Yahoo Tuning Groups Ultimate Backup crazy

FROM: mclaren
TO: New practical microtonality group
SUBJECT: Robert Walker's accurate & insightful points

Yes, Robert, you're exactly right that you *can* obtain
more accurate measurements if you use time-domain
methods like wave-counting _as well as_ frequency-
domain methods like the Fourier Transform.
The built-in limitation with frequency quantization still
does apply, however, and is dependent on the sampling
rate. Once you fix your sampling rate, you get a number
of artifacts. Interesting enough, no one appears to have
done adaptive sampling rate change on the fly in
hardwave (though you can zero-pad or interpolate fixed-sample-rate data aftterwards, but that's not the same
thing, since you don't really increase the measurement
refinement, you just recalculate).
Resampling might seem a pie-in-the-sky technique but
radio telescopes spread out over the surface of the earth
make massive use of it to resample to a nice square grid
so as to inversely Fourier Transform the data for minimal
artifacts. CD production also requires resampling if you
recorded the PCM encoded sound at 48 Khz and must
resample to 44.1 kHz for CD production.
Incidentally, PCM encoding (AKA digital audio recording)
is a time-domain method, like wave-counting. Linear PCM
encoding remains the winner and still champeen for artifact-
free recording methods, with spectral methods like minidisc
a very poor alternative.
Checking through a bunch of the state-of-the-art spectral
estimators a couple of years ago, I found that not one of 'em
uses exclusively frequency-domain analysis. Moreover, not
one of 'em is paramateric. All the state of the art spectral
estimators use time domain methods along with frequency
domain methods, typically in predictor-corrector toplogies likethe Runge-Kutta predictor-corrector partial differential equation
solving method. They're all non-parametric, too, which
means the user typically must input some info, and the algorithm
can possibly keep runinng forever (the user typically puts in
some error bound or some runtime beyond which the spectral
estimator retuns an error condition, which NEVER happens
with parametric methods like the Fourier Trasnform).
THe big advantage, by the way, of non-parametric methods
of spectral estimation is that they tyipcally give you an error residue
which can be related to the accuracy of the analysis. You get
this from LPC, for isntance, so LPC actually gives you a guesstimate
of how well the input signal matched the assumed analysis
parameter. You *never* get a guesstimate of how well the
input signal matched the basic assumpti8ons required by the FFT,
however, but that's a trade-off, since the FFT is guaranteed never
to keep running forever....unlike the LPC, an FFT will always
run in N*log base 2 of the number of points and reach completion, guaranteed, absolutely, no doubt. Non-parametric methods give you more info if they finish, but they might not, and might take quite a bit longer than you expected to run. As usual, it's a trade-off.
Probably the best-known non-parametric method of
spectral estimation is the maximum entropy method, AKA
linear predictive coding. Like wavelets, LPC does not
specify one particular required primitive set of orthogonal functions, so you can throw in anything you like after the fact to get neat
different resynthesis options -- exchange noise for sine & cosine
and you get musically interesting results.
-------------
Some of you, given the sobriquet "keeping it real," may wonder
what all this big-deal eerie theory math has to do with the real world.
Well, as Risset points out so eloquently, the musical utility of
an analysis method is best determined by testing it through resynthesis. If the resynthesis proves accurate, the analysis method probably fit the signal being analyzed. However, as Risset also points, there is no one ultimate method of analysis -- different methods seem to be required by different types of timbres..
This means that every method of analysis we have discussed has an overall "sound," sort of like a synthesizer. Weird, but true...various set sof integrals and mathematical functions have an overall "timbre" or "sound."

The "sound" of Fourier analysis/resynthesis is denatured, choirlike and strangely sterile in some cases or beautifully lucid (artificial but in a nice way) in others.

The "sound" of linear predictive coding is typically buzzy and fuzzy with some strange distortion products and artifacts whenever the sound's frequency or amplitude changes noticeably

The "sound" of subtractive synthesis is warm and hummy and low-pass-filtered

The "sound" of non-linear analysis/resynthesis methods tends to be a little rat-pedal-distortion-like, as though a heavy metal guitar was playing the timbre analyzed

The "sound" of Walsh analysis/resythesis is buzzy and almost clipped, as though digital clipping was larded onto the sound unless you use a WHOLE lot of Sal and Cal components

The "sound" of FM synthesis is metallic and rubbery.

Bottom line?
Since every method of synthesis has an overall "sound" that tinctures every timbre produced using that mathematical method, it follows that every method of mathematical analysis lends a certain distinctive timbral coloration to the sound in question. Best to bear this in mind when analyzing/resynthesizing.
--------------
Many thanks to Robert Walker for his wonderful work (ongoing) with Fractal Tune Smithy. For some reason, the better sounding the synth, the more rigidly it's locked into 12. Robert Walker has finally let us break through that Catch-22.
Thanks also to John Starrett for posting all that superb info about free scientific calculation software.
Lastly -- some of you might find interesting the article on Widmer's work in data-mining virtuoso piano performances of Mozart by computer to find "rules" which make the performance of a MIDI file more humanlike. Apparently he's getting good results. Unlike the gibberish spewed out at IRCAM, this use of technology in music seems to produce some useful results.
--------------
--mclaren

undefined

🔗xed@...

🔗genewardsmith@...