Re: [tuning] Spectro analysis needed.

In a message dated 3/14/00 2:34:28 AM !!!First Boot!!!,
PERLICH@ACADIAN-ASSET.COM writes:

> I didn't see any attachments to this e-mail. Could you put up this zipped
bitmap on the internet, or at least e-mail me a copy?

For those of you that missed my first post the internet URL is
http://hometown.aol.com/amiltonf

The only two files on the site are a 1 bar MIDI file and a zipped .bmp of its
spectrogram.

The question I posed earlier was "Where are the extra tones (not the upper
partials) coming from?".

AMiltonF@aol.com wrote,

>The question I posed earlier was "Where are the extra tones (not the upper
>partials) coming from?".

They are combinational tones. Take any two tones, either harmonics or
fundamentals, that are actually present in the sound you're trying to
produce. Take either the sum or the difference of the frequencies. That is
one of the combinational tones. All the extra tones you are seeing are
probably combinational tones of this kind (quadratic), but some may be cubic
combinational tones (the sum or difference between a quadratic combinational
tones and one of the original tones), or quartic combinational tones . . .
You would need to repeat the experiment with pure sine waves to be sure.

Combinational tones such as these are often produced by faulty sound
reproduction or equipment. The "THD" (Total Harmonic Distortion) rating on
amplification equipment measures the degree to which these "extra" tones are
produced. Driving an amplifier or speaker too hard is another common cause
of combinational tones. When subjected to loud volumes, the ear produces
"subjective" combinational tones, though sum tones are noticeably absent and
one cubic difference tone is anomalously loud for low-volume stimuli . . .

In your example, call the lower tone a and the upper tone b. They start at 2
and 4 times some frequency, and move up to 3 and 8 times that frequency.
(The lines are slightly curved since a linear rise in cents is an
exponential in frequency.) So:

a = 2-->3
b = 4-->8

So the lines you see are:

0-->0 (a-a, b-b, etc.)
0-->2 (b-2*a)
0-->4 (2*b-4*a)
2-->1 (3*a-b)
2-->3 (a)
2-->5 (b-a)
2-->7 (2*b-3*a)
4-->4 (2*b-4*a)
4-->6 (2*a)
4-->8 (b)
4-->10 (2*b-2*a)

etc.