Software

WEB-BASED CALCULATORS

Bain, Ratio to Cents

Yacavone, Xen-Calc

1. General Purpose Calculators
   
• Google, Calculator {support.google.com}
  Type an equation directly into Google's Search Box; e.g. 2 + 3 =,  or search for 'calculator'
2. Graphing Calculators
   
• Desmos, Graphing Calculator {Desmos.com}
• Apple, Graphing Calculator {Apple}
3. AI Calculators
   
• Anthropic, Claude
  
• Google, Gemini
• Microsoft, Copilot
• OpenAI, ChatGPT
4. Fraction Calculators
   Add (+), subtract (-), multiply (*) and divide (/) fractions
• Calculator Soup
• Convert Fraction to Decimal {CalculatorSoup}
• Convert Decimal to Fraction {CalculatorSoup}
• RapidTables, Fraction Calculator {RapidTables}
  
• Wolfram Alpha
• Simply Fractions {Wolfram Alpha}
• Fraction: Examples {Wolfram Alpha}
• Pie Charts and Tape Diagrams
5. Interval Calculators and Players
   
• Bain, Ratio to Cents - √
  A simple mobile Web app calculator that converts an interval frequency ratio to cents and provides the ratio's decimal expansion to three decimal places.
  
  
• Yacavone, Xen-Calc {About} - √
  A multi-purpose calculator/converter for microtonal music theory that supports conversion between cents, just ratios, EDO, FJS, and color notations. Also provides interval playback.
  
  Advanced
  
• Nicholson & Sabat, Plainsound Harmonic Space Calculator {Plainsound.org; User Guide}
  A tool for composers and musicians who are interested in discovering and working with properties of intervals tuned in just intonation
  
  
• Pierson & Melnikow, Partials Monster {https://partials.monster}
  Play intervals based on ratios found in the harmonic series
  
  
• Untwelve, JavaScript Interval Calculator {Untwelve.org}
  Calculates rational approximations (or semi-convergents) and EDO approximations for a given interval
  
  
• Winkler, Just intonation ratio player {Observable}
  Play ratio sequences as a scale or chord
  
  
• Zhu, Ratioscore: Just Interval Tool {Humdrum.org}
• Interval Grid
• Temperament Calculator
• Prime-limit intervals

WEB APPS

Lambdoma Player

1. Caspar Johannes Walter, Tonality Diamond {casparjohanneswalter.de}
2. TonalityDiamond, A Playable Tonality Diamond {TonalityDiamond.com}

Harmonic Series Spiral Player

1. Alexander Garsden, Erv's Spiral {Web app}
2. Giannotta and Løfvander, Overtones Spiral (1-16) {Suonoterapia.org}
3. Nicholson, Harmonic Series Spiral Synth (1-64) {Superparticular.com}
4. Norris, Harmonic Series Calculator {MichaelNorris.info}
5. Lowengard, The beauty of comparing harmonic intervals {jhhl.net}

Tone Circle Player

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

Tone Circle Maker

Villaseñor, Constant Structure Analyzer {Wilson-tunings.netify.app}

Lattice Maker

Sevish, Scale Workshop 2 {Sevish.com; Tutorials: Sevish.com; YouTube; GitHub} - √

Villaseñor, Lattice Maker {Wilson-tunings.netlify.app} - √

• Enter a scale and the program will create a tuning lattice
  e.g., enter the just (5-limit) scale 1/1 9/8 5/4 4/3 3/2 5/3 15/8 and the program will display the lattice shown in Figure 1

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

Keyboard/Scale Web Apps

1. Sevish, Scale Workshop 2 {Sevish.com; Tutorials: Sevish.com; YouTube; GitHub} - √
   Design microtonal scales and play them in your web browser
   
   
2. Plainsound, Hexatone {Plainsound.org}
   Customizable touch-screen keyboard with built-in sounds and MIDI input and microtonal (MIDI Tuning Standard) output
   
   
3. Terpstra, Keyboard WebApp {Terpstra}
• The Terpstra Keyboard Concept {YouTube}

Other Apps

1. Allami, Leimma & Aptome {isartum.net}
• Leimma Tutorial {Vimeo}
• Aptome Tutorial {Vimeo}
2. Alves, Just Intonation Ear Trainer
3. Jung, PitchGrid
   
4. Kline, Projective Tuning Space {ProjectiveTuningSpace.com}
5. Microsoft, Excel {Microsoft}
6. Mudd, Just Intonation Explorer {Tommudd.co.uk} - √
   
7. New Tonality, Xentonal Synthesizer {NewTonality.net}
   Calculate dissonance curves
   
• Tutorials: Part 1: Xentonal synth in your browser {YouTube}; Part 2 {YouTube}; Part 3 {YouTube}
8. Nicholson, Tools {superparticular.com}
• Plainsound Harmonic Synth Calculator
• Harmonic Series Spiral Synth
• Relations of tone as an analogy for relations of colour
9. The R Project for Statistical Computing {r-project.org}
   
10. Scullard, Interactive Circle of Fifths {randscullard.com}
11. Stilner, Moments of Symmetry in equal divisions of the octave calculator {anaphoria.com}
12. Tymoczko, Mad Musical Science {madmusicalscience.com}
• The Traditional Tonnetz
• The Generalized Tonnetz
  
13. Villaseñor, Tools for exploring some of Erv Wilson's scale concepts {wilson-tunings.netlify.app}
14. Walter, Music Calculators {CasparJohannesWalter.de}
15. Wilson Archives, Software Tools {anaphoria.com}
16. Wolfram, Demonstrations Project: Exploring Musical Tuning and Temperament {Wolfram}

1. Satellite, Wilsonic iPad App {Website}
2. AudioKit Pro {Website}
   
3. Peterson, iStrobeSoft {PetersonTuners.com}

STANDALONE SOFTWARE

1. Bain, String Length and Pitch Interval (SLAPI) {Website}
2. Centre for Digital Music, Sonic Visualiser - Visualization, analysis, and annotation of audio recordings {SonicVisualiser.org}
• CDM, Tony - High quality melody transcription {SonicVisualiser.org}
3. Microsoft, Excel {Microsoft}
4. Semantic Danielou – https://www.semantic-danielou.com
5. Sygyt Software UG, Voce Vista {VoceVista.com}
   Software for singers, singing teachers, speech language pathologists and anyone who analyzes sound

SCALA

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

• Scala Home Page
• Download
• File format
• Scale directory
• Scala files: http://quark.sccode.org/ScalaTunings/archive/
• Third-Party Tutorials:
• Walker, Scala for Dummies Tutorial
• Sevish
• How to export microtonal tuning files using Scala {YouTube}
• How to invent your own musical scales using Scala {YouTube}
• Other:
• Garritan, Aria Player, Scala file reference {Garritan}

MICROTONES IN ELECTRONIC MUSIC

Getting Started

1. Zheanna Erose, How to Microtune Easily {YouTube}
2. Sevish, Using Microtones in Electronic Music (2020) {YouTube}
3. Xenharmonic Wiki, List of Microtonal Software Plugins {XW}
4. Xenharmonic Wiki, List of DAWs {XW}
5. Sevish, Scale Workshop 3 {Plainsound}

Plugins

Xenharmonic Wiki, List of Microtonal Software Plugins {XW}

1. Arturia, Pigments
   
2. Node Audio, Entonal Studio {entonal.studio}
   
3. Fluid Synth: A Soundfont Synthesizer {fluidsynth.org}
   
• MTS compatible soundfonts for Fluidsynth (2023) {Plainsound}
  
4. Hπ Instruments
• Tonal Plexus {Hpi.com}
• Universal Tuning Editor {Hpi.com}
5. Infinitone: Dynamic Micro-Tuning Software {infinitone.com}
   
6. Modartt, Pianoteq {Modartt.com}
7. Naitive Instruments, Kontakt {Native-Instruments.com}
8. Spectrasonics, Omnisphere
9. Xfer, Serum

Keyboards

1. Hπ Instruments
• Tonal Plexus {Hpi.com}
• Universal Tuning Editor {Hpi.com}
2. Intuitive Instruments, Exquis {https://dualo.com}
3. Lumatone Isomorphic Keyboard {www.lumatone.io; YouTube}
4. Roli keyboards {roli.com}

MIDI

1. MIDI {WP; Midi.org}
   
2. Ways to microtune:
• MIDI Pitch bend {WP}
  
• MIDI Tuning Standard (MTS) {WP}
  
• MIDI Polyphonic Expression (MPE) {MIDI.org; ROLI}
  

Plainsound Music Edition, Just Intonation & Microtonal Resources – https://www.plainsound.org

The Wilson Archives, Tools and Treasures: Software: Tools for Exploring Some of Erv Wilson's Scale Concepts – https://www.anaphoria.com/wilsontreasure.html

Xeharmonic Wiki, List of DAWs {XW}; List of Music Software {XW}; List of Microtonal Software Plugins {XW}

References

Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician. Urbana: University of Illinois Press. {GB; Full text: TCL; Audio Examples}

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 13, 2026