The 3rd, 4th, 5th and 6th Revised Editions

Throughout the years after the initial 2008 Edition, the Unequal Temperaments eBook has been fully updated for completeness and consistency. In the process we identified a few topics that deserved clarification, enlargement and even individual research projects, resulting in the 3rd edition of May 2013, the 4th edition of August 2017, the 5th edition of August 2021 and the 6th edition of August 2026.

3rd Revised Edition (2013)

Please find below a list of topics with significant additions and enhancements:

• Temperaments: Werckmeister III, Vallotti/Young, Neidhardt and Leigh-Silver
• The search for J.S. Bach’s temperament
• Tuning for keyboard duets, trios and quartets
• Historical review of temperaments in performance
• Historical trends within the French tempérament ordinaire
• History of Variable Intonation for winds and strings
• Relevance of temperament for the stringing list of the harpsichord and clavichord
• Unequal Temperament Spreadsheet: please click in the Errata and Extras button

There have been many minor additions and improvements. Let us just mention:

• Temperaments: Schlick, history of meantone, Gallimard and Almost-Equal
• Intonation for brass wind instruments
• Mathematical coincidences in music
• Literature Cited: 49 new entries

4th Revised Edition (2017)

In this edition the book contains the following new sections:

• The temperament implied by Pachelbel’s harpsichord suites
• Monochord calibration and its accuracy for keyboard tuning
• The optimal tuning-fork note for instruments and ensembles

There are many minor additions and improvements, for example in the following topics:

• Temperaments: Pythagorean, Early Renaissance, Kirnberger, Werckmeister
• The practice of Good temperaments in the Baroque era
• New keyboard-tuning schemes for Meantone and French temperaments
• Playing in 17-note enharmonic meantone using a standard MIDI 12-note keyboard
• More details about intonation for wind instruments
• Literature Cited: 12 new entries

5th Revised Edition (2021)

This edition contains the following new sections:

• Two Theorems on the Pythagorean Comma and Regular Fifths
• A Taxonomy for Unequal Temperaments
• A Pioneering Achievement in Sicily

There are countless text and format improvements, as well as minor additions, for example in the following topics:

• Temperaments: J.S. Bach, Handel, Kirnberger
• Vicentino’s Arcicembalo
• Literature Cited: 21 new entries

6th Revised Edition (2026)

• The book has been fully reformatted for easier reading either onscreen or printed in either A4 or Letter paper
• Many minor improvements and additions have been carried throughout, mostly shown by a vertical bar "|" on the margin
• Literature Cited: 23 new entries