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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 Atlas of Consonance The author presents a graphical tool for the visualization of consonance and dissonance, based on an acoustical model of the interaction of musical tones. An Introduction to Historical Tunings On the development of tuning systems in Medieval Europe (Kirnberger, Young, and mean-tone systems). 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 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 Argument for Equal Temperament Lerdahl's cognitive constraints. Tuning and Temperament Bibliography Huge list of print books, magazines, and journal articles on 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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