1051edo - 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"

2026-03-13T13:31:38Z

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 57:		Line 57:
	! Temperaments		! Temperaments
	\|}		\|}
	<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 12:54, 21 February 2025

2025-02-21T12:54:33Z

← Older revision		Revision as of 12:54, 21 February 2025
Line 15:		Line 15:
	== 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]]
	! 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]] (¢)
Line 27:		Line 28:
	\| {{monzo\| 1666 -1051 }}		\| {{monzo\| 1666 -1051 }}
	\| {{mapping\| 1051 1666 }}		\| {{mapping\| 1051 1666 }}
	\| -0.0736		\| −0.0736
	\| 0.0736		\| 0.0736
	\| 6.45		\| 6.45
Line 41:		Line 42:
	\| {{monzo\| 40 7 -22 }}, {{monzo\| 63 -50 7 }}		\| {{monzo\| 40 7 -22 }}, {{monzo\| 63 -50 7 }}
	\| {{mapping\| 1051 1666 2441 }} (1051c)		\| {{mapping\| 1051 1666 2441 }} (1051c)
	\| -0.1562		\| −0.1562
	\| 0.1313		\| 0.1313
	\| 11.5		\| 11.5
Line 48:		Line 49:
	=== 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*
	! Associated<br>~~Ratio~~		! Cents*
			! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-
	\|}		\|}
			<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

2025-02-21T05:54:39Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:54, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1051~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.		1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.

Francium: +categories

2024-02-13T18:22:54Z

+categories

← Older revision		Revision as of 18:22, 13 February 2024
Line 58:		Line 58:

	== Music ==		== Music ==
	; [[~~User:Francium\|~~Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning		* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning

			[[Category:Listen]]

FloraC: Cleanup

2023-10-19T15:33:31Z

Cleanup

← Older revision		Revision as of 15:33, 19 October 2023
Line 25:		Line 25:
	\| 2.3		\| 2.3
	\| {{monzo\| 1666 -1051 }}		\| {{monzo\| 1666 -1051 }}
	\| {{~~val~~\| 1051 1666 }}		\| {{mapping\| 1051 1666 }}
	\| -0.0736		\| -0.0736
	\| 0.0736		\| 0.0736
Line 32:		Line 32:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -68 18 17 }}, {{monzo\| -26 -29 31 }}		\| {{monzo\| -68 18 17 }}, {{monzo\| -26 -29 31 }}
	\| {{~~val~~\| 1051 1666 2440 }} (1051)		\| {{mapping\| 1051 1666 2440 }} (1051)
	\| +0.0077		\| +0.0077
	\| 0.1298		\| 0.1298
Line 39:		Line 39:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 40 7 -22 }}, {{monzo\| 63 -50 7 }}		\| {{monzo\| 40 7 -22 }}, {{monzo\| 63 -50 7 }}
	\| {{~~val~~\| 1051 1666 2441 }} (1051c)		\| {{mapping\| 1051 1666 2441 }} (1051c)
	\| -0.1562		\| -0.1562
	\| 0.1313		\| 0.1313
Line 57:		Line 57:
	-->		-->

	== Music ==		== Music ==
	*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[~~User:Francium\|Francium~~]]		; [[User:Francium\|Francium]]
			* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning

BudjarnLambeth at 06:49, 9 July 2023

2023-07-09T06:49:35Z

← Older revision		Revision as of 06:49, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1051}}		{{EDO intro\|1051}}
	== Theory ==		== Theory ==

BudjarnLambeth at 05:23, 9 July 2023

2023-07-09T05:23:03Z

← Older revision		Revision as of 05:23, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1051}}		{{EDO intro\|1051}}
	== Theory ==		== Theory ==

FloraC: /* Theory */ plz note that subgroup is part of RTT perspective.

2023-05-08T08:23:03Z

Theory: plz note that subgroup is part of RTT perspective.

← Older revision		Revision as of 08:23, 8 May 2023
Line 2:		Line 2:
	{{EDO intro\|1051}}		{{EDO intro\|1051}}
	== Theory ==		== Theory ==
	1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit.		1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.
	From a regular temperament perspective, 1051edo only has a consistency limit of 3 and does poorly with approximating the harmonics 5 and 7. However, 1051edo has a good representation of the 2.3.11.13.15.17.19.35 subgroup.
	===Odd harmonics===		Assume the [[patent val]], 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|1051}}		{{Harmonics in equal\|1051}}
	===Subsets and supersets===
	1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.		=== Subsets and supersets ===
			1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3.

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"

FloraC: /* Regular temperament properties */ plz note 2.3.15 is equivalent to 2.3.5 and 2.3.15.35 is equivalent to 2.3.5.7. It doesn't seem to be supporting edson in any obvious way, either

2023-05-08T08:19:42Z

Regular temperament properties: plz note 2.3.15 is equivalent to 2.3.5 and 2.3.15.35 is equivalent to 2.3.5.7. It doesn't seem to be supporting edson in any obvious way, either

← Older revision		Revision as of 08:19, 8 May 2023
Line 8:		Line 8:
	===Subsets and supersets===		===Subsets and supersets===
	1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.		1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples 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\|1666 -1051}}		\| {{monzo\| 1666 -1051 }}
	\|{{val\|1051 1666}}		\| {{val\| 1051 1666 }}
	\| -0.0736		\| -0.0736
	\| 0.0736		\| 0.0736
	\| 6.45		\| 6.45
	\|-		\|-
	\|2.3.15		\| 2.3.5
	\|{{monzo\|-68 1 17}}, {{monzo\|42 -~~61 14~~}}		\| {{monzo\| -68 18 17 }}, {{monzo\| -26 -29 31 }}
	\|{{val\|1051 1666 ~~4106~~}}		\| {{val\| 1051 1666 2440 }} (1051)
	\| -0.~~0353~~		\| +0.0077
	\| 0.~~0810~~		\| 0.1298
	\| 7.09		\| 11.4
	\|-		\|-
	\|2.3.~~15.35~~		\| 2.3.5
	~~\|2460375/2458624, 4096000/4084101, 299072265625/297538935552~~		\| {{monzo\| 40 7 -22 }}, {{monzo\| 63 -50 7 }}
	\|{{~~val~~\|~~1051 1666 4106 5391~~}}		\| {{val\| 1051 1666 2441 }} (1051c)
	~~\| -0.0333~~		\| -0.1562
	~~\| 0.0702~~		\| 0.1313
	~~\| 6.15~~		\| 11.5
	\|-
	~~\|2.3.15.35.11~~
	~~\|6250/6237~~, ~~180224/180075, 2460375/2458624, 43923/43904~~
	\|{{~~val\|1051 1666 4106 5391 3636}}~~
	~~\| -0.0357~~
	~~\| 0.0630~~
	~~\| 5.52~~
	\|-
	~~\|2.3.15.35.11.13~~
	~~\|1716/1715, 4096/4095, 6250/6237, 91125/91091, 6656/6655~~
	~~\|{{val\|1051 1666 4106 5391 3636 3889~~}}
	~~\| -0.0214~~
	~~\| 0.0658~~
	~~\| 5.76~~
	\|-
	~~\|2.3.15.35.11.13.17~~
	~~\|1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 6656/6655~~
	\|{{val\|1051 1666 ~~4106 5391 3636 3889 4296~~}}
	\| -0.~~0214~~
	\| 0.~~0609~~
	\| ~~5.33~~
	\|-
	~~\|2.3.15.35.~~11.~~13.17.19~~
	~~\|1540/1539, 1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 41800/41769~~
	~~\|{{val\|1051 1666 4106 5391 3636 3889 4296 4465}}~~
	~~\| -0.0331~~
	~~\| 0.0648~~
	\| 5~~.68~~
	\|}		\|}
			<!--
	=== 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		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator<br>(~~reduced~~)		! Generator<br>(Reduced)
	! Cents<br>(~~reduced~~)		! Cents<br>(Reduced)
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
	\|1
	~~\|435\1051~~
	~~\|496.67~~
	~~\|5457/4096~~
	~~\|Edson~~
	\|}		\|}
			-->

	== Music ==		== Music ==
	*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium\|Francium]]		*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium\|Francium]]

Francium: Created page with "{{Infobox ET}} {{EDO intro|1051}} == Theory == 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376..."

2023-05-07T19:24:58Z

Created page with "{{Infobox ET}} {{EDO intro|1051}} == Theory == 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376..."

New page

{{Infobox ET}}
{{EDO intro|1051}}
== Theory ==
1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit.
From a regular temperament perspective, 1051edo only has a consistency limit of 3 and does poorly with approximating the harmonics 5 and 7. However, 1051edo has a good representation of the 2.3.11.13.15.17.19.35 subgroup.
===Odd harmonics===
{{Harmonics in equal|1051}}
===Subsets and supersets===
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples 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|1666 -1051}}
|{{val|1051 1666}}
| -0.0736
| 0.0736
| 6.45
|-
|2.3.15
|{{monzo|-68 1 17}}, {{monzo|42 -61 14}}
|{{val|1051 1666 4106}}
| -0.0353
| 0.0810
| 7.09
|-
|2.3.15.35
|2460375/2458624, 4096000/4084101, 299072265625/297538935552
|{{val|1051 1666 4106 5391}}
| -0.0333
| 0.0702
| 6.15
|-
|2.3.15.35.11
|6250/6237, 180224/180075, 2460375/2458624, 43923/43904
|{{val|1051 1666 4106 5391 3636}}
| -0.0357
| 0.0630
| 5.52
|-
|2.3.15.35.11.13
|1716/1715, 4096/4095, 6250/6237, 91125/91091, 6656/6655
|{{val|1051 1666 4106 5391 3636 3889}}
| -0.0214
| 0.0658
| 5.76
|-
|2.3.15.35.11.13.17
|1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 6656/6655
|{{val|1051 1666 4106 5391 3636 3889 4296}}
| -0.0214
| 0.0609
| 5.33
|-
|2.3.15.35.11.13.17.19
|1540/1539, 1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 41800/41769
|{{val|1051 1666 4106 5391 3636 3889 4296 4465}}
| -0.0331
| 0.0648
| 5.68
|}

=== 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
|435\1051
|496.67
|5457/4096
|Edson
|}

== Music ==
*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium|Francium]]