Temperament resources on the Web
Very rough order: bibliographies, pages on temperaments, software, special topics.
There is of course much overlap with what is discussed here, but with a different perspective, different way of saying things, and this often brings new insights.
Suggestions and corrections most welcome.
- Wikipedia's Tuning category
- Mario Igrec's excellent book Pianos Inside Out: a comprehensive reference work on the piano (2013), it includes a long chapter on tuning and the problems specific to the piano due to the inevitable inharmonicity of the strings. Tuning a harpsichord is, by comparison, much easier.
- A very complete bibliography (including historical and Web material) (600K! awesome) by Manuel Op de Coul
- Other tuning-related weblocations by Stichting Huygens-Fokker, including music fragments in various temperaments
- Also: WannaLearn, OpenHere
- A very thorough, well-researched and clear discussion of Pythagore's tuning by Margo Schulter, also with very complete discussion of later temperaments: a must-read for anyone seriously interested in tunings and temperaments (esp. for the medieval period)
- Chris Tyler's excellent site on temperaments (including a calculator)
- Lots of interesting stuff by Joe Monzo (starting on his meantone page)
- The temperamental Bach: demo CDs of various temperaments on harpsichord and organ
- Bach's musical temperament
- Temperament: A Beginner's Guide by Stephen Bicknell: less technical, with a lot more on historical perspective, and with some suggestions for CDs
- Temperament, a beginner's guide by Stephen Bicknell (also here) -- update of above?
- Comparison of temperaments by Andrew Purdam (also here)
- Alternate Temperaments: Theory and Philosophy by Terry Blackburn
- History of Tuning and Temperament by Howard Stoess
- Historical Tunings on the Modern Historical Concert Grand by Edward Foote
- The Meantone temperament home page
- Meantone and Temperament in Bach's Time by Daniel Pyle, adapted by Ben Chi
- Meantone Temperaments by Graham Breed, also other pages, e.g. Graham's microtonal software
- Lucy tuning by Charles Lucy (see some notes below)
- Just intonation network
- Just intonation by Kyle Gann, also An Introduction to Historical Tunings by Kyle Gann
- Applet on temperaments by Keith Griffin
- Tuning/temperament S/W compiled by Nicholas S. Lander
- Fred Nachbaur's MIDI tempering utilities
- Keyboard temperament analyzer/calculator by Bradley Lehman
- 12-tone equal temperament and 72-tone equal temperament
- Justesse a cappella à la renaissance par Yves Ouvrard, Jean-Pierre Vidal, Olivier Bettens
- The Mathematics of Tuning and Temperament by David Bartlett
- Algorithms for Mapping Diatonic Keyboard Tunings and Temperaments by Kenneth P. Scholtz
- Ear Training
The following are some notes on a few temperaments that may one
day work their way into my "Understanding temperaments" text.
Mostly adapted from email exchanges.
This is (my understanding) a regular temperament, about half-way
between Salinas and Aaron: both its major and minor thirds are
similarly out of tune (a distinctive characteristic).
All regular temperaments can be thought of as being a spiral
of fifths which is another way of saying that they are "open"
(in my context, because the way harpsichords and organs are
typically built, I have limited myself to 12 notes, but more notes
makes sense with this as well as all regular open temperaments).
As for its theoretical basis, I personally can't quite see how Pi can be
related to music. Pi is from a two-dimensional spatial environment, music and
sound happen in a one-dimensional time environment. But, I may just be blind
Lucy's temperament onto the JavaTuner (cent values to be entered):
Note Lucy JavaTuner
Name Cents Cents
C 313.5 +13.5
G 1009.0 +9.0
D 504.5 +4.5
A 0.0 0.0
E 695.5 -4.5
B 191.0 -9.0
F# 886.5 -13.5
C# 382.0 -18.0
G# 1077.5 -22.5
Eb 627.0 +27.0
Bb 122.5 +22.5
F 818.0 +18.0
(first two columns from Lucy's pages)
Dave Goggin's irregular temperament
French temperament ordinaire
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