Musical cells - Revision history

Fredg999: Mark term as idiosyncratic, misc. edits

2023-12-12T20:55:28Z

Mark term as idiosyncratic, misc. edits

← Older revision		Revision as of 20:55, 12 December 2023
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	'''Musical cells''' are a system of [[Mario Pizarro]] for constructing [[well temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.		'''Musical cells'''{{idiosyncratic}} are a system of [[Mario Pizarro]] for constructing [[well temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''"{{idiosyncratic}}. This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.

	== Musical cells ==		== Musical cells ==
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	== Toctave ==		== Toctave ==
	~~'''Toctave'''~~ (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro came up with in connection with his theory of musical cells.		The toctave (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro came up with in connection with his theory of musical cells.

	<math>Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots</math>		<math>Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots</math>
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	== See also ==		== See also ==

	* [[Octave]]		* [[Octave]]
	* [[Stretched tuning]]		* [[Stretched tuning]]

Fredg999: Replace Wikipedia link with internal link

2023-07-11T04:48:06Z

Replace Wikipedia link with internal link

← Older revision		Revision as of 04:48, 11 July 2023
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	* [[Octave]]		* [[Octave]]
	* [[~~Wikipedia:~~Stretched tuning]]		* [[Stretched tuning]]
	* [[Wikipedia:Stretched octave]]		* [[Wikipedia:Stretched octave]]

	[[Category:Well temperament]]		[[Category:Well temperament]]

Fredg999: Categories

2022-03-27T19:59:08Z

Fredg999: Added a section about musical cells

2022-03-27T19:58:07Z

Added a section about musical cells

← Older revision		Revision as of 19:58, 27 March 2022
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	'''Musical cells''' is a system of [[Mario Pizarro]] for constructing [[~~circulating~~ temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.		'''Musical cells''' are a system of [[Mario Pizarro]] for constructing [[well temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.

			== Musical cells ==
			Pizarro's musical cells are based on a set of three [[comma]]s:
			* M: (3<sup>8</sup> × 5)/2<sup>15</sup> ([[schisma]]);
			* J: (2<sup>25</sup> × 2<sup>1/4</sup>)/(3<sup>13</sup> × 5<sup>2</sup>);
			* U: (2<sup>12</sup> × 5<sup>2</sup> × 3<sup>1/2</sup>)/3<sup>11</sup>.

			Using combinations of these commas, he defined two "semitone factors" K and P, which he then put together to from the Piagui scale. This well-tempered scale follows an [[8L 4s]] pattern, with large steps K and small steps P. There are three variants (rotations) of this scale: Piagui I (KKP KKP KKP KKP), Piagui II (KPK KPK KPK KPK) and Piagui III (PKK PKK PKK PKK).

	== Toctave ==		== Toctave ==

Xenwolf: definition is there

2022-02-26T20:50:17Z

definition is there

← Older revision		Revision as of 20:50, 26 February 2022
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	* [[Wikipedia:Stretched octave]]		* [[Wikipedia:Stretched octave]]

	~~[[Category:Todo:add definition]]~~
	[[Category:Todo:expand]]		[[Category:Todo:expand]]

Xenwolf: /* See also */ +2 (moving "content" from Octove)

2022-02-26T20:47:33Z

See also: +2 (moving "content" from Octove)

← Older revision		Revision as of 20:47, 26 February 2022
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	* [[Octave]]		* [[Octave]]
			* [[Wikipedia:Stretched tuning]]
			* [[Wikipedia:Stretched octave]]

	[[Category:Todo:add definition]]		[[Category:Todo:add definition]]
	[[Category:Todo:expand]]		[[Category:Todo:expand]]

Xenwolf: cleanup

2020-11-06T08:00:55Z

cleanup

← Older revision		Revision as of 08:00, 6 November 2020
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	'''Musical cells''' is a system of [[~~Mario_Pizarro\|~~Mario Pizarro]] for constructing [[~~Circulating_Temperaments\|~~circulating ~~temperaments~~]]. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.		'''Musical cells''' is a system of [[Mario Pizarro]] for constructing [[circulating temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.

	= Toctave =		== Toctave ==
	'''Toctave''' (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro came up with in connection with his theory of musical cells.		'''Toctave''' (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro came up with in connection with his theory of musical cells.

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	Threads/Folders on the tuning list:		Threads/Folders on the tuning list:

	~~<ul><li>~~[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100894.html#100919 http://launch.groups.yahoo.com/group/tuning/message/100919] - "The True Octave"~~</li><li>~~[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101004.html http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"~~</li><li>~~[https://drive.google.com/drive/folders/1Zu20johQ1YcmVyFGv0V0_QtMDsCeRp7H?usp=sharing ~~http://launch.groups.yahoo.com/group/tuning/files/~~MarioPizarro/]~~</li></ul>~~		* [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100894.html#100919 http://launch.groups.yahoo.com/group/tuning/message/100919] - "The True Octave"
			* [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101004.html http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"
			* [https://drive.google.com/drive/folders/1Zu20johQ1YcmVyFGv0V0_QtMDsCeRp7H?usp=sharing MarioPizarro - Google Drive] - Collection of materials on the topic

	== ~~see~~ also ==		== See also ==
	~~<ul><li>~~[[~~Octave\|~~Octave]]~~</li></ul>~~
	[[Category:~~todo~~:~~add_definition~~]]		* [[Octave]]
	[[Category:~~todo~~:expand]]
			[[Category:Todo:add definition]]
			[[Category:Todo:expand]]

CritDeathX: Fixed Yahoo files link

2020-11-06T00:28:35Z

Fixed Yahoo files link

← Older revision		Revision as of 00:28, 6 November 2020
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	Threads/Folders on the tuning list:		Threads/Folders on the tuning list:

	<ul><li>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100894.html#100919 http://launch.groups.yahoo.com/group/tuning/message/100919] - "The True Octave"</li><li>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101004.html http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"</li><li>http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/</li></ul>		<ul><li>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100894.html#100919 http://launch.groups.yahoo.com/group/tuning/message/100919] - "The True Octave"</li><li>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101004.html http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"</li><li>[https://drive.google.com/drive/folders/1Zu20johQ1YcmVyFGv0V0_QtMDsCeRp7H?usp=sharing http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/]</li></ul>

	== see also ==		== see also ==

CritDeathX: Fixed two Yahoo links

2020-11-06T00:13:56Z

Fixed two Yahoo links

← Older revision		Revision as of 00:13, 6 November 2020
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	Threads/Folders on the tuning list:		Threads/Folders on the tuning list:

	<ul><li>http://launch.groups.yahoo.com/group/tuning/message/100919 - "The True Octave"</li><li>http://launch.groups.yahoo.com/group/tuning/message/101004 - "A new equal tempered scale?"</li><li>http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/</li></ul>		<ul><li>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100894.html#100919 http://launch.groups.yahoo.com/group/tuning/message/100919] - "The True Octave"</li><li>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101004.html http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"</li><li>http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/</li></ul>

	== see also ==		== see also ==

CritDeathX: Fixed Yahoo link

2020-11-06T00:06:57Z

Fixed Yahoo link

← Older revision		Revision as of 00:06, 6 November 2020
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	'''Musical cells''' is a system of [[Mario_Pizarro\|Mario Pizarro]] for constructing [[Circulating_Temperaments\|circulating temperaments]]. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[~~http~~://~~launch~~.~~groups~~.~~yahoo.com/group~~/tuning/~~message/100427~~ The corrected progression of musical cells]''.		'''Musical cells''' is a system of [[Mario_Pizarro\|Mario Pizarro]] for constructing [[Circulating_Temperaments\|circulating temperaments]]. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.

	= Toctave =		= Toctave =
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	Threads/Folders on the tuning list:		Threads/Folders on the tuning list:

	<ul><li>[http://launch.groups.yahoo.com/group/tuning/message/100919 ~~http://launch.groups.yahoo.com/group/tuning/message/100919]~~ - "The True Octave"</li><li>~~[http://launch.groups.yahoo.com/group/tuning/message/101004~~ http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"</li><li>~~[http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/~~ http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/]</li></ul>		<ul><li>http://launch.groups.yahoo.com/group/tuning/message/100919 - "The True Octave"</li><li>http://launch.groups.yahoo.com/group/tuning/message/101004 - "A new equal tempered scale?"</li><li>http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/</li></ul>

	== see also ==		== see also ==
	<ul><li>[[Octave\|Octave]]</li></ul> [[Category:todo:add_definition]]		<ul><li>[[Octave\|Octave]]</li></ul>
			[[Category:todo:add_definition]]
	[[Category:todo:expand]]		[[Category:todo:expand]]

← Older revision		Revision as of 19:59, 27 March 2022
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	* [[Wikipedia:Stretched octave]]		* [[Wikipedia:Stretched octave]]

	[[Category:~~Todo:expand~~]]		[[Category:Well temperament]]