Tuning Theory


Return to: MUSC 726T


  1. General Purpose
  2. Graphing
  3. Fraction
  4. Interval


Lambdoma and Tonality Diamond Players

  1. Roos, Pure Intervals: The Lambdoma {Loophole Letters}
  2. TonalityDiamond, A Playable Tonality Diamond {}

Harmonic Series Spiral Player

  1. Giannotta and Løfvander, Overtones Spiral (1-16) {}
  2. Nicholson, Harmonic Series Spiral Synth (1-64) {}
  3. Lowengard, The beauty of comparing harmonic intervals (1-256) {}

Tone Circle Player

  1. Bretschneider, Notenscheibe – {}
  2. Radical Data and Media, Harmonagon {}

Tone Circle Maker

Villaseñor, Constant Structure Analyzer {}

Lattice Maker

Villaseñor, Lattice Maker {}

Figure 1
. Tuning lattice for the diatonic scale in just (5-limit) intonation

Scale/Keyboard Web Apps

  1. Sevish et al., Scale Workshop {}
    Design microtonal scales and play them in your web browser
    Scale Workshop allows you to design microtonal scales and play them in your web browser
  2. Terpstra, Keyboard WebApp {Terpstra}
    Explore this generalized keyboard

Other Web Apps for Tuning Theory

  1. Allami, Leimma & Aptome {}
  2. Alves, Just Intonation Ear Trainer
  3. New Tonality, Xentonal Synthesizer {}
    Calculate dissonance curves
  4. Nicholson, Tools {}
  5. Scullard, Interactive Circle of Fifths {}
  6. Stilner, Moments of Symmetry in equal divisions of the octave calculator {}
  7. Villaseñor, Tools for exploring some of Erv Wilson's scale concepts {}
  8. Walter, Music Calculators {}
  9. Wolfram, Demonstrations Project: Exploring Musical Tuning and Temperament {Wolfram}


  1. Satellite, Wilsonic iPad App {App Store}
  2. Peterson, iStrobeSoft {}


Analysis & Transcription

Centre for Digital Music, Sonic Visualiser - Visualization, analysis, and annotation of audio recordings {}

CDM, Tony - High quality melody transcription {}

Tuning Specification Charts

Microsoft, Excel {Microsoft}

Tuning Apps made with Cycling '74's Max

  1. Bain, String Length and Pitch Interval (SLAPI) {Website}
  2. Mudd, Just Intonation Toolkit {Website; C74 Projects}

Rhythmic Loop Generator


Scala, by Op de Coul {WP}
Scala is an advanced application for tuning theory. It is freeware that runs on Windows, MacOS, and Linux.




  1. Cycling '74, Max {Cycling '74}
  2. IRCAM, OpenMusic {IRCAM}
  3. Mann, Tone.js {GitHub}
  4. McCartney, SuperCollider
  5. Vercoe, Csound {}

  1. Apple, Logic Pro X {Apple}
  2. Hπ Instruments, Universal Tuning Editor {Hpi}

See also: Xenharmonic Wiki, DAWs {XW}


Xeharmonic Wiki, List of Music Software {XW}


Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician. Urbana, IL: University of Illinois Press. {GB}

Mogini, Fabrice. 2011. "Ch. 17 Alternative Tunings with SuperCollider." In The SuperCollider Book, edited by Scott Wilson, David Cottle, and Nick Collins. Cambridge, MA: MIT Press. {GB}

Updated: January 20, 2024

Reginald Bain | University of South Carolina | School of Music