770edo - Revision history

ArrowHead294 at 12:32, 21 February 2025

2025-02-21T12:32:56Z

← Older revision		Revision as of 12:32, 21 February 2025
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" \| [[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]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
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	\| {{monzo\| 2441 -770 }}		\| {{monzo\| 2441 -770 }}
	\| {{mapping\| 770 2441 }}		\| {{mapping\| 770 2441 }}
	\| -0.0388		\| −0.0388
	\| 0.0388		\| 0.0388
	\| 2.49		\| 2.49
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	\| {{monzo\| 61 2 -29 }}, {{monzo\| 40 -28 21 }}		\| {{monzo\| 61 2 -29 }}, {{monzo\| 40 -28 21 }}
	\| {{mapping\| 770 2441 1788 }}		\| {{mapping\| 770 2441 1788 }}
	\| -0.0517		\| −0.0517
	\| 0.0365		\| 0.0365
	\| 2.34		\| 2.34
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	\| 43046721/43025920, 134217728/133984375, 1220703125/1219784832		\| 43046721/43025920, 134217728/133984375, 1220703125/1219784832
	\| {{mapping\| 770 2441 1788 2162 }}		\| {{mapping\| 770 2441 1788 2162 }}
	\| -0.0855		\| −0.0855
	\| 0.0666		\| 0.0666
	\| 4.27		\| 4.27
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	\| 9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367		\| 9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367
	\| {{mapping\| 770 2441 1788 2162 2664 }}		\| {{mapping\| 770 2441 1788 2162 2664 }}
	\| -0.0898		\| −0.0898
	\| 0.0602		\| 0.0602
	\| 3.86		\| 3.86

Francium: changed EDO intro to ED intro

2025-02-21T06:12:13Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:12, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|770~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T12:11:46Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:11, 2 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	770edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably tempers out [[9801/9800]].		770edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably [[tempering out\|tempers out]] [[9801/9800]].

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 770 factors into ~~2 × 5 × 7 × 11~~, 770edo has subset edos {{EDOs\| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.		Since 770 factors into {{factorization\|770}}, 770edo has subset edos {{EDOs\| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Rework on theory

2023-10-20T12:01:22Z

Rework on theory

← Older revision		Revision as of 12:01, 20 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|770}}		{{EDO intro\|770}}
	==Theory==
	770edo ~~tempers out 134217728/133984375,~~ [[~~703125/702464~~]]~~, 5250987/5242880 and 200120949/200000000 in~~ the 7-limit; 56723625/56689952, 161280/161051, 234375/234256, 2097152/2096325, 496125/495616, 151263/151250, 104857600/104825259, 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, 160083/160000, 766656/765625, 43923/43904, 20614528/20588575 and ~~781258401~~/~~781250000 in~~ the 11~~-limit~~.		== Theory ==
	===Odd harmonics===		770edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1\|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably tempers out [[9801/9800]].

			=== Odd harmonics ===
	{{Harmonics in equal\|770}}		{{Harmonics in equal\|770}}
	===Subsets and supersets===
	770 factors into 2 × 5 × 7 × 11 ~~with~~ subset edos {{EDOs\| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.		=== Subsets and supersets ===
	==Regular temperament properties==		Since 770 factors into 2 × 5 × 7 × 11, 770edo has subset edos {{EDOs\| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.

			== 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]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|2441 -770}}		\| {{monzo\| 2441 -770 }}
	\|{{~~val~~\|770 2441}}		\| {{mapping\| 770 2441 }}
	\| -0.0388		\| -0.0388
	\| 0.0388		\| 0.0388
	\| 2.49		\| 2.49
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|61 2 -29}}, {{monzo\|40 -28 21}}		\| {{monzo\| 61 2 -29 }}, {{monzo\| 40 -28 21 }}
	\|{{~~val~~\|770 2441 1788}}		\| {{mapping\| 770 2441 1788 }}
	\| -0.0517		\| -0.0517
	\| 0.0365		\| 0.0365
	\| 2.34		\| 2.34
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|43046721/43025920, 134217728/133984375, 1220703125/1219784832		\| 43046721/43025920, 134217728/133984375, 1220703125/1219784832
	\|{{~~val~~\|770 2441 1788 2162}}		\| {{mapping\| 770 2441 1788 2162 }}
	\| -0.0855		\| -0.0855
	\| 0.0666		\| 0.0666
	\| 4.27		\| 4.27
	\|-		\|-
	\|2.9.5.7.11		\| 2.9.5.7.11
	\|9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367		\| 9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367
	\|{{~~val~~\|770 2441 1788 2162 2664}}		\| {{mapping\| 770 2441 1788 2162 2664 }}
	\| -0.0898		\| -0.0898
	\| 0.0602		\| 0.0602
	\| 3.86		\| 3.86
	\|}		\|}
	==Scales==
			== Scales ==
	* [[Semidim8]]		* [[Semidim8]]
	* [[Semidim13]]		* [[Semidim13]]

Francium: Created page with "{{Infobox ET}} {{EDO intro|770}} ==Theory== 770edo tempers out 134217728/133984375, 703125/702464, 5250987/5242880 and 200120949/200000000 in the 7-limit; 56723625/5668995..."

2023-10-02T09:36:27Z

Created page with "{{Infobox ET}} {{EDO intro|770}} ==Theory== 770edo tempers out 134217728/133984375, 703125/702464, 5250987/5242880 and 200120949/200000000 in the 7-limit; 56723625/5668995..."

New page

{{Infobox ET}}
{{EDO intro|770}}
==Theory==
770edo tempers out 134217728/133984375, [[703125/702464]], 5250987/5242880 and 200120949/200000000 in the 7-limit; 56723625/56689952, 161280/161051, 234375/234256, 2097152/2096325, 496125/495616, 151263/151250, 104857600/104825259, 172032/171875, 369140625/369098752, 825000/823543, 180224/180075, 160083/160000, 766656/765625, 43923/43904, 20614528/20588575 and 781258401/781250000 in the 11-limit.
===Odd harmonics===
{{Harmonics in equal|770}}
===Subsets and supersets===
770 factors into 2 × 5 × 7 × 11 with subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.
==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]] (%)
|-
|2.9
|{{monzo|2441 -770}}
|{{val|770 2441}}
| -0.0388
| 0.0388
| 2.49
|-
|2.9.5
|{{monzo|61 2 -29}}, {{monzo|40 -28 21}}
|{{val|770 2441 1788}}
| -0.0517
| 0.0365
| 2.34
|-
|2.9.5.7
|43046721/43025920, 134217728/133984375, 1220703125/1219784832
|{{val|770 2441 1788 2162}}
| -0.0855
| 0.0666
| 4.27
|-
|2.9.5.7.11
|9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367
|{{val|770 2441 1788 2162 2664}}
| -0.0898
| 0.0602
| 3.86
|}
==Scales==
* [[Semidim8]]
* [[Semidim13]]