| > Since I don't have a visacard to order those wonderful books on
> computermusic over the net, I wonder if someone of you know some basic
> methods to calculate harmonic freqs from a given freq....Assume I have
> a sound with most emphasized freq is a 440Hz....Ok. Now I want to add
> some other sound, how can i alter the sound's main pitch so that it
> sounds harmonic with the previous sound ???
Well, the "harmonic frequencies" of a given fundamental frequency (the
lowest frequency in the sound) are simply the integer multiples of the
fundamental (times 2, times 3, and so on...). If your sounds are simple
sine waves, sticking to harmonics will *tend* to keep things from grating.
Even in that simple case, though, what you have to recognize is that when
you start to stack up sine waves, in effect you're creating chords. (This
is actually what Ravel was trying to do in "Bolero," albeit with already
complex tones.) As you start to layer notes with different (probably
non-harmonically-related fundamentals) and associated sequences of harmonic
overtones, it's almost guaranteed that some overtones in one note (here note
= fundamental + overtones) will beat against those in another note. Add to
this the fact that in real-world instruments much of the richness of the
timbre comes from the fact that the overtones have individual volume
envelopes and are out-of-phase with each other, and your task becomes
well-nigh impossible, at least as you've stated it. On the other hand, it
seems to me you're sort of micturating in the direction of the prevailing
atmospheric flow (to put it gently ). Were you actually able to
eliminate all the beating and heterodyning, you'd probably end up with a
pretty flat, banal sound, not the rich layering you describe in your next
paragraph.
> Most of my Csound time goes to constructing dronal, rich layered,slow
> ambient. A *HUGE* problem is that mostly my sounds are extremely
> overlapping, with (besides also in amplitude) slow changes in frequency,
> causing very annoying 'false'tones sometimes due to the pitch changes..
>
> I HAVE to find a way that I can tell Csound to take care that my
> overlapping sounds never sound false...How ???
Not doable. However, by sticking close to the frequency ratios that define
the major/minor/perfect intervals in the scale, you'll achieve a passable
approximation. Of course, it won't be perfect, both for the reasons I
mentioned above, and because most western scales, including the
well-tempered, don't actually exactly fit the harmonic overtone series.
(That's why the well-tempered scale took some time to gain acceptance: it's
a compromise that allows easy modulation between keys. Scales like the
just-tuned scale sound better in their home key, because they stick closer
to the overtone series, but they sound a bit strained when you need to do
something like modulate to a "related" key, do a temporary harmonization, or
play polychordal harmonies.)
In addition, the frequency ratios of the major/minor/perfect intervals don't
lie in the overtone series themselves. If you think about it, the first
harmonic is an octave above the fundamental. The second is a fifth above
that, and so on. The interval ratios are arrived at by dropping the upper
harmonics by one or more octaves as necessary to bring them within the ambit
of the octave. That's why chords in thirds or even fourths sound much
denser than the same notes played in "open" voicings. Increased beating due
to non-harmonicity. Those ratios are *related* but not exactly the same
thing as the true harmonics.
On the other hand, you shouldn't look at this as a drawback. I recall one
story my college physics professor told about the Hammond B-3. As you may
or may not know, the Hammond generates its overtone series by spinning
notched metal disks in front of electronic pickups, with the frequency
generated being determined by the number and spacing of the notches and the
speed of rotation. For many years people were at a loss to explain exactly
why the Hammond sounded so rich, especially when compared to the rather
cheesy sound of early "electronic" organs (remember the VOX, the darling of
the early American rock bands? Got a copy of "Inna-Gadda-Da-Vida" around?
) It turns out that they determined the necessary overtone frequencies
according to an incorrect acoustic theory (and partly because the mechanical
generator imposed certain constraints). Remember, this was sometime in the
twenties or thirties (not sure which). They were trying to get things
exactly harmonic, just as you are. They didn't get it right. Fortunately
for them . It's exactly the harmonic inaccuracies and the beating they
cause that make the Hammond sound so rich.
On a related tack, let me recommend two books you'll find very useful in
regard to questions of this sort (I could recommend *lots* more , but
these two are pretty well indispensable). First, "The Master Handbook of
Acoustics," 3rd ed. by F. Alton Everest, ISBN 0-8306-4437-7. Second, the
Yamaha "Sound Reinforcement Handbook," by Gary Davis and Ralph Jones, ISBN
0-88188-900-8. They should be easy to come by (I found both at the local
Barnes & Noble), and are around $35 each. Hope this helps.
Reid Sweatman
Programmer/Audio Engineer
|