The Significance of the French Baroque A-392

May 11th, 2009 by admin

The current issue of Strings, June 2009, asserts in a small review of the Bach Brandenburg Concertos that the conductor on this recording chose to perform them “in the French Baroque pitch of A = 392 Hz….”

The purpose of this short essay is to highlight the significance of that frequency in relation to natural pitch. I would like to set forth why I question this pitch as having been anything other than A flat in the time of Johann Sebastian Bach.

It was during the time of Bach that the vibrational rate per second of middle C was discovered to be 256 times per second. We call it 256 Hz now. Apparently this was the pitch for middle C commonly used in the time of Bach. It has been accepted by scientists as the pitch of middle C since that time.

Is there anything about that number that catches your attention? It is a power of two. That means that if you reduce it by halves you get 128, 64, 32, 16, 8, 4, 2, and finally 1.

Those numbers are all lower octaves of C. The one at 16 vibrations per second is the lowest that can be heard as a distinct pitch by the human ear. The lower numbers are still octaves of C.

This means that there is an immediate physical connection between one second of time and the standard of middle C at 256 Hz. If the interval of one second is a natural division of the diurnal rotation of the earth, then middle C of 256 is the natural middle C. This may explain why the pitch was standard before it was ever measured.

Using one cycle per second, we can derive other natural pitches by employing the simple rules of deriving overtones, or partials, from a fundamental pitch.

Two cycles per second is the octave C from one cycle. Three cycles per second is the fifth. It is G. Four cycles yields another C. Five per second gives us the third, E. Six cycles per second is an octave of the fifth. Seven cycles produces the lowered seventh, B flat.

Taking that pitch and multiplying by 7 we get the seventh of B flat, A flat.
That’s 49 vibrations per second. Double that for the octave and you have a tone that is 98 Hz. Double that and it’s 196 Hz. A final doubling gives you 392 Hz.

In short, if middle C in the time of Bach was 256 Hz, then the tone produced by 392 Hz would be perceived as an A flat.

It’s possible that violins might tune down their A and E strings a half step to sound brighter when accompanying the brass instruments. They might leave the G and D strings in standard tuning, playing in closed position on the lower strings, and open position on the higher strings. I’m just speculating here.

What is not conjecture is this assertion: if middle C is 256 Hz, then 392 Hz will sound like an A flat.