opaqueice wrote:

> By commensurate I mean related by an integer or simple rational number,
> as totoro correctly says.

Ah, right. I've not heard the term before.

> For real music I'm skeptical this will matter.  Still, it would be
> interesting to play with real tones that are pretty pure.  I may try
> recording my trumpet and then feeding it through an all-pass crossover
> to see if it makes a difference.

I think you'll find it does matter, particularly with multi-driver
speaker systems.

Real instruments generate harmonics at multiples of the fundamental
frequency. For example, an FFT analysis of a violin playing a single
note looks something like this:

http://ccp14.minerals.csiro.au/ccp/web-mirrors/isotropy/~stokesh/vspect.jpg

Now, imagine a two-way speaker system with the crossover point at 2kHz.

The fundamental tone and the first two harmonics will be played through
the LF driver, the third harmonic will sit right on the crossover point
 (who knows what will happen to that), and the upper harmonics will play
through the HF driver.

If the LF and HF drivers are not in phase then the tone of the violin
will be affect as the fundamental tone and the lower harmonics will not
play at the same time as the upper harmonics.

Let us know how your experiments come out.

R.

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