49edo - Revision history

Fredg999: Text replacement - "[[The Riemann zeta function and tuning|" to "[[Riemann zeta function|"

2026-07-16T18:55:35Z

Text replacement - "[[The Riemann zeta function and tuning|" to "[[Riemann zeta function|"

← Older revision		Revision as of 18:55, 16 July 2026
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	=== Zeta peaks ===		=== Zeta peaks ===
	The strongest [[~~The~~ Riemann zeta function ~~and tuning~~\|local zeta peak]] around 49edo is its second closest, 49.141 edo. One step is 24.419 cents, and two steps, 48.839 cents, is a good generator for [[Triple BP]].		The strongest [[Riemann zeta function\|local zeta peak]] around 49edo is its second closest, 49.141 edo. One step is 24.419 cents, and two steps, 48.839 cents, is a good generator for [[Triple BP]].

	== Approximation to irrational intervals ==		== Approximation to irrational intervals ==

Lucius Chiaraviglio: /* 21st century */ Bryan Deister's ''Prelude in 49edo'' (2026): Add full version

2026-07-16T17:20:24Z

21st century: Bryan Deister's ''Prelude in 49edo'' (2026): Add full version

← Older revision		Revision as of 17:20, 16 July 2026
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	* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026)		* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026)
	* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026)		* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026)
	* [https://www.youtube.com/watch?v=aNswQ1-1nlM&list=WL&index=275 ''<nowiki>~~Prelude in 49edo~~ [short clip]</nowiki>''] (2026)		* ''Prelude in 49edo'' (2026)
			** [https://www.youtube.com/watch?v=aNswQ1-1nlM&list=WL&index=275 <nowiki>[short clip]</nowiki>] (2026) (Lumatone view)
			** [https://www.youtube.com/watch?v=j1FEWPvHlGo <nowiki>[full version]</nowiki>] (2026)

	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]

Lucius Chiaraviglio: /* Intervals */ Add links to intervals that did not have them (some refer to pages that do not exist yet; some have corresponding pages); add the semisept generator 72/55 and its octave complement 55/36

2026-07-16T04:05:09Z

Intervals: Add links to intervals that did not have them (some refer to pages that do not exist yet; some have corresponding pages); add the semisept generator 72/55 and its octave complement 55/36

← Older revision		Revision as of 04:05, 16 July 2026
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	\| 10		\| 10
	\| 244.898		\| 244.898
	\| 125/108, 144/125		\| [[125/108]], [[144/125]]
	\| {{UDnote\|step=10}}		\| {{UDnote\|step=10}}
	\|-		\|-
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	\| 19		\| 19
	\| 465.306		\| 465.306
	\| 125/96, ''162/125''		\| [[72/55]], [[125/96]], ''[[162/125]]''
	\| {{UDnote\|step=19}}		\| {{UDnote\|step=19}}
	\|-		\|-
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	\| 30		\| 30
	\| 734.694		\| 734.694
	\| ''125/81'', 192/125		\| ''[[55/36]], [[125/81]]'', [[192/125]]
	\| {{UDnote\|step=30}}		\| {{UDnote\|step=30}}
	\|-		\|-
Line 216:		Line 216:
	\| 39		\| 39
	\| 955.102		\| 955.102
	\| 125/72, 216/125		\| [[125/72]], [[216/125]]
	\| {{UDnote\|step=39}}		\| {{UDnote\|step=39}}
	\|-		\|-

Lucius Chiaraviglio: /* Rank-2 temperaments */ 19\49 is 72/55, but table had 55/36 (octave complement) instead

2026-07-16T03:58:48Z

Rank-2 temperaments: 19\49 is 72/55, but table had 55/36 (octave complement) instead

← Older revision		Revision as of 03:58, 16 July 2026
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	\| 19\49		\| 19\49
	\| 465.3		\| 465.3
	\| 55~~/36~~		\| 72/55
	\| [[Semisept]]		\| [[Semisept]]
	\|-		\|-

Lucius Chiaraviglio: /* 21st century */ Add Bryan Deister's ''Prelude in 49edo [short clip]'' (2026)

2026-07-16T03:48:21Z

21st century: Add Bryan Deister's ''Prelude in 49edo [short clip]'' (2026)

← Older revision		Revision as of 03:48, 16 July 2026
Line 547:		Line 547:
	* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026)		* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026)
	* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026)		* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026)
			* [https://www.youtube.com/watch?v=aNswQ1-1nlM&list=WL&index=275 ''<nowiki>Prelude in 49edo [short clip]</nowiki>''] (2026)

	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]

Fitzgerald Lee: /* Approximation to JI */

2026-04-25T10:43:34Z

Approximation to JI

← Older revision		Revision as of 10:43, 25 April 2026
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	=== Interval mappings ===		=== Interval mappings ===
	{{Q-odd-limit intervals\|49}}		{{Q-odd-limit intervals\|49}}
			{{Q-odd-limit intervals\|49.1\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 49f val mapping}}

	=== Zeta peaks ===		=== Zeta peaks ===

Contribution: /* Nonoctave temperament */

2026-04-20T22:33:22Z

Nonoctave temperament

← Older revision		Revision as of 22:33, 20 April 2026
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	=== Nonoctave temperament ===		=== Nonoctave temperament ===
	The [[Triple BP\|triple Bohlen–Pierce scale]] is obtained by taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents~~; it is optimized as a~~ Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup ~~and~~ mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit.		The TE-optimized [[Triple BP\|triple Bohlen–Pierce scale]] is obtained by taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents. It realizes the Tenney–Euclidean regular temperament on the 3.5.7.11.13 subgroup mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit.

	== Scales ==		== Scales ==

Contribution: /* Nonoctave temperament */

2026-04-20T22:09:56Z

Nonoctave temperament

← Older revision		Revision as of 22:09, 20 April 2026
Line 482:		Line 482:

	=== Nonoctave temperament ===		=== Nonoctave temperament ===
	~~Taking~~ every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents ~~yields the [[Triple BP\|triple Bohlen–Pierce]] scale,~~ optimized as a Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup and mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit.		The [[Triple BP\|triple Bohlen–Pierce scale]] is obtained by taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents; it is optimized as a Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup and mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit.

	== Scales ==		== Scales ==

Contribution: /* Nonoctave temperament */

2026-04-20T22:02:35Z

Nonoctave temperament

← Older revision		Revision as of 22:02, 20 April 2026
Line 482:		Line 482:

	=== Nonoctave temperament ===		=== Nonoctave temperament ===
	Taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents yields the [[Triple BP\|triple Bohlen–Pierce]] scale, optimized as a Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup and mapped as [⟨78 114 138 170 182]].		Taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents yields the [[Triple BP\|triple Bohlen–Pierce]] scale, optimized as a Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup and mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit.

	== Scales ==		== Scales ==

Contribution: /* Nonoctave temperament */

2026-04-20T21:14:08Z

Nonoctave temperament

← Older revision		Revision as of 21:14, 20 April 2026
Line 482:		Line 482:

	=== Nonoctave temperament ===		=== Nonoctave temperament ===
	Taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents yields the [[Triple BP\|triple Bohlen–Pierce]] scale, optimized as a Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup and mapped as [~~⟨39 57 69 85 91~~]].		Taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents yields the [[Triple BP\|triple Bohlen–Pierce]] scale, optimized as a Tenney–Euclidean regular temperament in the 3.5.7.11.13 subgroup and mapped as [⟨78 114 138 170 182]].

	== Scales ==		== Scales ==