Gallery of projective tuning space images: Difference between revisions
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In the following images, unless otherwise specified: | In the following images, unless otherwise specified: | ||
<ul><li>numerals represent ETs (steps per '2')</li><li>multiple appearances of the same number are different mappings</li><li>rotation of the ET numbers indicates octave stretch of the TOP tuning of the ET (15 cents stretch = 90° clockwise rotation)</li><li>lines are temperaments (where a single comma is tempered out)</li><li>hexagons are contours of maximum Tenney-weighted damage of TOP tunings</li></ul> | <ul><li>numerals represent [[Edo|ETs]] (steps per '2')</li><li>multiple appearances of the same number are different mappings</li><li>rotation of the ET numbers indicates [[octave stretch]] of the [[TOP]] tuning of the ET (15 cents stretch = 90° clockwise rotation)</li><li>lines are [[temperaments]] (where a single [[comma]] is [[tempered out]])</li><li>hexagons are contours of maximum Tenney-weighted damage of TOP tunings</li></ul> | ||
=5-limit= | =[[5-limit]]= | ||
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=11-limit | =[[11-limit]] [[subgroup]]s= | ||
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=3.5.7, tritave (3-1) based= | =3.5.7, [[tritave]] (3-1) based= | ||
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Revision as of 05:37, 9 January 2024
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
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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, 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 |