The Road to equal temperament

What was the meaning of “Wohltemperierte” in Bach’s so-called “Wohltemperierte Klavier”? Did Bach’s title, “Wohltemperierte Klavier”, really mean “equal temperament”? No, it did not. It probably meant a clavier that could be played to a moderately distant key, or that could be tuned to a remote key with only minor adjustments.

Instruments that need to be tuned every time they are played are stringed instruments such as violins, harps, and guitars, as well as keyboard instruments with strings. Wind instruments cannot be tuned. Rather, wind instruments are “already tuned” when they are made, and are rarely re-tuned by the performer. Of course, this is not the case when the performer is also the maker. Therefore, from now on, when you hear the word “tuning,” unless you dare to say otherwise, please think of it as that of “keyboard instruments” or “string instruments.

As a side note, it is desirable for wind instruments to be tuned to “average tuning” as much as possible. This is because it is possible to create “genuine” harmony only when the instruments are in average tuning. However, this is not the case with the ancient instruments of the Baroque era. For example, in the flute, the f is high and does not sound good. On the other hand, the F# is low and sounds good. Therefore, the shape of the lips and the angle of the instrument had to be adjusted when playing.

Tonal music, or music with harmony, appeared in Europe during the Renaissance. Until then, which is mainly based on fourth and fifth degree parallels, genuine harmony would have been used. Later, in the Renaissance, the “third degree” appeared in harmony, and the music gradually began to have tonality (major and minor).

This is where the tricky issue of “tuning” comes in.

There is a term called “pure temperament”. In fact, this is a theoretical tuning, which is impossible in reality. In this tuning, the Pythagorean fifth degree and the major third of the meantone, which will be discussed later, are combined to produce three chords with no roar. However, this genuine harmony is absolutely impossible to use on a keyboard instrument. This is because it is a tuning that cannot go outside of a few chords in C major. As long as the pitches are fixed, it is a tuning method that cannot be realized. At the end of the 19th century, someone thought of a “split-key” organ to realize this tuning, but it was never practical.

So it is not as if genuine (tuning) is absolutely impossible. Of course, it is impossible with keyboard instruments. In fact, it is only possible for vocal ensembles, string ensembles, and wind ensembles. In these ensembles, it is possible for advanced players to instantly and “genuinely” match the so-called “keystone” triads of the melody, although it cannot be explained logically. However, the prerequisite for this is that each part knows perfectly the “sound” and “habits” of its own instrument. There is nothing more beautiful than a genuine harmony created in this way. I don’t have time to go into detail here, but it is surprisingly easy to obtain genuine chords through a physical phenomenon called “Tartini’s tones”.

The meantone tuning method was used from the early Baroque to the middle Baroque and partly to the beginning of the late Baroque. In terms of composers, Frescobaldi, Sweelinck, Louis Couperin, D’Anglebert, and Chambonniere were among those who used it. Sharps and flats were not used much in the music of those days. In addition, there were not many modulations to remote tones. This trend continued until Francois Couperin. There is no doubt that the most beautiful sounding tuning of these composers’ music is the meantone. However, when Rameau came along, there were pieces that meantone could not compete with . Then came Bach’s “Wohltemperierte Klavier” out at last.

It is often said that the recorders of the Baroque era were tuned in meantone, but this is a lie. To begin with, meantones are a tuning method unique to keyboard instruments, and they “always need to be changed”. In other words, in practice, the major third was raised or lowered here and there as needed according to the key of the piece being played.

In the meantone tuning, the four fifths(C-G,G-D,D-A,A-E) are narrowed so that starting from C major’s Do, the note of Mi is genuine to Do. Next, major thirds above and below “So, Re, La, and Mi” are adjusted to be genuine too. The “So #” is taken from the Mi note, but in the case of flat tunes, it is taken from the Do note downward to the genuine. In other words, it is not a “So♯” but a “La♭”. A keyboard instrument tuned in this way, with a meantone, can sometimes sound strange.）

For example, in the case of a C major minuet, the second minuet is in C minor. The first minuet is dominated by a genuine sound, but the second minuet is dominated by a dirty major third. The reason for this is that “Re♯” and “Mi♭”, “So♯” and “La♭”, etc. become different names. Also, at some point, you may hear the ultimate bad pitch in the meantone, the Wolf’s fifth degree. This is a “wrinkled” wide fifth caused by the narrowing of the fifth degree, and is an extremely unpleasant pitch.

It is the melody, rather than the chords, that gives us a real sense of the characteristics of a keyboard instrument tempered in meantone. The reason for this is that the semitones are wider in a meantone. When a trill is added to these wide semitones, it gives me an old-fashioned and elegant feeling.

In order to escape the contradictions and restrictions of the meantones, various tuning methods were developed in those days. I’ll leave the details for another time, but such tuning methods are known as Werckmeister’s tuning method and Kirnberger’s third tuning method in Germany, Young’s tuning method in England, Rameau’s tuning method and Rousseau’s tuning method in France. The idea behind all of these methods was to “dilute” the “murkiness,” so to speak, by distributing the Wolf’s fifth of the meantone appropriately so that all tones would sound “moderately beautiful” and all tones would sound “moderately dirty. This idea led to the modern “equal temperament”. It is highly probable that the tuning method used by Bach was one of these. Or perhaps Bach’s own tuning method existed. However, since Bach left no written record of his own tuning method, it is an eternal mystery as to what kind of tuning method he referred to as “Wohltemperierte Klavier” (well-tempered clavier).

I once wrote an entry about a film about Bach’s life. In it, a French musician, Louis Marchand, heard the sound of Bach tuning his harpsichord and said, “What is this tuning? I don’t want to fight with a musician who uses this kind of tuning method.” he said, and left the scheduled “harpsichord performance showdown. This is followed by the scene of Bach playing “Fantasy in C minor” by himself after Marchand had fled.

I don’t know much about the tuning of the lute instrument. However, most of the frets of the stringed instruments of the time were made of gut. This means that the frets are “movable”. In fact, the lute players I knew used to move these frets every time they tuned, sometimes shifting them diagonally (though I had no idea what that meant).However, this instrument is also capable (in principle) of equal temperament if it wanted to. However, that doesn’t mean that the lute player was always aware of equal temperament.