2960edo - Revision history

ArrowHead294 at 12:20, 21 February 2025

2025-02-21T12:20:32Z

← Older revision		Revision as of 12:20, 21 February 2025
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	The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave. These can be arranged in [[diatonic]] pattern to sound like a [[meantone]] scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.		The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave. These can be arranged in [[diatonic]] pattern to sound like a [[meantone]] scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.

	From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.		From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo ({{nowrap\|2955 + 5 {{=}} 2960}}), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
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	== Scales ==		== Scales ==
	* 474 474 295 474 474 474 295 - mercury "meantone" (major scale)		* 474 474 295 474 474 474 295 – mercury "meantone" (major scale)

	{{Todo\| review }}		{{Todo\| review }}

Francium: changed EDO intro to ED intro

2025-02-21T06:19:03Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:19, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2960~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Eliora: /* Theory */ readability, shorter sentences

2023-10-30T13:52:37Z

Theory: readability, shorter sentences

← Older revision		Revision as of 13:52, 30 October 2023
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	2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].		2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].

	The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave~~, which~~ can be arranged in [[diatonic]] pattern to sound like a meantone scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.		The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave. These can be arranged in [[diatonic]] pattern to sound like a [[meantone]] scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.

	From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.		From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.

Eliora: /* Theory */ clarify it's just the mercurial comma alone and not meantone

2023-10-30T13:52:01Z

Theory: clarify it's just the mercurial comma alone and not meantone

← Older revision		Revision as of 13:52, 30 October 2023
Line 5:		Line 5:
	2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].		2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].

	The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[~~mercury meantone~~]], which ~~tunes~~ the ~~meantone steps to~~ [[19/17]] and [[15/14]]. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the [[patent val]] fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3/2.		The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave, which can be arranged in [[diatonic]] pattern to sound like a meantone scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.

	From a regular temperament perspective, ~~mercury meantone~~ in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.		From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 16:		Line 16:

	== Scales ==		== Scales ==
	* 474 474 295 474 474 474 295 - mercury meantone (major scale)		* 474 474 295 474 474 474 295 - mercury "meantone" (major scale)

	{{Todo\| review }}		{{Todo\| review }}

FloraC: Rework theory; +subsets and supersets; mark todo (whether it supports mercury meantone must be thoroughly investigated)

2023-10-30T10:11:25Z

Rework theory; +subsets and supersets; mark todo (whether it supports mercury meantone must be thoroughly investigated)

← Older revision		Revision as of 10:11, 30 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2960}}		{{EDO intro\|2960}}

	== Theory ==		== Theory ==
	2960edo is ~~a dual~~-~~fifth system that~~ is ~~also an~~ excellent 2.5.9.11.17.19 subgroup ~~tuning.~~		2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].

	~~2960dh val {{val\|2960 4691 6873 '''8309''' 10240 10953 12099 '''12573'''}} is the unique mapping that supports both the 80th-octave temperament called~~ [[~~mercury~~]], and ~~the coincidentally similarly named~~ [[~~mercury meantone~~]], ~~which tunes the meantone steps to~~ [[19/17]] and [[15/14]].

	In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the patent val fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3\2.		The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]]. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the [[patent val]] fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3/2.

	From a regular temperament perspective, mercury meantone in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.		From a regular temperament perspective, mercury meantone in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|2960}}		{{Harmonics in equal\|2960}}

			=== Subsets and supersets ===
			Since 2960 factors into {{factorization\|2960}}, 2960edo has subset edos {{EDOs\| 2, 4, 5, 8, 10, 16, 20, 37, 40, 74, 80, 148, 185, 296, 370, 592, 740 and 1480 }}.

	== Scales ==		== Scales ==
	* 474 474 295 474 474 474 295 - mercury meantone (major scale)		* 474 474 295 474 474 474 295 - mercury meantone (major scale)

			{{Todo\| review }}

BudjarnLambeth at 07:03, 9 July 2023

2023-07-09T07:03:40Z

← Older revision		Revision as of 07:03, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2960}}		{{EDO intro\|2960}}
	== Theory ==		== Theory ==

BudjarnLambeth at 04:33, 9 July 2023

2023-07-09T04:33:03Z

← Older revision		Revision as of 04:33, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|2960}}		{{EDO intro\|2960}}
	== Theory ==		== Theory ==

Eliora: expanded upon mercury meantone and proposed an RTT interpretation

2023-04-15T21:27:13Z

expanded upon mercury meantone and proposed an RTT interpretation

← Older revision		Revision as of 21:27, 15 April 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2960}}		{{EDO intro\|2960}}
			== Theory ==
			2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning.

	~~2960edo~~ is ~~a dual~~-fifth ~~system that~~ is also ~~an excellent~~ 2.5.~~9.11.17.19 subgroup tuning~~.		2960dh val {{val\|2960 4691 6873 '''8309''' 10240 10953 12099 '''12573'''}} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]].

			In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the patent val fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3\2.

			From a regular temperament perspective, mercury meantone in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.

	2960dh val {{val\|2960 4691 6873 '''8309''' 10240 10953 12099 '''12573'''}} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]].		=== Odd harmonics ===
	{{harmonics in equal\|2960}}		{{harmonics in equal\|2960}}

			== Scales ==
			* 474 474 295 474 474 474 295 - mercury meantone (major scale)

Eliora: oops

2023-03-03T15:59:55Z

oops

← Older revision		Revision as of 15:59, 3 March 2023
Line 4:		Line 4:
	2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning.		2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning.

	2960dh val {{val\|2960 4691 '''~~6873~~''' ~~8309~~ 10240 10953 '''~~12099~~''' ~~12573~~}} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]].		2960dh val {{val\|2960 4691 6873 '''8309''' 10240 10953 12099 '''12573'''}} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]].
	{{harmonics in equal\|2960}}		{{harmonics in equal\|2960}}

Eliora: Created page with "{{Infobox ET}} {{EDO intro|2960}} 2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning. 2960dh val {{val|2960 4691 '''6873''' 8309 10240 1..."

2023-02-22T22:44:03Z

Created page with "{{Infobox ET}} {{EDO intro|2960}} 2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning. 2960dh val {{val|2960 4691 '''6873''' 8309 10240 1..."

New page

{{Infobox ET}}
{{EDO intro|2960}}

2960edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning.

2960dh val {{val|2960 4691 '''6873''' 8309 10240 10953 '''12099''' 12573}} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]].
{{harmonics in equal|2960}}

← Older revision		Revision as of 13:52, 30 October 2023
Line 5:		Line 5:
	2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].		2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[17/1\|17]], and [[19/1\|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1\|7]] and [[23/1\|23]], or [[21/1\|21]] and [[13/1\|13]].

	The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave~~, which~~ can be arranged in [[diatonic]] pattern to sound like a meantone scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.		The 2960dh [[val]] {{val\| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercurial comma]], which is the difference between a stack of 5 [[19/17]] and 2 [[15/14]] with the octave. These can be arranged in [[diatonic]] pattern to sound like a [[meantone]] scale. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps.

	From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.		From a regular temperament perspective, this in 2960edo can be potentially realized as [[893edo\|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.