LaripS.com, © Bradley Lehman, 2005-13, 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
These pages supplement the theory that is presented in the
Early Music article.
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]
- 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
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.
- New! 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
- "Temperament-killer" test pieces from Bach's repertoire, to confirm or weed out any proposed "Bach" temperaments empirically
- Updated! Some little test pieces for the Affekts of the keys. This page also describes the process of listening to Affekt.
- Updated! 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
- Updated! 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
See also the practical instructions, as theory and practice are so
tightly intertwined.... Some additional temperaments are provided there.
- Other "Bach"
- Cube puzzle
- Geometric 5ths
- TU & Schismas