Harmonic entropy of just intervals - Revision history

Eufalesio: dumb wording

2026-01-13T10:06:14Z

dumb wording

← Older revision		Revision as of 10:06, 13 January 2026
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	== Methodology ==		== Methodology ==
	This table was made with [[Scale Workshop]]. It was made by starting with ~~1080ed16 (~~[[270edo]] ~~but treating 16/1 as the [[period]])~~, then using "convert interval values > fraction" with a tolerance of 4.4{{c}} to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).		This table was made with [[Scale Workshop]]. It was made by starting with [[270edo]] across four octaves, then using "convert interval values > fraction" with a tolerance of 4.4{{c}} to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).

	Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).		Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).

ArrowHead294 at 15:07, 29 April 2025

2025-04-29T15:07:02Z

← Older revision		Revision as of 15:07, 29 April 2025
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	This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every ~~4-5~~ [[cents]].		This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every 4–5 [[cents]].

	The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].		The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].
Line 6:		Line 6:

	== Methodology ==		== Methodology ==
	This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values>fraction" with a tolerance of 4.4 ~~cents~~ to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).		This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values > fraction" with a tolerance of 4.4{{c}} to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).

	Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).		Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).

	== Table of intervals ==		== Table of intervals ==

	=== 1/1 to 2/1 ===		=== 1/1 to 2/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 0 to ~~1200¢~~		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 0 to 1200{{c}}
	\|-		\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
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	=== 2/1 to 4/1 ===		=== 2/1 to 4/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 1200 to ~~2400¢~~		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 1200 to 2400{{c}}
	\|-		\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
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	=== 4/1 to 8/1 ===		=== 4/1 to 8/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 2400 to ~~3600¢~~		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 2400 to 3600{{c}}
	\|-		\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
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	=== 8/1 to 16/1 ===		=== 8/1 to 16/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 3600 to ~~4800¢~~		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 3600 to 4800{{c}}
	\|-		\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)

BudjarnLambeth: /* See also */

2025-04-29T03:35:56Z

ArrowHead294 at 05:38, 25 January 2025

2025-01-25T05:38:10Z

← Older revision		Revision as of 05:38, 25 January 2025
Line 14:		Line 14:
	=== 1/1 to 2/1 ===		=== 1/1 to 2/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ Harmonic entropy of just intervals size 0 to 1200¢		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 0 to 1200¢
			\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	=== 2/1 to 4/1 ===		=== 2/1 to 4/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ Harmonic entropy of just intervals size 1200 to 2400¢		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 1200 to 2400¢
			\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	=== 4/1 to 8/1 ===		=== 4/1 to 8/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ Harmonic entropy of just intervals size 2400 to 3600¢		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 2400 to 3600¢
			\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	=== 8/1 to 16/1 ===		=== 8/1 to 16/1 ===
	{\| class="wikitable mw-collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
	\|+ Harmonic entropy of just intervals size 3600 to 4800¢		\|+ style="font-size: 105%;" \| Harmonic entropy of just intervals size 3600 to 4800¢
			\|-
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	* [[Runoff]]		* [[Runoff]]

	[[Category:Tables]][[Category:Harmonic entropy]]		[[Category:Tables]]
			[[Category:Harmonic entropy]]

BudjarnLambeth: /* 2/1 to 4/1 */ accidentally included copies of the later tables

2025-01-24T23:42:05Z

2/1 to 4/1: accidentally included copies of the later tables

Show changes

BudjarnLambeth: /* 1/1 to 2/1 */ accidentally included copies of the later tables

2025-01-24T23:41:24Z

1/1 to 2/1: accidentally included copies of the later tables

Show changes

BudjarnLambeth: /* Table of intervals */ Added table headings and made them properly collapsible

2025-01-24T06:08:49Z

Table of intervals: Added table headings and made them properly collapsible

← Older revision		Revision as of 06:08, 24 January 2025
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	=== 1/1 to 2/1 ===		=== 1/1 to 2/1 ===
	{\| class="wikitable collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
			\|+ Harmonic entropy of just intervals size 0 to 1200¢
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	=== 2/1 to 4/1 ===		=== 2/1 to 4/1 ===
	{\| class="wikitable collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
			\|+ Harmonic entropy of just intervals size 1200 to 2400¢
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	=== 4/1 to 8/1 ===		=== 4/1 to 8/1 ===
	{\| class="wikitable collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
			\|+ Harmonic entropy of just intervals size 2400 to 3600¢
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-
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	=== 8/1 to 16/1 ===		=== 8/1 to 16/1 ===
	{\| class="wikitable collapsible sortable"		{\| class="wikitable mw-collapsible sortable"
			\|+ Harmonic entropy of just intervals size 3600 to 4800¢
	! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)		! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
	\|-		\|-

BudjarnLambeth at 05:58, 24 January 2025

2025-01-24T05:58:00Z

← Older revision		Revision as of 05:58, 24 January 2025
Line 1:		Line 1:
	This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[8/1]]: roughly evenly spaced with about one interval every 4-5 [[cents]].		This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: roughly evenly spaced with about one interval every 4-5 [[cents]].

	The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].		The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].

BudjarnLambeth: /* Methodology */

2025-01-24T05:57:43Z

Methodology

← Older revision		Revision as of 05:57, 24 January 2025
Line 6:		Line 6:

	== Methodology ==		== Methodology ==
	This table was made with [[Scale Workshop]]. It was made by starting with ~~810ed8~~ ([[270edo]] but treating 8/1 as the [[period]]), then using "convert interval values>fraction" with a tolerance of 4.4 cents to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).		This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 as the [[period]]), then using "convert interval values>fraction" with a tolerance of 4.4 cents to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings).

	Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).		Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).

BudjarnLambeth: /* Table of intervals */ Complete Réyni 7.0 column, add intervals between 8/1 and 16/1

2025-01-24T05:57:23Z

Table of intervals: Complete Réyni 7.0 column, add intervals between 8/1 and 16/1

Show changes

← Older revision		Revision as of 03:35, 29 April 2025
Line 1,692:		Line 1,692:
	* [[Runoff]]		* [[Runoff]]

	[[Category:~~Tables~~]]		[[Category:Lists of intervals]]
	[[Category:Harmonic entropy]]		[[Category:Harmonic entropy]]