RATIONALE. This program is meant to be a pre-compositional tool
that scans and/or modifies chords along the dimension of
dissonance - an uneasy concept if there ever was one; here it
is perhaps best understood as referring to something like the
opacity of chords: the degree to which it might be difficult to
"hear through them" any new sound not already contained in them.
Be that as it may; we let the test measure what it does, in fact,
measure and its usefulness remain to be seen.
ASSUMPTIONS. A chord's dissonance is assumed to be a function of
its component intervals. Intervals within the octave are ordered
from dissonant to consonant (minor second - major seventh -
major second - minor seventh - augmented fourth/diminished
fifth - all thirds and sixths - perfect fourth - perfect fifth -
octave), and all intervals wider than those are proportionally
downgraded, a minor second plus octave taking the value of a
major seventh, a major seventh plus octave taking the value of a
major second, and so on. Furthermore, the possible contribution
of a tone that has also its own lower octave(s) in the chord is
correspondingly lessened.
USES. In the first place, the program may be used as a chord-
scanner. In that case, it displays four things: 1) each note's
contribution to the chord's overall dissonance, 2) the chord's
dissonance total, which is a number such that if you subtract
from it the contribution of any of the chord's component notes
(octaves make for exceptions here, sorry), you get the total of
another chord that is just like this one except for the absence
of that component note; 3) the dsg ("dissonance grading"), which
is twice that total divided by the number of component notes,
and 4) the dsg class, which positions the chord in one of the
five musically interesting subareas in the dissonance continuum
we have seen fit to number, roman-style, I through V, in the
following way: dsg class: I II III IV V
dsg: 0 -->3 -->8 -->21 -->55 -->
In the second place, the program may be used in some preparatory
stage of musical composition. It will try to increase or to
diminish, at your choice, the dissonance of any chord you care
to specify. It offers you the choice of two ways to do it:
(1) by setting it a target dsg, and letting it work its way
toward that target for as far as it can, or
(2) by parallel subset (semitone) motion.
When (after entering your starting chord) you choose the Target
option, the program prompts you for the dissonance to be real-
ized. It then sets about attaining this goal in the smallest
possible number of (minor or major second) steps, keeping you
informed of its progress through its screen and/or printer
output. In determining the steps to be taken it is guided by
principles essentially akin to those governing voice-leading,
such as: in diminishing dissonance, take first the tone con-
tributing most to it; do not conflate two tones into one,
etc., and the converse for increasing dissonance. This strategy
results in a tendency towards equal distribution of dissonance:
extremely unequal contributions of individual notes, which (I
think) make for the special combination of spiciness and
clarity of many jazz chords, become less likely as the program
proceeds in this mode. The other limitation inherent in the
target mode lies in the fact that, e.g., starting with eight
pitches within a space of an octave you obviously cannot get
below a certain dissonance. If you don't like these limita-
tions, use, or mix in, the parallel subset and the change-by-
hand modes.
When you choose this option, you accept primes as intervals -
two pitches, in working towards consonance, may get fused into
one. (The only way of achieving the converse, i.e. of splitting
a single tone in two, is to do it by hand.) Next, you actually
enforce change: if the chord was already maximally consonant,
and you try to make it more consonant still, you end up with a
slightly less consonant chord instead. Lastly, Parallel Subset
Motion, or PSM for short, brings home a freedom that every com-
poser working with this program will have to face: it does find
effective and elegant ways of changing a chord's dissonance,
but it does not tell you much about the precise spatial re-
lations of the resulting two consecutive chords. It may propose
you a subset motion of three pitches out of five: obviously, you
may do better by moving the other two, or by moving the whole
chord in steps of different lengths for its two subchords. (Note
that this goes not only for PSM: the results of the Target op-
tion leave you with exactly the same kind of freedom; as we all
know, letting an (almost) whole chord move in order to relieve
the dissonance of even a single motionless note is not unheard
of in good music.)
THE HINDEMITH ROOT. As an extra bonus, the user gets the chord's
root thrown in, as it is computed by applying a slightly gener-
alized version of the Hindemith Unterweisung im Tonsatz method.
Because of the generalizations results will not always coincide
with Hindemith's own. Thus, the program will not balk at chords
with less than three pitches; it will also assign their roots
to chords considered to be undecidable, such as the augmented
triad, the chord built up out of two perfect fourths, and the
diminished seventh chord, and it will do that by applying the
same methods as everywhere else. Most importantly, we are in dis-
agreement with the master because we think that his method, de-
pendent as it is on the analysis of isolated chords, provides no
solid basis at all for musical composition. (Composers are, as
always, on their own.) However, its results are never simply
foolish, which is why we have included it. An example. The user
should suspend any notions about chords being incomplete - for
the program, all chords are complete, and the chord c4-b4-d5 is
assigned b4 as its root, because the third is the best interval
contained in it. One might therefore say that, if the chord is
incomplete after all, the program would have preferred to add
f#4 and a4 to it rather than e4 and g4. Hindemith-style serious
results are to be expected only for complete chords.
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