An Arithmophone is a thing that turns numbers into sounds. Its name is derived from the ancient Greek words ἀριθμός (arithmos; number) and φωνή (phone; sound).
In its current form (version 4), The Arithmophone is a software instrument and midi controller for touchscreen devices. You can use it as a musical instrument, a source of melodic and harmonic inspiration or a tool for exploring the deep connection between music and numbers.
The Arithmophone works with 7-limit just intonation tuning. Rather than the standard 12 tone tempered tuning found on most Western musical instruments, it uses simple harmonic ratios like 3/2 and 7/5 to produce its notes. Even though these ratios only use combinations of the first four prime numbers (2, 3, 5 and 7), this provides all the familiar notes of standard tuning, plus many more tonal colours.
The Arithmophone web audio app is a self-contained software instrument that you can play from any tablet, phone or computer (a tablet in landscape orientation works best). You can play it straight from your browser, or install it as a standalone app. To start playing the Arithmophone, just hit the button below. The QuickStart Guide explains everything you need to know to begin making music.
The Arithmophone MPE (Midi Polyphonic Expression) is a MIDI controller for MPE enabled instruments. If you are used to working with hardware or software synthesizers and have a suitable device available, then is option is for you, as it will allow you to play the Arithmophone with low latency and full control over your own sounds. The MPE QuickStart guide will help you get everything set up.
Once you have the Arithmophone up and running, you might like to have a look at this booklet about scales & chords:
For details about the acoustic principles and design philosophy behind the Arithmophone, links to earlier versions of the Arithmophone and more, please visit these pages.
Arithmophone concept, design and development by Chiel Zwinkels © 2025