Gallery of projective tuning space images: Difference between revisions

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__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=

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

zoomed-out

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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 > ‎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|~~[[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]

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| | [[:File:pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg|~~[[File:tn_pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg|tn_pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg]]~~]]

| | [[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]

zoomed-in more

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

zoomed-in still more

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| | [[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]

zoomed way in

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

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| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z2.jpg|~~[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z2.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z2.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z2.jpg]]~~]]

| | [[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]

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| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z3.jpg|~~[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z3.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z3.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z3.jpg]]~~]]

| | [[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]

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| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z4.jpg|~~[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z4.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z4.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z4.jpg]]~~]]

| | [[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]

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| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z5.jpg|~~[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z5.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z5.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z5.jpg]]~~]]

| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z5.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10152643397784367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]

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| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z6.jpg|~~[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z6.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z6.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z6.jpg]]~~]]

| | [[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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]

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| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z7.jpg|~~[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z7.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z7.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z7.jpg]]~~]]

| | [[File:pts-2-3-5-e2-breed-twtop-tlin-z7.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10152643397989367&set=oa.389536071186621&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-26)]

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=11-limit subgroups=

== 11-limit subgroups ==

{| class="wikitable"

|-

| | [[File:pts-2-3-7-e2-twtop.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150090453304367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]

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

|-

| | [[File:pts-2-3-7-e2-twtop-z0.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150091440809367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[File:pts-2-3-9-e2-twtop.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150091485324367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[File:pts-2-3-11-e2-twtop.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150091496424367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[File:pts-2-5-7-e2-twtop.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150090453309367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]

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| | [[File:pts-2-5-9-e2-twtop.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150091482029367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[File:pts-2-5-11-e2-twtop.jpg|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150091500519367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[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 > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[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 > ‎The Xenharmonic Alliance (2011-02-06)]

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| | [[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 > ‎The Xenharmonic Alliance (2011-02-06)]

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=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|200px]]

| | [https://www.facebook.com/photo.php?fbid=10150090296744367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]

| [https://www.facebook.com/photo.php?fbid=10150090296744367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]

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

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[[Category:~~IMPORTDEBUG - Image in Link~~]]

[[Category:Lists]]

[[Category:Graphs]]

[[Category:Resources]]

@@ 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"
 |-
-| | [[: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
@@ Line 16: / Line 19: @@
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-| | [[:File:pts-2-3-5-e2-twtop.jpg|[[File:tn_pts-2-3-5-e2-twtop.jpg|alt=tn_pts-2-3-5-e2-twtop.jpg|tn_pts-2-3-5-e2-twtop.jpg]]]]
+| | [[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)]
@@ Line 28: / Line 31: @@
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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|[[File:tn_pts-2-3-5-e2-twtop-tlin-zo3.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zo3.jpg|tn_pts-2-3-5-e2-twtop-tlin-zo3.jpg]]]]
+| | [[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)]
 zoomed-out still more
 |-
-| | [[:File:pts-2-3-5-e2-twtop-tlin-zo2.jpg|[[File:tn_pts-2-3-5-e2-twtop-tlin-zo2.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zo2.jpg|tn_pts-2-3-5-e2-twtop-tlin-zo2.jpg]]]]
+| | [[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|[[File:tn_pts-2-3-5-e2-twtop-tlin-zo1.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zo1.jpg|tn_pts-2-3-5-e2-twtop-tlin-zo1.jpg]]]]
+| | [[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|[[File:tn_pts-2-3-5-e2-twtop-tlin.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin.jpg|tn_pts-2-3-5-e2-twtop-tlin.jpg]]]]
+| | [[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|[[File:tn_pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg|tn_pts-2-3-5-e2-twtop-tlin-graybg-zi2.jpg]]]]
+| | [[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|[[File:tn_pts-2-3-5-e2-twtop-tlin-zi3.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zi3.jpg|tn_pts-2-3-5-e2-twtop-tlin-zi3.jpg]]]]
+| | [[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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 |}
-=11-limit subgroups=
+== 11-limit subgroups ==
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 hexagons are contours of maximum Tenney-weighted damage of TOP tunings
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 |}
-=3.5.7, tritave (3-1) based=
+== 3.5.7 subgroup, tritave (3/1) based ==
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 projective tuning space based on {3,5,7}
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 |}
-[[Category:IMPORTDEBUG - Image in Link]]
+[[Category:Lists]]
+[[Category:Graphs]]
+[[Category:Resources]]