LaripS.com, © Bradley Lehman, 2005-22, all rights reserved.
All musical/historical analysis here on the LaripS.com web site is the personal opinion of the author,
as a researcher of historical temperaments and a performer of Bach's music.

Music theory in Bach's tuning and related methods

• Spring/summer 2006, the article "Bach's Art of Temperament" further explains this temperament from several additional practical angles.
• Practical instructions to set this temperament by ear [Beginning] [Intermediate] [Expert]
• Practical "twang" instructions, explaining the basic concept here for people who are accustomed to thinking of temperament as beat-counting
• A geometrical technique for quick tuning to set up any regular series of consistent fifths: the core C-G-D-A-E and/or F-C-G-D-A for any temperaments (including Bach's) that have them
• A diagram of the temperament, with brief remarks about scales and intervals
• Mathematical analysis of some of the musical results in this tuning's layout: cent charts, comma splits, tone and semitone measurements, etc.
• A clarification about the temperament's version for Bach's vocal music
• "Ordinary" and "Extraordinary" temperament
• Properties of regular or "meantone" temperaments; New! as of August 2006 includes beat-rate charts as well
• Graph of the enharmonic handling and scale structure
• The fifths and major thirds are explained using Brombaugh's "Temperament Units" and Sorge's 18th century model of schismas: a mini-lesson here on the basic mathematics of keyboard temperaments
• Comparisons with other temperaments
• Other "Bach" temperaments from 1966 to present, surveyed
• Updated! "Temperament-killer" test pieces from Bach's repertoire, to confirm or weed out any proposed "Bach" temperaments empirically
• Some little test pieces for the Affekts of the keys. This page also describes the process of listening to Affekt.
• Errata and clarifications for "Bach's extraordinary temperament: Our Rosetta Stone"
• The more complex enharmonic issues to be solved in keyboard tuning are expressible in a cube puzzle layout
• Outlines of the complete Early Music article, and of the Clavichord International article
• A digest of postings to HPSCHD-L clarifying research details and answering questions
• Lecture slides from October 2008: explaining the tuning theory in an hour, with as little math as possible. This was a guest lecture at James Madison University (Virginia).
• Lecture notes from October 2010, University of Colorado
• New! Fa, Ti, and Modulation - How the scale degrees interact when music modulates

See also the practical instructions, as theory and practice are so tightly intertwined.... Some additional temperaments are provided there.

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