Essays - Lara Speaks about Pure Intonation

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To: The Editor of the Globe & Mail
Re: Correction in November 7 review of St. John concert by David Miller

Concerning intonation in Bach works for solo instruments

This is a complex matter in classical music; violinists playing solo (i.e. without piano, clavichord, etc.) are wont to use what we term “expressive” or “just” intonation. This can be explained both scientifically and aesthetically.   Scientifically, “just” intonation applies to scale intervals being tuned to the pure harmonics of the natural overtone series, with these being exact multiples of a fundamental frequency. For example, the basic frequency of 100 cycles per second also vibrates at 200, 300, 400, etc. per second simultaneously. Historically, the notes of scale systems anywhere have been based on these 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 or “well” 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.

Your reviewer intimated that the Chaconne should be “tempered” which is historically, mathematically, aesthetically and absolutely false. Any string player instinctively feels the key differences and plays accordingly. This is the only way for a solo instrument to convey key and modulation, and therefore expression, by staying flexible instantaneously in real time. Equal temperament, presently on all pianos, is only a compromise, making all notes equally out of tune.

There is no earthly reason why a solo string instrument or voice, having the possibility to play or sing pure intonation, should want, or try, to be tempered.  I feel that the public has been misled by Mr. Miller’s paragraph about the Bach Chaconne, and I am writing this letter for the edification of your readers. This is an extremely important fact about solo string music, and I, having a very high standard of perfect pitch and of pitch relation, have always been fascinated by the subject.

My thanks to Mr. Miller for his time and comments.

Yours truly,

Lara St. John

November 9, 1998

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