Gallery of projective tuning space images
In the following images, unless otherwise specified:
- Numerals represent equal temperaments (steps per octave)
- Multiple appearances of the same number are different mappings
- Rotation of the ET numbers indicates octave stretch of the TOP tuning of the equal temperament (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
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{2,3,5} PTS with handwritten annotations
from A Middle Path |
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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 |
11-limit subgroups
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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 |
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Paul Erlich > The Xenharmonic Alliance (2011-02-06)
projective tuning space based on {2,3,7} zoomed way out! |
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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! |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 subgroup, tritave (3/1) based
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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 |