Gallery of projective tuning space images

Revision as of 05:37, 9 January 2024 by BudjarnLambeth (talk | contribs) (Added links to dead end pg)

In the following images, unless otherwise specified:

  • numerals represent ETs (steps per '2')
  • multiple appearances of the same number are different mappings
  • rotation of the ET numbers indicates octave stretch of the TOP tuning of the ET (15 cents stretch = 90° clockwise rotation)
  • lines are temperaments (where a single comma is tempered out)
  • hexagons are contours of maximum Tenney-weighted damage of TOP tunings

5-limit

  {2,3,5} PTS with handwritten annotations

from A Middle Path

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)

projective tuning space based on {2,3,5}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)

zoomed waaaay out

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)

zoomed-out still more

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)

zoomed-out more

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)

zoomed-out

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-04-10)

5-limit projective tuning space showing equal temperaments and good rank-two temperaments (or "temperament families"). Concentric hexagons indicate TOP damage (of TOP tuning) up to 10 in increments of 1.

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)

zoomed-in

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)

zoomed-in more

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)

zoomed-in still more

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)

zoomed way in

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)

zoomed way way in

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 0

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 1

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 2

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 3

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 4

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 5

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 6

  Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)

showing all three elements of each 5-limit breed

zoom level 7

11-limit subgroups

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)

projective tuning space based on {2,3,7}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,3,7}

zoomed way out!

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

"projective tuning space" "based on" "{2,3,9}"

numerals at "ETs" represent steps per '2'

hexagons are "contours" of "maximum Tenney-weighted damage" of "TOP tunings"

this one is not like the others! 9/3 is considered a different interval than 3, with complexity log(27) rather than log(3), and susceptibility to damage 1/log(27) instead of 1/log(3) -- whatever that means!

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,3,11}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)

projective tuning space based on {2,5,7}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,5,9}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,5,11}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,7,9}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,7,11}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)

projective tuning space based on {2,9,11}

numerals at ETs represent steps per '2'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings

3.5.7, tritave (3-1) based

  Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)

projective tuning space based on {3,5,7}

numerals at ETs represent steps per '3'

hexagons are contours of maximum Tenney-weighted damage of TOP tunings