🚀 go-pugleaf

In article <39616@linus.UUCP> eachus@mitre-bedford.arpa (Robert I. Eachus) writes:
>In article <8809071942.AA05026@cory.Berkeley.EDU> dillon@CORY.BERKELEY.EDU (Matt Dillon) writes:
>>>>    QUESTION#2)  Is it possible with software and hardware capabilities
>>>>                 to digitize a song and have the computer convert the
>>>>                 wavelengths into notes/sheetmusic and then print it
>>>>                 out?
>
>     This would certainly be doable on  an Amiga (not  in real-time of
>course),  and it would be  a lot of fun  (and a lot   of work).  First
>digitize the signal, then do a sequential  FFT with  a  sliding window
>128  samples long.  Use this to  decide when new   notes begin.  (Look
>every  16   samples  or   so to see   if succesive  power  spectra are
>proportional (same note increasing or decreasing) or not.

One problem is that FFTs are linear, and the musical scale is logarithmic.
When you do you 128 sample FFT, each of the 64 elements in the real and
imaginary result are spaced equally in the frequency domain.  Each of
the half steps you are trying to quantify this stuff into are spaced
by a factor of 2**1/12 (sorry fortran notation here).
Given this, your FFT sample must be much larger to account for the close
spacing at the low end (55 Hz for low, low, low A).

With the sliding window FFT, you must also take into account the the fact
that any wave (even one cycle) will appear to be in the spectra for the
length of one FFT sample.  Thus things appear to be on longer than they
truly are.

>
>     Now   transform each sample  interval   determined  above using a
>larger number of samples.  Determine the lowest fundamental frequency,
>and any notes within an octave above it.  Use templates (transforms of
>samples of a single  instrument playing a  single note) to do a linear
>regression best fit to  match  notes being  played to  the instruments
>playing  them.  Analyze the  residues   for notes in  the next highest
>octave and refit if necessary.

Oh, I see.  Use the first (cheap) FFT to get a rough feel of if there is
anything there at all.  I still don't see how this helps you with chords
that are spaced (in the half step domain) farther than one octave apart.

I guess you are presuming monophonic music.  It is not so easy for
polyphony.  What do you do for two trumpets or an oboe and a flute?
Even worse, how about a whole orchestra? Theoretically possible eh?
I don't mean to stiffle your creative juices, or have you stop commenting,
I've just thought about this issue a lot and don't have many people to
talk to about it).

You seem to know some about FFTs.  How does the phase of two instruments
playing the same note affect the result?

>
>     Do any ADSR (attack, delay,  sustain, release) analysis necessary
>to determine  when each  particular note  ends, and you  have  all the
>information necessary  to  print the music  (and to reconstruct it and
>subtract the power spectra) to make sure you got it right.
>
>					Robert I. Eachus

Well, there are other issues....  time signature recognition, tempo
and tempo changes,  time signature recognition, putting
in measure bars and rests, key signature recognition and accidentals
(this one is relatively easy), volume markings (piano, forte) and
crescendo's.

On the surface it seems simple.  I wish it was.  I've been thinking about
this subject for many years.  It's enough for a hobby of a lifetime.

                                                         kev
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