Mercurial comma - Revision history

Overthink: /* Temperaments */ fix info

2025-12-07T05:23:41Z

Temperaments: fix info

← Older revision		Revision as of 05:23, 7 December 2025
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	== Temperaments ==		== Temperaments ==
	Tempering this comma out in the full 19-limit produces the rank-19 '''mercurial''' temperament.		Tempering this comma out in the full 19-limit produces the rank-7 '''mercurial''' temperament.

	Subgroup:		Subgroup: 2.3.5.7.11.13.17.19

	Comma list: 557122275/556583944		Comma list: 557122275/556583944

VectorGraphics at 09:44, 14 August 2025

2025-08-14T09:44:29Z

← Older revision		Revision as of 09:44, 14 August 2025
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	As the ratio between these intervals is very close to phi, a diatonic scale consisting of a 19/17 as the tone and 15/14 as the semitone represents a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence. This is particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials. Hence, the mercurial comma is named after the chemical element mercury due to its adjacency to gold, since mercury meantone is adjacent to golden meantone.		As the ratio between these intervals is very close to phi, a diatonic scale consisting of a 19/17 as the tone and 15/14 as the semitone represents a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence. This is particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials. Hence, the mercurial comma is named after the chemical element mercury due to its adjacency to gold, since mercury meantone is adjacent to golden meantone.

	It is worth noting that per principles of regular temperament theory, a temperament produced by the mercurial comma is a rank-7 19-limit temperament, which would naturally have the name mercurial.		It is worth noting that per principles of regular temperament theory, a temperament produced by the mercurial comma is a rank-7 19-limit temperament, which would naturally have the name mercurial. Alternately, there is a temperament produced in the 2.3.5.7.17.19 subgroup, which is a rank-5 temperament. This can be easily added to the commas of septimal meantone and [[256/255]] to produce a rank-2 temperament in the meantone family which supports the mercurial relation.

	== Temperaments ==		== Temperaments ==

Eliora: expand and clarify that a mere stack of 19/17s and 15/14s in a diatonic way is not a "temperament" and this comma like any others has a full rank temperament to it

2025-08-12T03:35:53Z

expand and clarify that a mere stack of 19/17s and 15/14s in a diatonic way is not a "temperament" and this comma like any others has a full rank temperament to it

@@ Line 6: / Line 6: @@
 }}
-'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.
+'''557122275/556583944''', or the '''mercurial comma''', is an unnoticeable comma measuring 1.673649 [[cent]]s. It represents the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave, thus being of importance in [[5L 2s]] diatonic scale.
 == Etymology ==
-It is named after the chemical element mercury due to its adjacency to gold, since mercury meantone is adjacent to golden meantone.
+As the ratio between these intervals is very close to phi, a diatonic scale consisting of a 19/17 as the tone and 15/14 as the semitone represents a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence. This is particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials. Hence, the mercurial comma is named after the chemical element mercury due to its adjacency to gold, since mercury meantone is adjacent to golden meantone.
-It is unrelated to the [[Mercury|80th-octave temperament]] by the same name.
+It is worth noting that per principles of regular temperament theory, a temperament produced by the mercurial comma is a rank-7 19-limit temperament, which would naturally have the name mercurial.
 [[Category:Meantone]]
 [[Category:Mercurial]]
 [[Category:Commas named after elements]]

BudjarnLambeth at 02:15, 16 November 2024

2024-11-16T02:15:12Z

← Older revision		Revision as of 02:15, 16 November 2024
Line 15:		Line 15:
	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Mercurial]]		[[Category:Mercurial]]
			[[Category:Commas named after elements]]

Eliora at 21:25, 8 September 2023

2023-09-08T21:25:22Z

← Older revision		Revision as of 21:25, 8 September 2023
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	'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.		'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.

			== Etymology ==
			It is named after the chemical element mercury due to its adjacency to gold, since mercury meantone is adjacent to golden meantone.

			It is unrelated to the [[Mercury\|80th-octave temperament]] by the same name.

	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Mercurial]]		[[Category:Mercurial]]

Francium: Added color name

2023-09-08T05:27:50Z

Added color name

← Older revision		Revision as of 05:27, 8 September 2023
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	\| Ratio = 557122275/556583944		\| Ratio = 557122275/556583944
	\| Name = mercurial comma		\| Name = mercurial comma
			\| Color name = 19o<sup>5</sup>17u<sup>5</sup>rryy-3, quinnosu-abiruyo negative 3rd
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:47:48Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:47, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 557122275/556583944		\| Ratio = 557122275/556583944
	~~\| Monzo = -3 2 2 -2 0 0 -5 5~~
	~~\| Cents = 1.673649~~
	\| Name = mercurial comma		\| Name = mercurial comma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name =~~
	~~\| Sound~~ =
	}}		}}

	'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.		'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.

	~~[[Category:19-limit]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Mercurial]]		[[Category:Mercurial]]

Fredg999 category edits: Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

2022-03-20T22:01:54Z

Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

← Older revision		Revision as of 22:01, 20 March 2022
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	[[Category:19-limit]]		[[Category:19-limit]]
	[[Category:Unnoticeable ~~comma~~]]		[[Category:Unnoticeable commas]]
	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Mercurial]]		[[Category:Mercurial]]

Fredg999: Misc. edits, categories

2022-01-22T05:26:03Z

Misc. edits, categories

← Older revision		Revision as of 05:26, 22 January 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 557122275/556583944		\| Ratio = 557122275/556583944
	\| Monzo = -3 2 2 -2 0 0 -5 5		\| Monzo = -3 2 2 -2 0 0 -5 5
	\| Cents = 1.673649		\| Cents = 1.673649
	\| Name = ~~Mercurial Comma~~		\| Name = mercurial comma
	\| Color name =		\| Color name =
			\| FJS name =
	\| Sound =		\| Sound =
	}}		}}

	'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent~~\|cents~~]], and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[~~Golden_meantone\|~~golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.		'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent]]s, and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.

	[[Category:19-limit]]		[[Category:19-limit]]
	[[Category:~~Interval]]~~		[[Category:Unnoticeable comma]]
	~~[[Category:Ratio]]~~
	~~[[Category:Unnoticeable_comma]]~~
	~~[[Category:Just interval~~]]
	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Mercurial]]		[[Category:Mercurial]]

Flirora at 22:20, 6 February 2021

2021-02-06T22:20:32Z

← Older revision		Revision as of 22:20, 6 February 2021
Line 9:		Line 9:
	}}		}}

	'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent\|cents]], and is the amount by which five justly tuned [[19/17]]'s and two [[15/14]]'s ~~exceeds~~ an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[Golden_meantone\|golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.		'''557122275/556583944''', or the '''mercurial comma''', has a value of 1.673649 [[cent\|cents]], and is the amount by which five justly tuned [[19/17]]s and two [[15/14]]s exceed an octave. As the ratio between these intervals is very close to phi, this is a strong harmonic entropy minimum adjacent to the [[Golden_meantone\|golden meantone]] sequence, particularly well suited to stringed instruments that are normally tuned with slight octave stretches due to the inharmonicity of their partials.

	[[Category:19-limit]]		[[Category:19-limit]]