20ed5 - Revision history

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:20:44Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:20, 1 August 2025
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	\| just major third plus two octaves		\| just major third plus two octaves
	\|}		\|}

	~~[[Category:Edonoi]]~~

	{{todo\|add sound example}}		{{todo\|add sound example}}

Fredg999 category edits: Removing from Category:Ed5 using Cat-a-lot

2025-08-01T18:39:02Z

Removing from Category:Ed5 using Cat-a-lot

← Older revision		Revision as of 18:39, 1 August 2025
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	\|}		\|}

	~~[[Category:Ed5]]~~
	[[Category:Edonoi]]		[[Category:Edonoi]]

	{{todo\|add sound example}}		{{todo\|add sound example}}

ArrowHead294 at 18:19, 13 March 2025

2025-03-13T18:19:38Z

← Older revision		Revision as of 18:19, 13 March 2025
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	'''[[Ed5\|Division of the 5th harmonic]] into 20 equal parts''' (20ED5) is known as '''Hieronymus' Tuning'''. The step size is about 139.3157 cents, corresponding to 8.6135 [[EDO]].		'''[[Ed5\|Division of the 5th harmonic]] into 20 equal parts''' (20ED5) is known as '''Hieronymus' Tuning'''. The step size is about 139.3157 cents, corresponding to 8.6135 [[EDO]].

	A [[harmonic entropy]] minimum, that has better approximations of a variety of [[just interval]]s than [[~~Bohlen Pierce~~]] (of course, not the same intervals) among which are 13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are (at most) ~4.3 pentaves within [[human hearing range]]; imagine if that were the case with octaves (yes that is a helpful analogy).		A [[harmonic entropy]] minimum, that has better approximations of a variety of [[just interval]]s than [[Bohlen–Pierce]] (of course, not the same intervals) among which are 13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are (at most) ~4.3 pentaves within [[human hearing range]]; imagine if that were the case with octaves (yes that is a helpful analogy).

	One way of looking at it comes by constructing it via four tempered 3/2 ([[meantone]] without octaves) each of which is divided into five tones, which in turn approximate 11/8, 13/8, 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but ''turned entirely inside-out''. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.		One way of looking at it comes by constructing it via four tempered 3/2 ([[meantone]] without octaves) each of which is divided into five tones, which in turn approximate 11/8, 13/8, 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but ''turned entirely inside-out''. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.

BudjarnLambeth: /* Harmonics */

2024-10-06T01:18:09Z

Harmonics

← Older revision		Revision as of 01:18, 6 October 2024
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	== Harmonics ==		== Harmonics ==
			{{Harmonics in equal
	{{~~harmonics~~ in equal\|20\|5\|1}}		\| steps = 20
			\| num = 5
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 20
			\| num = 5
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

	== Intervals ==		== Intervals ==

BudjarnLambeth: Added headings, added table of harmonics

2024-01-15T09:49:13Z

Added headings, added table of harmonics

← Older revision		Revision as of 09:49, 15 January 2024
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	Adding octaves makes it [[Meantone family#Jerome\|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo\|43EDO]], and 5\43 can be used as a generator.		Adding octaves makes it [[Meantone family#Jerome\|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo\|43EDO]], and 5\43 can be used as a generator.

			== Harmonics ==

			{{harmonics in equal\|20\|5\|1}}

			== Intervals ==

	{\| class="wikitable"		{\| class="wikitable"

Plumtree: Infobox ET added

2022-10-05T20:39:23Z

Infobox ET added

← Older revision		Revision as of 20:39, 5 October 2022
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			{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 20 equal parts''' (20ED5) is known as '''Hieronymus' Tuning'''. The step size is about 139.3157 cents, corresponding to 8.6135 [[EDO]].		'''[[Ed5\|Division of the 5th harmonic]] into 20 equal parts''' (20ED5) is known as '''Hieronymus' Tuning'''. The step size is about 139.3157 cents, corresponding to 8.6135 [[EDO]].

Xenwolf: simplify internal links and table markup

2022-03-24T07:17:53Z

simplify internal links and table markup

Show changes

Xenllium at 01:01, 29 August 2021

2021-08-29T01:01:12Z

@@ Line 1: / Line 1: @@
-th root of 5 "Hieronymus' Tuning"
+'''[[Ed5|Division of the 5th harmonic]] into 20 equal parts''' (20ED5) is known as '''Hieronymus' Tuning'''. The step size is about 139.3157 cents, corresponding to 8.6135 [[EDO]].
-A [[Harmonic_Entropy|harmonic entropy]] minimum, that has better approximations of a variety of [[just_interval|just interval]]s than [[Bohlen_Pierce|Bohlen Pierce]] (of course, not the same intervals) among which are <span style="">13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are (at most) ~4.3 pentaves within [[human_hearing_range|human hearing range]]; imagine if that were the case with octaves (yes that is a helpful analogy).</span>
+A [[Harmonic_Entropy|harmonic entropy]] minimum, that has better approximations of a variety of [[just_interval|just interval]]s than [[Bohlen Pierce]] (of course, not the same intervals) among which are 13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of strict 5/1 equivalence and high-limit harmony, it also approximates the harmonics and their pentave reductions: ‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents. Note that there are (at most) ~4.3 pentaves within [[human_hearing_range|human hearing range]]; imagine if that were the case with octaves (yes that is a helpful analogy).
-<span style="">One way of looking at it comes by constructing it via four tempered 3/2</span> ([[Meantone|meantone]] without octaves) <span style="">each of which is divided</span> into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but ''turned entirely inside-out''. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.
+One way of looking at it comes by constructing it via four tempered 3/2 ([[Meantone|meantone]] without octaves) each of which is divided into five tones, which in turn approximate 11/8, 13/8, 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but ''turned entirely inside-out''. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.
-Adding octaves makes it [[Meantone_family#Jerome|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo]], and 5\43 can be used as a generator.
+Adding octaves makes it [[Meantone_family#Jerome|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo|43EDO]], and 5\43 can be used as a generator.
 [[Category:Ed5]]

Xenwolf: upd cats

2020-11-29T13:20:36Z

upd cats

← Older revision		Revision as of 13:20, 29 November 2020
Line 6:		Line 6:

	Adding octaves makes it [[Meantone_family#Jerome\|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo]], and 5\43 can be used as a generator.		Adding octaves makes it [[Meantone_family#Jerome\|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo]], and 5\43 can be used as a generator.
	[[Category:~~ed5~~]]
	[[Category:~~edonoi~~]]		[[Category:Ed5]]
	[[Category:~~todo~~:~~add_sound_examples~~]]		[[Category:Edonoi]]

			[[Category:Todo:add sound example]]

Inthar at 12:02, 4 July 2020

2020-07-04T12:02:52Z

← Older revision		Revision as of 12:02, 4 July 2020
Line 5:		Line 5:
	<span style="">One way of looking at it comes by constructing it via four tempered 3/2</span> ([[Meantone\|meantone]] without octaves) <span style="">each of which is divided</span> into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but ''turned entirely inside-out''. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.		<span style="">One way of looking at it comes by constructing it via four tempered 3/2</span> ([[Meantone\|meantone]] without octaves) <span style="">each of which is divided</span> into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1, wherein the scale repeats itself. By analogy to common practice, this is familiar extended meantone but ''turned entirely inside-out''. Interestingly, while Hieronymus does not repeat at the octave or even approximate it well, factors of 2 are nevertheless important to its perception and structure; it might even be helpful to think of the 3/2 intervals as a cellular structure of sorts.

	Adding octaves makes it [[Meantone_family#Jerome\|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo]], and ~~its~~ 5\43 ~~interval~~ can be used as a generator.		Adding octaves makes it [[Meantone_family#Jerome\|jerome temperament]], with generator a meantone fifth divided in five, and Hieronymus is the generator chain of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, or even higher limit system. It is related to [[43edo]], and 5\43 can be used as a generator.
	[[Category:ed5]]		[[Category:ed5]]
	[[Category:edonoi]]		[[Category:edonoi]]
	[[Category:todo:add_sound_examples]]		[[Category:todo:add_sound_examples]]