Tuning Systems

Tuning and Temperament Bibliography   - Extensive list of print books, magazines, and journal articles on tuning systems.

Alternate Temperaments: Theory and Philosophy - Introduction to tuning systems, based on the Western cents system. Written by Terry Blackburn.

The Argument for Equal Temperament - Fred Lerdahl's paper regarding the use of equal temperament over just tuning.

Comparison of Temperaments - Table comparing various Western and Non-Western temperaments.

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 temperament style 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.

Historical Tunings on the Modern Concert Grand - Tradational tunings of the grand piano and Beethoven's specific tunings.

An Introduction to Historical Tunings - Discusses the development of tuning systems in Medieval Europe.

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

Larpis.com - Previously unknown temperament found on the autograph title page of the "Well-Tempered Clavier"; published 2005. Includes explanations and links to scholarly articles.

Musical Tunings and Temperaments - Color-coded descriptions of tunings and temperaments from the 9th Century through the 16th Century.

Pitch and Scale of the Great Highland Bagpipe - Describes proper tunings and scale construction for the Great Highland Bagpipe.

Pythagorean Tuning and Medieval Polyphony - Article by Margo Schulter written in 1998.

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.