Thursday, December 06, 2007

from the Strad December'07 issue :):):)

Making Waves
.
Intonation is a lifelong challenge for string players - which is not surprising, since perfect intonation is mathematically impossible. A note is in tune only in relation to other notes, specifically their pitches. Pitch and tone colour are the subjective perceptions of the objective phenomenon of frequency. Frequency relationships are simply numerical ratios, and this fact allows us to think about them mathematically.
.
Perfect intonation is mathematically impossible because the relationships among notes depend on how you get from one note to the next. By way of demonstration, try this:
1. Tune your open strings until they're beatless (in tuning open 5ths, we match the third harmonic of the lower string to the second of the upper and tune until the beats slow down and disappear).
2. Play a beatless, pure major 6th, open G to E. The E in this pure, beatless major 6th will be considerably lower than the E one whole step above open D.
3. Now play this E against the open A. It will be very flat.
.
You could call the distance between D and E tuned to the open A a 'major whole tone', and the distance between D and E tuned to the open G a 'minor whole tone'.
.
The greatest conflict in intonation is the difference between intervals played sequentially and intervals played simultaneously. For example, an F sharp played as a pure double-stop with D is a much lower note than an F sharp leading note resolving on to G.

COOL.
;)


stomached it at
4:43 PM