Lara Speaks about Pure Intonation

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:

One thought on “Lara Speaks about Pure Intonation

  1. I am currently doing doctoral research on teaching intonation in instrumental ensembles and, quite accidentally, came across a quote from you on the topic of just intonation. I work primarily with wind players, and have had some challenges generalizing some of the current ideas about just intonation to string players and vocalists. Thanks for your comments on the topic and best wishes for continued success!

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