PIFE comma: Difference between revisions

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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>

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

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== 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 ==

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[[Category:~~Commas]]~~

[[Category:Comma]]

~~[[Category:Theory~~]]

[[Category:Todo:expand]]

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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>
 A '''S-PIFE comma''' (or '''spife''') is a [[superparticular]] pife<ref name="def" />.
@@ Line 9: / Line 9: @@
 == 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 ==
@@ Line 22: / Line 22: @@
 <references />
-[[Category:Commas]]
+[[Category:Comma]]
-[[Category:Theory]]
 [[Category:Todo:expand]]