Tonalsoft Encyclopedia, by Joe Monzo - Homepage

Math and Music

Microtonal and Just-intonation Theory

Just-intonation tuning and microtonal music-theory form the conceptual basis of many musical scales and tuning systems. From the Sumerians 4000 years ago and ancient Greeks centuries later, right through the middle-ages and renaissance, musicians have studied math and music, and these two topics were inseparable. Unfortunately, during most of the 20th century and largely continuing to the present, Western music has generally ignored its own math-and-music foundations. Composers, theorists, and instrumentalists have focused on the rote learning of unchangable symbolic rules and musical scales, thereby remaining ignorant of the fundamental relationship between math and music.

The 4-strand helical lattice of the standard 31-tone meantone tuning, produced in Tonescape

Microtonal and just intonation composers and theorists have recently been working to re-establish the connection between math and music through the development of microtonal music theory. This vibrant, growing community of microtonal music theorists, composers, and software developers has been making tremendous contributions to our knowledge and understanding of a variety of topics in contemporary and historic music theory:

• Just-intonation scales, chords, and chord progressions
• New musical scales and tuning-systems based on the expanded resources of musical pioneers such as Partch, Fokker, and Wilson.
• Equal temperaments, unequal temperaments and how they relate to just-intonation music theory
• The application of advanced mathematics such as group theory, integer programming, and N-dimensional Grassmann Algebra for the development and categorization of musical scales (tuning systems).

This Encyclopedia of Microtonal Music Theory is a group project and a work in progress. It contains entries, data, clarifications, and corrections from dozens of direct contributors, and includes thousands of direct and indirect contributions. If you would like to contribute to the encyclopedia or ask a question, please don't hesitate to contact us.

We hope you can fulfill your needs for information regarding just intonation and microtonal music theory right here in the encyclopedia. If there's something you can't find, check out the latest encyclopedia entries and the latest essays on microtonal and just intonation music theory at the inTune news column, right here on the Tonalsoft site.

Please make a donation to help keep Tonalsoft online. A recurring monthly contribution would be apprecitated.

Thank you!