1637edo - Revision history

Francium: +comma

2025-02-24T06:07:36Z

+comma

← Older revision		Revision as of 06:07, 24 February 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1637edo is [[consistent]] to the [[7-odd-limit]], but the error of its [[harmonic]] [[3/1\|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. In the 2.5.11.17.23.43 subgroup it tempers out [[10880/10879]].		1637edo is [[consistent]] to the [[7-odd-limit]], but the error of its [[harmonic]] [[3/1\|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. In the 2.5.11.17.23.43 subgroup it tempers out [[4301/4300]] and [[10880/10879]].

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 12:52, 21 February 2025

2025-02-21T12:52:07Z

← Older revision		Revision as of 12:52, 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" \|[[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \|Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning ~~Error~~		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	\|-		! colspan="2" \| Tuning error
	![[TE error\|Absolute]] (¢)		\|-
	![[TE simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.9		\| 2.9
Line 39:		Line 40:
	\| {{monzo\|-7 -2 13 -6}}, {{monzo\|-24 12 0 -5}}, {{monzo\|22 5 -3 -11}}		\| {{monzo\|-7 -2 13 -6}}, {{monzo\|-24 12 0 -5}}, {{monzo\|22 5 -3 -11}}
	\| {{mapping\|1637 5189 3801 4596}}		\| {{mapping\|1637 5189 3801 4596}}
	\| -0.0141		\| −0.0141
	\| 0.0488		\| 0.0488
	\| 6.66		\| 6.66
Line 46:		Line 47:
	\| 2359296/2358125, 820125/819896, 50014503/50000000, 275653125/275365888		\| 2359296/2358125, 820125/819896, 50014503/50000000, 275653125/275365888
	\| {{mapping\|1637 5189 3801 4596 5663}}		\| {{mapping\|1637 5189 3801 4596 5663}}
	\| -0.0075		\| −0.0075
	\| 0.0456		\| 0.0456
	\| 6.22		\| 6.22
Line 53:		Line 54:
	\| 4096/4095, 67392/67375, 3720087/3718000, 225000/224939, 6125625/6117748		\| 4096/4095, 67392/67375, 3720087/3718000, 225000/224939, 6125625/6117748
	\| {{mapping\|1637 5189 3801 4596 5663 6058}}		\| {{mapping\|1637 5189 3801 4596 5663 6058}}
	\| -0.0188		\| −0.0188
	\| 0.0487		\| 0.0487
	\| 6.64		\| 6.64

Francium: changed EDO intro to ED intro

2025-02-21T05:58:03Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:58, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1637~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +music

2025-01-15T14:57:00Z

+music

← Older revision		Revision as of 14:57, 15 January 2025
Line 57:		Line 57:
	\| 6.64		\| 6.64
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Kasivo" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/6QCT4t1o2dd1CMDgdmlSAv Spotify] \| [https://francium223.bandcamp.com/track/kasivo Bandcamp] \| [https://www.youtube.com/watch?v=X-OVkgCF8IY YouTube] – in Kaguyic, 1637edo tuning

FloraC: /* Theory */ nullity-1 temps are best given by commas

2024-11-08T12:47:55Z

Theory: nullity-1 temps are best given by commas

← Older revision		Revision as of 12:47, 8 November 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1637edo is [[consistent]] to the [[7-odd-limit]] ~~and~~ the error of its [[harmonic]] [[3/1\|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. It [[~~support]]s [[kaguyic~~]].		1637edo is [[consistent]] to the [[7-odd-limit]], but the error of its [[harmonic]] [[3/1\|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. In the 2.5.11.17.23.43 subgroup it tempers out [[10880/10879]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	1637edo is the 259th [[prime ~~EDO~~]]. [[3274edo]], which doubles it, gives a good correction to the harmonic 3.		1637edo is the 259th [[prime edo]]. [[3274edo]], which doubles it, gives a good correction to the harmonic 3.

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

Francium: Created page with "{{Infobox ET}} {{EDO intro|1637}} == Theory == 1637edo is consistent to the 7-odd-limit and the error of its harmonic 3 is quite large. Using the 2.9.5.7...."

2024-11-03T17:29:28Z

Created page with "{{Infobox ET}} {{EDO intro|1637}} == Theory == 1637edo is consistent to the 7-odd-limit and the error of its harmonic 3 is quite large. Using the 2.9.5.7...."

New page

{{Infobox ET}}
{{EDO intro|1637}}

== Theory ==
1637edo is [[consistent]] to the [[7-odd-limit]] and the error of its [[harmonic]] [[3/1|3]] is quite large. Using the 2.9.5.7.11.13.17.19.23 [[subgroup]], it tempers out [[4096/4095]], 67392/67375, [[14400/14399]], [[6175/6174]], [[11016/11011]], [[1863/1862]], [[3060/3059]] and 152361/152320. It [[support]]s [[kaguyic]].

=== Odd harmonics ===
{{Harmonics in equal|1637}}

=== Subsets and supersets ===
1637edo is the 259th [[prime EDO]]. [[3274edo]], 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|-5189 1637}}
| {{mapping|1637 5189}}
| +0.0193
| 0.0193
| 2.63
|-
| 2.9.5
| {{monzo|-53 5 16}}, {{monzo|-56 77 -81}}
| {{mapping|1637 5189 3801}}
| +0.0125
| 0.0185
| 2.52
|-
| 2.9.5.7
| {{monzo|-7 -2 13 -6}}, {{monzo|-24 12 0 -5}}, {{monzo|22 5 -3 -11}}
| {{mapping|1637 5189 3801 4596}}
| -0.0141
| 0.0488
| 6.66
|-
| 2.9.5.7.11
| 2359296/2358125, 820125/819896, 50014503/50000000, 275653125/275365888
| {{mapping|1637 5189 3801 4596 5663}}
| -0.0075
| 0.0456
| 6.22
|-
| 2.9.5.7.11.13
| 4096/4095, 67392/67375, 3720087/3718000, 225000/224939, 6125625/6117748
| {{mapping|1637 5189 3801 4596 5663 6058}}
| -0.0188
| 0.0487
| 6.64
|}