Tuning In (by Mr.Wilkinson)

Could anybody post the list of errors of the book "Tuning in,
Microtonality in electronic music" by Mr.Wilkinson???

Thanks!!!

Tony Salinas

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TONY SALINAS wrote:
>
> I can see two clear groups of tunings:
>
> A) The ones using fractions as ratios
>
> B) The ones using roots to determine the ratio

It's interesting to note the the ones using roots
still use ratios as the interval for which a root
is found. Most often, the ratio for which roots
are found is 2:1, but not always.

I think there are more categories.

What about equal temperaments of transcendental numbers (the most
abundant numbers), which are neither ratios nor roots of ratios?

What about "modulated equal temperaments"? These would be
pitch sets which are sort of like equal temperaments but
which vary in step size along the "scale" according to a given
curve. For example, using a sine curve, the widths would
cycle from narrow to wide and back again as you move up the
"scale". I think either a slanted line or a log scale applied
to a modulated equal temperament would produce an harmonic
series.

What about sets of "found" pitches--pitches which are determined
randomly or from some natural data (like stock prices). I read
a neat post in the archives, but lost it again, which described
how someone would find the most comfortable finger positions for
a wood flute before drilling the holes. That determined the
pitch set for the instrument, for which music was then composed.

There are conceivably as many pitch set categories as there are
categories of numbers and number sets. I suspect, as John Starret
here wrote, that "...we may be hardwired for mathematical
understanding of all that we can understand mathematically, and
that may spill over into musical understanding...". I think we
can perceive different qualities in pitch sets derived by
different mathematical means, given that the instrument has
good enough resolution to distinguish them and that the actual
pitch differences are large enough to fall above the threshold
of perception.

Matt Nathan

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