Website of the Huygens-Fokker Foundation, centre for microtonal music.

Pythagorean Tuning and Medieval Polyphony Table of Contents Introduction Remarks and acknowledgements Basic concepts Pythagorean tuning and Gothic polyphony Simple vertical intervals Ideal fifths and fourths Active thirds and sixths Milder major seconds and minor sevenths Coloristic harmony Stable trines (8/5, 8/4) The split fifth (5/3) Quintal/quartal sonorities (9/5, 5/4, 5/2, 7/4) Cadential ...

Historic music tuning problem described and solution provided with Pitch Palette software tunes a microtunable synthesizer to just intonation, world scales, historic scales and user scales in real time.

Overview of historical temperaments on keyboard instruments ...

Bibliography containing references to literature about musical tuning, temperament, scales, microtonality and intonation with links to relevant sites ...

Excel spreadsheet that analyzes keyboard temperaments: gives beat rates for tuning, and harmonic-tension charts in all keys.

Alternate Temperaments: Theory and Philosophy (The beginner's field guide to alternate temperaments) Introduction Very, very brief history Circle of fifths and the harmonic series Do the Math... The Comma Why equal temperament Why study alternate temperaments My temperament analysis project Analysis of historic temperaments Footnotes Merchandise! DISCLAIMER INTRODUCTION: Are you feeling just a ...

An Introduction to Historical Tunings By Kyle Gann 1. Tuning in Pre-20th Century Europe 2. Meantone Tuning 3. Werckmeister III and Bach's W.T.C. 4. Well Temperament and 18th-Century Music 5. A Word about Pythagorean Tuning 6. Conclusion Just Intonation - a whole other subject 1. Tuning in Pre-20th Century Europe Those who attack equal temperament, the tuning of our modern pianos - as I do on my ...

Tantrum: A Tool for the Study of Temperament Anomalies Download tantrum.sea.hqx (60K) -- Macintosh freeware Go to Music Animation Machine main page Send us email Tantrum Description Because musical pitch classes repeat at the octave, the gamut of pitch classes may be conveniently arrayed around a circle. Where, precisely, on the circle should the pitch classes be placed in order to accurately ...

WELCOME TO THE WORLD SCALE DEPOSITORY AT THIS STAGE, WE ARE IN THE BEGINNING STAGE OF ASSEMBLING A WORLD BANK OF SCALES. OUR CONCERN IS MASSING TOGETHER THE RAW DATA OF DIFFERENT TUNINGS FOUND AROUND THE WORLD. IT IS A TASK BEYOND THE CAPABILITIES OF EVEN A HOST OF VOLUNTEERS AND RELIES ON THOSE AT LARGE TO AUGMENT OUR OWN RESEARCH WITH SUBMISSIONS. SUCH SUBMISSIONS ARE INDISPENSABLE IF SUCH A ...

This paper explores the use of simple ratios to tune musical intervals and chords. Included are a tutorial, a set of computer programs, and a re-tuned two-part invention by J.S. Bach.

Press play for Albeniz' Aragon from his Suite Espanola. Comparison of Temperaments Below is a table comparing various temperaments, including Equal Temperament, Pythagorean, another natural tuning, two mean-tone tunings, several Well temperaments, two Indian tunings, two Persian tunings. The discussion is carried out using the key of C as example. By compare, I mean with respect to using - say - ...