Tuning Systems

Alternate Temperaments: Theory and Philosophy - Introduction to tuning systems, based on the Western cents system. Written by Terry Blackburn.
www.terryblackburn.us/music/temperament/index.html

The Argument for Equal Temperament - Fred Lerdahl's paper regarding the use of equal temperament over just tuning.
eamusic.dartmouth.edu/~kov/lerdahl/EqTemp.html

A Beginner's Guide To Temperament - Written for the electronic mailing list Piporg-l by Stephen Bicknell.
www.users.dircon.co.uk/~oneskull/3.6.04.htm

Comparison of Temperaments - Table comparing various Western and Non-Western temperaments.
members.pcug.org.au/~apurdam/tempers.html

The Development of Musical Tuning Systems - The historical development of musical tuning systems from ancient Greek origins to the development of equal temperament.
www.midicode.com/tunings/

Dictionary of Microtonal Music Theory - Dictionary of common terms used in just tuning and equal temperament style tunings.
www.tonalsoft.com/enc/encyclopedia.aspx

Equal Temperament Tuning - An introduction to equal temperament for guitarists who have problems tuning their guitars.
users.adelphia.net/~cygnusx_1/equal_temperament.html

Historical Tuning - Includes information on the differences between equal temperament and well temperament and why Bach rejected equal temperament and celebrated well temperament.
users.bestweb.net/~rmp/

Historical Tunings on the Modern Concert Grand - Tradational tunings of the grand piano and Beethoven's specific tunings.
www.uk-piano.org/edfoote/

An Introduction to Historical Tunings - Discusses the development of tuning systems in Medieval Europe.
www.kylegann.com/histune.html

Justonic Tuning Inc. - Pitch Palette software tunes a microtunable synthesizer to just intonation, world scales, historic scales and user scales in real time.
www.justonic.com/

Keyboard temperament analyzer/calculator - Excel spreadsheet that analyzes keyboard temperaments: gives beat rates for tuning, and harmonic-tension charts in all keys.
www-personal.umich.edu/~bpl/temper.html

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.
www.larips.com

Musical Tunings and Temperaments - Color-coded descriptions of tunings and temperaments from the 9th Century through the 16th Century.
www.j2b.co.uk/tuning/

Pitch and Scale of the Great Highland Bagpipe - Describes proper tunings and scale construction for the Great Highland Bagpipe.
www-personal.umich.edu/~emacpher/pipes/acoustics/pipescale.html

Pythagorean Tuning and Medieval Polyphony - Article by Margo Schulter written in 1998.
www.medieval.org/emfaq/harmony/pyth.html

Tantrum - Tool for the study of temperament anomalies.
www.musanim.com/mam/tantrum.html

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.
www.redshift.com/~dcanright/harmser/

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.
www.leeds.ac.uk/music/studio/rproj_swss/tuning/tuning.htm

Understanding Temperaments - Tunings used for harpsichords.
pages.globetrotter.net/roule/temper.htm

World Scale Depository - Construction of a reference center of scale measurements throughout the world.
www.anaphoria.com/depos.html