From: mclaren
Subject: sensory versus musical consonance
--
Kami Rousseau has suggested stretching just
intonation scales so that the octaves will be
heard as perceptual octaves, the fifths as
perceptually "pure" fifths, and so on. This
idea is interesting and innovative. However,
it's important to point out a source of
possible confusion here.
My posts on pyschoacoustics have described
in detail the fact that the mathematical and
perceptual octave are different entities,
especially when the octave is heard as an
isolated interval. Psychoacoustic experiments
do indeed show that isolated intervals are
heard as "too flat" and "too narrow" and "impure"
when they are tuned to a precise 2:1 ratio,
whereas an interval of approximately 1208-1215
cents is heard as "pure" and "in tune" and "just."
However, what we are discussing here is
*sensory consonance.* This is consonance
as measured by psychoacoustic experiments.
It is the consonance perceived by observers
under experimental conditions. It is consonance
of isolated intervals in a non-musical setting.
This is not necessarily the same thing
as *musical consonance.*
Musical consonance is dependent on *context*.
It is judged in a musical setting. Musical
consonance is dependent not only on timbre
and beats and the width of the critical band,
it is also dependent on the preceding harmonies,
the nature of the music's melodic stucture,
and most importantly it is determined by the
intonation itself.
It is very important to make this distinction
between *sensory consonance* and *musical
consonance* because the two are not generally
distinguished in music theory. In fact Hermann
Helmholtz intentionally and purposely conflated
the two--Helmholtz claimed that sensory
consonance was completely equivalent to
musical consonance.
Yet it is clear that this is often not the case.
One of the best examples is the stretched Balinese
octave. Heard as an isolated interval, this 1215-cent
octave can sound questionable. But it is never
played in isolation in Balinese music.
When a Balinese gamelan plays, there's a constant
tinkling shimmering gonging interplay of partials
that make the partials seem to sizzle in the air,
and the beats thus produced are integral to the
musical effect. Individual intervals sound quite
different in terms of their consonance from the
same intervals played in rhythmic counterpoint
with mass masses of other notes, whose timbre
blends into one huge shimmering klangfarbenmelodie.
Indonesian gamelan tuners know this so well that
they point out that an individual metallophone cannot
be fully tuned until the entire gamelan has been
rough-tuned; the entire timbral wash is needed
to fine-tune any one metallophone in the
ensemble.
This is a *very* important point.
Our ears have a remarkable ability to
pick up on the structure embedded within
an intonation and to fit various harmonic
and melodic progressions into that
embedded structure. A great deal of
subconscious processing goes on when
we listen to music; our ear/brain system
is extraordinarily sophisticated at
extracting and recognizing patterns
buried in the intonation of the music
to which we listen.
The net result is that we must be careful
not to pursue sensory consonance at the
expense of musical consonance. While
as Johan Sundberg points out it is vital
not to mistake mathematical for perceptual
intervals, it is even more vital *not* to
give up musical consonance in the pursuit
of sensory consonance.
Thus Kami's suggestion of stretching just
intonation tunings makes good sense as
far as increasing the sensory consonance
of the intervals. However, stretching the
intervals in a just array disarranges most
of the mathematical relationships between
the octave and the component just intervals.
This can be a significant loss if those
relationships are used musically. Moreover,
this is not just a matter of mathematics;
the ear can hear the musical structure
embedded with a just intonation scale.
Disjointing this structure for the sake of
improving sensory consonance might prove
musically successful--or it might not. My
guess is that it will depend on the musical
context.
--
On another point:
An extremely superficial understanding of
my criticisms of theories of just intonation
on this forum leads to the false conclusion
that I am out to debunk just intonation.
Nothing could be further from the truth. If
this is what people have come away with
by reading my posts on psychoacoustics
then they have completely misunderstood
my point.
Instead, my point is that the arguments used
by JI advocates in favor of just intonation do
Instead, my point is that the arguments used
by JI advocates in favor of just intonation do
not hold water. Hermann Helmholtz and
Partch (following Helmholtz's lead) both
tried to claim that western music was based
on the harmonic series, and that therefore
sensory consonance could be directly equated
to musical consonance, and that therefore
just intonation is musically superior and
musically preferable to any other system
because just intonation offers maximal
sensory consonance and direct use of the
harmonic series in music.
These arguments in favor of just intonation
have actually been extremely damaging to
the cause of JI. As psychoacoustics and
digital synthesis have progressed by leaps
and bounds, it has become increasingly
clear over the last 100 years that sensory
consonance is not at all necessarily the same
thing as musical consonance, and that as a
result many exotic and beuatiful yet
inharmonic timbres and intonations can
be developed which nonetheless sound
musically effective and very beautiful.
The problem with the Helmholtz/Partch/
Johnston/Doty argument in favor of just
intonation is that it creates a Manichean
dichotomy: once we accept the premise that
the harmonic series is the end-and and the
be-all of music, all musical structures not
based on the harmonic/subharmonic series
must be regarded as musically inferior, to
be purged, expurgated, reviled, cast down
into darkness.
This is a big problem because it immediately
puts the listener in the position of having to
revile and abjure all the music s/he has
heard over a lifetime...since virtually all of
the music all of us hear while we grow up
is, of course, 12 tone equal temperament.
Yet anyone interested enough to spend years
studying music theory must love 12-tet music
dearly indeed. So this creates a huge problem
for the just intonation advocate: you are now
in the position to having to convince your
audience that all the music they love is
a debased abomination, a falling-away from
the true faith of the harmonic series.
This is not a good way to attract converts
and gain followers.
The sensory consonance argument for JI
is also lethally flawed, because anyone
with a reasonable knowledge of pyschoacoustics
can destroy it by citing the experimental
evidence. For that matter, you can utterly
annihilate the Helmholtz/Partch sensory
consonance argument simply by playing
pieces of music by Risset, Chowning,
Dashow, Harvey, et al. which use extremely
inharmonic timbres but which nonetheless
sounds beautiful.
Inharmonic digitally-generated timbres and
computer-produced and -controlled inharmonic
series could not be heard prior to the mid-1970s.
The computer power to produce such music was
simply not available. Now that everyone can hear
and experiment with such musical timbres and
inharmonic series tunings, it has become starkly
apparent that arguments for just intonation on
inharmonic series tunings, it has become starkly
apparent that arguments for just intonation on
the basis of sensory consonance do *not*
necessarily lead to sensory consonance. (Inharmonic
timbres with harmonic series chords produce musical
effects completely *unlike* those of just intonation.
John R. Pierce, Max Mathews, William Sethares,
myself and many others have produced demonstation
tapes showing this effect.)
The point of all this is that my systematic
demolition of the sensory consonance argument
for just intonation is in fact necessary to create
a firm foundation for the musical use of JI.
Otherwise, we are building on a foundation of
quicksand. As for the the claim that the harmonic
series is the basis of all consonance intervals
and timbres, and that sensory consonance can
series is the basis of all consonance intervals
and timbres, and that sensory consonance can
best be obtained from the members of the
harmonic series, and that therefore JI is
the most musical intonation because it
maximizes sensory consonance... Well, as
we have seen, all of these arguments are
incorrect because all of the premises are
false. And so, to use these lethally flawed
arguments for just intonation is merely to
create a wonderful oportunity for those
hostile to new music to shoot down just
intonation wthout even hearing it.
A much more powerful argument for just
intonation is the "Mount Everest" argument.
Like Everest, just intonation is there--
why not explore it?
While it's extremely easy for any narrow-
minded conservative hater of new music
like the abysmally ignorant Paul Griffiths
(current music critic for the New Yorker)
to demolish the "natural interval" or
"harmonic series" or "sensory consonance"
justification of JI, it's extremely hard
for even the most narrow-minded musical
reactionary to convince anyone that we'd
all be better off if we didn't open our
ears and explore potentially beautiful new
JI harmonies and melodies.
This argument for JI puts the shoe on the
other foot--reactionaries like Griffiths must
now show their true colors and argue against open-
mindedness if they want to prevent anyone
from trying JI on this basis.
--
To return to the original point, then, Kami's
idea of stretching JI scales is an interesting
one. However, it's important not to confuse
sensory consonance with musical consonance,
and not to confuse either of those with
musical concordance.
Stretching a JI scale might heighten the
perceptual purity of intervals while lowering
the musical utility of those intervals. If
stretching the scale warps or destroys the
internal structure of the intonation,
sensory consonance might be enhanced at
the price of creating musical discordance.
As always, all three quantities must be
balanced, and they are inextricably bound
up with the musical context in which
this occurs.
It would be nice to give a simpler or shorter
evaluation of Kami's idea...but given the
complexity of human hearing and the subtlety
of even the simplest-sounding intonation,
that just isn't possible.
--mclaren
