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 | 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> | ||
Revision as of 18:36, 19 July 2021
A prime-limit-inclusive fully dimensionally entangled comma (PIFE comma or pife) is a comma that takes a system of n dimensions and reduces it to (n − 1) dimensions, with all of the previous dimensions now being tangled together onto (n − 1) composite dimensions.[1]
The term was coined by Scott Dakota [1]. 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."[2]
A S-PIFE comma (or spife) is a superparticular pife[1].
A pife-like comma is fully dimensionally entangled for the subgroup targets to be approximated only[1].
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) — perfect pife comma in 17 limit
- "[-7, -1, 1, 1, 1⟩ (385:384) — perfect pife comma in 11-limit
"Pife commas also make up super important 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 commas pumps and pivot opportunities each temperament description provides."[3]
See also
References
- ↑ 1.0 1.1 1.2 1.3 Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866332500729397289
- ↑ Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866330104199905311
- ↑ Dakota, Scott. https://discord.com/channels/332357996569034752/516067802864549890/866335583802097715