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.

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

Chord-based (eg tritriadic, tetrachordal)

• Cv scales – epimorphic scales with three major and two minor tetrads
• Hahn_7 – Paul Hahn's scale with 32 consonant 7-limit dyads. TL '99
• Major clus – Chalmers' Major Mode Cluster
• Major wing – Chalmers' Major Wing with 7 major and 6 minor triads
• 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
• Barton – Jacob Barton, tetratetradic scale on 6:7:9:11

Detempering-based

• 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, Just Zither Me (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 – 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

CPS-based

• 1-3-5-7 by 9/5 bihexany
• 1-3-5-9 by 7/5 bihexany
• 1-5-9-13 by 3/2 bihexany
• 3-5-15-19 by 9/8 bihexany
• Bihexanymyna
• 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.)
• Dekany-cs – Cps({1,3,7,9,11}, 2) union {77/72, 77/64}; Grady-Narushima
• Duohex – a scale with two hexanies
• Duohexmarvwoo
• Duohexmean
• GW Smith bihexany 14 Feb 2011 – hole around [0, 1/2, 1/2, 1/2]
• Hexanys – 1.3.5.7.9 hexanies
• Hexanys-valentino
• 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

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 – Alexander Malcolm's Monochord (1721)
• Malcolm2 – Alexander Malcolm's 1721 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
• Secor5_23TX – George Secor's synchronous 5/23-comma temperament extraordinaire

Hobbits, dwarves & related

• Centaur – a 7-limit tuning discovered by Kraig Grady
  • Chris Vaisvil, 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 – Chris Vaisvil's 11 limit JI hobbit
  • Chris Vaisvil, The Forgotten Glory of Wolf’s Motor Court (play)

Originating from a composition

• Biggulp – Big Gulp tuning
  • Chris Vaisvil, improv (details)
• Harrison_cinna – Lou Harrison, "Incidental Music for Corneille's Cinna"
• Margo Scale – 13-limit subgroup detempering of Pepperoni used in a song by Tristan Bay
• Oljare – Mats Öljare, scale for "Tampere" (2001)
• Prentwind – Prent Rodgers' scale for Dry Hole Canyon for Woodwind Quintet
• Riley rosary – Terry Riley, tuning for Cactus Rosary (1993)
• 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
• Young-lm_piano – La Monte Young's scale from "The Well-Tuned Piano"

Overtone/undertone-based scales

• Carlos harm – Wendy Carlos Harmonic Scale
  • Chris Vaisvil, 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 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, piano improvisation
• Omaha – a 2.3.11 subgroup scale
• Portsmouth – a 2.3.7.11 subgroup scale
• Serafini-11 – Serafini's 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 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
  • Sweeney's Agony
  • Atonement to a Centaur
• Breedball3 – the third breed ball around 49/40-7/4
• Chalmers_ji1 – based loosely on Wronski's and similar JI scales
• Eagle JI - John O'Sullivan
• Glumma – a <12 19 27 34|-epimorphic rectangular scale
• Gutierrez-Lambeth chromaticized sunbreak scale: 187/175 - 9/8 — 20/17 — 14/11 — 34/25 — 25/17 — 280/187 - 11/7 — 17/10 — 16/9 — 350/187 - 2/1
• Hahn12 – Hahn-reduced 12 note scale
• HahnZ – Paul Hahn's scale Z, TL '99
• Harrisonm_rev – Michael Harrison's 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