Gallery of projective tuning space images: Difference between revisions

Latest revision as of 09:14, 3 December 2024

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

	{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 subgroup, 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

Gallery of projective tuning space images: Difference between revisions

Latest revision as of 09:14, 3 December 2024

Contents

5-limit

11-limit subgroups

3.5.7 subgroup, tritave (3/1) based

Navigation menu

@@ Line 1: / Line 1: @@
 __FORCETOC__
 In the following images, unless otherwise specified:
+* Numerals represent [[edo|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
-<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>
+== 5-limit ==
-=5-limit=
 {| class="wikitable"
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-| | [[:File:pts-2-3-5-e2-amp-hand-annotated-gray.jpg|[[File:tn_pts-2-3-5-e2-amp-hand-annotated-gray.jpg|alt=tn_pts-2-3-5-e2-amp-hand-annotated-gray.jpg|tn_pts-2-3-5-e2-amp-hand-annotated-gray.jpg]]]]
+| | [[File:pts-2-3-5-e2-amp-hand-annotated-gray.jpg|200px]]
 | | {2,3,5} PTS with handwritten annotations
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+| | [[File:pts-2-3-5-e2-twtop.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10150090296739367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-04)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin-zo4.jpg|157px]]
 | | [https://www.facebook.com/photo.php?fbid=10152632247244367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
 zoomed waaaay out
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+| | [[File:pts-2-3-5-e2-twtop-tlin-zo3.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152632247269367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin-zo2.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152632247314367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin-zo1.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152632247409367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152310913269367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-04-10)]
 -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|[[File:tn_pts-2-3-5-e2-twtop-tlin-graybg-zi1.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-graybg-zi1.jpg|tn_pts-2-3-5-e2-twtop-tlin-graybg-zi1.jpg]]]]
+| | [[File:pts-2-3-5-e2-twtop-tlin-graybg-zi1.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152640895264367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152640895159367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin-zi3.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152640895094367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
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-| | [[:File:pts-2-3-5-e2-twtop-tlin-zi4.jpg|[[File:tn_pts-2-3-5-e2-twtop-tlin-zi4.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zi4.jpg|tn_pts-2-3-5-e2-twtop-tlin-zi4.jpg]]]]
+| | [[File:pts-2-3-5-e2-twtop-tlin-zi4.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152641282619367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
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+| | [[File:pts-2-3-5-e2-twtop-tlin-zi5.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152641282779367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z0.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152643397394367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z1.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152643397459367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory  (2014-08-26)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z2.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152643397549367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory  (2014-08-26)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z3.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152643397614367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance  - Mathematical Theory (2014-08-26)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z4.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152643397709367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z5.jpg|200px]]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z6.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10152643397899367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]
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+| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z7.jpg|200px]]
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 |}
-=11-limit subgroups=
+== 11-limit subgroups ==
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 | | [https://www.facebook.com/photo.php?fbid=10150090453304367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-04)]
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 hexagons are contours of maximum Tenney-weighted damage of TOP tunings
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 | | [https://www.facebook.com/photo.php?fbid=10150091500519367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-06)]
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-| | [[:File:pts-2-7-9-e2-twtop.jpg|[[File:tn_pts-2-7-9-e2-twtop.jpg|alt=tn_pts-2-7-9-e2-twtop.jpg|tn_pts-2-7-9-e2-twtop.jpg]]]]
+| | [[File:pts-2-7-9-e2-twtop.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10150091540804367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-06)]
@@ Line 235: / Line 238: @@
 {| class="wikitable"
 |-
-| | [[:File:pts-2-7-11-e2-twtop.jpg|[[File:tn_pts-2-7-11-e2-twtop.jpg|alt=tn_pts-2-7-11-e2-twtop.jpg|tn_pts-2-7-11-e2-twtop.jpg]]]]
+| | [[File:pts-2-7-11-e2-twtop.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10150091506389367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-06)]
@@ Line 247: / Line 250: @@
 {| class="wikitable"
 |-
-| | [[:File:pts-2-9-11-e2-twtop.jpg|[[File:tn_pts-2-9-11-e2-twtop.jpg|alt=tn_pts-2-9-11-e2-twtop.jpg|tn_pts-2-9-11-e2-twtop.jpg]]]]
+| | [[File:pts-2-9-11-e2-twtop.jpg|200px]]
 | | [https://www.facebook.com/photo.php?fbid=10150091508499367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-06)]
@@ Line 257: / Line 260: @@
 |}
-=3.5.7, tritave (3-1) based=
+== 3.5.7 subgroup, tritave (3/1) based ==
 {| class="wikitable"
 |-
-| | [[:File:pts-3-5-7-e3-twtop.jpg|[[File:tn_pts-3-5-7-e3-twtop.jpg|alt=tn_pts-3-5-7-e3-twtop.jpg|tn_pts-3-5-7-e3-twtop.jpg]]]]
+| [[File:pts-3-5-7-e3-twtop.jpg|200px]]
-| | [https://www.facebook.com/photo.php?fbid=10150090296744367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-04)]
+| [https://www.facebook.com/photo.php?fbid=10150090296744367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich &gt; ‎The Xenharmonic Alliance (2011-02-04)]
 projective tuning space based on {3,5,7}
@@ Line 271: / Line 274: @@
 |}
-[[Category:IMPORTDEBUG - Image in Link]]
+[[Category:Lists]]
+[[Category:Graphs]]
+[[Category:Resources]]

Gallery of projective tuning space images: Difference between revisions

Latest revision as of 09:14, 3 December 2024

5-limit

11-limit subgroups

3.5.7 subgroup, tritave (3/1) based

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