PIFE comma

From Xenharmonic Wiki
Jump to navigation Jump to search

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].


"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