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Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
sonance
The relative
consonance/dissonance
of an interval.
Rather than use the above phrase (as Partch did), I have adopted
the single term sonance, because I agree with the assertion
- made by both Schoenberg and Partch, among others -
that rather than describing two diametrically-opposed
sensations, consonance and dissonance refer instead to
the opposite poles of a single continuum of sensation.
(An early and influential expression of this idea was
presented by Helmholtz - see below.)
My own theory of sonance actually holds that
there are two separate continua of sensation,
one determined by the values of the
prime-factors
of the ratios interpreted by the listener
as being that of the two tones in the interval,
and the other determined by the values of the exponents
of those factors. Dissonance increases
(and consonance simultaneously decreases) as both the prime-factors and
the values of the exponents of those factors become larger.
This idea was expressed earlier
by Ben Johnston and others; the earliest reference
to it which I have seen is in
The true character of modern music, written in 1764
by the mathematician
Leonhard Euler.
Harmonic lattice diagrams are
a graphical representation of this theory of sonance.
My own theory thus allows that the actual tuning of the
interval may be a ratio with far higher primes or exponents,
or in fact may not be rational at all (as in the case of
temperaments), but that the listener
will, at least to some extent, interpret or understand
that interval as a rational one with the smallest prime-factors
and exponents recognized by his aural
and/or music-theoretical experience.
Recent speculation among tuning theorists (mid-1999)
has raised the idea
that consonance and dissonance may actually be two separate and
not mutually-exclusive dimensions of sonance. I have extrapolated
this to the idea that each
prime factor may in fact be responsible for
a separate dimension of sonance that does not necessarily exclude
any of the others.
It is also important to note that sonance is usually determined
not merely as an auditory phenomenon, but rather as a result of
musical context, highly dependent on the style of a particular
composer or era. Many tuning theorists have recently (1999) come
to the consensus that the term
cordance (describing the
continuum from concordance to discordance) should be used for
the former, restricting sonance for the latter.
see also
roughness,
harmonic entropy,
critical band,
cordance.
[from Joe Monzo, JustMusic: A New Harmony]
I recommend we distinguish between "sensory consonance" (aka
roughness,
sonance etc.) and "contextual consonance" as Tenney does in his
History of Consonance and Dissonance.
[from John Chalmers,
Tuning Forum posting]
Consonance is a continuous, dissonance an intermittent sensation of tone.
... We have found that from the most perfect consonance to the
most decided dissonance there is a continuous series of degrees,
of combinations of sound, which continually increase in roughness,
so that there cannot be any sharp line drawn between consonance
and dissonance, and the distinction would therefore seem to be
merely arbitrary.
[from Hermann Helmholtz,
On the Sensations of Tone, p 226 and 227]
(Immediately after this quote, Helmholtz devotes three pages
to a discussion of Euler's
theories of consonance and dissonance.)
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