A few of Pythagoras' Recent Findings, as Explained to the Layman
1) The Equal Distance Fretted Lute
Since Pythagoras didn't feel comfortable about the equidistant scale
steps
of the well tempered piano, he would rather approximate the frequencies
on a subharmonic scale. This idea turned out to be well suited to the
fact
that the oud-like instrument that was going to be used could have its
frets
placed at equal distances, which facilitates its building. In terms of
a comb filter: the delay times could be approximated by milliseconds
with
two decimals of precision, which gives a fairly good approximation at
low
frequencies, but becomes more and more out of tune with increasing
frequency.
However, according to Pythagoras, it's in tune all the way.
convol.aiff
2) The Groove of a Silver Spoon
Pythagoras decided to believe, that there had to be an Einhet der
musikalischer
Zeit somewhere, and if there were, at that time, no actual physical
phenomena corresponding to such an idea, at least it should be possible
to construct one in the laboratory. What about generating rhythms from
a spectral analysis of the sound of a silver spoon? Try this: first
lower
the pitch and speed about 10 octaves, then choose every positive (or
negative)
peek in the wave form generated through additive synthesis of various
components
of the spectrum. These peeks are then used to position rhythmic events.
Any spoon playing virtuoso knows there are simpler ways to achieve
this.
silver.aiff
3) Melodic Convolution
Surely Pythagoras knew about Cartesian products and tensor products
even
before they were invented by others, but maybe this technique is more
accurately
described as the convolution of two musical objects. But most of all it
resembled a special case of the canon: Each note in one of the musical
objects was taken as the point of departure for the whole second
object,
both in pitch and time.
convol.aiff (if you don't mind
hearing it once more.)
4) A Silver Scale
As Pythagoras noted very early in his career, it is often the case that
the scale systems in use in a particular musical community show a
strong
correlation to the spectra of favored instruments. This hypothesis is
well
known to musicologists, but why not use it constructively? So, for a
musical
phrase played on the piano, to be transposed to an inharmonic bell
sound,
the scale would be changed accordingly. A new scale is easily generated
from the set of transposition ratios between successive partials.
piano ---> bell
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