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Re: Auditory wheel

Kindly excuse my posting on an old topic, but I am currently going through
a great deal of old e-mail.

There are definitely circularities or wheels in music theory.

With respect to the circle of fifths, the interval of the fifth implies a
dominant-tonic relationship in harmony.  Moving from G to C, the
progression is V-I.  If you have V/V - V- I, then you have three points in
the circle of fifths.  Harmony provides other chord progressions that work
aurally other than the dominant-tonic relationship.  The exploration of
such circularities is the basis for the composition of the first movement
of the symphony.  It starts in the tonic, moves to the dominant or the
relative key, and works its way back trough a series of modulations.  The
originality of the construction of the loop gives the symphony its

Another way to form loops is via the scale networks described in papers
and a recent book by Dmitri Tymoczko.  Here the scales are related by
means of adjacencies (scales that differ by one note are adjacent) and
these are arranged into geometrical structures.  These are related to
rule-based definitions of scales (such as no consecutive minor seconds, or
no major thirds).  My analysis of Act. IV, Sc. IV of Debussy's Pelleas et
Melisande shows the presence of some of these network adjacencies and
their use in projecting the meaning of the text.

My third comment is that one could contruct loops or circles anywhere in
the vector space of a multidimensional scaling result. You would gradually
progress to areas that are perceptually different and then back to the
starting point.

Linda Seltzer