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Gallery of 12-tone just intonation scales: Difference between revisions

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Adding Wilson-middle-rank-12 to gallery. The scale is a subset of Wilson's 7-limit 22-enharmonic (marimba) scale.
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Just Intonation is an infinite universe. A justly-intoned pentatonic can be very effective in the hands of a sensitive composer, and in this electronic age that same composer on another day can use a scale with hundreds of notes in an octave.
[[Just intonation]] is an infinite universe. A justly-intoned [[pentatonic]] can be very effective in the hands of a sensitive composer, and in this electronic age that same composer on another day can use a [[scale]] with hundreds of notes in an [[octave]].


One approach to making just intonation not only practical but easy is to map an [[Periodic_scale|octave-repeating]] 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a [[Gallery_of_12-tone_Tempered_Scales|companion page]] does the same for tempered scales.
One approach to making just intonation not only practical but easy is to map an [[Periodic_scale|octave-repeating]] 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a [[Gallery_of_12-tone_Tempered_Scales|companion page]] does the same for tempered scales.


{{todo|cleanup|inline=1}}
== [[Chain of fifths|Interval circle]]-based ==
* [[Rectoo]] – Hahn reduced circle of fifths via <12 19 27 34|
* [[Secor5_23TX]] – [[George Secor]]'s synchronous 5/23-comma temperament extraordinaire


*[[wilson-middle-rank-12]] - Wilson 7-limit, 12-note middle rank of 22 marimba scale
== Chord-based (eg [[tritriadic scale|tritriadic]], [[tetrachord|tetrachordal]]) ==
*[[12highschool1]] - first 12-note highschool scale
* [[Cv_scales|Cv scales]] – [[Periodic_scale|epimorphic scales]] with three major and two minor tetrads
*[[12highschool2|12highschool2]] - second 12-note highschool scale
* [[Hahn_7|Hahn_7]] – [[Paul Hahn]]'s scale with 32 consonant 7-limit dyads. TL '99
*[[44_39-12|44_39-12]] - 12-note chromatic tuning with 352:351, 364:363 by Margo Schulter
* [[Major_clus|Major clus]] – Chalmers' Major Mode Cluster
*[[pre-archytas|pre-archytas]] - tuning by Gene Ward Smith
* [[Major_wing|Major wing]] – Chalmers' Major Wing with 7 major and 6 minor triads
**Chris Vaisvil, [http://micro.soonlabel.com/just/pre-archytas-hobbit/daily20110621_zither_ji.mp3 Just Zither Me] [http://chrisvaisvil.com/?p=983 (details)]
* [[Max_scales|Max scales]] – 31 dyads 26 triads 6 tetrads 2 pentads
*[[augdommean|augdommean]] - Fokkerization of Centaur
* [[Minor_clus|Minor clus]] – Chalmers' Minor Mode Cluster, Genus [333335]
*[[barton|barton]] - Jacob Barton, tetratetradic scale on 6:7:9:11
* [[Minor_wing|Minor wing]] – Chalmers' Minor Wing with 7 minor and 6 major triads
*[[bicycle|bicycle]] - George Secor's (also Wilson's and Heathwaite's) 13-limit harmonic bicycle
* [[Barton]] – [[Jacob Barton]], tetratetradic scale on 6:7:9:11
*[[biggulp|biggulp]] - Big Gulp tuning
**Chris Vaisvil, [http://micro.soonlabel.com/tuning-survey/daily20100611-Big%20Gulp.mp3 improv] [http://chrisvaisvil.com/?p=164 (details)]
*[[bihexany|bihexany]] - hole around [0, 1/2, 1/2, 1/2]
*[[blue-ji|blue-ji]] - John O'Sullivan and Carl Lumma
**[https://alonetone.com/vaisvil/tracks/sweeneys-agony-remix-by-johnny-pumphandle.mp3 Sweeney's Agony]
*[http://micro.soonlabel.com/blue-tuning/daily20110119-atonement-in-blue-JI.mp3 Atonement to a Centaur]
*[[bluesji|bluesji]] - Graham Breed's Blues scale in a 7-limit JI version
*[[Bozuji Tuning]] - Bostjan Zupancic's tuning based on combining the ideas of ergotonics (i.e. defining tones by their musical functionality), adaptive step sizes (i.e., defining steps rather than intervals), and the further extrapolation of Gioseffo Zarlino's expansion of the Ptolemeic JI scale.
*[[breedball3|breedball3]] - the third breed ball around 49/40-7/4
*[[canton|canton]] - a 2.3.11/7.13/7 subgroup scale
*[[carlos_harm|carlos_harm]] - [[Wendy_Carlos|Wendy Carlos]] Harmonic Scale
**Chris Vaisvil, [http://micro.soonlabel.com/carlos-harmonic/daily20090806-piano-valles-marineris-harmonic-wah.mp3 Valles Marineris]
*[[centaur|centaur]] - a 7-limit tuning [http://www.anaphoria.com/centaur.html discovered by Kraig Grady]
**Chris Vaisvil, [http://micro.soonlabel.com/centaur_tuning/daily20100823-centaur-ver2.mp3 Centaur’s Pasture]
*[[chalmers_ji1.scl|chalmers_ji1.scl]] - based loosely on Wronski's and similar JI scales
*[[collapsar|collapsar]] - an 11-limit patent val superwakalix
*[[cv_scales|cv scales]] - [[Periodic_scale|epimorphic scales]] with three major and two minor tetrads
*[[dekany-cs|dekany-cs]] - [[Combination_product_sets|Cps]]({1,3,7,9,11}, 2) union {77/72, 77/64}; Grady-Narushima
*[[domdimpajinjschis|domdimpajinjschis]] - superwakalix
*[[domdimpajinjmean|domdimpajinjmean]] - superwakalix, same as miller7, parizek_ji1
*[[duodene|duodene]] - the Ellis duodene = Dwarf(<12 19 28|) = syndie3 = Euler(675) = Gandhar tuning
*[[duodene_skew|duodene_skew]] - rotated duodene = magsyn3
*[[duohex|duohex]] - a scale with two hexanies
*[[dwarf12_7|dwarf12_7]] - the 7-limit 12-note dwarf
*[[dwarf12_11|dwarf12_11]] - the 11-limit 12-note dwarf
*[[genovese_12|genovese_12]] - Denny Genovese's superposition of harmonics 8-16 and subharmonics 6-12
*[[glumma|glumma]] - a <12 19 27 34|-epimorphic rectangular scale
*[[hexanys|hexanys]]
*[[hobbit_11_limit|hobbit_11_limit]] - Chris Vaisvil's 11 limit JI hobbit
**Chris Vaisvil, [http://chrisvaisvil.com/the-forgotten-glory-of-wolfs-motor-court/ The Forgotten Glory of Wolf’s Motor Court] [http://micro.soonlabel.com/hobbit_scales/20130923_hobbit_11_limit.mp3 (play)]
*[[locomotive|locomotive]] - a 2.9.11.13 subgroup scale
*[[major_clus|major_clus]] - Chalmers' Major Mode Cluster
*[[major_wing|major_wing]] - Chalmers' Major Wing with 7 major and 6 minor triads
*[[minor_clus|minor_clus]] - Chalmers' Minor Mode Cluster, Genus [333335]
*[[minor_wing|minor_wing]] - Chalmers' Minor Wing with 7 minor and 6 major triads
*[[Max_scales|max scales]] - 31 dyads 26 triads 6 tetrads 2 pentads
*[[mdevelde|mdevelde]] - a 2.3.5.19 subgroup scale
*[[nofives|nofives]] - a 3 & 7 scale discovered by Gene Ward Smith
**Aaron Krister Johnson, [https://www.youtube.com/watch?v=n7mxHWdkV04 piano improvisation]
*[[omaha|omaha]] - a 2.3.11 subgroup scale
*[[otones12-24|otones12-24]] - a.k.a. Mode 12 of the [[OverToneSeries|Harmonic Series]]
*[[part12|part12]] - 9+3=12 partition scale <12 19 27| epimorphic
*[[portsmouth|portsmouth]] - a 2.3.7.11 subgroup scale
*[[prentwind|prentwind]] - [[Prent_Rodgers|Prent Rodgers]]' scale for [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/prentrodgers+dryholecanyonforwoodwindquintet.mp3 Dry Hole Canyon for Woodwind Quintet]
*[[prism|prism]] - [[Carl_Lumma|Carl Lumma]] scale
*[[pris|pris]] - optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale
*[[ptolex|ptolex]] - [[Jon_Lyle_Smith|Jon Lyle Smith]]'s extended septimal Ptolemy
**Jon Lyle Smith, [http://www.notonlymusic.com/board/download/file.php?id=1993 Te Deum Laudamus]
*[[hahn12|hahn12]] - [[Hahn-reduced|Hahn-reduced]] 12 note scale
*[[hahn_7|hahn_7]] - [[Paul_Hahn|Paul Hahn]]'s scale with 32 consonant 7-limit dyads. TL '99
*[[hahnZ|hahnZ]] - [[Paul_Hahn|Paul Hahn]]'s scale Z, TL '99
*[[harrison_cinna|harrison_cinna]] - [[Lou_Harrison|Lou Harrison]], "Incidental Music for Corneille's Cinna"
*[[harrisonm_rev|harrisonm_rev]] - Michael Harrison's [http://www.michaelharrison.com/harmonic-tunings.html Revelation Tuning]
*[[hexy|hexy]] - maximized 9-limit harmony containing a hexany
*[[johnston|johnston]] - Ben Johnston's combined otonal-utonal 11-limit Fokker block
*[[malcolm|malcolm]] - Alexander Malcolm's Monochord (1721)
*[[malcolm2|malcolm2]] - Alexander Malcolm's 1721 scale
*[[mohajira-to-slendro|mohajira-to-slendro]] - Dudon's "From Mohajira to Aeolian and Slendros"
*[[oljare|oljare]] - Mats Öljare, scale for "Tampere" (2001)
*[[ramis|ramis]] - monochord of Ramos de Pareja (Ramis de Pareia), Musica practica (1482)
**[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Impromptu%20in%20F%20Minor.mp3 Impromptu in F Minor] by [[Zach_Curley|Zach Curley]]
*[[rectoo|rectoo]] - Hahn reduced circle of fifths via <12 19 27 34|
*[[riley_rosary|riley_rosary]] - Terry Riley, tuning for Cactus Rosary (1993)
*[[Secor5_23TX|Secor5_23TX]] - George Secor's synchronous 5/23-comma temperament extraordinaire
*[[serafini-11|serafini-11]] - Serafini's [http://electro-music.com/forum/topic-14631.html 11's chromatic scale], an 11-limit tuning discovered by [[Carlo_Serafini|Carlo Serafini]]
*[[Sevish (scale)|sevish]] - Sean "Sevish" Archibald's scale for [https://www.archive.org/download/FNet021/02.Sevish-Trapped_in_a_Cycle.mp3 Trapped in a Cycle]
*[[simp12|simp12]] - Stiltner-Vaisvil 12 note 2.3.5.7.13 scale
**[http://micro.soonlabel.com/just/JI/simpl10plus13.mp3 Simpl10plus13] by Chris Vaisvil
*[[sonbirkezsorted|sonbirkezsorted]] Sonbirkez Huzzam scale
*[[steel|steel]] - an 11-limit tuning discovered by [[Lou_Harrison|Lou Harrison]] and Bill Slye
**see David B. Doty's [http://www.dbdoty.com/SteelSuiteIntro.html Steel Suite]
*[[stelhex|stelhex]] - stellated two out of 1 3 5 7 hexany
*[[stelhex2|stelhex2]] - stellated two out of 1 3 5 9 hexany
*[[stelhex5|stelhex5]] - stellated two out of 1 3 7 9 hexany, stellation is degenerate
*[[terrain|terrain]] - in effect a generated scale in 2.9/5.9/7 subgroup
*[[thirteendene|thirteendene]] - 2.3.5.7.13 marveldene transversal
*[[unimajor|unimajor]] - a 2.3.11/7 subgroup scale
*[[wilson_class|wilson_class]] - [[Erv_Wilson|Erv Wilson]]'s class
*[[wilsonistic|wilsonistic]] - [[Margo_Schulter|Margo Schulter]]'s Wilsonistic Pivot on C
**Chris Vaisvil, [http://micro.soonlabel.com/just/wilson/daily20101225--wilsonistic_pivot_C-ji.mp3 A Blue Christmas for Erv]
*[[yekta|yekta]] - Rauf Yekta's 12-tone tuning suggested in 1922 Lavignac Music Encyclopedia
*[[young-lm_piano|young-lm_piano]]- La Monte Young's scale from "The Well-Tuned Piano"
*[[zeta12|zeta12]] - Margo Schulter's Zeta Centauri tuning, inspired by Kraig Grady's Centaur


== See also ==
== [[Detempering]]-based ==
* [[Gallery of 12-tone tempered scales]]
* [[Duodene_skew]] – rotated duodene = magsyn3
* [[Pre-archytas]] – tuning
* [[Mohajira-to-slendro]] – Dudon's "From Mohajira to Aeolian and Slendros"by [[Gene Ward Smith]]
** [[Chris Vaisvil]], [http://micro.soonlabel.com/just/pre-archytas-hobbit/daily20110621_zither_ji.mp3 Just Zither Me] [http://chrisvaisvil.com/?p=983 (details)]
* [[Septimal Canright]] – A 7-limit detemper of 12edo used by [[David Canright]]
* [[Thirteendene]] – 2.3.5.7.13 marveldene transversal
 
=== [[Wakalix]]-based ===
* [[Collapsar]] – an 11-limit patent val superwakalix
* [[Domdimpajinjschis]] – superwakalix
* [[Domdimpajinjmean]] – superwakalix, same as miller7, parizek_ji1
 
== [[Erv Wilson]]-related ==
* [[Wilson_class|Wilson class]] – [[Erv Wilson]]'s class
* [[Wilson helix]]
* [[Wilsonistic]] – [[Margo Schulter]]'s Wilsonistic Pivot on C
* [[Wilson-middle-rank-12]] – Wilson 7-limit, 12-note middle rank of 22 [[marimba]] scale
** Chris Vaisvil, [http://micro.soonlabel.com/just/wilson/daily20101225--wilsonistic_pivot_C-ji.mp3 A Blue Christmas for Erv]
 
=== [[CPS]]-based ===
* [[Bihexany]] – hole around [0, 1/2, 1/2, 1/2]
* [[User:BudjarnLambeth/435zpi|CPS (1 of 3 5 9 11 15 19 25 27 29 33 37 41) (untempered ver.)]]
* [[User:BudjarnLambeth/435zpi|CPS (11 of 3 5 9 11 15 19 25 27 29 33 37 41) (untempered ver.)]]
* [[Dekany-cs]] – [[Combination_product_sets|Cps]]({1,3,7,9,11}, 2) union {77/72, 77/64}; Grady-Narushima
* [[Duohex]] – a scale with two hexanies
* [[Hexanys]] – 1.3.5.7.9 hexany
* [[Hexy]] – maximized 9-limit harmony containing a hexany
* [[Stelhex]] – stellated two out of 1 3 5 7 hexany
* [[Stelhex2]] – stellated two out of 1 3 5 9 hexany
* [[Stelhex5]] – stellated two out of 1 3 7 9 hexany, stellation is degenerate
 
== [[Fokker block]]-based ==
* [[Augdommean]] – Fokkerization of Centaur
* [[Johnston]] – [[Ben Johnston]]'s combined otonal-utonal 11-limit Fokker block
 
== [[Historical temperaments|History]]-related ==
* [[Bozuji Tuning]] – [[Bostjan Zupancic]]'s tuning based on combining the ideas of ergotonics (i.e. defining tones by their musical functionality), adaptive step sizes (i.e., defining steps rather than intervals), and the further extrapolation of [[Gioseffo Zarlino]]'s expansion of the Ptolemeic JI scale.
* [[Malcolm (scale)|Malcolm]] – [[Alexander Malcolm]]'s Monochord (1721)
* [[Malcolm2]] – Alexander Malcolm's 1721 scale
* [[Ptolex]] – [[Jon Lyle Smith]]'s extended septimal Ptolemy
** Jon Lyle Smith, [http://www.notonlymusic.com/board/download/file.php?id=1993 Te Deum Laudamus]
* [[Ramis]] – monochord of Ramos de Pareja (Ramis de Pareia), Musica practica (1482)
** [http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Impromptu%20in%20F%20Minor.mp3 Impromptu in F Minor] by [[Zach Curley]]
* [[Secor5_23TX]] – [[George Secor]]'s synchronous 5/23-comma temperament extraordinaire
 
== [[Hobbit]]s, [[dwarves]] & related ==
* [[Centaur]] – a 7-limit tuning [http://www.anaphoria.com/centaur.html discovered by Kraig Grady]
** Chris Vaisvil, [http://micro.soonlabel.com/centaur_tuning/daily20100823-centaur-ver2.mp3 Centaur’s Pasture]
* [[Duodene]] – the Ellis duodene = Dwarf(<12 19 28|) = syndie3 = Euler(675) = Gandhar tuning
* [[Dwarf12_7]] – the 7-limit 12-note dwarf
* [[Dwarf12_11]] – the 11-limit 12-note dwarf
* [[Hobbit_11_limit|Hobbit 11-limit]] – Chris Vaisvil's 11 limit JI hobbit
** Chris Vaisvil, [http://chrisvaisvil.com/the-forgotten-glory-of-wolfs-motor-court/ The Forgotten Glory of Wolf’s Motor Court] [http://micro.soonlabel.com/hobbit_scales/20130923_hobbit_11_limit.mp3 (play)]
 
== Originating from a composition ==
* [[Biggulp]] – Big Gulp tuning
** Chris Vaisvil, [http://micro.soonlabel.com/tuning-survey/daily20100611-Big%20Gulp.mp3 improv] [http://chrisvaisvil.com/?p=164 (details)]
* [[Harrison_cinna]] – [[Lou Harrison]], "Incidental Music for Corneille's Cinna"
* [[User:Tristanbay/Margo Scale|Margo Scale]] – 13-limit subgroup detempering of [[Subgroup temperaments#Pepperoni|Pepperoni]] used in a song by [[User:Tristanbay|Tristan Bay]]
* [[Oljare]] – Mats Öljare, scale for "Tampere" (2001)
* [[Prentwind]] – [[Prent Rodgers]]' scale for [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/prentrodgers+dryholecanyonforwoodwindquintet.mp3 Dry Hole Canyon for Woodwind Quintet]
* [[Riley_rosary|Riley rosary]] – [[Terry Riley]], tuning for Cactus Rosary (1993)
* [[Sevish (scale)|sevish]] – [[Sean Archibald]] (Sevish)'s scale for [https://www.archive.org/download/FNet021/02.Sevish-Trapped_in_a_Cycle.mp3 Trapped in a Cycle]
* [[Simp12]] – Stiltner-Vaisvil 12 note 2.3.5.7.13 scale
** [http://micro.soonlabel.com/just/JI/simpl10plus13.mp3 Simpl10plus13] by Chris Vaisvil
* [[Young-lm_piano]] – [[La Monte Young]]'s scale from "The Well-Tuned Piano"
 
== Overtone/undertone-based scales ==
* [[Carlos_harm|Carlos harm]] – [[Wendy Carlos]] Harmonic Scale
** Chris Vaisvil, [http://micro.soonlabel.com/carlos-harmonic/daily20090806-piano-valles-marineris-harmonic-wah.mp3 Valles Marineris]
* [[Genovese_12]] – [[Denny Genovese]]'s superposition of harmonics 8-16 and subharmonics 6-12
* [[Otones12-24]] – a.k.a. Mode 12 of the [[OverToneSeries|Harmonic Series]]
 
== [[Subgroup]]- or [[limit]]- based ==
''(Only added to this subheading if it doesn't belong under another subheading.)''
* [[Bicycle]] – [[George Secor]]'s (also Wilson's and Heathwaite's) 13-limit harmonic bicycle
* [[Bluesji]] – [[Graham Breed]]'s Blues scale in a 7-limit JI version
* [[Canton]] – a 2.3.11/7.13/7 subgroup scale
* [[Locomotive]] – a 2.9.11.13 subgroup scale
* [[Mdevelde]] – a 2.3.5.19 subgroup scale
* [[Nofives]] – a 3 & 7 scale discovered by Gene Ward Smith
** Aaron Krister Johnson, [https://www.youtube.com/watch?v=n7mxHWdkV04 piano improvisation]
* [[Omaha]] – a 2.3.11 subgroup scale
* [[Portsmouth]] – a 2.3.7.11 subgroup scale
* [[Serafini-11]] – Serafini's [http://electro-music.com/forum/topic-14631.html 11's chromatic scale], an 11-limit tuning discovered by [[Carlo Serafini]]
* [[Steel]] – an 11-limit tuning discovered by [[Lou Harrison]] and [[Bill Slye]]
** see David B. Doty's [http://www.dbdoty.com/SteelSuiteIntro.html Steel Suite]
* [[Terrain]] – in effect a generated scale in 2.9/5.9/7 subgroup
* [[Unimajor]] – a 2.3.11/7 subgroup scale
 
== Others ==
* [[12highschool1]] – first 12-note highschool scale
* [[12highschool2]] – second 12-note highschool scale
* [[44_39-12]] – 12-note chromatic tuning with 352:351, 364:363 by [[Margo Schulter]]
* [[Blue-ji]] – [[John O'Sullivan]] and [[Carl Lumma]]
** [https://alonetone.com/vaisvil/tracks/sweeneys-agony-remix-by-johnny-pumphandle.mp3 Sweeney's Agony]
** [http://micro.soonlabel.com/blue-tuning/daily20110119-atonement-in-blue-JI.mp3 Atonement to a Centaur]
* [[Breedball3]] – the third breed ball around 49/40-7/4
* [[Chalmers_ji1.scl|Chalmers_ji1]] – based loosely on Wronski's and similar JI scales
* [[Eagle 53|Eagle JI]] - [[John O'Sullivan]]
* [[Glumma]] – a <12 19 27 34|-epimorphic rectangular scale
* [[Hahn12]] – [[Hahn-reduced]] 12 note scale
* [[HahnZ|HahnZ]] – [[Paul Hahn]]'s scale Z, TL '99
* [[Harrisonm_rev]] – [[Michael Harrison]]'s [http://www.michaelharrison.com/harmonic-tunings.html Revelation Tuning]
* [[Part12]] – 9+3=12 partition scale <12 19 27| epimorphic
* [[Pris]] – optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale
* [[Prism]] – [[Carl Lumma]] scale
* [[Sonbirkezsorted]] Sonbirkez Huzzam scale
* [[Yekta]] – [[Rauf Yekta]]'s 12-tone tuning suggested in 1922 Lavignac Music Encyclopedia
* [[Zeta12]] – Margo Schulter's Zeta Centauri tuning, inspired by [[Kraig Grady]]'s Centaur
 
{{Navbox scale gallery}}


[[Category:Lists of scales|12-tone just intonation scales]]
[[Category:Lists of scales|12-tone just intonation scales]]
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