Gallery of projective tuning space images: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Wikispaces>FREEZE
No edit summary
PreImportHandFixes>Battaglia01
Mike - changed malformed links, removed "thumbnail" png's and replaced with locally generated thumbnails. May create unused files
Line 8: Line 8:
{| class="wikitable"
{| 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
| | {2,3,5} PTS with handwritten annotations


Line 16: Line 16:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance (2011-02-04)]
| | [https://www.facebook.com/photo.php?fbid=10150090296739367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]


Line 28: Line 28:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-3-5-e2-twtop-tlin-zo4.jpg|[[File:tn_pts-2-3-5-e2-twtop-tlin-zo4.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zo4.jpg|tn_pts-2-3-5-e2-twtop-tlin-zo4.jpg]]]]
| | [[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)]
| | [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
zoomed waaaay out
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
| | [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)]


zoomed-out still more
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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
| | [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)]


zoomed-out more
zoomed-out more
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-22)]
| | [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
zoomed-out
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-04-10)]
| | [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.
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)]
| | [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)]


zoomed-in
zoomed-in
|-
|-
| | [[: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)]
| | [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
zoomed-in more
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
| | [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
zoomed-in still more
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance - Mathematical Theory (2014-08-25)]
| | [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
zoomed way in
|-
|-
| | [[:File:pts-2-3-5-e2-twtop-tlin-zi5.jpg|[[File:tn_pts-2-3-5-e2-twtop-tlin-zi5.jpg|alt=tn_pts-2-3-5-e2-twtop-tlin-zi5.jpg|tn_pts-2-3-5-e2-twtop-tlin-zi5.jpg]]]]
| | [[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)]
| | [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)]


Line 81: Line 81:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z0.jpg|[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z0.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z0.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z0.jpg]]]]
| | [[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)]
| | [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)]


Line 88: Line 88:
zoom level 0
zoom level 0
|-
|-
| | [[:File:pts-2-3-5-e2-breed-twtop-tlin-z1.jpg|[[File:tn_pts-2-3-5-e2-breed-twtop-tlin-z1.jpg|alt=tn_pts-2-3-5-e2-breed-twtop-tlin-z1.jpg|tn_pts-2-3-5-e2-breed-twtop-tlin-z1.jpg]]]]
| | [[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)]
| | [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)]


Line 95: Line 95:
zoom level 1
zoom level 1
|-
|-
| | [[: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)]
| | [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)]


Line 102: Line 102:
zoom level 2
zoom level 2
|-
|-
| | [[: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)]
| | [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)]


Line 109: Line 109:
zoom level 3
zoom level 3
|-
|-
| | [[: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)]
| | [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)]


Line 116: Line 116:
zoom level 4
zoom level 4
|-
|-
| | [[: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)]
| | [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)]


Line 123: Line 123:
zoom level 5
zoom level 5
|-
|-
| | [[: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)]
| | [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)]


Line 130: Line 130:
zoom level 6
zoom level 6
|-
|-
| | [[: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)]
| | [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)]


Line 142: Line 142:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-3-7-e2-twtop.jpg|[[File:tn_pts-2-3-7-e2-twtop.jpg|alt=tn_pts-2-3-7-e2-twtop.jpg|tn_pts-2-3-7-e2-twtop.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150090453304367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]


Line 151: Line 151:
hexagons are contours of maximum Tenney-weighted damage of TOP tunings
hexagons are contours of maximum Tenney-weighted damage of TOP tunings
|-
|-
| | [[:File:pts-2-3-7-e2-twtop-z0.jpg|[[File:tn_pts-2-3-7-e2-twtop-z0.jpg|alt=tn_pts-2-3-7-e2-twtop-z0.jpg|tn_pts-2-3-7-e2-twtop-z0.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150091440809367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 161: Line 161:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-3-9-e2-twtop.jpg|[[File:tn_pts-2-3-9-e2-twtop.jpg|alt=tn_pts-2-3-9-e2-twtop.jpg|tn_pts-2-3-9-e2-twtop.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150091485324367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 175: Line 175:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-3-11-e2-twtop.jpg|[[File:tn_pts-2-3-11-e2-twtop.jpg|alt=tn_pts-2-3-11-e2-twtop.jpg|tn_pts-2-3-11-e2-twtop.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150091496424367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 187: Line 187:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-5-7-e2-twtop.jpg|[[File:tn_pts-2-5-7-e2-twtop.jpg|alt=tn_pts-2-5-7-e2-twtop.jpg|tn_pts-2-5-7-e2-twtop.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150090453309367&set=gm.10150170038074482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-04)]


Line 199: Line 199:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-5-9-e2-twtop.jpg|[[File:tn_pts-2-5-9-e2-twtop.jpg|alt=tn_pts-2-5-9-e2-twtop.jpg|tn_pts-2-5-9-e2-twtop.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150091482029367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 211: Line 211:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[:File:pts-2-5-11-e2-twtop.jpg|[[File:tn_pts-2-5-11-e2-twtop.jpg|alt=tn_pts-2-5-11-e2-twtop.jpg|tn_pts-2-5-11-e2-twtop.jpg]]]]
| | [[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)]
| | [https://www.facebook.com/photo.php?fbid=10150091500519367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 223: Line 223:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[: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 > ‎The Xenharmonic Alliance (2011-02-06)]
| | [https://www.facebook.com/photo.php?fbid=10150091540804367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 235: Line 235:
{| class="wikitable"
{| 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 > ‎The Xenharmonic Alliance (2011-02-06)]
| | [https://www.facebook.com/photo.php?fbid=10150091506389367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 247: Line 247:
{| class="wikitable"
{| 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 > ‎The Xenharmonic Alliance (2011-02-06)]
| | [https://www.facebook.com/photo.php?fbid=10150091508499367&set=gm.10150170037959482&type=1&permPage=1 Paul Erlich > ‎The Xenharmonic Alliance (2011-02-06)]


Line 261: Line 261:
{| class="wikitable"
{| 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 > ‎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)]


Line 270: Line 270:
hexagons are contours of maximum Tenney-weighted damage of TOP tunings
hexagons are contours of maximum Tenney-weighted damage of TOP tunings
|}
|}
[[Category:IMPORTDEBUG - Image in Link]]

Revision as of 18:13, 19 August 2018

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

{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, 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

Retrieved from "https://en.xen.wiki/index.php?title=Gallery_of_projective_tuning_space_images&oldid=31045"