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Tek Platonics?

🔗J Gill <JGill99@imajis.com>

12/9/2001 11:55:53 AM

In regards to my curiosity regarding "superparticularity", I came across
some info which indicates ancient fondness for such "inequalities", but my
knowledge of historical texts to this effect is virtually non-existant.
Does anyone know of (or have the text of) early writings addressing
"rationales" as to why "superparticular" ratios are found (by some)
pleasing to the ear?

At the site: http://humanities.uchicago.edu/classes/zbikowski/week4sum.html
I found the following info describing writings of Aurelianus Reomensis
(Aurelian of Réome), The Discipline of Music

Scolica enchiriadis, part 3
After discussing the relationships between different parts of the
quadrivium at the end of part 2 (in particular noting that music, astronomy and geometry are founded on mathematics), the disciple and master delve
into mathematical issues.

The third part opens with definitions of terms including: multitude (which
is accumulated in units), magnitude (which is divisible into units) and the
five different kinds of inequality (multiple, superparticular,
superpartient, multiple-superparticular and multiple superpartient).

When the disciple asks, "How are the phthongi of music known to have the
measures given above, when [the measures] are perceivable neither by sight
nor by touch?" the master answers, following Plato, that anything in the
world that can be joined compatibly is linked by commensurable or
connumerable (i.e. multiple or superparticular) ratios. The Platonic answer
is given first. This, however, leads to "experiential" or
"phenomenological" reasoning (following Boethius) about the correspondence
of specific ratios with specific intervals. The master argues that "...
given number or line, nothing is easier to recognize with the eye or reason
than its double, as, for example, 12 to 6 ... And because the recognition
of the duple is easier, it is justly assigned to that consonance which is
easier and which our critical faculty perceives more clearly ... the
diapason." (p. 82) Following this the "practical" argument of tones
produced by different string lengths is presented.