Negri extensions - Revision history

FloraC: FloraC moved page Negri/Extensions to Negri extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

2025-08-06T11:57:48Z

FloraC moved page Negri/Extensions to Negri extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

← Older revision	Revision as of 11:57, 6 August 2025
(No difference)

Lériendil: Text replacement - "Eigenmonzo
(unchanged-interval)" to "Unchanged interval
(eigenmonzo)"

2025-06-21T06:56:24Z

Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"

← Older revision		Revision as of 06:56, 21 June 2025
Line 197:		Line 197:
	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! [[Eigenmonzo\|~~Eigenmonzo~~<br>(~~unchanged-interval~~)]]		! [[Eigenmonzo\|Unchanged interval<br>(eigenmonzo)]]
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
Line 387:		Line 387:
	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! ~~Eigenmonzo~~<br>(~~unchanged-interval~~)		! Unchanged interval<br>(eigenmonzo)
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
Line 577:		Line 577:
	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! ~~Eigenmonzo~~<br>(~~unchanged-interval~~)		! Unchanged interval<br>(eigenmonzo)
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
Line 767:		Line 767:
	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! ~~Eigenmonzo~~<br>(~~unchanged-interval~~)		! Unchanged interval<br>(eigenmonzo)
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

Lériendil: Lériendil moved page Negri extensions to Negri/Extensions: if that's the new consensus

2025-06-04T16:58:42Z

Lériendil moved page Negri extensions to Negri/Extensions: if that's the new consensus

← Older revision	Revision as of 16:58, 4 June 2025
(No difference)

Lériendil at 23:33, 19 April 2025

2025-04-19T23:33:08Z

← Older revision		Revision as of 23:33, 19 April 2025
Line 1:		Line 1:
			{{Breadcrumb\|Negri}}

	[[Negri]] has various competing [[extension]]s to the [[11-limit]]. This is evidenced by the fact that its [[support]]ing equal temperaments, [[10edo\|10]] and [[19edo\|19]], do less well in the 11-limit. The extensions are:		[[Negri]] has various competing [[extension]]s to the [[11-limit]]. This is evidenced by the fact that its [[support]]ing equal temperaments, [[10edo\|10]] and [[19edo\|19]], do less well in the 11-limit. The extensions are:
	* '''Undecimal negri''' (10 & 19) – tempering out 45/44, 49/48, and 56/55		* '''Undecimal negri''' (10 & 19) – tempering out 45/44, 49/48, and 56/55
Line 947:		Line 949:
	[[Category:Negri]]		[[Category:Negri]]
	[[Category:Temperament extensions]]		[[Category:Temperament extensions]]
			[[Category:Rank-2 temperaments]]

FloraC: /* Tuning spectra */ +9edo

2024-12-06T09:14:54Z

Tuning spectra: +9edo

← Older revision		Revision as of 09:14, 6 December 2024
Line 552:		Line 552:
	\| 5/4		\| 5/4
	\| 128.771		\| 128.771
			\|
			\|-
			\| 1\9
			\|
			\| 133.333
	\|		\|
	\|-		\|-
Line 727:		Line 732:
	\| 15/11		\| 15/11
	\| 132.610		\| 132.610
			\|
			\|-
			\| 1\9
			\|
			\| 133.333
	\|		\|
	\|-		\|-
Line 917:		Line 927:
	\| 5/4		\| 5/4
	\| 128.771		\| 128.771
			\|
			\|-
			\| 1\9
			\|
			\| 133.333
	\|		\|
	\|-		\|-

FloraC: Simplify the ratios in the tuning spectra

2024-12-06T09:12:42Z

Simplify the ratios in the tuning spectra

Show changes

FloraC: Expand

2024-12-05T19:21:23Z

Expand

← Older revision		Revision as of 19:21, 5 December 2024
Line 4:		Line 4:
	* '''Negric''' (10e & 19e) – tempering out 33/32, 49/48, and 77/75		* '''Negric''' (10e & 19e) – tempering out 33/32, 49/48, and 77/75
	* '''Negroni''' (10 & 19e) – tempering out 49/48, 55/54, and 225/224		* '''Negroni''' (10 & 19e) – tempering out 49/48, 55/54, and 225/224

			The most important of these is undecimal negri, in which the generator, representing 13/12, 14/13, 15/14, and 16/15, goes one step further to stand in for ~12/11. The poor accuracy comes with a not overly complex mapping, as you can find ~16/11 just five generator steps away. Its evil cousin, negric, finds ~11/8 where negri will find ~15/11, which is of course conflated with [[4/3]].

			The other pair of extensions are of higher complexity, but are well rewarded with better intonation. Negril finds ~11/8 where negroni will find ~15/11 and vice versa. They unite in [[29edo]], which can be recommended as a tuning for both.

	Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to [[wilsec]]. This has the effect of slicing the generator in two, and is supported by [[20edo\|20]], [[29edo\|29]], and [[38edo\|38df]].		Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to [[wilsec]]. This has the effect of slicing the generator in two, and is supported by [[20edo\|20]], [[29edo\|29]], and [[38edo\|38df]].
Line 33:		Line 37:
	\| 1		\| 1
	\| 125.4		\| 125.4
	\| 16/15, 15/14, 14/~~13, 13/12~~		\| 13/12, 14/13, 15/14, 16/15
	\| 12/11		\| 12/11
	\|		\|
Line 41:		Line 45:
	\| 2		\| 2
	\| 250.7		\| 250.7
	\| '''8/7'''~~, 7/6~~, 15/13		\| 7/6, '''8/7''', 15/13
	\| 13/11		\| 13/11
	\|		\|
Line 73:		Line 77:
	\| 6		\| 6
	\| 752.1		\| 752.1
	\| 14/9, 32/21~~, 20/13~~		\| 14/9, 20/13, 32/21
	\|		\|
	\|		\|

FloraC: +interval chain

2024-12-05T18:38:41Z

+interval chain

Show changes

FloraC: Intro

2024-12-05T12:59:45Z

Intro

← Older revision		Revision as of 12:59, 5 December 2024
Line 1:		Line 1:
	[[Negri]] temperament has various ~~extensions~~ to the [[11-limit]].		[[Negri]] temperament has various competing [[extension]]s to the [[11-limit]]. This is evidenced by the fact that its [[support]]ing equal temperaments, [[10edo\|10]] and [[19edo\|19]], do less well in the 11-limit. The extensions are:
			* '''Undecimal negri''' (10 & 19) – tempering out 45/44, 49/48, and 56/55
			* '''Negril''' (10e & 19) – tempering out 49/48, 100/99, 225/224
			* '''Negric''' (10e & 19e) – tempering out 33/32, 49/48, 77/75
			* '''Negroni''' (10 & 19e) – tempering out 49/48, 55/54, 225/224

			Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to [[wilsec]]. This has the effect of slicing the generator in two, and is supported by [[20edo\|20]], [[29edo\|29]], and [[38edo\|38df]].

	== Tuning spectra ==		== Tuning spectra ==
Line 264:		Line 270:
	\| 4/3		\| 4/3
	\| 124.511		\| 124.511
	\| 7, 9, 11, 13 and 15 limit minimax		\| 7-, 9-, 11-, 13- and 15-odd-limit minimax
	\|-		\|-
	\|		\|
Line 274:		Line 280:
	\| {{vector\|0 -136 21 -14 98 -21}}		\| {{vector\|0 -136 21 -14 98 -21}}
	\| 124.764		\| 124.764
	\| 13 limit least squares		\| 13-odd-limit least squares
	\|-		\|-
	\|		\|
Line 304:		Line 310:
	\| 30517578125/26795786661		\| 30517578125/26795786661
	\| 125.469		\| 125.469
	\| 7 limit least squares		\| 7-odd-limit least squares
	\|-		\|-
	\|		\|

FloraC: -gencoms (irrelevant to tuning and trivial to derive). Misc. cleanup

2024-12-05T12:50:51Z

-gencoms (irrelevant to tuning and trivial to derive). Misc. cleanup

Show changes

Negri extensions - Revision history

FloraC: FloraC moved page Negri/Extensions to Negri extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

Lériendil: Text replacement - "Eigenmonzo(unchanged-interval)" to "Unchanged interval(eigenmonzo)"

Lériendil: Lériendil moved page Negri extensions to Negri/Extensions: if that's the new consensus

Lériendil at 23:33, 19 April 2025

FloraC: /* Tuning spectra */ +9edo

FloraC: Simplify the ratios in the tuning spectra

FloraC: Expand

FloraC: +interval chain

FloraC: Intro

FloraC: -gencoms (irrelevant to tuning and trivial to derive). Misc. cleanup

Lériendil: Text replacement - "Eigenmonzo
(unchanged-interval)" to "Unchanged interval
(eigenmonzo)"