Posted by js on June 04, 2003 at 23:05:04:
In Reply to: Tuning to A440? posted by jlb on June 04, 2003 at 10:37:04:
"A" above "middle C" on a standard well-tuned piano has frequency 440 Hz. It is often called A440 and is the pitch the oboe player plays to tune an orchestra. The pitch called "A" which is an octave below has half the frequency (220 Hz). The equal temperament system of tuning divides an octave logarithmically into twelve segments:
A_ 220
Bb 233.082
B_ 246.942
C_ 261.626
C# 277.183
D_ 293.665
Eb 311.127
E_ 329.628
F_ 349.228
F# 369.994
G_ 391.995
G# 415.305
A_ 440
Bb 466.164
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In other words, when Bb (your typical band tuning pitch) sounds at about 466 (or, in the case of tubas, two octaves lower at around 116.5) vibrations per second, the pitch called "A-concert" is still 440 vibrations per second, and pitch level of the tuning of your band is still referred to as "A440".
Math isn't my specialty at all, but I believe the 12th root of 2 is used to calculate these "equal temperament" values in "vibrations per second".
Someone else will probably elaborate or correct.
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I personally question the wisdom of the "bottom-up" tuning method for "absolute" tuning unless it is done like your band director does it - monitoring it with an electronic tuner.