Don said:
Any nonlinear devicee generates harmonics.
They are integral multiples because of fundamental trig identities.
Except on the paino where lateral stiffness makes the overtones
different from the harmonics.
This is a bit misleading. The "except" is implying something that is not
correct. Harmonics are by *definition* integral to the fundamental,
always. The piano don't make harmonics not equal to overtones. Its an
example where harmonics are not equal to overtones.
What instruments produces are "overtones". These are the natural
resonant frequencies of the instrument due to its physical construction.
This overtones may or may not be close to a harmonic. For strings the
overtones are very close to harmonics, so the words are often used
interchangeable, although their definitions are completely independent.
For an instrument such as a guitar, the bridge saddles of the bridge are
individually adjusted to ensure that the harmonic frequency is the same
as the overtone at the 12th fret. This is because the effective
vibration length of the string is slightly shorter then its physical
length, and progressively shorter as sting thickness goes up. That is,
the string dose not start vibrating at its end point, but slightly away
from the end point. Some obtuse individuals, for reasons unknown, may
like to simply state "lateral stiffness" as the reason, but this is
about as useful as knowing the date of the battle of Trafalgar as an
explanation to the battle tactics.
Drum overtones are way off from harmonics of the fundamental. They are
actually related to the roots of Bessel functions, not sine functions.
The first overtone is at 2.4f.
Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.