Yahoo Tuning Groups Ultimate Backup tuning Yale Boy heads for the hills

FROM: mclaren
TO: The new practical microtonality list
SUBJECT: Yale Boy heads for the hills

In his parting post, Paul Erlich relies (as
always) on a handful of outdated and disproven
hearing theories by a tiny coeterie of researchers--
Terhardt, Wightman, and Goldstein.
Sadly, these outdated theories date from the
early 1970s -- and they all conflict in many important
ways with the results a number of more modern
psychoacoustic experiments from the 1980s and 1990s.
Ernst Terhardt is a European psychoacoustician who
has gained plenty of attention for his theory of human
hearing from the early 1970s. Terhardt's theory basically
revamps Rameau's theory of the "basse fundamental" and
spit-shines it with Fourier Transforms. In a nutshell,
Terhardt hypothesizes that the human ear/brain system
operates entirely by Fourier (that is, spectral) analysis
and that musical consonance therefore consists of 2
parts: so-called "harmonic consonance" (which is nothing
more than Rameau's "basse fundamentale" under a new name)
and virtual pitch purported produced by pattern recognition
acting on a spectral analysis of the harmonies concerned.
Sadly, Ernst Terhardt's theory of human hearing
fails the test of experiment:

"However, predictions based on Terhardt's theory
of harmonic consonance are not met. According to
Terhardt's (1977) theory, the relative ambiguity of
the `fundamental root' of the triad denotes the degree
of perceived consonance or dissonance. Our analysis
of equal-tempered major, minor, diminsihed, and augmented
triads indicated that the fundamental pitch of the major
triad is totally unambiguous whereas the fundamental
pitches of the other three triads are about equally
ambiguous. Clearly Terhardt's model does not account
for the data." [Roberts, Linda A. and Marilyn L. Shaw,
"Perceive Structure of Triads," Music Perception,
Vol. 2, No. 1, 1984, pg. 108]

Naturally Paul Erlich does not realize this, since
he cites Terhardt's theory as though there existed no
disproof of its predictions. In Terhardt's outdated
theory from the 1970s, the sole action of the human
auditory system is alleged to be Fourier analysis. Other
auditory effects--such as virtual pitch--Terahrdt tries
to argue out of existence as "secondary sensations" derived
entirely from Fourier analysis.
To derive virtual as a so-called "secondary sensation,"
Ernst Terhardt offers an algorithm for extracting virtual
pitch from the spectrum of the harmony. Unfortunately,

"The predictions of the algorithm, calculated
from the formulas given in Terhardt et al. (1982),
are shown in Fig. 14. The figure shows predictions
for -4% and +4% mistuning; the predictions for other
values of mistuning actually used in our experiments lie
ebtween the curves for -4% and +4%. The algorithm
predicts a shift for zero mistuning (harmonic
complex), approximately midway between curves for
-4% and +4%, although Peters et al. (1983) did not
find such shifts.
"Comparing the predicted shifts with the observed
shifts shows that he algorithm correctly predicts
the trends of the data when the mistuning is positive.
When te mistuning is negative, however, the algorithm
fails completely. Experimentally, negative mistuning
usually leads to negative pitch shifts. By contrast,
the algorithm predicts positive pitch shifts for negative
mistuning. (..) The fact that [Terhardt's] algorithm fails
so badly for negative mistuning suggests that there is
something quite wrong with the idea that pitch shifts
are mainly determined by partial masking." [Hartmann,
W. M., McAdamas, S., and Smith, B. K., "Hearing a Mistuned
Harmonic In An Otherwise Periodic Complex Tone,"
J. Acoust. Soc. Am., Vol. 88, No. 4, 1990, pg. 1722]

Naturally Paul Erlich fails to mention either of these
crucially important experimental disproofs of Ernst
Terhardt's outdated 1970s theory of hearing because, in
the grand Yale tradition, Paul Erlich is too arrogant
to realize that experimental tests of Terhardt's theory
of hearing have disproven Terhardt's theoretical predictions
BOTH for "harmonic consonance" AND for the virtual pitch algorithm.
Erlich is also too ignorant of the psychoacoustic literature
to realize that Terhardt's antique 1970s theory of hearing
fails other important listening tests, and of course
Paul Erlich is too incompetent as a scholar to be
aware of the post-1970s modern literature on the
human ear/brain system which has moved beyond Ernst
Terhardt's obsolete theory.

If we look at more modern citations from the psychoacoustic
literature than the musty antique results from 1952 and 1971
cited by Erlich, we quickly discover that the experiments I
discuss above are not the only ones which disprove Terhardt's
theory. Other experiments for which Terhardt's theory fails to
accurately predict results include those documented in:
"Pitch of Components of a Complex Tone," Peters,
R. W., Moore, B. C. J., and Glasberg, B.R., Journal of
the Acoustical Soc. Am., Vol. 73, 1983, pp. 924-929.

So not only does Terhardt's theory badly fail the test
of 3 different basic psychoacoustic experiments (op cit.),
Terhardt's entire theory of virtual pitch as a "secondary
effect" (allegedly derived from the operation of the basilar
membrane) ignores a significant body of psychoacoustic
evidence.
This body of evidence from the modern post-1970s
psychoacoustic literature points to the operation of
temporal mechanisms of pitch perception... Moreover,
there exists a large amount of modern evidence *against*
the place theory as a valid explanation for human hearing
throughout much of the musical range.
Why, for instance, doesn't the ear seem to use
basilar membrane information to detect pitch
below about 500 Herz?
Terhardt (and Paul Erlich) deals with this serious
problem by ignoring it.
Yet the experiments are striking. They have given
us important information about the ear/brain system.
They cannot be ignored.
David M. Green performed some of the most crucial
experiments in 1970. In that experiment, Green found
that "waveforms having identical energy spectra were
generated using a technique developed by Huffman.
A pair of such waveform differ only in their
phase spectra. The discriminability of such
waveforms was measured under various
conditions. (..) The results of these experiments
suggest that the ear can discriminate differences
in temporal order as small as 2.5 msec." [Green,
D. M. and Patterson J. H., "Discrimination of Transient
Signals Having Identical Energy Spectra," J. Acoust.
Soc. Am., Vol. 48, No. 4, pp. 894-905]
Green's experiments show clearly and unambiguously
that the ear can reliably discriminate between a waveform
and its time-inverse. But if this is the case,
then clearly the ear is not using Fourier analysis
in that frequency range -- since a waveform and its
time-inverse have exactly identical Fourier magnitude
spectra.
Clearly, below 250 Hz the human ear does not detect
pitch via frequency analysis. Instead, it uses time-based
analysis.
Green's experiments, along with many others, offer
proof positive that the human ear MUST use time-based
analysis throughout much of the audible range. Moreover,
Green's experiments (along with many others) prove
conclusively that below about 250 Hz the ear uses ONLY
time-based analysis to detect pitch and process
sounds.
Terhardt's model of the ear as a spectrum analyzer with
virtual pitch produced as a "secondary effect" cannot
explain Green's experiments, nor can it explain Newman
Guttman's series of experiments from 1960 and 1961.
How does Terhardt deal with these serious problems
in his theory?
Terhardt ignores them.
Other, more reputable, investigators have not ignored
these serious problems with Terhardt's theory.
John R. Pierce details some of the overwhelming
and extensive evidence that the ear uses time-based
methods of analysis (as well as spectral analysis) in "The
Science of Musical Sound," 2nd ed., 1992, pg. 149.
See also "Tone Segregation by Phase: On the Phase
Sensitivity of the Single Ear," Kubovy and Jordan,
J. Acoust. Soc. Am., Vol. 66, No. 1, 1979, pp. 100-
106.
As Kubovy and Jordan point out, "This tone-
segregation by phase raises doubts concerning several
current theories of pitch perception. (..) Insofar
as these results support temporal fine-structure
theories of pitch perception, they are incompatible
with the theories of pitch perception we cited
at the beginning of this paper (Goldstein, 1973;
Terhardt, 1973; Wightman 1973b)." [op cit., pp. 102-3]
Notice that Kubovy and Martin *specifically*
identify Terhardt's, Wightman's and Goldstein's
models of human hearing as *incompatible* with their
experimental results.
Other embarrassing problems with Terhardt's
Fourier theory of consonance include an unwonted
sensivity to the phase of high harmonics in
determining the virtual pitch of the tone complex.
According to Terhardt's theory, the ear/brains system
should ignore phase, but in fact phase is vitally
important to determining fundamental pitch below
500 Hz and above about 5000 Hz.
In fact, interestingly enough, the ear's reliable
pitch discrimination ends at exactly the point at
which the ear's time-based analysis mechanisms poop
out...namely, for fundamental frequencies above 5khz.
This evidence strongly suggests that time-based
mechanisms of analysis are not only present, but
absolutely indispensible, for the detection of
pitch throughout the audible range.
--
Further proof of the presence of time-based
pitch mechanisms (and thus disproof of Terhardt's
model) of human hearing comes from John R.
Pierce.
Pierce points out that:
"Investigations of just noticeable differences
(jnd's) of pitch continue to indicate the
plausibility of two `pitch mechanisms,' the first
operating on resolved harmonics, and the second
'periodicity pitch' mechanism on unresolved
clusters of harmonics (Houtsma and Smurzynski, 1990)
as discussed earlier by de Boer (1976). (..)
"The shape of the curve of jnd versus pulse rate
suggests a transition between two mechanisms between
62.5 and 500 pulses per second.
"Such a transition is supported by experiments on
matches between periodic all-positive pulses and
periodic patterns of positive and negative pulses,
carried out by Flanagan and Guttman (1960), Guttman
et al. (1964), and Rosenberg (1966). At low frequencies
the match is on pulse rate; at higher frequencies the '
match is on fundamental frequency." [Pierce, J. R.,
"Periodicity and Pitch Perception," J. Acoust. Soc.
Am., 90 (4), October 1991, pg. 1989]

The failure of the ear's Fourier analysis below
250 Hz to account for observed pitch perception
is a long-standing weakness of place theories of
hearing, and since Terhardt's theory is a pure place
theory it fails to explain all these important
psychoaacoustic results. Once again, Ernst
Terhardt deals with these problems by ignoring
them. Terhardt's many papers never mention
or explain the results of Guttman & Newman's
1960 experiments. Terhardt's paper never mentions
or explains the results of David M. Green's 1970
experiments. Terhardt's paper never mentions or
explains the results of Kubovy & Jordan's experiments.
Ask yourself:
Would you believe a scientific theory against which
considerable scientific evidence has been amassed,
if the author of that theory never bothered to
discuss or even acknowledge all the contrary
scientific evidence?
This is what Ernst Terhardt has done.
While Terhardt prefers to ignore the results of
all these experiments, reputable psychoaucistics
researchers cannot. These experiments cannot be
ignored because they're crucial to our
understanding of the presence of periodicity
mechanisms of pitch perception.
One of the most serious problems for a theory
of place-type pitch perception like Terhart's
(in which time-based auditory mechanisms of pitch
perception are conjured away with smoke and mirrors
and labelled as "secondary sensations") is that while
a purely spectral Fourier analysis model gets
central processor models are forced on us, nonetheless
phase remains crucially important to the perception
of pitch below about 250 Hz and above 5000 Hz.
A central processor model of some kind is
forced on us by the finding that
dichotic harmonics 3, 4 and 5 are most important to
the perception of virtual pitch. For more details, see
Ritsma, R. J., "Frequencies Dominant in the
Perception of the Pitch of Complex Sounds," J. Acoust.
Soc. Am., Vol. 42, 1967, pp. 191-198; also Plomp, R.,
"Pitch of Complx Tones, J. Acoust. Soc. Am., Vol. 41,
1967, pp. 1526-1533) and particularly the finding
by Houtsma and Goldstein (1972) that 2 successive
simultaneous harmonics with frequencies nf[o] and
(n+1)f[o] are presented to different ears they evoke
a fundamental pitch percept equally as effect as
a monotic or diotic presentation of the same two
harmonics.
The fact remains, however, that despite the
requirement for some sort of central processor
processor model to explain the above results,
phase remains crucially important to the perception
of pitch below 250Hz and above 5000 Hz. But phase
is a time-based auditory mechanism. And whenever
phase becomes important in pitch perception, by
definition the mechanism of hearing which detects
phase must be temporal and not spectral.
Moreover, in an intriguing experiment in which "the
perception of musical pitch was investigated in
postlinguistically deaf subjects with cochlear implants,"
the pure periodicity theory of hearing received a shot
in the arm. "Within a range of low pulse rates, subjects
defined the intervals mediated by electrical pulse
rate by the same ratios which govern musical intervals
of tonal frequencies in normal-hearing listeners.
It may be concluded that tempral cues are sufficient
for the mediation of musical pitch, at least for
the lower half of the range of fundamental frequencies
commonly used in music." [Pijl, S., and Schwartz, D. W. F.,
"Melody Recognition and Musical Interval Perception by
Deaf Subjects Stimulated with Electrical Pulse Trains
Through Single Cochlear Implant Electrodes," J. Acoust.
Soc. Am., 98(2), August 1995, pg. 886]
This provides strong evidence in favor of a strictly
temporal mechanism of pitch perception at low frequencies.
If you directly stimulate the auditory nerve periodically,
by definition the nerve is receiving only periodicity
information. The fact that subjects hear recognizable
sounds with cochlear implants disproves conclusively
Ernst Terhardt's claim that time-based processing
does not occur in the auditory range spectacularly fails
to account for this evidence, which cannot be conjured
out of existence as "secondary senstions" -- since
direct electric stimulation of the auditory nerve
produces ONLY time-based representations of acoustic
stimuli, with NO place stimulation of the basilar
membrane whatsoever.
Paul "All Boasts, No Scholarship" Erlich's reliance
on Terhardt's 20-year-old disproven theories of hearing
remains puzzling, since all contemporary computer
models of human hearing have systematically abandoned
Terhardt's Fourier analysis paradigm for the operation
of the human ear/brain system.
Instead, in D. P. W. Ellis' 1996 "Prediction-Driven
Comptuational Auditory Analysis," unpublished PhD thesis,
MIT, 1996 and Eric David Sheirer's "Computer Listening
Systems," unpublished PhD thesis, MIT, 1999,
Terhardt's 20-year-old outdated and disproven
pure Fourier analysis model of human hearing
fails so many crucial tests that both Sheirer and
Ellis abandoned Fourier analysis entirely as a
mechanism for analyzing acoustic inputs to their
computer listening systems.
Instead, both Ellis and Sheirer use autocorrelograms
in their computer listening systems. By following James
Moorer in his earlier 1975 Stanford PhD thesis "On the
Analysis and Segmentation of Real-Time Musical Sounds,"
in which Moorer abandoned Fourier analysis as unworkable
(because even slight changes in the transfer function
caused by room acoustics produced unacceptable alternations
in the Fourier spectrum of the input sound), both Daniel
Ellis and Eric Sheirer have found themselves forced to
throw out Fourier representations of the human ear/brain
system in favor of time-based models of the human
ear/bain system based on some form of autocorrelation.
As Eric Sheirer points out in his thesis, despite
an entire book written by Richard Parncutt based on
Terhardt's theory of human hearing, no one has yet
tested Terhardt's hearing algorithm with real-world
musical inputs (as opposed to artificial bleeps and
bloops generated by computer). And as mentioned above,
those of Terhardt's general predictions which *have*
been tested, systematically *FAIL.*

Bottom line?
By clinging to Terhardt's 30-year-old pure-Fourier-
analysis model of human hearing, which has failed at
least 3 different important psychoacoustic tests, Paul
"All Speculation, No Scholarship" Erlich once again
shows us the gross inadequancy of his knowledge of
psychoacoustics.
If we look at a more recent reference on psychoacoustics
to sum up the evidence, as opposed to Paul "All outdated
references, no modern results" Erlich's antique 1971 and
1952 citations, we find that:

"Several theories have been proposed to account for
residue pitch. Theories prior to 1980 may be divided
into two broad classes. The first, spectral theories,
propose that the perception of the pitch of a complex
involves [Fourier analysis followed by] a pattern
recognizer which determines the pitch pitch of a
complex involves [Fourier analysis followed by] a
pattern recognizer which determines the pitch
of the complex from the frequencies of the unresolved
components (Goldstein 1973; Terhardt 1974). (..)
"The alternative, temporal theories, assume that
pitch is based on the time pattern of the waveform at a
point on the basilar membrane responding to the higher
harmonics. (..) For these theories, the upper unresolved
harmonics should determine the pitch that is heard.
"Some recent theories (spectro-temporal theories)
assume that both frequency analysis and time-pattern
analysis are involved in pitch perception (Moore 1982,
1989; Srulovicz and Goldstein 1983; Patterson 1987;
Yost and Sheft, Chapter 6." [Yost, William A., Arthur N.
Popper and Richard R. Fay, "Human Psychophysics,"
Springer-Verlag, New York, 1993, pg. 98]

The references for these more recent spectro-temporal
theories of pitch perception include:

Moore, B.C.J., "An Introduction to the Psychology of
Hearing," 2nd Ed., London: Academic Press, 1982.
Moore, B.C.J., ditto, 3rd edition, 1989.
Srulovicz, P. and J. L. Goldstein, "A central spectrum
model: A synthesis of auditory-nerve timing
and place cues in monaural communication of
frequency spectrum," J. Acoust. Soc. Am., Vol.
73, pp. 1266-1276, 1983
Patterson, R.D., "A pulse ribbon model of monaural
phase perception," J. ACoust. Soc. Am., Vol. 82, pp.
1560-1586, 1987
Hall, J. W., Haggard, M.P., and Fernandes, M. A.,
"Detection in noise by spectro-temporal pattern
analysis," J. Acoust. Soc. Am., Vol. 76, No. 1, July
1984, pp. 50-56
Cohen, M. A., Grossberg, S., and Wyse, L. L., "A
Spectral Network Model of Pitch Perception,"
J. Acoust. Soc. Am., Vol. 98, No. 2, August 1995,
pp. 862-879.
-------
Notice 3 important points here:

[1] Paul Erlich is unaware that Ernst Terhardt's
theory of human hearing has been disproven by 3
different important psychocaoustic tests (as cited above)

[2] Paul Erlich's references are musty antiques
dating from 1971 and 1952 -- as compared to the far more
modern references I have cited above, which date from
between 1984 to 1999. Ask yourself -- which results
are more likely to be correct: outdated antique
citations from 1971 and 1952...or more modern psycho-
acoustic experimental results from 1984 and 1987 and
1993 and 1995 and 1996 and 1999?

[3] Lastly, notice that J. L. Goldstein is the same
author Paul Erlich quotes to support his disproven
and debunked "harmonic entropy" scheme. But Goldstein
cooked up his subsequent spectro-temporal theory in
the 1990s to patch the glaring holes in his 1973
central processor theory--namely, Goldstein's complete
inability to explain experiments like those summarized in
David M. Green's 1970 paper.

In fact Goldstein's early theory (which Erlich is so
fond of citing) is so inadequate that Goldstein himself
had to deep-six and come up with a better theory,
so many and so serious were its problems.

"Frequency difference limens are very much smaller
than critical bands. Two mechanisms are possible.
For instance, the subject may detect shifts in the
place of excitation of the cochlea. This is called the
'place theory.' Or he may use temporal information. We
know that the firing in the auditory nerve is phase-locked
'place theory.' Or he may use temporal information. We
know that the firing in the auditory nerve is phase-locked
to the stimulus waveform up to about 5 khz. In this
theory, called the 'temporal' [that is, 'periodicity'] theory,
the subject discriminates the two tones by using the
time interval between the neural firings. It is not clear
which of the two mechanisms is used. Indeed the controversy
has been active for more than 100 years, and the fact
that it is not yet settled shows that we still do not
have adequate evidence. Auditory physiologists
divide into three groups, namely those that think
only temporal information is used, thouse that think
only place information is used, and an eclectic group,
who suppose that temporal information is used at
low frequencies, and only place information at high."
[Pickles, J. O., "An Introduction to the Physiology of
Hearing," Academic Press, 2nd ed., 1988, pg. 271]
--
By placing excessive reliance on Terhardt's disproven
9170s theory of human hearing -- which systematically
contradicts the psychoacoustic data in a number of cases,
as cited -- Paul Erlich has yet again proven himself a
true Yale graduate. As we all know, arrogance combined
with ignorance and incompetence is the true imprimatur of
a Yale education, and in all respects Erlich has upheld the
low standards of that intellectual sewer known as Yale
with his parting post.

So let's see what we've got here...
Paul Erlich drags in the corpses of dead disproven
antique theories from the psychoacoustic literature
from 1971 and 1952...even while he systematically
ignores a host of more modern psychoacoustic theories
and psychoacoustic experiments (op cit.), including
Eric Sheirer's and Daniel Ellis' 1999 and 1996 PhD
theses on computer models of the human ear/brain system.

And T*H*I*S is what Paul Erlich describes as being
"a perfectionist" in his theories...?
--
At this point it behooves us to move on to the
larger issue of the dead antique superstition which
Paul Erlich styles "harmonic entropy."
To put it as simply as possible, "harmonic entropy"
asks the question: What is the smallest integer ratio
an isolated dyad will be heard as?
The problem with using this scheme as any kind
of measure for real music in the real world is
obvious, and it was discussed in detail by Leonard
B. Meyer in 1956:

"The attempt to explain and understand music as
a succession of separable, discrete sounds and sound
complexes is the error of atomism. (..) For the tested
pleasure-displeasure reactions are not what most of
the psychologists tacitly assumed them to be: they are
not universals (good for all times and all places) but
products of learning and experience. (..) Attempts to
explain the effect of the minor mode of Western music,
to cite but one example, in terms of consonance and
dissonance or in terms of the harmonic series have
resulted in uncontrolled speculations and untenable
theories. Even those not thus haunted by the ghost
of Pythagoras have contributed little to our
understanding of musical meaning and its communication.
For, on the whole, music theorists have concerned
themselves with the grammar and syntax of music
rather than with its meaning or the affective
experiences to which it gives rise." [Meyer, Leonard
B., "Emotion and Meaning in Music," The University
of Chicago Press: Chicago, 1956, pp. 7-8]

Naturally since this reference dates from 1956,
Paul Erlich is unaware of it. Presumably this
reference is too modern and too futuristic for
Erlich to have read -- Erlich appears to prefer
psychoacoustic research done in 1952 (!).

Of course L. B. Meyer is not the only music theorist
who has pointed out the crass and obvious logical error
in efforts like Paul Erlich's doomed attempt to extract
meaningful musical information from a numerical measure
of the acoustic smoothness or acoustic roughness of
isolated musical intervals:

"Helmholtz, Wundt, Stumpf, and other psychologists...
based their inquiries on the assumption that music was a
form of _pleasurable sensation_...this gave rise to an
aesthetic based on liking and disliking, a hunt for a
sensationist definition of beauty... But beyond a
description of tested pleasure-displeasure reactions to
simple sounds or elementary sound complexes...this
approach has not taken us very far." [Langer, Suzanne
K., "Philosophy in A New Key," Mentor Book Co.: New
York, 1951]

Paul Erlich's concept of "harmonic entropy" is
nothing more a mathematical operation on "simple sounds
or elementary sound complexes" inteded to yeild a measure
of acoustic smoothness -- which is to say, the degree to
which that isoalted sound complex produces a pleasurable
sensation when heard in total isolation.
But even the least competent musician instantly
recognizes the utter folly of the attempt to mathematically
gauge the purported "pleasurable sensation" produced
by a dyad or a chord heard in total isolation -- the
effort is foolish and inevitably doomed because in real
music we NEVER heard dyads or chords in total isolation.
We NEVER judge dyads or chords solely by the purported
"pleasurable sensation" they produce when heard in
total isolation...instead, listeners A*L*W*A*Y*S judge
dyads and chord according to the musical context in
which they occur.

"One reason for the difficulty has been an initial
assumption of distinct sensory atoms in perception. Even
in the study of judgments of isolated intervals, pure
tones have been consistently used--tones which may have
a laboratory value, but which are not found in music.
Musical perceptions do not arise from tones, they arise
from structural relations among tones. The relations
cannot be uncovered by observing and measuring response
to isolated interval-qualities." [Cazden, Norman, "Musical
Consonance and Dissonance: A Cultural Criterion," Journal
of Aesthetics and Art Criticism, Vol. 4, No. 1, 1945,
pg. 4]

"Historically, there have been two major difficulties
with the treatment of consonance and dissonance. First,
many writers have equated consonance with pleasantness
and dissonance with unpleasantness; and second, judgments
of consonance and dissonance have sometimes been made
to isolated sounds and sometimes to sounds presented
in a musical context." [Gulick, W. Lawrence, George
A. Geschneider and Robert D. Frisina, "Hearing:
Physiological Acoustics, Neural Coding, and Psychoacoustics."
Oxford University Press: New York, 1989, pg. 289]

So Paul Erlich's "harmonic entropy" is at its
core nothing more than a resuscitation of the truly
antique Victorian sensationist theories of music
purveyed by Stumpf and Wundt in the 1890s (!)
How could someone who graduated from Yale offer up
with a straight face a so-called "theory" of music
(viz., "harmonic entropy") which is basically nothing
more than a turgid numerological gloss on debunked
sensationist theories of music dating back to the 1890s...?
Precise *because* Paul Erlich graduated from Yale.
Having been infected with the fatal arrogance typical
of the Ivy League, Erlich merely assumed that since he
stumbled across his "harmonic entropy" scheme, he did
not need to do any scholarly research to ascertain whether
other substantially identical theories of music had been
advanced and disproven in earlier eras.
After all, what need?
Erlich graduated from Yale -- therefore he knew
everything. "I am the master of Yale college, and if
I don't know it, it isn't knowledge," goes the refrain
of the Ivy League.
And we get numerological mumbo-jumbo like "harmonic
entropy" palmed off as a serious theory of music, instead
of the antique regurgitation of debunked 1890s "pleasure/pain"
theories of music that it really is.

"The conclusions of Rameau's successors were evidently
examples of reasoning from the particular to the general.
Argument proceeded in a vicious circle. A theory of harmony,
based on the facts of acoustics as a branch of physics...
was accepted by academic musicians because musical illustrations
of its tenets could readily be found in music of the classical
period. In turn the theorist clung to his speculations because
they earned the approval of academic musicians.
"The fallacy of the theory, from the point of
view of music, is obvious: it considered chords as things
in themselves, existing timelessly, with no reference
to what had gone before, and little to what was to
come after." [Lloyd, L. S., "Helmholtz and the Musical
Ear," Musical Quarterly, Vol. 5, 1939, pg. 170]

"Perceptions of interval qualities, though they do not
arise on natural foundations, are neither arbitrary nor
accidental. They are conditioned responses derived from
the structural relations of a specific musical language
and its history. (..) Thus the materials of musical art
are not to be discovered in natural phenomena taken in
isolation, in tones and the responses to them, but in
the more complex systems of tonal relations which are
the historical products of human culture. These systems
cannot be reduced to their constituent elements without
losing their essential properties as organized wholes,
and without losing their human context." [Cazden, Norman,
"Musical Consonance and Dissonance: A Cultural Criterion,"
Journal of Aesthetics and Art Criticism, Vol. 4, No. 1,
1945, pg. 10]

As the crowning disproof of Erlich's claim that
the "harmonic entropy" measurement has any valid
musical meaning, the fact that the relative musical
effect of a chord depends on its musical context
was experimentally proven all the way back in 1945:

"According to Helmholtz's well-known theory,
the consonance or dissonance of a chord depends on
the extent to which its component fundamental tones
and their overtones produce beats. Even a cursory
study of the methods of musicians, however, and the
experience of listening to music, make it seem
possible that in actual practice the degree of
harshness of dissonances varies considerably according
to the way in which they are used and on their
context of surrounding chords. A short experiment
was planned to test this possibility. (..) From
these data it must be inferred that the dissonance
of a chord depends even more upon the relation in
which it stands to its surrounding chords than on
the nature of the chord itself. The objection might
be raised that the subjects were simply judging the
dissonance (or consonance) of given chords in
comparison with more (or less) dissonant chords
on either side of them. This objection, however,
is met by the results for settings C and F, which
consisted of the test chord itself, transposed one
tone up or down." [Gardner, P. A. D. and R. W.
Pickford, "Relation Between Dissonance and Context,"
Nature, Septemeber 25, 1943, Volume 152, pg. 358]

--------
To sum up, Erlich's "harmonic entropy" rests
on a quicksand foundation of error piled upon error,
folly heaped upon folly, debunken Victorian superstition
dumped atop antique disproven Victorian supersition:

[1] Insofar as it attempts to discern the acoustic
smoothness of an isolated chord or dyad,
"harmonic entropy" involves the long-debunked
error of sensationism, the faulty 19th-century
effort to reduce music to a mere acoustical
banana split, a mere matter of auditory pleasure
or pain;

[2] By utterly ignoring the context in which the
dyad or chord occurs, "harmonic entropy" entails
the error of msuical atomism, which assumes
pitches and/or chords can be usefully analyzed
as isolated things rather than as part of a
musical context;

[3] By entirely disregarding cultural and stylistic
influences on music, "harmonic entropy" foolishly
assumes that the same acoustic interval will be
heard and can be nmeasured numericall in the same
way regardless of the musical style in which it
occurs;

[4] By ignoring the existing experimental literature
which shows that the human ear/brain system
cannot be modeled solely as a Fourier spectral
analysis system, "harmonic entropy" presumes
that harmony is basic to music -- whereas all
contemporary psychoacoustic and computer listening
research indicates that melody is far more important
to music and that therefore the acoustic roughness
or smoothness of isolated tone-complexes proves
trivial by comparison with the melodic context in
which they occur;

[5] By entirely disregarding the question of the
connection twixt the syntax of the musical surface
and acoustic roughness/smoothness, "harmonic
entropy" embodies a musically meaningless
measure of purely sensory qualities which does
not relate to the musical meaning of a chord,
since the musical significance of any chord
derives from its connection twixt acoustic
smoothness and the musical syntax in question;

[6] Last but not least, John Chalmers has pointed out
that "harmonic entropy" involves nothing more than
an unnecessarily complex numerological method
for inaccurately determining the acoustic smoothenss
of an isolated interval, and consequently "harmonic
entropy" boils down to nothing more than a turgid
layer of numerology applied to Plomp & Levelt's
critical band theory -- but since Plomp & Levelt's
theory of the critical band already explains
the auditory roughness of musical intervals entirely
well from a purely empirical standpoint, there
is no need for Paul Erlich's additional veneer of
numerology larded on top of Plomp & Levelt's far
simpler and more accurate empirical description.

So there we have it.
Paul Erlich's "harmonic entropy" fails numerically,
it fails historically, it fails philosophically, it fails
conceptually, it fails Occam's Razor (why not simply use
Plomp & Levelt's simpler empirical description instead?),
it fails at every level and in every way.

We are now in a position to understand why Paul
Erlich makes use of such laughably antique psychoacoustic
results from 1952 (!). Erlich probably recognizes that
his "harmonic entropy" scheme fails in so many ways, on
so many levels, that he must cast his fishing line all
the way back to the 1950s to scavenge plausible-sounding
citations from the psychoacoustic literature, for the
more modern results would conclusively debunk his
"harmonic entropy" scheme.
We are likewise now in a position to see why Erlich
clings with such a death grip to the antique debunked
1970s theory of human hearing advanced by Ernst Terhardt.
Erlich's theory is based on such obsolete 19th
century notions about music (viz., Wundt's "pleasure/pain"
model of music as a mere series of acoustical sensations)
that only a theory of human hearing as antique as Terhardt's,
based solely on Fourier analysis, will support such an
obsolete conceptual structure.
More modern theories of the human ear/brain system,
such as those advanced by D. P. W. Ellis and Eric Sheirer
(1996, 1999, respectively, op cit.), which abandon Fourier
analysis, imply strongly that melody and musical context
prove far more important than the acoustic properties of
dyads and chords considered as isolated entitities.
Since Erlich's laughable "harmonic entropy" superstition
boils down to precisely the effort to numerically calculate
the acoustic properties of dyads and chords considered as
isolated entitities, it stands to reason that Erlich must
embrance Terhardt's obsolete 1970s theory of hearing and
systematically ignore more modern and more accurate
spectrotemporal theories of hearing based on
context-sensitive prediction-driven computations of
time-domatin autocorrellograms.
--------
Lastly, it might prove interesting to know why
Paul Erlich mentions the "central pitch processor" theories
of Wightman and Goldstein when discussing "harmonic
entropy." These were hybrid theories which became
fashionable about 25 years ago in a number of guises.
Erlich dredges up Goldstein's and Wightman's central
processor theories of hearing from the early 1970s
because Erlich desperately needs to find a way to
boil all of music down to a single numerical measure
(like the one implied by his "harmonic entropy").
However, it might also prove interesting to
learn that Goldstein offers one version, Wightman
another, more recently (in 1991) Meddis and Hewitt:
"Virtual Pitch and Phase sensitivity of a computer model
of the auditory periphery," I & II, 1991, J.
Acoust. Soc. Am., Vol. 89., pp. 2866-2894.
Wightman's pattern transformation theory
suffered a severe blow in 1979--see A. J. M.
Houtsma, "Musical pitch of 2-tone complexes
and predictions by modern pitch theories,"
J. Acoust. Soc. Am., Vol. 66, No. 1, July 1979,
ppg. 87-98.

"Among the three popular pitch theories only
the optimum processor theory [Goldstein's]
is able to account for most of the data
is a quantitative sense. The virtual pitch theory,
which in its original formulation can account for
most phenomena only in a qualitative sense, can
be brought into quantitative agreement with most
experimental results through some modifications
which make it yield results very similar to the
optimal processor theory. The pattern transformation
theory was found to be significantly less supported
by empirical results, especially by results obtained
with successive harmonic two-tone complexes that
were already available in the literature. Attempts to
find a suitable modification of this theory that would
bring its predicitions and experimental results in
closer agreement were not successful. None of the
theories presently accounts in a quantitative way
for the apparent constant rivalry between analytic
and synthetic mode pitch perception which is always
present in experiments that use complex tones."
[Houstmas, A. J. M., op cit., 1979, pg. 98]

And so Wightman's and Goldstein's models have been
supplanted in the 1980s and 1990s by spatio-temporal
theories of the kind exemplified by Eric Sheirer's
model in "Computer Listening Systems," unpublished
PhD thesis, MIT, 1999, and Daniel P. W. Ellis'
"Prediction-Driven Comptuational Auditory Analysis,"
unpublished PhD thesis, MIT, 1996.
See also Beerends, J. G., J. Acoust. Soc. Am.,
86(5), 1989, pg. 1835-1844 ("subjects tend to switch
to the analytic mode of pitch perception when when
complex tones are shortened--i.e., they tend
to hear the psectral pitches instead of the
virtual ones") and Cross, West and Howell's
"Pitch Relations and the Formation of Scalar
Structure," Music Perception, 1985, 2(3),
pp. 329-344 ("Experimental results indicate
that important aspects of musical judgment
are well accounted for by logical consequences
of such formal definitions, without the necessity
of invoking either simplicity of frequency ratios
or musical `well-formedness.'"), and the effects
noted in "Brightness and Octave Position: Are Changes
in Spectral Envelope and In Tone Height
Perceptually Equivalent?" Contemporary Music
Review, 1993, 9(1&2), pp. 83-95, ("Rapid changes
in spectral envelope have been reported to
influence estimation of octave position by
musically trained listeners"), and Jan Nordmark's
results in "Mechanisms of Frequency Discrimination,"
J. Acoust. Soc. Am., 44(6), 1968, pp. 1533-
1539 ("the main difficulties of the place theory:
why a well-defined pitch could be heard corresponding
to the fundamental of a complex sound even when
the fundamental was wek or absent, and why one
coudl be heard also for very short tones. (..) The
second difficult of the place throy arises from
the fact that the pitch dscirimination of which
human beings are capable seems to indicate a sharp
resonance and consequently a very low degree of
damping on the basilar membrane. The short
time required for a clear tonal impresison, on the other
hand, pointed to a high degree of damping"), as well
as Irwin Pollack's results in "Ohm's Acoustical Law
and Short-Term Auditory Memory,' J. Acoust. Soc.
Am., 36(12), 1964, pp. 2340-2345 ("Contrary to the
expectation of Ohm's acoustical law, listeners were
relatively unable to accurately `extract' components
from nonharmonicaly related tone combinations.")
---------
Since Ernst Terhardt's theory of human hearing
fails all these important psychoacoustic listening
tests, and since Terhardt's theory of hearing also
fails to account for large amounts of the psychoacoustic
experimental literature, and since Terhardt's model
of the human ear/brain system (Fourier analysis) has
been systematically abandoned by all the current
cutting-edge computer listening systems which
model human hearing with computer algorithms...
why, it stands to reason that Paul Erlich must
ignore all these gaping holes and glaring disproofs
of Ernst Terhardt's theory of human hearing, and
instead of cling to antique 1971 and 1952 papers
as alleged "support" for Erlich's own claims about
human hearing.
---------
It's all standard stuff. Wherever we look
throughout the length and breadth of Paul Erlich's
so-called "theories" of music, we find antique
and outdated and pervasively disproven references
like the 1971 Terhardt citation Erlich drags in
during his parting post on this discussion group.
Given the sheer bulk of experimental evidence
disproving Erlich's antique 1971 and 1952
citations (cited in this post), it's no surprise
that Paul Erlich has now fled this discussion
group like a cockroack scuttling away from a
blast of RAID. When faced with genuine scholarship
like the citations above which disprove and refute
Erlich's antique and outdated citations, what
else can Erlich do but run away?
Run far, Paul Erlich. Run fast. Skitter like
a bug fleeing the Orkin Man. If those pathetic
1971 and 1952 citatins are the best you can dredge
up (as opposed to the 27 different separate modern
psychouacoustic references I cite in this post),
no wonder you're running scared, Erlich.
No wonder you've soiled yourself with fear
and have now abandoned this tuning list in panic,
Paul Erlich. You know your scholarship is
ludicrously outdated and fifth-rate, like the
debunked "harmonic entropy" scheme you base
on it.
---------
--mclaren

Yale Boy heads for the hills

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