Pitch & Frequency (was:Re: FS and "AKO Phasing" update)

List, Chris Chris.List at sc.siemens.com
Fri Jan 16 21:29:36 CET 1998

>Hang on a minute, I always thought that perceived pitch is the same as
>received frequency. Would someone explain why it isn't the case?

To increase my own comfort level with this stuff, I've outlines a simple
real life example....

Let's say you have a sine wave at 440Hz. You hear a tone, A4 (or is it
3? - we'll call it A4). You run it through a pitch shifter and a
frequency shifter each set so that the output of each one is a sine wave
at 880Hz - double the frequency, one octave higher, you hear A5. The
thing is that the pitch shifter does this by doubling the input and the
frequency shifter does it by adding 440Hz to the input.

Now, lets say you change your source, and make it two sine waves, mixed
together, one at 440Hz (A4) and another a perfect 5th up - that'd be E4,
and that'd be 440 * (2 ^ (7/12)) = 660Hz (ahhh the beauty of math and
music - yes, perfect 5ths are 3/2 times the frequency of their roots -
it's no wonder they sound smooth).

Your pitch shifter would double the frequency of all input (raise by an
octave), so your output would be two mixed sine waves, at 880Hz (A5) and
1320Hz (E5), and you'd still hear a perfect 5th.

The frequency shifter, however, would add the same offset to all
partials. Since it was set to <<add>> 440Hz to your input, your output
would be two mixed sine waves, one at 880Hz (A5), and the other at
1000Hz (somewhere between B5 and C5 - if I've got my match right).
Obviously not a perfect fifth - more like an "illin' second" hence the
"does not maintain harmonic relationships" observation.

BTW, the output of a ringmod (aka "multiplier") with this same input
would also be two sine waves - one at 220Hz (A2) and one at 1010Hz (just
south of C5).

- CList

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