AudioBanter.com - View Single Post - Fourier Analyses, or, how the Orchestra learned to play "Jet Engine"

(Scott Dorsey) wrote in message ...

Hi Scott. How have you been? Heard anymore Sonic Youth of late?

Ryan wrote:
I'm looking to find out more about writing some software that will use
traditional classical instruments to emulate "natural" or "non musical
sounds." The software will perform some type of analyses on an audio
file, I imagine FFT would be used at some point, but the problem with
FFT is that it only tells you what "perfect" or pure sine wave based
frequencies are present in a sound.

No. ANY arbitrary waveform can be decomposed down to sine waves. When you
put the sines back together, you can reconstitute the original wave. This is
the WHOLE POINT of the Fourier series. The time domain and frequency domain
representations of the waveform are equivalent and you can convert from one
to the other and back with impunity.

So what I have to do is perform FFT on each of my sound "samples", the
squeak of a vilon played behind the bridge, a viol's "dry string"
sounds, regular arco, pizzicato, etc, ect, all the ohter instruments,
etc. And then perform an FFT on any given sound file I'm interested
in emulating. After that, what kind of math would be used to sort
through all the samples and figure what goes best where?

Samplitude features an FFT analyses window. It just looks like a
regular EQ anlysis to me. Is it the case that if I take each
frequency as a sine wave and apply it to the given amplitude that I
will have achieved X's sound? Is there anyway to simplify that? Even
the simplest natural sounds have about a 5khz range. Do I have to
create 5000 individual sine waves? The FFT graph only shows frequency
over time, How do I find out about the relationships between the
frequencies as far as timming? For example say a put a sine wave at
2Khz and 1Khz. Obviously the 2Khz occilates twice as fast as the 1
Khz, but beyond that, the starting/ending points (where y=0) might not
sink up. The 2Khz sine may start, say, 300ths of a second after the
1Khz. I don't think info like this can be found out by the FFT
window, can it?

Do I have this right at all, or am I still nopt grasping Fourier
transforms?

Besides the flute, not much else
in an orchestra has anything close to a sine wave output. After this
analysis is done, the software will look through a library of sounds
made by traditional instruments. These sounds will include every
noise and playing style every traditional instrument can produce. The
software will then juggle the sounds around at various dynamic levels
in various rhythms and etc until it comes up with the closest
combination to the original sound.

Why use a computer for this anyway? George Gershwin did a perfectly good
job of this by ear.
--scott

The hope is to use this as a learning tool and eventually stop using
it, not unlike training wheels on a bicycle. I could probably do a
decent job of this in a tonal 4/4 world, but most real life sounds
contain dissonant and microtonal intervals, as well as many
"co-rhythms" that work together to create larger aspects of the sound,
such as pulses, and trigonometric polynomials. Making something that
sounds like a train whistle is one thing. I imagine it would have
been rather difficult for a composer of even Gershwin's skill to
notate out the sound of a babbling brook during a rain storm, with a
distant propeller airplane heard off in the far distance. It would
break my head, not to mention take a considerable amount of time for
me to do this by ear. Whereas with a system of this sort, I could run
twenty analyses and in a day know far more about this type of
orchestration than I would in a month if I did it all in my head. I
would gain a good overall knowledge that I can use as starting points
for future works, I would have a "feel for it". On the other hand,
doing this all by ear until I figure out how to make it work, is like
finding out the details first and only later getting the overall
picture--not the most efficient way of working. Like trying to
complete a jigsaw puzzle with no picture of what the finished puzzle
looks like. Learning the individual interactions between the parts
does not always lead to a good understanding of the whole. Anyway, I
learn best working from the outside in.