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A Beginner's Guide to Temperament
- Written by Stephen Bicknell for the electronic mailing list Piporg-l.
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.
Alternate Temperaments: Theory and Philosophy
- Introduction to tuning systems, based on the cents system. Written by Terry Blackburn.
An Introduction to Historical Tunings
- On the development of tuning systems in Medieval Europe (Kirnberger, Young, mean-tone systems, etc.)
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.
Equal Temperament Tuning
- An introduction to equal temperament for guitarists who have problems tuning their guitars.
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
Johann Sebastian Bach: Well Tempered Tuning (Wohltemperirt)
- Paper on the history of the tuning system, as well as information about tuning a harpsichord in this system.
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.
Modes and Scales in Indian Music
- Article by David Courtney.
Pythagorean Tuning and Medieval Polyphony
- Article by Margo Schulter.
Tantrum
- Tool for the study of temperament anomalies.
The Alternate Tuning Internet Mailing List
- For exchanging ideas relevant to alternate tunings, including just intonation, paratactical tunings, experimental musical instrument design, and non-standard equal temperaments.
The Argument for Equal Temperament
- Lerdahl's cognitive constraints.
The History of Musical Tuning and Temperament
- Two academic papers, covering music before 1750, and music during the Classical and Romantic periods.
Tuning and Temperament Bibliography
- Huge list of print books, magazines, and journal articles on tuning systems. A must-visit for people seriously researching 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.
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