Gallery of projective tuning space images
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
[[:File:pts-2-3-5-e2-amp-hand-annotated-gray.jpg| ]]
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{2,3,5} PTS with handwritten annotations
from A Middle Path |
[[:File:pts-2-3-5-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-3-5-e2-twtop-tlin-zo4.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-22)
zoomed waaaay out |
[[:File:pts-2-3-5-e2-twtop-tlin-zo3.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-22)
zoomed-out still more |
[[:File:pts-2-3-5-e2-twtop-tlin-zo2.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-22)
zoomed-out more |
[[:File:pts-2-3-5-e2-twtop-tlin-zo1.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-22)
zoomed-out |
[[:File:pts-2-3-5-e2-twtop-tlin.jpg| ]]
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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. |
[[:File:pts-2-3-5-e2-twtop-tlin-graybg-zi1.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-25)
zoomed-in |
[[:File:pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-25)
zoomed-in more |
[[:File:pts-2-3-5-e2-twtop-tlin-zi3.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-25)
zoomed-in still more |
[[:File:pts-2-3-5-e2-twtop-tlin-zi4.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-25)
zoomed way in |
[[:File:pts-2-3-5-e2-twtop-tlin-zi5.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-25)
zoomed way way in |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z0.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 0 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z1.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 1 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z2.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 2 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z3.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 3 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z4.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 4 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z5.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 5 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z6.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance - Mathematical Theory (2014-08-26)
showing all three elements of each 5-limit breed zoom level 6 |
[[:File:pts-2-3-5-e2-breed-twtop-tlin-z7.jpg| ]]
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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
[[:File:pts-2-3-7-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-3-7-e2-twtop-z0.jpg| ]]
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Paul Erlich > The Xenharmonic Alliance (2011-02-06)
projective tuning space based on {2,3,7} zoomed way out! |
[[:File:pts-2-3-9-e2-twtop.jpg| ]]
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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! |
[[:File:pts-2-3-11-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-5-7-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-5-9-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-5-11-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-7-9-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-7-11-e2-twtop.jpg| ]]
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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 |
[[:File:pts-2-9-11-e2-twtop.jpg| ]]
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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
[[:File:pts-3-5-7-e3-twtop.jpg| ]]
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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 |