Next Post from McLaren

From: mclaren
Subject: the audility and audible coherence
of inharmonic progressions of inharmonic tones
Part 2 of 2
--
Inharmonic timbres are the final frontier of
microtonality. Thus it's important to be
clear on whether they are musically useful
or not.
We have seen why experiments on inharmonic
tones gave deceptive results prior to the 1970s.
Before the wide availability of computers,
it was not practical for most auditory researchers
to generate inharmonic tones digitally. Thus,
most early experiments with inharmonic tones
were done with analog circuits. These circuits
offered early researchers almost no control at
all over the fine structure of the inharmonic tones
thus produced. In particular, researchers couldn't specify
detailed amplitude or frequency envelopes for each
inharmonic partial, nor did early researchers have even
crude control over the exact frequencies of the
inharmonic partials used.
Typically, FM or AM techniques were used to
generate inharmonic timbres. These methods
generated large sets of audibly unrelated and
individually uncontrollable partials from an input
periodic waveform. Prior to the use of computers,
there was thus no scale-like relationship twixt
adjacent inharmonic partials, as is found (say)
in an inharmonic tone produced by setting each
partial to the closest value in 19-tone equal
temperament.
By the 1980s the notion that inharmonic sounds
necessarily failed to fuse into a single percept, or
necessarily exhibited a fundamental pitch
unrelated to the pitches of the partials, had
been disproven. Geary, for example, points
out that "This paper examines the hypothesis
that pairs of strongly inharmonic sounds can
also cause the perception of a kind of consonance
if the two have frequency components in common,
and dissonance if components at each make
near misses. This hypothesis is verified by
experiments in which subjects were asked
to choose which of two inharmonic sound
pairs seemed more consonant. The data show
significant agreement with predictions based
ont he missing and matching of spectral
components." [Geary, J. M., "Consonance and
dissonance of pairs of inharmonic sounds,"
J. Acoust. Soc. Am., Vol. 67, No. 5, May 1980,
pg. 1785]
Geary goes on to conclude: "Clearly, it cannot
be claimed that the perceptions are exactly
the same, since inharmonic and harmonic
tones themselves sound different to the ear.
However, the experiments do establish a
similarity between the consonance-dissonance
phenomenon in harmonic and inharmonic sounds.
Most of the subjects had prior familiarity with
the conventional meanings of the words consonant
and dissonant (especially the latter) and
conventional harmonic intervals were played and
identified for each subjec before the experiment.
Consequently one would expect the subjects'
judgments to be made according to the conventional
sensations of consonance and dissonance. The
similarity of perceptions in the harmonic and
inharmonic cases is further established by the
high scores of people with substantial musical
experience. (..) That such people chose the
predicted dyads in spite of their conventionally
dissonant relationships between their
fundamentals, and rejected other dyads with
conventionally consonant fundamental
relationships, is strong confirmation of
the hypothesis of this paper." [op. cit., pg. 1788]
Geary further mentions that "the concept of
inharmonic consonance and dissonance raises
intriguing possibilities for experimentation
in electronic and computer music. Consonance
and dissonance are responsible for much of
the structure of conventional music, such as
that in scales, chords, and harmonic practice.
If this structure is due to the configuration
of spectral components of harmonic sounds,
then it might be possible to alter such
structure by electornically relocating the
spectral components to inharmonic positions.
New intervals, scales, and chords might be
possible, as well as timbres unobtainable
with harmonic spectra." [op cit., pg. 1789]
By the mid-1980s, with many computer-generated
inharmonic progressions in many different
compositions as audible examples, it had
become clear that inharmonic tones could
and did exhibit consonance, dissonance,
modes and cadences akin to those found
in harmonic-series-based compositions.
Examples include James Dashow's compositions
--take your pick: Whispers Out Of Time,
Sequence Symbols, etc.,; Risset's compositions,
against take your pick: Mutations II, Inharmonique,
Songes, etc. Jonathan Harvey's Mortuos Plango
Vivos Voco, and so on and so on.
Slaymaker, in 1970, described some perceptual &
musical characteristics of harmony and melody
which uses inharmonic tunings and inharmonic
timbres: "Not all musical instruments [use
harmonic series timbres], however. The cast
bell carillon and tubular chimes, for example,
have tones that are not made up of harmonics.
Many of the intervals traditionally defined
as consonant sound quite dissonant on these
instruments; therefore, true chords are
seldom played on either of them, and chimes
are usually used in the orchestra only for
special effects. Conversely--a situation
seldom realized--some of the intervals
that have been classed as dissonant can
sound quite smooth on these inharmonic
instruments. Consonant sounds can also
be produced from synthetic tones having
partials that are spaced by a constant
ratio, as long as the partials appearing
in a chord are not spaced closer than
the critical bandwidth of the ear."
[Slaymaker, F. H., "Chords From Tones
Having Stretched Partials," J. Acoust.
Soc. Am., Vol. 47, No. 6, 1970, pg. 1569]
Slaymaker goes on to describe the effect
of increasing timbral inharmonicity while
playing a traditional chord sequence:
"The impression of traditional predictability
still persisted, though the tone quality
gradually became more chime-like and the
intervals of the scale became more noticeably
different from the familiar tempered scale;
i.e., the sequence began to sound 'out-of-
tune.' The change in the S value from 1.083333
to 1.261839 resulted in a completely
different impression for the chord sequence,
compared to tfe impression for the values of
S nearer unity. All of the traditional
predictability was gone. The chords sounded
smooth and nondissonant but strange and
somewhat eerie. The effect was so different
from the tempered scale that there was no
tendency to judge in-tuneness and out-of-
tuneness. It seemed like a peek into a new and
unfamiliar musical world, in which none of the
old rules applied and the new ones, if any, were
yet undiscovered." [ op. cit., pg. 1569]
With the advent of William Sethares' landmark
paper "Local consonance and the relationship
between timbre and scale," J. Acoust. Soc. Am.,
Vol. 94, No. 3, 1993, pp. 218-1228, those
rules became clear.
Demonstrations like Slaymaker's sounded
"out-of-tune" as the inharmonicity of the
timbres increased, because the chord
progressions were based on traditional
Western musical intervals...which are
themselves closely related to low members
of the harmonic series.
If instead the chord progressions of inharmonic
tones are based on an *inharmonic series* (and
not simply a set of arbitrarily stretched
members of the harmnic series, but rather
a coherent self-contained inharmonic series-
viz., the vibrational modes of the free-free
metal bar, or of the free metal tube) then
the inharmonic chord progressions will
produce a sense of finality and cadence.
This is also the reason why Mathews and
Pierce reported that extreme values of
partial stretch resulted in a destruction of
the finality of the cadences--Mathews and
Pierce were also using cadences whose triadic
root movements were based on
*harmonic-series-related* intervals.
However, I have used the commercial resynthesis
package FdSoft to analyze and resynthesize
sampled sounds. Although this package is
greatly inferior to the LEMUR Fourier analysis/
resynthesis software available for the Macintosh
(which I cannot run since I have only a Mac Plus),
FdSoft does analyze and resynthesize some
timbres relatively well. For instance, solo
brass instruments, strong (not whispered)
vocal timbres, and some solo woodwinds and
double reed instruments retain their identity
well upon Fourier analysis/resynthesis without
modification.
Using FdSoft, I have determined that most timbres
retain their identity well when resynthesized with
slightly inharmonic partials--for example, setting
the partials of a resynthesized trumpet or trombone
or clarinet or english horn note to the closest
values available in 41-TET produces an inharmonic
sound which is virtually unchanged perceptually
from the original sampled sound, yet exhibits
subtly increased sensory consonance when used
in 41-TET triads.
Warping the partial frequencies by larger values
(for instance, setting them to the nearest
approximations available in 11-TET or 13-TET)
produces a slight perceptual distortion of the
trumpet or trombone or clarinet or english horn
note upon resynthesis... The effect is somewhat
similar to very slight ring modulation. These
timbres, however, exhibit greatly increased
sensory consonance upon resynthesis.
Pushing this method to its uttermost extreme,
I have determined that some sounds even retain
their identity well upon radical timbre-mapping.
For example, a trombone note retains its identity
very well even when mapped into the closest
partials of the free-free metal bar scale (with
all partials not close to members of the metal
bar scale deleted). The resulting timbre sounds
slightly denatured and empty because large numbers
of partials have been deleted, but the sound is
still recognizably a trombone--but, weirdly,
it sounds like a trombone crossed with a chime.
The effect is very strnage--as though you could
somehow put a mouthpiece on a metal bar and
instead of striking the bar, produce sound
by blowing through the mouthpiece. (A perceptual
paradox I've also heard in the Yamaha series
of physical modelling synthesizers, which allow
you to "put a mouthpiece" on a bowed string
instrument and "blow" instead of bow a violin
or cello or viola.)
Most sounds do not retain their iden
well
when their component partials are mapped into
such a radical non-just non-equal-tempered scale,
but *all* such resynthesized sounds retain the
sense of spectral fusion--no doubt because all
the original auditory cues are still present:
synchronous fluctuations of amplitude envelope in
each partial, the slight trajectory in frequency for
each partial, the initial identical "blip" of the attack
of all the partials, the overall synchrony of
the partial envelopes and the ensemble effect
produced by their synchronized decay, etc.
My experiments in this area, however, pale
before William Sethares' investigations.
William Sethares has produced many musical
examples using inharmonic timbres and
inharmonic tunings. The tunings sound
convincing, consonance and dissonant are
present, and cadences exist--yet they are
unlike those present in harmonic-series-
based music.
With typical clarity, Sethares points out
that "One subtlety that arises when
dealing with nonharmonic partials is
that it is important for the partials to
fuse, to be perceived holistically as
a single entity rather than as a collection
of oddly placed sine waves. Fusing is
greatly helped by commonalities in the
partials: similar pitch vibrato, similar
amplitude fluctuations, similar onset
times and similar envelopes." [Sethares,
W., "Local Consonance and the Relationship
between Timbre and Scale," J. Acoust. Soc.
Am., Vol. 94, No3., Sept. 1993, pg. 1227]
William Sethares' music is the most
convincing example yet of the falsity of
Erlich's contention. From now on, people,
please read the literature before making
these kind of claims. Please get the facts
straight, and do the reserach. Let
us hear no more of verifiably false claims that
inharmonic timbres cannot spectrally
fuse, or that they necessarily produce
(via virtual pitch) unrelated and bizarre
fundamental pitches: anyone who doubts that
inharmonic timbres can be used to
produce convincing and entirely
musical cadences & harmonies
need only e-mail William Sethares
and ask for a copy of his demonstration
tapes. Or, if you prefer, simply persue the
article "Applying Psychoacoustics
in Composition: `Harmonic' Progressions
of `Nonharmonic' Sonorities," Parncutt, R.
and H. Strasburger, Perspectives of New
Music, Vol. 39, Nos. 1-2, 1995, pp.
88-127
--mclaren


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