19edf - Revision history

ArrowHead294 at 14:52, 8 July 2025

2025-07-08T14:52:29Z

BudjarnLambeth: add todo:expand, add harmonics, make table collapsible

2024-12-20T08:29:10Z

add todo:expand, add harmonics, make table collapsible

← Older revision		Revision as of 08:29, 20 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''19EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent\|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of \|-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.		'''19EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent\|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of \|-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.

			==Harmonics==
			{{Harmonics in equal\|19\|3\|2}}
			{{Harmonics in equal\|19\|3\|2\|start=12\|collapsed=1}}

	==Intervals==		==Intervals==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 19edf
	\|-		\|-
	! \| degree		! \| degree
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	\|		\|
	\|}		\|}

			{{todo\|expand}}

FloraC: -irrelevant shit

2024-05-07T13:23:28Z

-irrelevant shit

← Older revision		Revision as of 13:23, 7 May 2024
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	\|		\|
	\|}		\|}
	~~==Scale tree==~~
	If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant\|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.

	~~If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.~~

	~~Generator range: 36.09023 cents (4\7/19 = 4\133) to 37.89474 cents (3\5/19 = 3\95)~~
	~~{\| class="wikitable center-all"~~
	~~! colspan="7" \| Fifth~~
	~~!Cents~~
	~~! Comments~~
	\|-
	~~\| 4\7\|\| \|\| \|\| \|\| \|\| \|\| \|\| 36.0902\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|27\47\|\|36.2822\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|23\40\|\| \|\|36.3158 \|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|42\73 \|\|36.3374 \|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| 19\33\|\| \|\| \|\|36.{{Overline\|36}}\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|53\92\|\|36.3844\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|34\59\|\| \|\|36.3961\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|49\85\|\|36.4087 \|\|~~
	\|-
	~~\| \|\| \|\| \|\|15\26\|\| \|\| \|\| \|\|36.43725\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|56\97\|\|36.4633\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| 41\71\|\| \|\|36.4175\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|67\116\|\| 36.4791\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| 26\45\|\| \|\| \|\|36.4912\|\|[[Flattone]] is in this region~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|63\109\|\|36.5041\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|37\64\|\| \|\|36.5132\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|48\83 \|\| 36.52505\|\|~~
	\|-
	~~\| \|\| \|\|11\19\|\| \|\| \|\| \|\| \|\| 36.5651\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\| 51\88\|\|36.6029\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|40\69 \|\| \|\|36.6133\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|69\119\|\| 36.6210\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| 29\50\|\| \|\| \|\|36.6316\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\| 76\131\|\|36.6412\|\|[[Golden meantone]] (696.2145¢)~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|47\81\|\| \|\|36.6472\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|65\112\|\|36.6541\|\|~~
	\|-
	~~\| \|\| \|\| \|\|18\31\|\| \|\| \|\| \|\|36.6723\|\|[[Meantone]] is in this region~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|61\105\|\|36.6917\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|43\74\|\| \|\|36.6999\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|68\117\|\|36.70175\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\|25\43\|\| \|\| \|\|36.7197\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|57\98\|\|36.7347\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|32\55\|\| \|\|36.7464\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|39\67\|\|36.76355\|\|~~
	\|-
	~~\| \|\|7\12\|\| \|\| \|\| \|\| \|\| \|\|36.8421\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|36.9231\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|36.9414\|\|The fifth closest to a just [[3/2]] for EDOs less than 200~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|36.9541\|\|[[Garibaldi]] / [[Cassandra]]~~
	\|-
	~~\| \|\| \|\| \|\| \|\|24\41\|\| \|\| \|\|36.9705\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|65\111\|\|36.98435\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|41\70\|\| \|\|36.9925\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|58\99\|\|37.0016\|\|~~
	\|-
	~~\| \|\| \|\| \|\|17\29\|\| \|\| \|\| \|\|37.0236\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|61\104\|\|37.0445\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|44\75\|\| \|\|37.0526\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|71\121\|\|37.0596\|\|Golden neogothic (704.0956¢)~~
	\|-
	~~\| \|\| \|\| \|\| \|\|27\46\|\| \|\| \|\|37.0709\|\|[[Neogothic]] is in this region~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|64\109\|\|37.0835\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|37\63\|\| \|\|37.0927\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|47\80\|\|37.1053\|\|~~
	\|-
	~~\| \|\| \|\|10\17\|\| \|\| \|\| \|\| \|\|37.1517\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|43\73\|\|37.2026\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|33\56\|\| \|\|37.21805\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|56\95\|\|37.2299\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\|23\39\|\| \|\| \|\|37.2470\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|59\100\|\|37.2632\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|36\61\|\| \|\|37.2735\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|49\83\|\|37.2388\|\|~~
	\|-
	~~\| \|\| \|\| \|\|13\22\|\| \|\| \|\| \|\|37.3206\|\|[[Archy]] is in this region~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|42\71\|\|37.3610\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|29\49\|\| \|\|37.3792\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|45\76\|\|37.3961\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\|16\27\|\| \|\| \|\|37.4269\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|35\59\|\|37.46655\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\|19\32\|\| \|\|37.5000\|\|~~
	\|-
	~~\| \|\| \|\| \|\| \|\| \|\| \|\|22\37\|\|37.5533\|\|~~
	\|-
	~~\|3\5\|\| \|\| \|\| \|\| \|\| \|\| \|\|37.8947\|\|~~
	\|}Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.
	~~[[Category:Edf]]~~
	~~[[Category:Edonoi]]~~

Moremajorthanmajor at 00:47, 26 March 2023

2023-03-26T00:47:20Z

@@ Line 204: / Line 204: @@
+|
 |}
 [[Category:Edf]]
 [[Category:Edonoi]]

Plumtree: Infobox ET added

2022-10-05T18:37:40Z

Infobox ET added

← Older revision		Revision as of 18:37, 5 October 2022
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			{{Infobox ET}}
	'''19EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent\|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of \|-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.		'''19EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 19 parts of 36.945 [[cent\|cents]] each, corresponding to 32.4807 [[edo]] (similar to every second step of [[65edo]]). It tempers out the same commas as 65edo with the addition of \|-103/19 65/19> (1.425 cents) resulting from its inexact 4/1.

Moremajorthanmajor at 18:25, 1 June 2021

2021-06-01T18:25:09Z

← Older revision		Revision as of 18:25, 1 June 2021
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	! \| comments		! \| comments
	\|-		\|-
	\| colspan="2"\| 0		! colspan="2" \| 0
	\| \| '''exact [[1/1]]'''		\| \| '''exact [[1/1]]'''
	\| \|		\| \|

Moremajorthanmajor at 22:34, 19 August 2019

2019-08-19T22:34:54Z

← Older revision		Revision as of 22:34, 19 August 2019
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	! \| comments		! \| comments
	\|-		\|-
	\| ~~\| 0~~		\| colspan="2"\| 0
	\| \| 0
	\| \| '''exact [[1/1]]'''		\| \| '''exact [[1/1]]'''
	\| \|		\| \|

Moremajorthanmajor at 22:30, 5 March 2019

2019-03-05T22:30:33Z

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Xenllium at 13:08, 6 February 2019

2019-02-06T13:08:48Z

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Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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