Estimated reading time 4 minutes
Table of Contents
Introduction
Do you like Johann Sebastian Bach’s Well-Tempered Clavier (WTC) but wonder what the “well-tempered” in the title means? Bach advocated for the well-temperaments which are circular tuning systems that allow keyboardists to play in any key without restrictions, similar to equal temperament. Thus, WTC was written to showcase well-temperaments. Keep reading What Precisely Did Bach Mean by Well-Tempered Clavier to learn how it works.
This article uses musical terms. For definitions, see the Glossary at the end of the post.
What Did Bach Mean by Well-Tempered Clavier: What Is the WTC?
J.S. Bach is a major composer who was so important that music historians end the Baroque period on the date of his death:
- Despite his fame today, back in the Baroque period, he was known more as a keyboard virtuoso than as a composer.
- Therefore, it makes sense that he would compose for the instrument that brought him his fame.
- He wrote his influential keyboard work, the Well-Tempered Clavier, in two parts. Each part consists of 24 preludes and fugues, covering all the major and minor keys.
That begs the question, “What is a well-temperament?” Keep Reading to learn more.
What Did Bach Mean by Well-Tempered Clavier: What Does Circular Tuning Mean?
Narrowing Select Fifths
The “well-tempered” part of the WTC name refers to a class of circular tunings for keyboard instruments.
- Unlike meantone temperament, circular tunings allow you to use all the major and minor keys.
- Thus, the name circular.
- Why? Because you can modulate around the circle of fifths.
How do you do this? By narrowing the fifths:
- Unlike equal temperament, not all the fifths are narrowed, nor are they all narrowed by the same amount.
- More importantly, tuning the fifths that way will also affect how narrow the major thirds are.
- This means that some chords and keys are better in tune than others.
The result is that each key has its own sound, which is called key coloration.
How It Impacts the Major Thirds
For example, according to The New Grove Dictionary of Music and Musicians, the organ at Queens college in Oxford has this tuning:
- C 0
- C#/Db 94.7
- D 197.3
- D#/Eb 296.5
- E 394.5
- F 500
- F#/Gb 594.5
- G 698.6
- G#/Ab 794.9
- A 895.9
- A#/Bb 998.4
- B 1094.5
(The numbers next to the note names are the cent values.)
In Western music, the major thirds are the most important intervals in the tuning scheme. Let’s look at the cent values for the major thirds from the Oxford organ:
- C/E = 394.5
- Db/F = 405.3
- D/F# = 397.2
- Eb/G = 402.1
- E/G# = 400.4
- F/A = 395.9
- Gb/Bb = 403.9
- G/B = 395.9
- Ab/C = 405.1
- A/C# = 398.8
- Bb/D = 398.9
- B/D# = 402
The major thirds range from as narrow as 394.5 cents to as wide as 405.3 cents. The narrower the major third, the better the major chord will sound:
- Thus, the C, F, and G chords in the key of C major will all sound good. However, the Db, Gb, and Ab chords in the key of Db major will tend to sound harsh.
- This is just one of many schemes that fall under the umbrella of circular tunings, but they all have this general pattern.
- The main thing that changes is which fifths get narrowed and by how much.
So, how exactly did Bach tune his keyboard instruments?
What Did Bach Mean by Well-Tempered Clavier: How Exactly Did He Tune His Keyboard Instruments?
There’s a theory that J.S. Bach left us a clue in his score showing exactly how he tuned his keyboard instruments. This video sums it up:
Video: Well-Tempered Tuning Explained
In the above video, an animated Bach character explains how he tunes the harpsichord:
- At the end of the video (time stamp 4:44) he says that the curlicues at the top of the page hold a clue to the secret of his well-temperament for clavier.
- It implies that if you can crack the code, you’ll be able to know exactly how he tuned.
- This is based upon a popular theory that has been circulating for some years now.
However, The New Grove Dictionary of Music and Musicians states:
It is doubtful whether J.S. Bach had any one secret mathematical formula of his own; he was not so mathematically inclined in matters of theory…
… J.S. Bach was probably no less exacting; according to his son C.P.E. Bach, no one else could tune a keyboard instrument to his satisfaction.
C.P.E. Bach’s own tuning advice allows for a few 5ths to be left untempered (implying a slightly unequal temperament)… (27: 276).
Therefore, there’s a good chance that we’ll never know exactly how J.S. Bach intended his music to sound:
- However, the performer in the following video shows what a Bach prelude would sound like in the Kirnberger III circular tuning on clavichord (time stamp 14:46 – 16:50), which gives a good approximation of Bach’s keyboard sound.
- In addition, the performer has a discussion of equal temperament vs. well-temperament (time stamp 5:37 – 8:00).
- For performers in general, getting the harpsichord or clavichord into the right tuning is important, because unlike piano, harpsichord and clavichord will sound jangly and harsh in equal temperament.
Therefore, pianists can use the cent values in the section “How It Impacts the Major Thirds” to tune a microtonal keyboard to the correct temperament while also playing with the correct sound: clavichord, harpsichord, or organ.
Video: Bach Prelude in Three Different Temperaments
Final Thoughts
The takeaway points:
- J.S. Bach’s well-tempered clavier is in two parts and consists of 24 preludes and fugues each, covering all the major and minor keys.
- The “well-tempered” part of the WTC name refers to a class of circular tunings for keyboard instruments.
- These are uneven tunings that allow all keys to be used, but each key will have its own characteristic sound.
Have fun!
Related Posts
- Simple Instructions for Pythagorean Tuning
- Intonation and Supplemented Equal Temperament
- How to Tune Your Incredibly Cool Microtonal Keyboard
© 2025 Geoffrey Keith
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