Equal temperament is a tuning system that divides 1 octave evenly into 12 semitones, and it became popular in the latter half of the 19th century. This made it possible to obtain the same sound when playing in any of the 24 keys and to modulate freely, but it also created a situation in which every chord sounds muddy and ugly. First, let’s experience just how ugly it is through performances by Hatsune Miku. Listening to the first 1 minute of each is enough.
- Fugue from The Well-Tempered Clavier, Book 2, No. 9, BWV 878 (equal-temperament version)
- Fugue from The Well-Tempered Clavier, Book 2, No. 9, BWV 878 (Kirnberger III version)
And once more:
- Fugue from The Well-Tempered Clavier, Book 2, No. 9, BWV 878 (equal-temperament version)
Doesn’t that make you think, “What?!” Equal temperament is ugly. I cannot bear to listen to it.
But you might say, “Didn’t Bach write it for equal temperament? After all, it is called The Equal-Tempered Clavier.”
Bzzzt. Wrong. Bach did not write anything called “The Equal-Tempered Clavier.” That is a mistranslation. The original title is
- Das Wohltemperierte Klavier (The Well-tempered Keyboard / well-tempered keyboard instrument), collection
. And this “well temperament” is not “equal temperament.” It appears certain that he used an unequal temperament1.
This Kirnberger temperament became popular in the 19th century after Bach’s death, and it seems that Beethoven and Chopin wrote using this temperament. I plan to write more about that in due course.
Incidentally, temperaments like this are compromises for pianos and organs, which cannot freely change pitch. Orchestras and choirs that do not include instruments such as pianos or organs can freely change pitch, so they can perform in just intonation2. This makes the harmonies sound even more beautiful than with the unequal temperaments described above. I will give one example below. It is a Russian Orthodox hymn arranged by Tchaikovsky. Instruments are not permitted in Russian Orthodox music. It is therefore sung by an a cappella choir (= meaning “in the style of the church”…). Immerse yourself in the transparent sound of just intonation.
- though apparently not the Kirnberger temperament above…. There is also a theory that Bach’s actual tuning method is written on the cover of Das Wohltemperierte Klavier. The paper is here → Bradley Lehman: Das Wohltemperierte Klavier http://nymetro-ems.com/images/pdf_music/Bach%27sExtraordinaryTemperament-PartI.pdf
- Just intonation is a tuning system based on the natural harmonic series, which gives its harmonies a pleasing sound. Melodically, on the other hand, Pythagorean tuning is often felt to be more beautiful. But in places with a great deal of reverberation, such as churches, even a single melody produces a harmonic effect, so the benefits of using just intonation are greater. Thinking about it this way, in places where reverberation is not very long, it seems best to play the principal melody in Pythagorean tuning and add harmony above it in just intonation. Or rather, I think string quartets normally do exactly that…. That is what it means to tune by ear, isn’t it?
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