103edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:45Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
Line 209:		Line 209:
	\| [[Neptune]]		\| [[Neptune]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Overthink: /* Regular temperament properties */ note absolute error

2026-01-11T02:23:31Z

Regular temperament properties: note absolute error

← Older revision		Revision as of 02:23, 11 January 2026
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	\| 5.10		\| 5.10
	\|}		\|}

			* 103et (103h val) has lower absolute errors than any smaller equal temperaments in the [[13-limit\|13-]], [[17-limit\|17-]], and [[19-limit]]s, being beaten by [[111edo\|111]] in all of them.

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

ArrowHead294: /* Approximation to JI */

2025-03-20T14:44:43Z

Approximation to JI

← Older revision		Revision as of 14:44, 20 March 2025
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	== Approximation to JI ==		== Approximation to JI ==
			=== Interval mappings ===
			{{Q-odd-limit intervals}}

	=== Zeta peak index ===		=== Zeta peak index ===
	{~~\| class="wikitable"~~		{{ZPI
	\|-		\| zpi = 596
	~~! colspan="3"~~ \| ~~Tuning~~		\| steps = 102.936629522070
	~~! colspan~~=~~"3" \| Strength~~		\| step size = 11.6576577800491
	~~! colspan="2"~~ \| ~~Closest edo~~		\| tempered height = 8.543510
	~~! colspan~~=~~"2" \| Integer limit~~		\| pure height = 5.620365
	\|-		\| integral = 1.340775
	~~! ZPI~~		\| gap = 18.270998
	~~! Steps per octave~~		\| octave = 1200.73875134506
	~~! Step size (cents)~~		\| consistent = 15
	~~! Height~~		\| distinct = 15
	~~! Integral~~		}}
	~~! Gap~~
	~~! Edo~~
	~~! Octave (cents)~~
	~~! Consistent~~
	~~! Distinct~~
	\|-
	~~\| [[596zpi]]~~
	\| 102.936629522070
	\| 11.6576577800491
	\| 8.543510
	\| 1.340775
	\| 18.270998
	\| ~~103edo~~
	\| 1200.73875134506
	\| 15
	\| 15
	\|}

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

ArrowHead294 at 16:46, 18 February 2025

2025-02-18T16:46:37Z

← Older revision		Revision as of 16:46, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|103~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Consolidate sections

2025-01-19T10:10:40Z

Consolidate sections

@@ Line 15: / Line 15: @@
 == Intervals ==
 {{Main|Table of 103edo intervals}}
 == Regular temperament properties ==
@@ Line 22: / Line 54: @@
 ! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br />8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve stretch (¢)
 ! colspan="2" | Tuning error
 |-
@@ Line 75: / Line 107: @@
 |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
 |-
-! Periods<br />per 8ve
+! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br />ratio*
+! Associated<br>ratio*
 ! Temperaments
 |-
@@ Line 189: / Line 221: @@
 | [[Neptune]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 == Music ==

ArrowHead294: Formatting

2025-01-19T02:43:22Z

Formatting

← Older revision		Revision as of 02:43, 19 January 2025
Line 5:		Line 5:
	In 103edo, all intervals within the [[17-odd-limit]] are [[consistent]], with the sole exception of [[9/8]] and its octave complement [[16/9]], which barely miss (relative error 50.2%). Its closest [[zeta peak index]], [[596zpi]], [[stretched and compressed tuning\|stretches the octave]] by +0.739 cents. This expansion is uniquely consistent within the 15-integer-limit.		In 103edo, all intervals within the [[17-odd-limit]] are [[consistent]], with the sole exception of [[9/8]] and its octave complement [[16/9]], which barely miss (relative error 50.2%). Its closest [[zeta peak index]], [[596zpi]], [[stretched and compressed tuning\|stretches the octave]] by +0.739 cents. This expansion is uniquely consistent within the 15-integer-limit.

	103edo is a good [[miracle]] tuning, especially for the [[7-limit]], and for [[Gamelismic clan #Miracle\|benediction]] and [[Gamelismic clan #Miracle\|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out\|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.		103edo is a good [[miracle]] tuning, especially for the [[7-limit]], and for [[Gamelismic clan #Miracle\|benediction]] and [[Gamelismic clan #Miracle\|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out\|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]], and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]], and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.

	=== Prime harmonics ===		=== Prime harmonics ===
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	== Zeta properties ==		== Zeta properties ==
	===Zeta peak index===		=== Zeta peak index ===
	{\| class="wikitable"		{\| class="wikitable"
	~~! colspan="3" \|Tuning~~
	~~! colspan="3" \|Strength~~
	~~! colspan="2" \|Closest EDO~~
	~~! colspan="2" \|Integer limit~~
	\|-		\|-
	!~~ZPI~~		! colspan="3" \| Tuning
	!~~Steps per octave~~		! colspan="3" \| Strength
	~~!Step size (cents)~~		! colspan="2" \| Closest EDO
	~~!Height~~		! colspan="2" \| Integer limit
	~~!Integral~~
	~~!Gap~~
	!EDO
	!~~Octave (cents)~~
	~~!Consistent~~
	~~!Distinct~~
	\|-		\|-
	\|[[596zpi]]		! ZPI
	\|102.936629522070		! Steps per octave
	\|11.6576577800491		! Step size (cents)
	\|8.543510		! Height
	\|1.340775		! Integral
	\|18.270998		! Gap
	\|103edo		! EDO
	\|1200.73875134506		! Octave (cents)
	\|15		! Consistent
	\|15		! Distinct
			\|-
			\| [[596zpi]]
			\| 102.936629522070
			\| 11.6576577800491
			\| 8.543510
			\| 1.340775
			\| 18.270998
			\| 103edo
			\| 1200.73875134506
			\| 15
			\| 15
	\|}		\|}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]

Contribution at 23:10, 18 January 2025

2025-01-18T23:10:59Z

@@ Line 191: / Line 191: @@
 <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 == Music ==
 ; [[Francium]]

ArrowHead294 at 14:19, 16 January 2025

2025-01-16T14:19:58Z

← Older revision		Revision as of 14:19, 16 January 2025
Line 189:		Line 189:
	\| [[Neptune]]		\| [[Neptune]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Forest Tribe Dance" from ''Mysteries'' (2023) ~~–~~ [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] \| [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] \| [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube]		* "Forest Tribe Dance" from ''Mysteries'' (2023) – [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] \| [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] \| [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube]

	[[Category:Benediction]]		[[Category:Benediction]]
	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Miracle]]		[[Category:Miracle]]

ArrowHead294: Partial undo

2024-11-16T12:23:11Z

Partial undo

← Older revision		Revision as of 12:23, 16 November 2024
Line 17:		Line 17:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 60:		Line 69:
	\| 0.595		\| 0.595
	\| 5.10		\| 5.10
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
Line 172:		Line 188:
	\| 7/5		\| 7/5
	\| [[Neptune]]		\| [[Neptune]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==

ArrowHead294 at 04:50, 16 November 2024

2024-11-16T04:50:20Z

← Older revision		Revision as of 04:50, 16 November 2024
Line 17:		Line 17:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! 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]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 68:		Line 60:
	\| 0.595		\| 0.595
	\| 5.10		\| 5.10
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 186:		Line 172:
	\| 7/5		\| 7/5
	\| [[Neptune]]		\| [[Neptune]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Forest Tribe Dance" from ''Mysteries'' (2023) – [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] \| [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] \| [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube]		* "Forest Tribe Dance" from ''Mysteries'' (2023) – [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] \| [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] \| [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube]

	[[Category:Benediction]]		[[Category:Benediction]]
			[[Category:Listen]]
	[[Category:Miracle]]		[[Category:Miracle]]
	~~[[Category:Listen]]~~