Gallery of 12-tone just intonation scales

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 octave-repeating 12-tone JI scale to a standard keyboard. This page collects some of these scales, and a companion page does the same for tempered scales.

• 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
• Pre-archytas – tuning by Gene Ward Smith
  • Chris Vaisvil, Just Zither Me (details)
• Augdommean – Fokkerization of Centaur
• Barton – Jacob Barton, tetratetradic scale on 6:7:9:11
• Bicycle – George Secor's (also Wilson's and Heathwaite's) 13-limit harmonic bicycle
• Biggulp – Big Gulp tuning
  • Chris Vaisvil, improv (details)
• Bihexany – hole around [0, 1/2, 1/2, 1/2]
• Blue-ji – John O'Sullivan and Carl Lumma
  • Sweeney's Agony
  • Atonement to a Centaur
• 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 – the third breed ball around 49/40-7/4
• Canton – a 2.3.11/7.13/7 subgroup scale
• Carlos harm – Wendy Carlos Harmonic Scale
  • Chris Vaisvil, Valles Marineris
• Centaur – a 7-limit tuning discovered by Kraig Grady
  • Chris Vaisvil, Centaur’s Pasture
• Chalmers_ji1 – based loosely on Wronski's and similar JI scales
• Collapsar – an 11-limit patent val superwakalix
• CPS (1 of 3 5 9 11 15 19 25 27 29 33 37 41) (untempered ver.)
• CPS (11 of 3 5 9 11 15 19 25 27 29 33 37 41) (untempered ver.)
• Cv scales – epimorphic scales with three major and two minor tetrads
• Dekany-cs – Cps({1,3,7,9,11}, 2) union {77/72, 77/64}; Grady-Narushima
• Domdimpajinjschis – superwakalix
• Domdimpajinjmean – superwakalix, same as miller7, parizek_ji1
• Duodene – the Ellis duodene = Dwarf(<12 19 28|) = syndie3 = Euler(675) = Gandhar tuning
• Duodene_skew – rotated duodene = magsyn3
• Duohex – a scale with two hexanies
• Dwarf12_7 – the 7-limit 12-note dwarf
• Dwarf12_11 – the 11-limit 12-note dwarf
• Genovese_12 – Denny Genovese's superposition of harmonics 8-16 and subharmonics 6-12
• Glumma – a <12 19 27 34|-epimorphic rectangular scale
• Hahn12 – Hahn-reduced 12 note scale
• Hahn_7 – Paul Hahn's scale with 32 consonant 7-limit dyads. TL '99
• HahnZ – Paul Hahn's scale Z, TL '99
• Harrison_cinna – Lou Harrison, "Incidental Music for Corneille's Cinna"
• Harrisonm_rev – Michael Harrison's Revelation Tuning
• Hexanys – 1.3.5.7.9 hexany
• Hexy – maximized 9-limit harmony containing a hexany
• Hobbit 11-limit – Chris Vaisvil's 11 limit JI hobbit
  • Chris Vaisvil, The Forgotten Glory of Wolf’s Motor Court (play)
• Johnston – Ben Johnston's combined otonal-utonal 11-limit Fokker block
• Locomotive – a 2.9.11.13 subgroup scale
• Major clus – Chalmers' Major Mode Cluster
• Major wing – Chalmers' Major Wing with 7 major and 6 minor triads
• Malcolm – Alexander Malcolm's Monochord (1721)
• Malcolm2 – Alexander Malcolm's 1721 scale
• Margo Scale – 13-limit subgroup detempering of Pepperoni used in a song by Tristan Bay
• Max scales – 31 dyads 26 triads 6 tetrads 2 pentads
• Minor clus – Chalmers' Minor Mode Cluster, Genus [333335]
• Minor wing – Chalmers' Minor Wing with 7 minor and 6 major triads
• Mdevelde – a 2.3.5.19 subgroup scale
• Mohajira-to-slendro – Dudon's "From Mohajira to Aeolian and Slendros"
• Nofives – a 3 & 7 scale discovered by Gene Ward Smith
  • Aaron Krister Johnson, piano improvisation
• Oljare – Mats Öljare, scale for "Tampere" (2001)
• Omaha – a 2.3.11 subgroup scale
• Otones12-24 – a.k.a. Mode 12 of the Harmonic Series
• Part12 – 9+3=12 partition scale <12 19 27| epimorphic
• Portsmouth – a 2.3.7.11 subgroup scale
• Prentwind – Prent Rodgers' scale for Dry Hole Canyon for Woodwind Quintet
• Pris – optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale
• Prism – Carl Lumma scale
• Ptolex – Jon Lyle Smith's extended septimal Ptolemy
  • Jon Lyle Smith, Te Deum Laudamus
• Ramis – monochord of Ramos de Pareja (Ramis de Pareia), Musica practica (1482)
  • Impromptu in F Minor by Zach Curley
• Rectoo – Hahn reduced circle of fifths via <12 19 27 34|
• Riley rosary – Terry Riley, tuning for Cactus Rosary (1993)
• Secor5_23TX – George Secor's synchronous 5/23-comma temperament extraordinaire
• Septimal Canright – A 7-limit detemper of 12edo used by David Canright
• Serafini-11 – Serafini's 11's chromatic scale, an 11-limit tuning discovered by Carlo Serafini
• sevish – Sean Archibald (Sevish)'s scale for Trapped in a Cycle
• Simp12 – Stiltner-Vaisvil 12 note 2.3.5.7.13 scale
  • Simpl10plus13 by Chris Vaisvil
• Sonbirkezsorted Sonbirkez Huzzam scale
• Steel – an 11-limit tuning discovered by Lou Harrison and Bill Slye
  • see David B. Doty's Steel Suite
• 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
• Terrain – in effect a generated scale in 2.9/5.9/7 subgroup
• Thirteendene – 2.3.5.7.13 marveldene transversal
• Unimajor – a 2.3.11/7 subgroup scale
• 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, A Blue Christmas for Erv
• Yekta – Rauf Yekta's 12-tone tuning suggested in 1922 Lavignac Music Encyclopedia
• Young-lm_piano – La Monte Young's scale from "The Well-Tuned Piano"
• Zeta12 – Margo Schulter's Zeta Centauri tuning, inspired by Kraig Grady's Centaur