THEORY - www.larips.com

Bach's schematic, as it appears on the page

LaripS.com, © Bradley Lehman, 2005-8, 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.

New! 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.
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
New! A digest of postings to HPSCHD-L clarifying research details and answering questions

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

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v Introduction
v Articles
v FAQ
v Practice
* Theory
  - Measurements
  - Comparisons
  - Other "Bach"
  - [Extra]ordinary
  - Regular/Mean
  - Enharmonics
  - Cube puzzle
  - Geometric 5ths
  - TU & Schismas
v History
v Etc
v Recordings