024-11-16T13:09:25Z

Partial undo

← Older revision		Revision as of 13:09, 16 November 2024
Line 21:		Line 21:

	== 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
Line 36:		Line 45:
	\| 0.2182		\| 0.2182
	\| 7.31		\| 7.31
	~~{{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
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	\| 4/3<br />(200/189)		\| 4/3<br />(200/189)
	\| [[Bischismic]] (402c, 7-limit)		\| [[Bischismic]] (402c, 7-limit)
	~~{{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 02:14, 16 November 2024

2024-11-16T02:14:24Z

← Older revision		Revision as of 02:14, 16 November 2024
Line 21:		Line 21:

	== 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 44:		Line 36:
	\| 0.2182		\| 0.2182
	\| 7.31		\| 7.31
	\|}		{{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
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	\|-		\|-
	\| 2		\| 2
	\| 167\402<br>(34\402)		\| 167\402<br />(34\402)
	\| 498.51<br>(101.49)		\| 498.51<br />(101.49)
	\| 4/3<br>(200/189)		\| 4/3<br />(200/189)
	\| [[Bischismic]] (402c, 7-limit)		\| [[Bischismic]] (402c, 7-limit)
	\|}		{{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: -rank-3 temps that are obvious from the commas ("parahemwuer" is just an alias for hemimean); note abigail and bischismic in the table of rank-2 temps

2024-04-15T12:43:35Z

-rank-3 temps that are obvious from the commas ("parahemwuer" is just an alias for hemimean); note abigail and bischismic in the table of rank-2 temps

← Older revision		Revision as of 12:43, 15 April 2024
Line 8:		Line 8:
	* {{val\| 402 637 '''934''' 1129 }} (402c)		* {{val\| 402 637 '''934''' 1129 }} (402c)

	Using the patent val, it tempers out [[4375/4374]], 7381125/7340032 and 3200000/3176523 in the 7-limit. It ~~supports~~ [[~~ragismic~~]] ~~and~~ [[abigail]].		Using the patent val, it tempers out the [[semicomma]] in the 5-limit; [[4375/4374]], 7381125/7340032 and 3200000/3176523 in the 7-limit. It [[support]]s [[abigail]].

	Using the 402d val, it tempers out [[250047/250000]], 1500625/1492992 and 2460375/2458624 in the 7-limit~~. It supports the [[landscape]] temperament~~.		Using the 402d val, it tempers out [[250047/250000]], 1500625/1492992 and 2460375/2458624 in the 7-limit.

	Using the 402c val, it tempers out [[3136/3125]], 321489/320000 and 13060694016/12867859375 in the 7-limit. It supports [[bischismic~~]] and [[parahemwuer~~]].		Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000 and 13060694016/12867859375 in the 7-limit. It supports [[bischismic]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 402 factors into 2 × 3 × 67, 402edo has subset edos {{EDOs\| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the ~~harmonic~~ 7.		Since 402 factors into 2 × 3 × 67, 402edo has subset edos {{EDOs\| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 59:		Line 59:
	\| 271.64		\| 271.64
	\| 75/64		\| 75/64
	\| [[Orson]]		\| [[Orson]] (402)
	\|-		\|-
	\| 1		\| 1
Line 65:		Line 65:
	\| 343.28		\| 343.28
	\| 8000/6561		\| 8000/6561
	\| [[Raider]]		\| [[Raider]] (402)
			\|-
			\| 2
			\| 70\402
			\| 208.96
			\| 44/39
			\| [[Abigail]] (402)
			\|-
			\| 2
			\| 167\402<br>(34\402)
			\| 498.51<br>(101.49)
			\| 4/3<br>(200/189)
			\| [[Bischismic]] (402c, 7-limit)
	\|}		\|}
	<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

FloraC: Review

2024-04-15T12:31:44Z

Review

← Older revision		Revision as of 12:31, 15 April 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~402et~~ is only consistent to the 5-limit~~, tempering out the [[semicomma~~]]. There are three possible mappings in the 7-limit:		402edo is only [[consistent]] to the [[5-odd-limit]]. There are three possible mappings in the 7-limit:
	* {{val\|402 637 933 1129}} (patent val)		* {{val\| 402 637 933 1129 }} ([[patent val]])
	* {{val\|402 637 '''~~934~~''' ~~1129~~}} (~~402c~~)		* {{val\| 402 637 933 '''1128''' }} (402d)
	* {{val\|402 637 ~~933~~ '''~~1128~~'''}} (~~402d~~)		* {{val\| 402 637 '''934''' 1129 }} (402c)

	Using the patent val, it tempers out 4375/4374, 7381125/7340032 and 3200000/3176523 in the 7-limit. It supports [[ragismic]] and [[abigail]].		Using the patent val, it tempers out [[4375/4374]], 7381125/7340032 and 3200000/3176523 in the 7-limit. It supports [[ragismic]] and [[abigail]].

	Using the ~~402c~~ val, it tempers out ~~3136~~/~~3125~~, ~~321489~~/~~320000~~ and ~~13060694016~~/~~12867859375~~ in the 7-limit. It supports [[~~bischismic]] and [[parahemwuer~~]].		Using the 402d val, it tempers out [[250047/250000]], 1500625/1492992 and 2460375/2458624 in the 7-limit. It supports the [[landscape]] temperament.

	Using the ~~402d~~ val, it tempers out ~~250047~~/~~250000~~, ~~1500625~~/~~1492992~~ and ~~2460375~~/~~2458624~~ in the 7-limit. It supports ~~the~~ [[~~landscape~~]] ~~temperament~~.		Using the 402c val, it tempers out [[3136/3125]], 321489/320000 and 13060694016/12867859375 in the 7-limit. It supports [[bischismic]] and [[parahemwuer]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	402 factors into 2 × 3 × 67, ~~with~~ subset edos {{EDOs\|2, 3, 6, 67, 134, and 201}}. [[804edo]], which doubles it, gives a good correction to the harmonic 7.		Since 402 factors into 2 × 3 × 67, 402edo has subset edos {{EDOs\| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonic 7.

	== 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\|-637 402}}		\| {{monzo\| -637 402 }}
	\|{{mapping\|402 637}}		\| {{mapping\| 402 637 }}
	\| 0.1459		\| 0.1459
	\| 0.1459		\| 0.1459
	\| 4.89		\| 4.89
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|2109375/2097152, {{monzo\|25 -48 22}}		\| 2109375/2097152, {{monzo\| 25 -48 22 }}
	\|{{mapping\|402 637 933}}		\| {{mapping\| 402 637 933 }}
	\| 0.2752		\| 0.2752
	\| 0.2182		\| 0.2182
Line 50:		Line 50:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~*		! Generator*
	! Cents~~<br>(reduced)~~*		! Cents*
	! Associated<br>Ratio*		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|91\402		\| 91\402
	\|271.64		\| 271.64
	\|75/64		\| 75/64
	\|[[Orson]]		\| [[Orson]]
	\|-		\|-
	\|1		\| 1
	\|115\402		\| 115\402
	\|343.28		\| 343.28
	\|8000/6561		\| 8000/6561
	\|[[Raider]]		\| [[Raider]]
	\|}		\|}

	<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: /* Rank-2 temperaments */

2023-11-22T07:10:17Z

Rank-2 temperaments

← Older revision		Revision as of 07:10, 22 November 2023
Line 67:		Line 67:
	\|[[Raider]]		\|[[Raider]]
	\|}		\|}
	\|}
			<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|402}} == Theory == 402et is only consistent to the 5-limit, tempering out the semicomma. There are three possible mappings in the 7-limit: * {{..."

2023-11-22T07:09:24Z

Created page with "{{Infobox ET}} {{EDO intro|402}} == Theory == 402et is only consistent to the 5-limit, tempering out the semicomma. There are three possible mappings in the 7-limit: * {{..."

New page

{{Infobox ET}}
{{EDO intro|402}}

== Theory ==
402et is only consistent to the 5-limit, tempering out the [[semicomma]]. There are three possible mappings in the 7-limit:
* {{val|402 637 933 1129}} (patent val)
* {{val|402 637 '''934''' 1129}} (402c)
* {{val|402 637 933 '''1128'''}} (402d)

Using the patent val, it tempers out 4375/4374, 7381125/7340032 and 3200000/3176523 in the 7-limit. It supports [[ragismic]] and [[abigail]].

Using the 402c val, it tempers out 3136/3125, 321489/320000 and 13060694016/12867859375 in the 7-limit. It supports [[bischismic]] and [[parahemwuer]].

Using the 402d val, it tempers out 250047/250000, 1500625/1492992 and 2460375/2458624 in the 7-limit. It supports the [[landscape]] temperament.

=== Odd harmonics ===
{{Harmonics in equal|402}}

=== Subsets and supersets ===
402 factors into 2 × 3 × 67, with subset edos {{EDOs|2, 3, 6, 67, 134, and 201}}. [[804edo]], 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 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-637 402}}
|{{mapping|402 637}}
| 0.1459
| 0.1459
| 4.89
|-
|2.3.5
|2109375/2097152, {{monzo|25 -48 22}}
|{{mapping|402 637 933}}
| 0.2752
| 0.2182
| 7.31
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)*
! Cents (reduced)*
! Associated Ratio*
! Temperaments
|-
|1
|91\402
|271.64
|75/64
|[[Orson]]
|-
|1
|115\402
|343.28
|8000/6561
|[[Raider]]
|}
|}