417edo - 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"

2026-03-13T13:33:14Z

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 13:33, 13 March 2026
Line 86:		Line 86:
	\| [[Tertiosec]]		\| [[Tertiosec]]
	\|}		\|}
	<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

2025-02-21T06:26:18Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:26, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|417~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:49, 15 January 2025

2025-01-15T17:49:48Z

← Older revision		Revision as of 17:49, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	417et is only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out [[589824/588245]], [[43046721/43025920]], [[33554432/33480783]] and [[65625/65536]] in the 7-limit; 78121827/77948684, 20155392/20131375, 10333575/10307264, 1019215872/1019046875, 46656/46585, 1366875/1362944, 78675968/78594219, [[536870912/535869675]], 7168000/7144929, 496125/495616, 514714375/514434888, 2359296/2358125, [[540/539]], 1265625/1261568, 17561600/17537553, 180224/180075, 1375/1372, 645922816/645700815, [[3025/3024]], 9453125/9437184 and 1362944/1361367 in the 11-limit. It [[support]]s [[familia]] and 5-limit [[fortune]].		417et is only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out [[589824/588245]], [[43046721/43025920]], [[33554432/33480783]], and [[65625/65536]] in the 7-limit; 78121827/77948684, 20155392/20131375, 10333575/10307264, 1019215872/1019046875, 46656/46585, 1366875/1362944, 78675968/78594219, [[536870912/535869675]], 7168000/7144929, 496125/495616, 514714375/514434888, 2359296/2358125, [[540/539]], 1265625/1261568, 17561600/17537553, 180224/180075, 1375/1372, 645922816/645700815, [[3025/3024]], 9453125/9437184, and 1362944/1361367 in the 11-limit. It [[support]]s [[familia]] and 5-limit [[fortune]].

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	417 factors into ~~3 × 139~~, with [[3edo]] and [[139edo]] as its subset edos.		417 factors into {{factorisation\|417}}, with [[3edo]] and [[139edo]] as its subset edos.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| {{monzo\|661 -417}}		\| {{monzo\|661 -417}}
	\| {{mapping\|417 661}}		\| {{mapping\|417 661}}
	\| ~~−0~~.0641		\| −0.0641
	\| 0.0641		\| 0.0641
	\| 2.23		\| 2.23
Line 40:		Line 40:
	\| 16875/16807, 65625/65536, 1600000/1594323		\| 16875/16807, 65625/65536, 1600000/1594323
	\| {{mapping\|417 661 968 1171}}		\| {{mapping\|417 661 968 1171}}
	\| ~~−0~~.0418		\| −0.0418
	\| 0.2331		\| 0.2331
	\| 8.10		\| 8.10
Line 47:		Line 47:
	\| 540/539, 3025/3024, 496125/495616, 7168000/7144929		\| 540/539, 3025/3024, 496125/495616, 7168000/7144929
	\| {{mapping\|417 661 968 1171 1443}}		\| {{mapping\|417 661 968 1171 1443}}
	\| ~~−0~~.1029		\| −0.1029
	\| 0.2416		\| 0.2416
	\| 8.40		\| 8.40
Line 86:		Line 86:
	\| [[Tertiosec]]		\| [[Tertiosec]]
	\|}		\|}
	<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

2024-11-16T13:18:38Z

Partial undo

← Older revision		Revision as of 13:18, 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
Line 41:		Line 50:
	\| 0.2416		\| 0.2416
	\| 8.40		\| 8.40
	~~{{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 69:		Line 85:
	\| 16/15		\| 16/15
	\| [[Tertiosec]]		\| [[Tertiosec]]
	~~{{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 01:39, 16 November 2024

2024-11-16T01:39:33Z

← Older revision		Revision as of 01:39, 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
	\| {{monzo\|661 -417}}		\| {{monzo\|661 -417}}
	\| {{mapping\|417 661}}		\| {{mapping\|417 661}}
	\| -0.0641		\| −0.0641
	\| 0.0641		\| 0.0641
	\| 2.23		\| 2.23
Line 40:		Line 31:
	\| 16875/16807, 65625/65536, 1600000/1594323		\| 16875/16807, 65625/65536, 1600000/1594323
	\| {{mapping\|417 661 968 1171}}		\| {{mapping\|417 661 968 1171}}
	\| -0.0418		\| −0.0418
	\| 0.2331		\| 0.2331
	\| 8.10		\| 8.10
Line 47:		Line 38:
	\| 540/539, 3025/3024, 496125/495616, 7168000/7144929		\| 540/539, 3025/3024, 496125/495616, 7168000/7144929
	\| {{mapping\|417 661 968 1171 1443}}		\| {{mapping\|417 661 968 1171 1443}}
	\| -0.1029		\| −0.1029
	\| 0.2416		\| 0.2416
	\| 8.40		\| 8.40
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator<br />(reduced)*
	! Cents<br />(reduced)*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 85:		Line 69:
	\| 16/15		\| 16/15
	\| [[Tertiosec]]		\| [[Tertiosec]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:58, 16 November 2024

2024-11-16T00:58:26Z

← Older revision		Revision as of 00:58, 16 November 2024
Line 13:		Line 13:
	== 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\|661 -417}}		! rowspan="2" \| [[Comma list\|Comma List]]
	\|{{mapping\|417 661}}		! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve Stretch (¢)
			! colspan="2" \| Tuning Error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
			\|-
			\| 2.3
			\| {{monzo\|661 -417}}
			\| {{mapping\|417 661}}
	\| -0.0641		\| -0.0641
	\| 0.0641		\| 0.0641
	\| 2.23		\| 2.23
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|1600000/1594323, {{monzo\|-80 8 29}}		\| 1600000/1594323, {{monzo\|-80 8 29}}
	\|{{mapping\|417 661 968}}		\| {{mapping\|417 661 968}}
	\| +0.0580		\| +0.0580
	\| 0.1806		\| 0.1806
	\| 6.28		\| 6.28
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|16875/16807, 65625/65536, 1600000/1594323		\| 16875/16807, 65625/65536, 1600000/1594323
	\|{{mapping\|417 661 968 1171}}		\| {{mapping\|417 661 968 1171}}
	\| -0.0418		\| -0.0418
	\| 0.2331		\| 0.2331
	\| 8.10		\| 8.10
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|540/539, 3025/3024, 496125/495616, 7168000/7144929		\| 540/539, 3025/3024, 496125/495616, 7168000/7144929
	\|{{mapping\|417 661 968 1171 1443}}		\| {{mapping\|417 661 968 1171 1443}}
	\| -0.1029		\| -0.1029
	\| 0.2416		\| 0.2416
Line 53:		Line 54:
	=== 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		\|-
	! Generator<br>(reduced)*		! Periods<br />per 8ve
	! Cents<br>(reduced)*		! Generator<br />(reduced)*
	! Associated<br>Ratio*		! Cents<br />(reduced)*
			! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|77\417		\| 77\417
	\|221.58		\| 221.58
	\|8388608/7381125		\| 8388608/7381125
	\|[[Fortune]]		\| [[Fortune]]
	\|-		\|-
	\|1		\| 1
	\|118\417		\| 118\417
	\|339.57		\| 339.57
	\|243/200		\| 243/200
	\|[[Amity]]		\| [[Amity]]
	\|-		\|-
	\|1		\| 1
	\|121\417		\| 121\417
	\|348.20		\| 348.20
	\|60/49		\| 60/49
	\|[[Eris]]		\| [[Eris]]
	\|-		\|-
	\|3		\| 3
	\|39\417		\| 39\417
	\|112.23		\| 112.23
	\|16/15		\| 16/15
	\|[[Tertiosec]]		\| [[Tertiosec]]
	\|}		\|}
			{{orf}}
	~~<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 */

2023-12-23T19:02:24Z

Rank-2 temperaments

@@ Line 60: / Line 60: @@
 ! Temperaments
 |-
 |-
 |1
@@ Line 66: / Line 77: @@
 |60/49
 |[[Eris]]
 |}

Francium: Created page with "{{Infobox ET}} {{EDO intro|417}} == Theory == 417et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 589824/588245, 43046721/43025920,..."

2023-12-23T18:56:42Z

Created page with "{{Infobox ET}} {{EDO intro|417}} == Theory == 417et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 589824/588245, 43046721/43025920,..."

New page

{{Infobox ET}}
{{EDO intro|417}}

== Theory ==
417et is only consistent to the [[5-odd-limit]]. Using the patent val, it tempers out [[589824/588245]], [[43046721/43025920]], [[33554432/33480783]] and [[65625/65536]] in the 7-limit; 78121827/77948684, 20155392/20131375, 10333575/10307264, 1019215872/1019046875, 46656/46585, 1366875/1362944, 78675968/78594219, [[536870912/535869675]], 7168000/7144929, 496125/495616, 514714375/514434888, 2359296/2358125, [[540/539]], 1265625/1261568, 17561600/17537553, 180224/180075, 1375/1372, 645922816/645700815, [[3025/3024]], 9453125/9437184 and 1362944/1361367 in the 11-limit. It [[support]]s [[familia]] and 5-limit [[fortune]].

=== Prime harmonics ===
{{Harmonics in equal|417}}

=== Subsets and supersets ===
417 factors into 3 × 139, with [[3edo]] and [[139edo]] 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 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|661 -417}}
|{{mapping|417 661}}
| -0.0641
| 0.0641
| 2.23
|-
|2.3.5
|1600000/1594323, {{monzo|-80 8 29}}
|{{mapping|417 661 968}}
| +0.0580
| 0.1806
| 6.28
|-
|2.3.5.7
|16875/16807, 65625/65536, 1600000/1594323
|{{mapping|417 661 968 1171}}
| -0.0418
| 0.2331
| 8.10
|-
|2.3.5.7.11
|540/539, 3025/3024, 496125/495616, 7168000/7144929
|{{mapping|417 661 968 1171 1443}}
| -0.1029
| 0.2416
| 8.40
|}

=== 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
|121\417
|348.20
|60/49
|[[Eris]]
|}