PIFE comma - Revision history

ArrowHead294 at 13:12, 14 March 2025

2025-03-14T13:12:16Z

← Older revision		Revision as of 13:12, 14 March 2025
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	A '''prime-limit-inclusive fully-dimensionally-entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>		A '''prime-limit-inclusive fully-dimensionally-entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to {{nowrap\|(''n'' − 1)}} dimensions, with all of the previous dimensions now being tangled together onto {{nowrap\|(''n'' − 1)}} composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>

	The term was coined by [[Scott Dakota]] <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a [[tempered]] space with a dented [[JI]] dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>		The term was coined by [[Scott Dakota]] <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a [[tempered]] space with a dented [[JI]] dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>
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	== Properties ==		== Properties ==

	"Some pife commas also seem to be pretty portable across multiple systems, because they tend to have short [[Taxicab distance\|taxicab]] extent in each JI dimension they are touching - therefore, there's more range where the component intervals can be tuned various ways, but not have the short connections so tuning-dented they don't make sense any more.		"Some pife commas also seem to be pretty portable across multiple systems, because they tend to have short [[Taxicab distance\|taxicab]] extent in each JI dimension they are touching – therefore, there's more range where the component intervals can be tuned various ways, but not have the short connections so tuning-dented they don't make sense any more.

	* "[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714\|715:714]]) — perfect pife comma in 17 limit		* "[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714\|715:714]]) – perfect pife comma in 17 limit
	* "[-7, -1, 1, 1, 1⟩ ([[385/384\|385:384]]) — perfect pife comma in 11-limit		* "[-7, -1, 1, 1, 1⟩ ([[385/384\|385:384]]) – perfect pife comma in 11-limit

	"Pife commas also make up super important [[Dyadic_chord#Essentially_tempered_dyadic_chords\|dyadic essentially tempered chords]] that are extremely characteristic of the [[Temperament families and clans\|temperament families]] they are attractor points for. These dyadic essentially tempered chords are some of the key objects for playing through the [[Comma pump\|commas pumps]] and pivot opportunities each temperament description provides."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866335583802097715</ref>		"Pife commas also make up super important [[Dyadic_chord#Essentially_tempered_dyadic_chords\|dyadic essentially tempered chords]] that are extremely characteristic of the [[Temperament families and clans\|temperament families]] they are attractor points for. These dyadic essentially tempered chords are some of the key objects for playing through the [[Comma pump\|commas pumps]] and pivot opportunities each temperament description provides."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866335583802097715</ref>

BudjarnLambeth: Add links

2024-12-21T07:27:47Z

Add links

← Older revision		Revision as of 07:27, 21 December 2024
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	A '''prime-limit-inclusive fully-dimensionally-entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>		A '''prime-limit-inclusive fully-dimensionally-entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>

	The term was coined by Scott Dakota <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>		The term was coined by [[Scott Dakota]] <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a [[tempered]] space with a dented [[JI]] dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>

	A '''S-PIFE comma''' (or '''spife''') is a [[superparticular]] pife<ref name="def" />.		A '''S-PIFE comma''' (or '''spife''') is a [[superparticular]] pife<ref name="def" />.
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	== Properties ==		== Properties ==

	"Some pife commas also seem to be pretty portable across multiple systems, because they tend to have short taxicab extent in each JI dimension they are touching - therefore, there's more range where the component intervals can be tuned various ways, but not have the short connections so tuning-dented they don't make sense any more.		"Some pife commas also seem to be pretty portable across multiple systems, because they tend to have short [[Taxicab distance\|taxicab]] extent in each JI dimension they are touching - therefore, there's more range where the component intervals can be tuned various ways, but not have the short connections so tuning-dented they don't make sense any more.

	* "[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714\|715:714]]) — perfect pife comma in 17 limit		* "[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714\|715:714]]) — perfect pife comma in 17 limit
	* "[-7, -1, 1, 1, 1⟩ ([[385/384\|385:384]]) — perfect pife comma in 11-limit		* "[-7, -1, 1, 1, 1⟩ ([[385/384\|385:384]]) — perfect pife comma in 11-limit

	"Pife commas also make up super important [[Dyadic_chord#Essentially_tempered_dyadic_chords\|dyadic essentially tempered chords]] that are extremely characteristic of the temperament families they are attractor points for. These dyadic essentially tempered chords are some of the key objects for playing through the [[Comma pump\|commas pumps]] and pivot opportunities each temperament description provides."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866335583802097715</ref>		"Pife commas also make up super important [[Dyadic_chord#Essentially_tempered_dyadic_chords\|dyadic essentially tempered chords]] that are extremely characteristic of the [[Temperament families and clans\|temperament families]] they are attractor points for. These dyadic essentially tempered chords are some of the key objects for playing through the [[Comma pump\|commas pumps]] and pivot opportunities each temperament description provides."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866335583802097715</ref>

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

FloraC: Recategorize

2024-01-09T10:13:46Z

Recategorize

← Older revision		Revision as of 10:13, 9 January 2024
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	<references />		<references />

	[[Category:~~Commas~~]]		[[Category:Comma]]
	[[Category:Todo:expand]]		[[Category:Todo:expand]]

Fredg999: Grammar

2023-08-22T02:25:42Z

Grammar

← Older revision		Revision as of 02:25, 22 August 2023
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	A '''prime-limit-inclusive fully dimensionally entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>		A '''prime-limit-inclusive fully-dimensionally-entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>

	The term was coined by Scott Dakota <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>		The term was coined by Scott Dakota <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2023-03-05T05:32:47Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 05:32, 5 March 2023
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	[[Category:Commas]]		[[Category:Commas]]
	~~[[Category:Theory]]~~
	[[Category:Todo:expand]]		[[Category:Todo:expand]]

Fredg999 category edits: Moving from Category:Comma to Category:Commas using Cat-a-lot

2022-03-20T21:27:52Z

Moving from Category:Comma to Category:Commas using Cat-a-lot

← Older revision		Revision as of 21:27, 20 March 2022
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	<references />		<references />

	[[Category:~~Comma~~]]		[[Category:Commas]]
	[[Category:Theory]]		[[Category:Theory]]
	[[Category:Todo:expand]]		[[Category:Todo:expand]]

Fredg999: /* See also */ Removed link to S-PIFE comma

2021-07-19T18:37:46Z

Fredg999: Revert addition of a pair of quoting marks in the previous edit

2021-07-19T18:36:09Z

Revert addition of a pair of quoting marks in the previous edit

← Older revision		Revision as of 18:36, 19 July 2021
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	A '''prime-limit-inclusive fully dimensionally entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that "takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions."<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>		A '''prime-limit-inclusive fully dimensionally entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>

	The term was coined by Scott Dakota <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>		The term was coined by Scott Dakota <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>

Fredg999: Added S-PIFE, added references for definitions

2021-07-19T18:34:38Z

Added S-PIFE, added references for definitions

← Older revision		Revision as of 18:34, 19 July 2021
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	A '''prime-limit-inclusive fully dimensionally entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.		A '''prime-limit-inclusive fully dimensionally entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that "takes a system of ''n'' [[Rank_and_codimension\|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions."<ref name="def">Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289</ref>

	The term was coined by Scott Dakota. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>		The term was coined by Scott Dakota <ref name="def" />. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>

	A '''pife-like comma''' is fully dimensionally entangled for the subgroup targets to be approximated only.		A '''S-PIFE comma''' (or '''spife''') is a [[superparticular]] pife<ref name="def" />.

			A '''pife-like comma''' is fully dimensionally entangled for the subgroup targets to be approximated only<ref name="def" />.

	== Properties ==		== Properties ==

Fredg999: From Scott Dakota's posts on Discord XA

2021-07-19T18:29:15Z

From Scott Dakota's posts on Discord XA

New page

A '''prime-limit-inclusive fully dimensionally entangled comma''' ('''PIFE comma''' or '''pife''') is a [[comma]] that takes a system of ''n'' [[Rank_and_codimension|dimensions]] and reduces it to (''n'' − 1) dimensions, with all of the previous dimensions now being tangled together onto (''n'' − 1) composite dimensions.

The term was coined by Scott Dakota. He explains that pifes are "in contrast to commas that leave some of the initial dimensions still somewhat floating off to the side, like a tempered space with a dented JI dimension sitting off to the side of the now tempered object."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311</ref>

A '''pife-like comma''' is fully dimensionally entangled for the subgroup targets to be approximated only.

== Properties ==

"Some pife commas also seem to be pretty portable across multiple systems, because they tend to have short taxicab extent in each JI dimension they are touching - therefore, there's more range where the component intervals can be tuned various ways, but not have the short connections so tuning-dented they don't make sense any more.

* "[-1, -1, 1, -1, 1, 1, -1⟩ ([[715/714|715:714]]) — perfect pife comma in 17 limit
* "[-7, -1, 1, 1, 1⟩ ([[385/384|385:384]]) — perfect pife comma in 11-limit

"Pife commas also make up super important [[Dyadic_chord#Essentially_tempered_dyadic_chords|dyadic essentially tempered chords]] that are extremely characteristic of the temperament families they are attractor points for. These dyadic essentially tempered chords are some of the key objects for playing through the [[Comma pump|commas pumps]] and pivot opportunities each temperament description provides."<ref>Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866335583802097715</ref>

== See also ==
* [[S-PIFE comma]]
* [[TIFE comma]]

== References ==
<references />

[[Category:Comma]]
[[Category:Theory]]
[[Category:Todo:expand]]

← Older revision		Revision as of 18:37, 19 July 2021
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	== See also ==		== See also ==
	* [[S-PIFE comma]]
	* [[TIFE comma]]		* [[TIFE comma]]