MacWorld 1999 January - Disc 2/Macworld (1999-01) (Disk 2).dmg/Serious Demos/Symbolic Composer 4.2/Environment/Projects/Questions & Answers/Q&A Programming Music/Minimum number of samples

Text File | 1998-10-26 | 4KB | 71 lines

DETERMINING MINIMUM NUMBER OF SAMPLES

>    My question is this:  is there a way to determine the minimum number of
>samples needed to accurately represent a given vector?  A method that will
>work with complex algorithms such as the output of Vector-Mix and
>Vector-Amplify as well as with simple ones such as Gen-sin?

I would say that it depends on the purpose. If the material is a cyclic
wave-like data then you should select the number of samples so that you
will be recognizing the form. Minimizing the number of sample points
while maximizing perceptional distinction is the main rule. Often 8-16
elements can describe a melodic wave in 1/16 rhythm and if there are more
then the material will sound too redundant. Ear is sensitive in catching
the meaning from tiny patterns. And then it likes that these patterns
are organized in a second level. I have made interesting melodies starting
from a couple of 4 element length waves which are then inverted and
retrograded and then appended into a 16 element wave, which is then
used as a pattern and itself inverted and retrograded. Controller
data should be sent 1/32 to sound smooth and hundreds of sample points
are needed to represent wavy data.

    The waveform freqency to smaple ratio issues is a larger problem than one
may think.  For instance, here is the most basic example I can give:  In
the visualizer, graph the following:

    (gen-sin 16 1 64 0)    ;and then graph
    (gen-sin 16 1 63 0)      ; as you can see, the waveform does not represent
the algorithm which was used to generate it...  The problem worsens
however...
    (gen-sin 16 1 65 0)    ;  one would think, under the assumption that this
is somethin akin to ailiasing, that once the samples were safely above a
given number that distortion would be eliminated.  As shown, this is not
the case.  In fact graph these:

    (gen-sin 16 1 127 0)
    (gen-sin 16 1 128 0)
    (gen-sin 16 1 129 0)

    With simple waveforms it is possible though tedious to determine the right
sample numbers and fit them into the larger score structure, but with more
complex algorithms it is much more difficult.  This worries me in that what
I think that I may be programming may not be exactly what is reproduced.
Creating melodies is especially critical.  Randomness is nice, when that is
what I want, but that is what gen-white noise or is for!  ;-)  Can you
offer any further explanation of this or do you suggest I post the question
to the discussion list?

>is somethin akin to ailiasing, that once the samples were safely above a
>given number that distortion would be eliminated.  As shown, this is not
>the case.  In fact graph these:
>    (gen-sin 16 1 127 0)
>    (gen-sin 16 1 128 0)
>    (gen-sin 16 1 129 0)

>But, even 32 values of sin fool the ear to perceive a continuous
>wave when applied to a filter sweep. It all depends on where you
>draw the mark on the water.

    But I am NOT talking about "how many points must one use to accurately
represent a given waveform to human perception?"  I AM talking about, "How
many samples are needed, due to the structure of the program and
mathematics behind it, to represent a given waveform without getting sample
values that are not found on the waveform when an infinite number of
samples are taken?"  What I am reporting, and it needs to be said that
perhaps I am perceiving things incorrectly, is that if an "unfit" or
"improper" number of samples are used, sampler points which are later
converted to symbols or vector lists or whatever, are given which are not
in accordance with the shape of the waveform;  they are in error!  They are
not found on the continuous line of the waveform.  This is what is not
acceptable;  this is what i am trying to guard against.