Lara St. John on Intonationby Lara St. John
/ April 1, 2000
Violinists playing solo (without piano, clavichord, etc.) are wont to use what we term "expressive" or "just" intonation. This can be explained both scientifically and aesthetically. Historically, the notes of scale systems anywhere have been based on pure harmonics. Singing, or playing a non-tempered instrument in "just" intonation requires slight shifts in pitch for any note, as exemplified below:
In the first 3 notes of a C major scale (C, D, E) "D" is 9/8 times the frequency of the first note, and the "E" is 5/4 times the frequency of the first, therefore:
C = 1/1 x 528 = 528 cycles per second
D = 9/8 x 528 = 594 cycles per second
E = 5/4 x 528 = 660 cycles per second
However, to start in D, we face a problem:
D = 1/1 x 594 = 594 cycles per second
E = 9/8 x 594 = 668.25 cycles per second
Mathematically, as soon as the "key" or initial note changes, the difference for the note "E" is 8.25 cycles per second (in this example). In "just" intonation, all pitches must have the capacity to move. This is not an obstacle for instruments such as the violin or voice, where the performer has direct power over the pitch of every note. However, for fixed tone instruments (piano, organ, etc.), this becomes a major problem.
The historical "solution" of this dilemma is the totally contrived equal-tempered scale developed in 1685 and ultimately adopted by all piano makers. Bach, however, with the exception of his Well-Tempered Clavier (an experiment in equal temperament) wrote for "just" intonation. If works such as the Chaconne for Solo Violin were heard in equal temperament, the full beauty of his harmony would be compromised.
The notion that the Chaconne should be "tempered" is historically, mathematically, aesthetically, and absolutely false. This is extremely important for solo string music. Having a very high standard of perfect pitch and of pitch relation, I have always been fascinated by the subject.