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Alternate Temperaments: Theory and Philosophy
Introduction to tuning systems, based on the cents system. Written by Terry Blackburn.
The Argument for Equal Temperament
Lerdahl's cognitive constraints.
Comparison of Temperaments
Table comparing various temperaments, including Equal Temperament, Pythagorean, another natural tuning, two mean-tone tunings, two Well temperaments, two Indian tunings, and two Persian tunings.
The Development of Musical Tuning Systems
The historical development of musical tuning systems from ancient Greek origins to the development of equal temperament.
Dictionary of Microtonal Music Theory
Dictionary of common terms used in just tuning and equal temperment style tunings.
Equal Temperament Tuning
An introduction to equal temperament for guitarists who have problems tuning their guitars.
Historical temperament tunings for the concert piano
Tradational tunings of the grand piano and Beethoven's specific tunings.
Historical Tuning
Includes information on the differences between equal temperament and well temperament and why Bach rejected equal temperament and celebrated well temperament.
Huygens-Fokker Foundation
Center for microtonal music. Promotes microtonal music in all its forms
An Introduction to Historical Tunings
On the development of tuning systems in Medieval Europe (Kirnberger, Young, and mean-tone systems).
J. S. Bach's recently discovered 1722 keyboard tuning
The previously unknown temperament found on the autograph title page of the "Well-Tempered Clavier", and published 2005; explanation and links to the scholarly article about this discovery
Julian Carrillo and the Thirteenth Sound
(1875-1965), Mexican music creator of the microtonal system called the 13th Sound. He reformed the theory of music, invented a new musical written based in numbers and built instrument capable to produce those small intervals.
Justonic Tuning Inc.
Pitch Palette software tunes a microtunable synthesizer to just intonation, world scales, historic scales and user scales in real time.
Keyboard temperament analyzer/calculator - Bradley Lehman
Excel spreadsheet that analyzes keyboard temperaments: gives beat rates for tuning, and harmonic-tension charts in all keys.
Musical tunings and temperment
Color-coded descriptions of tunings and temperments from the 9th Century through 16th Century.
Pythagorean Tuning and Medieval Polyphony
Article by Margo Schulter.
Stephen Bicknell
A Beginner's Guide to Temperament - written for the electronic mailing list Piporg-l.
Tantrum
Tool for the study of temperament anomalies.
A Tour Up The Harmonic Series
Basic introduction to the Pythagorean circle of fifths and the physical basis for the need for alternative tuning systems.
Tuning by Ratios
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.
Understanding Temperaments
Tunings used for harpsichords.
World Scale Depository
Construction of a reference center of scale measurements throughout the world.
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