1216/1215 - Revision history

BudjarnLambeth at 02:16, 16 November 2024

2024-11-16T02:16:16Z

← Older revision		Revision as of 02:16, 16 November 2024
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	[[Category:Eratosthenes]]		[[Category:Eratosthenes]]
			[[Category:Commas named after polymaths]]
			[[Category:Commas with unknown etymology]]{{todo\|add etymology\|comment=add etymology for “password”}}

BudjarnLambeth at 23:41, 18 September 2024

2024-09-18T23:41:47Z

← Older revision		Revision as of 23:41, 18 September 2024
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	== Etymology ==		== Etymology ==
	This comma was named after {{w\|Eratosthenes}}, the Ancient Greek polymath. According to an analysis by [[Joseph Monzo]], Eratosthenes made use of this comma by employing "standard" [[3-limit]] pitches in his diatonic genus, but substituting 19-limit ratios which are very close by in pitch in his chromatic and enharmonic genera.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_26618.html Yahoo! Tuning Group \| ''ratios in ancient Greek tetrachords (was: Byzantine and Serb Church Music)'']</ref>		This comma was named after {{w\|Eratosthenes}}, the Ancient Greek polymath. According to an analysis by [[Joseph Monzo]], Eratosthenes made use of this comma by employing "standard" [[3-limit]] pitches in his diatonic [[genus]], but substituting 19-limit ratios which are very close by in pitch in his chromatic and enharmonic genera.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_26618.html Yahoo! Tuning Group \| ''ratios in ancient Greek tetrachords (was: Byzantine and Serb Church Music)'']</ref>

	== See also ==		== See also ==

FloraC: +source of one of the names

2024-08-23T10:25:19Z

+source of one of the names

← Older revision		Revision as of 10:25, 23 August 2024
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	}}		}}

	'''1216/1215''', the '''password''' or '''Eratosthenes' comma''', is a [[19-limit]] (also 2.3.5.19 subgroup) ~~unnoticeable~~ comma. It is the amount by which [[19/15]] exceeds the [[81/64\|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243\|Pythagorean minor second (256/243)]]. It is also the difference between [[19/18]], the undevicesimal semitone and [[135/128]], the major chroma, and in addition, between the [[513/512\|undevicesimal comma]] and the [[schisma]].		'''1216/1215''', the '''password''' or '''Eratosthenes' comma''', is an [[unnoticeable comma\|unnoticeable]] [[19-limit]] (also 2.3.5.19-[[subgroup]]) [[comma]]. It is the amount by which [[19/15]] exceeds the [[81/64\|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243\|Pythagorean minor second (256/243)]]. It is also the difference between [[19/18]], the undevicesimal semitone and [[135/128]], the major chroma, and in addition, between the [[513/512\|undevicesimal comma]] and the [[schisma]].

	== Commatic relations ==		== Commatic relations ==
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	== Temperaments ==		== Temperaments ==
	By tempering out this comma is defined the '''eratosthenes temperament''', which enables the [[eratosthenes chords]]. ~~EDOs~~ supporting this temperament includes {{Optimal ET sequence\| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692}}.		By tempering out this comma is defined the '''eratosthenes temperament''', which enables the [[eratosthenes chords]]. Edos supporting this temperament includes {{Optimal ET sequence\| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 }}.

			== Etymology ==
			This comma was named after {{w\|Eratosthenes}}, the Ancient Greek polymath. According to an analysis by [[Joseph Monzo]], Eratosthenes made use of this comma by employing "standard" [[3-limit]] pitches in his diatonic genus, but substituting 19-limit ratios which are very close by in pitch in his chromatic and enharmonic genera.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_26618.html Yahoo! Tuning Group \| ''ratios in ancient Greek tetrachords (was: Byzantine and Serb Church Music)'']</ref>

	== See also ==		== See also ==
	* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			== Notes ==

	[[Category:Eratosthenes]]		[[Category:Eratosthenes]]

Dummy index: /* Commatic relations */

2024-05-11T12:20:12Z

Commatic relations

← Older revision		Revision as of 12:20, 11 May 2024
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	== Commatic relations ==		== Commatic relations ==
	This comma is the difference between the following superparticular pairs:		This comma is the difference between the following superparticular pairs:
	* [[76/75]] and [[81/80]]		* [[76/75]] and [[81/80]] *
	* [[136/135]] and [[153/152]]		* [[136/135]] and [[153/152]]
	* [[190/189]] and [[225/224]]		* [[190/189]] and [[225/224]]
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	* [[676/675]] and [[1521/1520]]		* [[676/675]] and [[1521/1520]]
	* [[1156/1155]] and [[23409/23408]]		* [[1156/1155]] and [[23409/23408]]
	<nowiki>*</nowiki> ~~all is~~ within the 2.3.5.19 subgroup		<nowiki>*</nowiki> both of these commas are also within the 2.3.5.19 subgroup.

	It factors into the following superparticular pairs:		It factors into the following superparticular pairs:

Dummy index: /* Commatic relations */ mark the subgroup-strict decomposition

2024-05-10T16:17:57Z

Commatic relations: mark the subgroup-strict decomposition

← Older revision		Revision as of 16:17, 10 May 2024
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	* [[256/255]] and [[324/323]]		* [[256/255]] and [[324/323]]
	* [[352/351]] and [[495/494]]		* [[352/351]] and [[495/494]]
	* [[361/360]] and [[513/512]]		* [[361/360]] and [[513/512]] *
	* [[456/455]] and [[729/728]]		* [[456/455]] and [[729/728]]
	* [[676/675]] and [[1521/1520]]		* [[676/675]] and [[1521/1520]]
	* [[1156/1155]] and [[23409/23408]]		* [[1156/1155]] and [[23409/23408]]
			<nowiki>*</nowiki> all is within the 2.3.5.19 subgroup

	It factors into the following superparticular pairs:		It factors into the following superparticular pairs:

FloraC: +commatic relations

2023-09-02T12:03:06Z

+commatic relations

@@ Line 5: / Line 5: @@
 }}
-'''1216/1215''', the '''password''' or '''Eratosthenes' comma''', is a [[19-limit]] (also 2.3.5.19 subgroup) unnoticeable comma. It is the amount by which [[19/15]] exceeds the [[81/64|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243|Pythagorean minor second (256/243)]]. It is also the difference between [[19/18]], the undevicesimal semitone and [[135/128]], the major chroma, and in addition, between the [[256/255|septendecimal kleisma]] and the [[324/323|nusu comma]], between the [[361/360|go comma]] and the [[513/512|undevicesimal comma]], and between the undevicesimal comma and the [[schisma]].
+'''1216/1215''', the '''password''' or '''Eratosthenes' comma''', is a [[19-limit]] (also 2.3.5.19 subgroup) unnoticeable comma. It is the amount by which [[19/15]] exceeds the [[81/64|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243|Pythagorean minor second (256/243)]]. It is also the difference between [[19/18]], the undevicesimal semitone and [[135/128]], the major chroma, and in addition, between the [[513/512|undevicesimal comma]] and the [[schisma]].
-By tempering it out is defined the '''eratosthenes temperament''', which enables the [[eratosthenes chords]]. EDOs supporting this temperament includes {{Optimal ET sequence| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692}}.
+== Commatic relations ==
 == See also ==

Xenllium at 15:14, 20 July 2023

2023-07-20T15:14:37Z

← Older revision		Revision as of 15:14, 20 July 2023
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	'''1216/1215''', the '''password''' or '''Eratosthenes' comma''', is a [[19-limit]] (also 2.3.5.19 subgroup) unnoticeable comma. It is the amount by which [[19/15]] exceeds the [[81/64\|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243\|Pythagorean minor second (256/243)]]. It is also the difference between [[19/18]], the undevicesimal semitone and [[135/128]], the major chroma, and in addition, between the [[256/255\|septendecimal kleisma]] and the [[324/323\|nusu comma]], between the [[361/360\|go comma]] and the [[513/512\|undevicesimal comma]], and between the undevicesimal comma and the [[schisma]].		'''1216/1215''', the '''password''' or '''Eratosthenes' comma''', is a [[19-limit]] (also 2.3.5.19 subgroup) unnoticeable comma. It is the amount by which [[19/15]] exceeds the [[81/64\|Pythagorean major third (81/64)]], or [[20/19]] falls short of the [[256/243\|Pythagorean minor second (256/243)]]. It is also the difference between [[19/18]], the undevicesimal semitone and [[135/128]], the major chroma, and in addition, between the [[256/255\|septendecimal kleisma]] and the [[324/323\|nusu comma]], between the [[361/360\|go comma]] and the [[513/512\|undevicesimal comma]], and between the undevicesimal comma and the [[schisma]].

	By tempering it out is defined the '''eratosthenes temperament''', which enables the ~~'''~~eratosthenes chords~~'''~~. EDOs supporting this temperament includes {{~~EDOs~~\| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692}}.		By tempering it out is defined the '''eratosthenes temperament''', which enables the [[eratosthenes chords]]. EDOs supporting this temperament includes {{Optimal ET sequence\| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692}}.

	== See also ==		== See also ==

TallKite at 02:29, 10 January 2023

2023-01-10T02:29:59Z

← Older revision		Revision as of 02:29, 10 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = password, Eratosthenes' comma		\| Name = password, Eratosthenes' comma
	\| Color name = s19og2, Sanogu comma		\| Color name = s19og2, sanogu 2nd,<br>Sanogu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

TallKite: added color name

2022-12-04T01:34:04Z

added color name

← Older revision		Revision as of 01:34, 4 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = password, Eratosthenes' comma		\| Name = password, Eratosthenes' comma
			\| Color name = s19og2, Sanogu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T14:04:32Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 14:04, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~		\| Name = password, Eratosthenes' comma
	~~\| Ratio = 1216/1215~~		\| Comma = yes
	~~\| Monzo = 6 -5 -1 0 0 0 0 1~~
	~~\| Cents = 1.42430~~
	\| Name = password, ~~<br>~~Eratosthenes' comma
	\| ~~Color name =~~
	~~\| Sound~~ =
	}}		}}

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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~[[Category:19-limit]]~~
	~~[[Category:Superparticular]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Eratosthenes]]		[[Category:Eratosthenes]]