Yahoo Tuning Groups Ultimate Backup tuning Boomsliter & Creel

FROM: mclaren
TO: new practical microtonality list
SUBJECT: Boomsliter & Creel

In Message 729 on 26 July, Kraig Grady wrote:

"OK, I am going to push the `Devils Advocate' on this one. (..)
"My basic point being is that one cannot dissect even one aspect
"of a work of art."

But that's just what you're doing, Kraig, when you try to use
Boosmliter & Creel's results and the harmonic series and mythical
"integer ratio detectors" inside people's heads to support JI.
It's exactly what you're doing when you say that "If you put
different pitches in different ears the ear will hear difference
tones. JI intervals will have these in tune and will beat
less." -- Kraig Grady, Message 729, op cit.

What you're doing here, Kraig, is dissecting art down to
a particularly crude and blunt level -- the level of beats.
Less beats = good, more beats = bad. Therefore JI is
good, according to your argument.

First, it seems to me that your claim "one cannot dissect
even one aspect of a work of art" by means of math or physics
is far closer to the truth than crude caricatures like counting
beats per second or mythical "integer ratio detectors" inside
people's heads (which have been shown not to exist).
Efforts to use such startlingly crude caricatures to
justify one particular tuning or class of musical composition
are stupefyingly simplistic, Kraig, and for that reason they
have never worked -- and never will work. Euler tried it with
his Gradus Suavitatus, and he got laughed out of court. Helmholtz
tried it with his Klangverwandschaft scheme, and in order to
make his concoction work Helmholtz had to claim that the 7th
overtone does not exist in the timbre of Western instruments.
These kinds of bizarre and foolish results come from overly
simplistic schemes for classifying and categorizing music.
Incredibly cartoonish methods of dissecting musical artworks
like "count beats/sec" or "match-ups between harmonic overtones"
are so caricaturish that they seem to me about on the level
of, say, deciding who is a good physicist by looking at the
guy's haircut, or deciding whether you want to marry a girl
by asking "How white are her teeth?"
These kinds of criteria are so crude and so simplistic
that they don't even come close to telling us anything useful.
In music, such incredibly simplistic cartoonish criteria
are things like difference tones, beats, "the chord of nature,"
the harmonic series, and Boomsliter and Creel's claims about
extended reference.
These ideas are incredibly simplistic because they all boil
down to doing baby math. Are they integers, and if so, how
small are the integers? Subtract the integers. Add the
integers.
If music were really this simple, we would sit in gape-
jawed adoration of the screech from a smoke detector, whose
"pure perfect natural" overtones form a "perfect chord of
nature" generated by the "pure perfect natural chord of
nature."
Ever HEAR the screech from a smoke detector?
Yeesh.
It's the most stultifyingly boring timbre known to man.
The human brain is complex, Kraig, and craves change
and variation and variance and departures from regularity.
This is as true of music and musical timbre as it is of
art -- who wants to sit in a music looking at a big square
or pure red or a big square of pure green on the wall? Can
you imagine anything more boring? More cartoonish? More
simplistic?
But the rods and cones in our eyes are adapted to detect
particular primary colors, Kraig, so according to your
kind of argument the most perfect art should consist of
big blocks of pure primay colors...just as the most perfect
music should supposedly consist of the pure perfect natural
overtones of the harmonic series moving in lockstep with one
another in tunings made up of sections of the harmonic series.
That's far too crude and too simplistic, Kraig, because
in between the ear and the mind lies the brain. Just as
in between the retina and the mind lies the brain.
Our brain is complicated and designed to detect mainly
change, not things which are stationary and trivial and
simple. As a result, our brains crave irregularity and asymmetry
and complexity and subtlety, and we get bored without it.
This is why cartoonish ideas like "small integers"
results in what one member of this discussion group (whom I
shall not name) called "music so bland I can't stand it."
Boomsliter and Creel merely change this question (Are the
integers small) very slightly by asking: Are the musical
DISTANCES from one melodic key center to another very small
integers? rather than the traditional crude question: Are
the pitches of the melodic notes themselves very small integers?
The idea that this is all there is to the human ear/brain
system seems insulting not only to humans, but to biology
itself.
Kraig, we've got upwards of 100 billion (with a B) brain
cells in our heads. Each brain cell is connected to about
10,000 others. Each brain cell is more complex than the
computer on your desktop.
And after feeding all that complexity with 30 or 40 or
50 years of hands-on context-dependent relational knowledge
and experience...
...Human hearing boils down to small integers?
Please.
IT doesn't even pass the straight-face test. It's like
claiming that the purpose of the proton-antiproton collider
at CERN must be...to boil water.

However, the second issue (aside from the sheer crudity
and cartoonish triviality of simplistic numerical schemes
like Boomsliter and Creel's, or Euler's, or Pythagoras') is
that Boomsliter and Creel's results came from badly flawed
procedures and had a lot of problems.

Let's talk about those problems.

Since you haven't yet quoted a single line from
Boomsliter and Creel's 1963 paper in the Journal of Music
Theory, it's not clear whether you've actually read the
paper. Probably you have. For those of you who haven't,
B&C's 1963 paper is called "Extended Reference: An
Unrecognized Dynamic In Melody," Journal of Music Theory,
1963, and in it Paul Boomsliter and Warren Creel claimed
that the human ear operates by difference tones, and
that in effect the real pitches played by real musicians
in the real world were created by using intervals
relative to temporary melodic JI pitch centers. This
made the pitches numerically complex, but audibly simple,
according to Boomsliter and Creel.
The term "extended reference" comes from B&C's description
of how we supposedly hear melodies. At first we reference
the melodic pitches to the 1/1, but as the melody moves away
from the 1/1, B&C claim we reference new melodic pitches
to pitches different from the 1/1 -- perhaps the 3/2, or
the 6/5, etc.
This results in complicated ratios, but the pitch differences
(which is what we really hear) between local melodic notes
and the local extended reference pitch remain simple.

Here is what B&C themselves wrote about extended reference:

"To this we can add that the audience would have
noticed, and -- improbable as it may at first seem --
would have been disturbed, if the singers had sung
the notes `on pitch,' in the theoretically correct
tunings prescribed by the just scale or equal
temperament. (..)
"Music theorists have customarily taken harmony as
the source of melody, treating a melodic sequence
as the surface of a harmony or of a chord progression,
again a form of direct reference. Yet difficulties
arise when this is applied to a specific melodic
sequence. Let us take as example the opening strain of
The Marseillaise, Figure 3. The tuning, selected on
the Search Organ by Robert Enman, music teacher at the
Emma Willard school in Troy, New York, begins: Sol
Sol Sol Day Day Re Re Say May Day. Of course classical
just intonation would be Do instead of Day, Sol instead
of Say, and Mi instead of May. Mr. Enman starts with Sol,
a direct reference, 3/2 to Do, it has multiple references,
being 1/1 on the second level, and 4/3 on the third. The
melody goes promptly into extended reference, to Day, 9/5
to the third reference. (The cent values and ratios of
all notes are shown on Figure 2). Played in just tuning
the melody does not have the quality of a good Marseillaise;
it sounds dull. The just notes Sol Do Re Mi and Sol, sounded
as a chord or combination of chords, do not have the quality
of the Marseillaise. This opening phrase is notably
electrifying melody, and it has the Marseillalse quality in
Mr. Enman's tuning. The effect cannot plausibly be described
as that of any chord. Sol and Day sounded together do not
harmonize, yet the tuning the ear wants in this melodic
sequence is Day, while the sound of Do is rejected as
wrong and dull.
"Conventional theory explains melodic vitality, or
melodic tension, by a principle of consonance and
dissonance which cannot be narrowly applied, and by
the tendency of certain notes to serve as points of
rest, and the tendency of other notes to pull toward
these, which can indeed be observed if one plays up
the scale, treating the scale as a melody. However, we
submit that in this phrase of The Marseillaise the
tension is not heard simply as a pull of some notes
toward other notes which sound restful. In addition to
any tensions between note and note, the whole phrase
has tension, which may well be caused by the tense
relationship, the extended reference, to the tonic.
"It is observable that all melodies have, throughout
their course, an effect of something started but not
yet finished, of motion toward a destination that
is known, but not yet reached. It is also true that
all melodies begin by establishing a tonic and going
into extended reference to it, and they stay in
extended reference until the end, which is accomplished
by a return to direct reference and, normally, to the
tonic. We submit then, that extended reference is
the characteristic organization of melody; it is
possibly the chief source (although certainly not
the only source) of the tension and relaxation that
go on in melody.
"To illustrate in detail: The note Day has the
ratio 81/80 to the tonic. This is impossibly complex
as a direct ratio. In terms of the partial series it
is the relationship between the 81st partial and
the 80th - impracticably high. With a maximum of
transposing down it is the relation between the 81st
partial and the 5th - still impracticable, it cannot
be explained by cultural conditioning to the tempered
scale, since the tempered first is Do, zero cents,
exactly like just Do. This note, and others in its
sequence, can be explained as an auditory result of
organization in simple ratios, if we assume that the
auditory system can handle simple ratios in linkages,
or chains.
"The implications of this hypothesis for auditory
theory are discussed at some length in the Second
interim Report. In brief, we hold that...we select and
organize the various partials of a normal complex
tone by the fact that the partials synchronize;
they are in step with each other. We exclude
interfering vibratlons from the sensation because
they do not keep step; thus we perform the essential
operation of hearing through interference. This
normal organization by direct synchronization is the
constant function of our hearing in all tones, and
it is altogether too ordinary to be musically
interesting. It is child's play. The auditory nerve
network, equipped for synchronization by the necessities
of normal hearing, is also able to project a matrix
that organizes synchronizations linked together one
after another, in a pattern different from the
partial series. Now this is interesting. It stimulates
and rivets the attention because it is not the same
easy partial series pattern. it requires effort to
maintain the linked matrix (keep the key). Such a
linked matrix of simple ratios, although manageable,
is unusual, therefore tense, and requires resolution
by return to direct reference to end the pattern. Thus
melodic tunings, except at the start and end of a
melody, are organized to depart from the partial
series. At the same time these tunings are organized
by extended applications of synchronization -- the
process that organizes the partial series." [Boosmliter,
Paul and Warren Creel, "Extended Reference: An Unrecognized
Dynamic In Melody," Journal of Music Theory, 1963, op cit.]

You can see some of the problems with Boomsliter &
Creel's procedure right off.
For one thing, they are essentially talking about
modeling human hearing as difference tones. But that
scheme was tried by Felix Krueger in 1906 and was
conclusively debunked by Carl Stumpf in 1908.

"Krueger regarded consonance and dissonance as
determined by another factor extrinsic to the interval
itself, namely the difference tones generated by it.
(..) ...According to Krueger, the consonance or dissonance
of any interval depends on the simplicity or complexity
of its structure of difference tones. Much criticism has
been leveled at...these theories, and it may safely be
said that they have been proved entirely untenable." [Mursell,
James L. "The Psychology of Music," W. W. Norton & Company
Inc.: New York, 1937, pg. 93]

I have written about the difference tone myth elsewhere
in "Myths and Misconceptions about Just Intonation."
The myth that difference tones "explain" music or "explain"
human hearing or "explain" harmony or "explain" melody is
yet another dead debunked superstition, like the myth
that small integers = musical consonance, the myth that
the human ear/brain system has integer ratios inside it,
the myth that music evolves from simpler to more complex
forms, the myth that harmony evolved historically through
the overtone series, the myth that history is on a constant
progression toward more and more musical chromaticism so
that atonality represents the irresistable endpoint of
an inevitable historical process, and countless other
musical myths and old wive's tales.

To summarize my discussion which elsewhere discusses
the vast amounts of evidence that disprove the old wive's
tale that human hearing dependson differenc tones:

SUMMARY OF THE FAILURES OF DIFFERENCE TONE THEORIES

Difference tones fail to explain human hearing because:

[1] If human hearing depended solely or even mainly on
difference tones, then all musical cultures throughout
the world would hear the same musical intervals as
sounding musically consonant. Ethnomusiclogy tells us
that they don't.

[2] If human hearing depended on difference tones, Western
European music history would show a consistent judgment
of certain musical intervals as always consonant, and
other musical intervals as always dissonant. Music
history tells us the opposite. Throughout Western European
musical history, some intervals have been considered
dissonant which were previously heard as consonant and
vice versa. Intervals constantly change their perceptual
status according to the style of musical composition
popular in a given historical period, not according to
mythical difference tone detectors engraved inside our ears.

[3] If human hearing depended on difference tones, then because
the loudness of difference tones depends disproprtionately
on the loudness of the component tones, ppp minor seconds
and major sevenths would sound more consonant than ffff octaves.
No observer ever reports such a musical perception. No Western
music textbook has ever made this claim. Western music utterly
discounts the loudness of tones in a musical interval when
classifying the interval as consonant or dissonant, yet this
is crucial for creating various levels of difference tones,
for the louder the 2 tones the more audible difference tones
occur and therefore the greater the interference twixt all
newly-audible difference tones.

[4] If human hearing depended on difference tones, then the frequency
spectrum of tones in an interval would exert an overwhelming
influence on its audible consonance. For example, a perfect
fifth sounded between two clarinets would theoretically produce
a very different musical effect than a perfect fifth sounded
between two flutes (since clarinets produce mainly odd numbered
overtones, while flutes tend to produce even numbered overtones).
But listeners do not report this. Instead, listeners prove able
to reliably identify musical intervals regardless of the overtone
structure of the instruments on which they are sounded, and
listeners and composers hear and use musical intervals uniformly
within the constraints of a musical style regardless of the
instruments which produce them. Thus, for example, Bach never
composes flute duets in which the harmony consists entirely of
minor seconds. Likewise, Bartok almost never composes pieces
which
consist entirely of Palestrina-like major and minor triads,
regardless of the timbres Bartok calls for in the composition.

[5] The phenomenon of categorical perception systematically
contradicts
claims for human hearing based on on difference tones. Listeners
universally report pitches and intervals far away from their
nominal frequencies as sounding nonetheless "in tune," and this
effect has been so comprehensively documented that it cannot be
denied.

[6] Listeners outside a given culture also often prove unable to hear
musical effects reported by listeners familiar with the musical
culture. This again argues against the purported musical
importance
of sensory percepts like difference tones.

[7] Listeners who are not musically educated report an entirely
different ranking for dyadic musical intervals than listeners
who are musically educated. This indicates that the main component
of musical listening is acculturation--NOT the physical acoustics
of difference tones.

[8] Within a single composition, the same musical interval can sound
both musically consonant at one point, and musically dissonant at
another point--depending on context. This again tends to disprove
claims of human hearing according to numerical physical
interactions
like difference tones, since the same identical interval, with
identical difference tones, should produce identical numerical
physical interactions due to difference tones.

[9] The pervasive practice of tempering musical intervals should
produce horrible effects, according to the theory of difference
tone hearing, since detuning an interval slightly produces a
much greater detuning in the difference tones. (You can see this
mathematically by noticing that every slight detunings like
20,001/10,000
produce an enormously large difference tone.) Listeners do not
report that tempering or detuning intervals produces
disproportionate
musical dissonance, and this in turn indicates that difference
tones are not significant in our musical perception of intervals.

[10] If the theory that our ears hear by detecting difference tones
is
correct, then intervals played on inharmonic instruments like
carillons or chimes or tubulongs should sound unbearably
dissonant.
Once again, this doesn't happen.

[11] Among all the world's musical cultures, ONLY India and Western
Europe have developed theories of music which place importance on
mathematics and acoustics and abstract computations like
difference
tones. The other 85% of the world's population does not think of
music in terms of mathematics and has no interest in trying to
mathematically derive or explain the effects of its music. This
indicates that the Western European attempt to derive and explain
its music by means of mathematics is as much a superstition as
the
attempt of certain Amazon indian tribes to explain their music by
reference to "gods of the river" and "gods of the air."

[12] Theories of difference tones fail when consonant intervals are
octave-inverted. For example, the perfect fourth is sometimes
classed as a dissonance because its difference tones clash with
the notes of the perfect fourth interval. But if this is correct,
then the just minor sixth should also be classed as a dissonance
because its difference tones also clash with the notes of the
interval. In fact, ALL octave-inverted JI consonances (major
third, minor third, perfect fifth) theoretically produce
difference tones which clash with the fundamental and therefore
ALL
octave-inverted consonant JI intervals should sound dissonant.
Listeners do not report this.

[13] Psychoacoustic experiments show that difference tones prove
far too faint to be audible under most musical circumstances.
Theorists try to argue this laboratory data out of existence
by claiming that "the ear unconsciously processes the very
faint difference tones, even though they sound inaudible under
ordinary musical conditions." But this sophistry creates even
larger problems for the music theorist, for having allowed
inaudible difference tones into hi/r theory, the theorist can
no longer justify ignoring the vast number of very faint
combination tones which occur between the 2nd overtone of one
note in a dyad and the 2nd overtone of the other note, the
3rd overtone of one note in a dyad and the 3rd overtone of the
other note, the 4th overtone of one note in a dyad and the
4th overtone of the other note, and so on, tens of difference
tones and scores of difference tones and hundreds of difference
tones. All of which must now be taken into consideration in
theoretical determinations of musical consonance--since the
theorist has prestigitated out of existence the overwhelming
laboratory evidence that actual difference tones between real
musical notes in the real world prove inaudible, thus opening
the door to a flood of inaudible and hitherto ignored difference
tones of the 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th,
12th, 13th, 14th and higher order.

[14] Calculations involving difference tones lead to mathematically
invariant conclusions which ought to dictate a uniform response
by all members of a given culture in a given context to a given
musical interval. But psychoacoustic experiments show that
different
listeners respond differently to the same musical interval even
if
that interval be presented to members of the same musical culture
with the same musical training within the same musical context:

"We were very surprised to observe that subjects showed two
distinct
patterns. Nine subjects (top three rows of Fig 1) had `M' patterns,
in
which chords deviating from just intonation by +15 and -15 cents were
judged to be most in tune and chords with just intonation or
deviating
from just intonation by +30 and -30 cents are judged to be less in
tune.
For reasons to be discussed later, we describe these subjects as
`rich'
listeners. A second distinct pattern is apparent for the four
subjects
shown on the bottom of Fig. 1. It shows inverted `V' patterns, in
which
just chords were preferred to all others. We refer to this group as
`pure' listeners. The grouping of the listeners does not correspond
to
any classification according to training that we have been able to
discover. (..) </B></FONT></P>
"From this experiment we conclude that...listeners fall into two
groups: one of which, the `pure' group, prefers chords with just
intonation and the other of which, the `rich' group, prefers chords
which deviate enough from just intonation so a pleasant beating can
be heard." [Mathews, M. V., J. R. Pierce, and L. A. Roberts, "Harmony
and New Scales," in J. Sundberg (ed.), "Harmony and Tonality,"
Stockholm:
Royal Swedish Academy of Music, 1986]

[15] Physiological experiments have proven conclusively that the
nonlinear distortion in the inner ear does not conform to
Helmholtz's
hypothesized frequency-independent power law. Rather, the amplitude
of nonlinear distortion depends crucially on the frequency of the
tones -- which plays havoc with theories like Boomsliter & Creel's.

-------

Given the overwhelming eveidence against any musical important of
difference tones for human hearing, it's clear that Boomsliter &
Creel's theory rests on a foundation which has already been
demmolished. In fact, no serious psychoacoustician or audiologist
or music researcher today believes that difference tones provide
an adequate explanation of musical structures or a credible
model for human hearing, since so much evidence against the
alleged musical importance of difference tones has been amassed
over the last 90 years.

So the first big problem with Boomsliter & Creel's theory of
extended reference is that it starts with assumptions about
human hearing which have been proven incorrect.

"Difference tones were observed by Tartini as early as 1714,
[29] and were applied by him as an aid to judgments of intonation
for double-stops on the violin. Only the first order difference
tone was known to Tartini, and even this estimated incorrectly.
Nevertheless he demonstrates practically that any two tones
forming an interval give rise automatically to a `terza suono,'
and that this `third sound' does not result merely from suggestion
but is present to the ear. Tartini regards this resultant tone
as the natural bass of the whole, and on this principle he constructs
a valuable theory of harmonic practice. Hindemith [30] follows the
same principle, though describing it as an original discovery.
"Krueger attributes consonance to the absence of disturbance
caused by difference tones of the several orders; or, alternatively,
to their reinforcement of the lower tone of an interval, or of its
lower octave. `This relative intensification of the lowest difference
tone is the greater, the more consonant the primary interval, the
simpler its vibration ratio, the fewer difference tones other than
the characteristic one are still possible; stated otherwise: the
more tones coincide in it.' [31] It follows from his calculations
that `the phenomena, due to differene tones, are in exact
correspondence
to the degrees of consonance and dissonance. The most perfect
consonances (unisone and octave) have no distinct difference
consonance, the larger the number of difference-tones and the
greater the consequent danger of mutual disturbance.' [32]
"We need not follow here the intricate mathematical
constructions by which Krueger carries out difference tones
up to five orders to make explicit how they determine consonance
response. Stumpf criticizes both the results and the assumptions
involved. He shows that by Krueger's formula, such frequency
combinations as 800 and 1100 cycles, in ratio 8:11, would not
show disturbances of the type Krueger identifies as the source
of dissonance. `Even triads can be constituted in which all three
tones indubitably are mutually dissonant, without the difference
tones arising according to Krueger's rules producing more than
the mildest beats or disturbances.' [33] Thus a combination of
tones in the ratios 3:7:10:17:27 would turn out not to be
dissonant by Krueger's definition. Finally, Stumpf argues that
to attribute consonance to an agreement among difference tones and
their progenitors requires a prior assumption of just what
constitutes consonant agreement, and that is the very issue
involved. `Always, therefore, the existence and operation of
consonance must already be grounded somehow upon other
characteristics.' [34] The awkwardness of Hindemith's manipulation
of `natural' difference tone roots [35] is due in some measure to
a similar rationalizing assumption of what was to be demonstrated.
Experimental evidence shows further that the sensing of combination
tones is very much dependent upon the loudness of the primary tones,
[36] so that the theory would necessarily have to posit a variation
of consonance and dissonance response as a function of loudness,
which is hardly tenable, and on the other hand would be unable
to account for any such response below a loudness level of about
42 db above threshold, at which combination tones become barely
distinguishable.
"While the sensory phenomena of combination tones do not
appear to explain the perception of consonance, they may well
affect the euphonious properties of isolated sonorities. [37]
`Now in the defective intonation of the perfect consonances, at
least the octave and the fifth, difference tones actually play
a role.' [38] Thus from the known characteristics, difference
tones are useful to practical judgments of precision in the
intonation of double stops, just as Tartini found initially.
"They do not count for the perception of consonance." [Cazden,
Norman. "Sensory Theories of Musical Consonance," Journal of
Aesthetics and Art Criticism, Vol. 20, pp. 301-319, 1962]

"The influence of difference tones on consonance perception
also is not very probable in view of the data reproduced in
Figs. 1 and 2. Moreover, experiments of one of the authors on
the audibility of combination tones [21] showed that the nonlinear
distortion of the hearing organ is so small that it cannot be
regarded as a constitutive base for consonance." [Plomp, R.
and W.J.M. Levelt, "Tonal consonance and critical bandwidth," Journal
of the Acoustical Society of America, Vol. 38, 1965, pp. 548-568.]

The second big problem with Boomsliter & Creel's theory
of extended reference is that it boils down to unsupported personal
preference.
In the quote from B&C above, you can hear that B&C merely
claim that the extended reference version of The Marselleise
"sounds more electrifying," but they provide no proof of it.
This is important, because when we examine the procedure
B&C used to produce their listening tests, we find it's
critically flawed.
Boomsliter and Creel did not use a double-blind experimental
procedure.
What I am saying here is that Boomsliter & Creel did not
provide listeners with samples of melodies which neither the
listener nor the experimenters to be extended reference or
12-equal.
Instead, the "experimental procedure" consisted of B&C
FIRST getting a small group of musicians to produce melodies
on a monochord, then using a "by guess and by God" method
which can only be termed "perceptions verging on the extrasensory"
to somehow guess the alleged "extended reference" pitches
produced by that group of musicians on the monochord...
And finally B&C built a "search organ" with a bunch
of different JI pitches for each note.
A variety of listeners were then asked to use the search
organ to produce what sounded to them like the "best" or
"most effective" or "most musical" version of the melody.

Well, you can see the whole plaethora of problems with
Boomsliter & Creel's test procedure.
First, since B&C present while the listener used the
search organ, they could have influenced hi/r without
meaning to.
Second, the listener being tested always knew which
pitches on the search organ he was playing, so there was
a vast opportunity for bias, depending on the test subject's
innate theoretical bias. I.e., if s/he believed in JI
as the basis of music you'd naturally expect the test
subject to search for various JI pitches on the search
organ and use 'em.
Third, the test subjects were ONLY given a choice
of pitches already chosen on the search organ by Boomsliter
& Creel, which intolerably and unacceptably biases the
entire experiment. Shoot, I can "prove" that all listeners
prefer 12 equal for melodies if you allow me to select
the pitches used on a search organ. For that matter, by
appropriate fiddling and twiddling with the source set
of pitches, I can probably bias the experiment in such
a way that listeners prefer any ET or JI system, merely
by tainting the search organ by deliberately excluding
some pitches and deliberately including others for each
musical note. This is the classic error of observational
selection.
Fourth, the procedure by which B&C boiled down
the conflicting and imprecise pitches sounded on the
monochord to a limited set of "extended reference" pitches
can only be described as witchcraft. There is no empirical
basis for it, no proof that B&C "extended reference" pitches
are actually related to the pitches the test subjects played
on the monochord, and worst of all -- monochords built
without a very tough steel or aluminum pipe running down
under the box are notoriously imprecise, because the high
string tension will cause the box of the monochord to
flex slightly and change the string's pitch when a
listener stops off the pitch. We don't know how well
B&C monochord was built, but it's safe to say it wasn't
as precise as the world-class monochord's Bill Colvig
builds. Thus all of B&C monochord measurements are
strongly suspect to start with, and since these data
points provide the starting pitches for the search organ,
the whole procedure is hopelessly tainted from the outset.
Fifth, lots of experiments show that performers
tend to compress musical intervals smaller than a
minor third and expand musical intervals larger than a
minor third. This is probably what the test subjects were
doing, and they merely chose the nearest available JI
pitches even though JI has nothing to do with what was
going on.
Sixth, B&C did not provide an adequate set of
alternatives for listeners. They should have provided
12 equal AND extended reference pitches AND a whole
set of non-just non-equal-tempered pitches. But B&C
couldn't do that because their search organ was
very limited in the total number of alternate pitches
it could allow for each musical notes. To put it bluntly,
the search organ was a piss poor idea from the outset
because you can only have so many keys on any keyboard-
based musical instrument.

This is why I stated that

> There is not one shred of evidence for the false claim that
> singers or string players "naturally play in just intonation,"
> and there much evidence against the musical old wive's tale that
> solo performers "naturally play in JI." -- mclaren

As we can now discern quite clearly, Boomsliter and Creel
never tested what performers "naturally" do -- instead, B&C
forced performers to choose from a limited set of pitches
available on their search organ, and these pitches came
out of the brains of Boomsliter & Creel with no hard
evidence to back 'em up.
Thus, we have no idea what B&C's test subjects would
do under "natural" conditions, since the search organ was
forced upon them like a Procrustean bed.

Much more reliable tests of what performers do "naturally,"
that is, in actual performance are (logically enough)
obtained from measurements of the actual pitches played
by actual performers during actual musical performers.
Such measurements systematically disprove B&C's claims.

Lastly, we may note that Boomsliter & Creel's approach
is a typical Western mathematical reductionist approach
to music. First, the issue to be studied is stripped of
its complexity by removing it from the real world (instead
of playing free pitches, the performer is forced to choose
from among the predigested pitches available on the search
organ). Then the issue to be studied is boiled down
further to a mathematical skeleton (i.e., B&C's extended
reference scheme). The final stage occurs when the
researcher declares the original rich complexity of
the real intonation in real music in the real world
irrelevant, and substitutes the dessicated mathematical
skeleton for the rich living original as the "real"
version.
This typical Western reductionist approach to music
fails and fails badly because it wholly ignores the
overwhelming importance of culture and emotion to
music, as opposed to math and physics (viz., extended
reference difference tones as dreamed up by B&C):

"[Much Western music theory] seems to suggest that it
ought to be possible to create a way of measuring or assessing
musical compositions...related, in some way or another, to
the compositions' `musicalness'--the degree to which we think
it's good or interesting music.
"This seems like a project that might not succeed...because...
music is actually a contingent combination of sounds whose
emotional resonances are entirely dependent on the audience's
personal and shared histories as listeners. By `contingent' I
mean that it could have been otherwise. Music didn't have to
consist of the elements and structures that it happens to
consist of -- and indeed it consists of quite other ones in
other cultures, as anyone attending a concert of classical
Thai music will soon realize. (I once attended such a concert
in Bangkok that was totally mystifying. I could see that
the audience was utterly enraptured, swooning at moments of
apparently overwhelming emotional beauty that made no impression
on me whatsoever; not only that, I couldn't distinguish them
from any other moments in the piece. (..) I had no cultural
background against which to set this particular adventure.)
"(..) The reason we can be moved by a single voice singing
a simple song is clearly not because it has internal complexity,
but because we do: we don't just hear sounds, but hosts of
associations and historical, social and cultural undertones.
A single voice is powerful to us because it is different in
particular ways from most of our other musical experiences,
and because this particular voice is different in particular
ways from other voices we've heard. Aesthetically, what we
respond to are differences, not `absolutes.' That is why
it is possible for a group of Lebanese to become ecstatic
about the way Fairuz turns a phrase, while a non-aficionado
of Arabic music will fail to get the point at all. What
those Arab listeners are responding to is how she does
it differently. So when they hear it, they hear it against
an enormous repertoire of other possible ways of doing
it, of other possible emotional resonances and associations.
"This is a very important cultural issue, since it sets
up a major division between two different ways of looking
at cultural objects. In the traditional classical view,
art-objects are containers of some kind of aesthetic value.
In this view, the value was put into them by the artist
(who got it from God) and it now radiates back out to
those who behold it. It was thus that missionaries played
gramophone records of Bach to Africans with the expectation
that it would civilize them; they would somehow be enriched
by the flood of goodness washing over them. We now see the
arrogance of this assumption, but I think few people
understand what is really wrong-headed about it...culture
objects have no notable identity outside of that that which
we confer on them. Their `value' is entirely a product of
the interaction that we have with them." [Eno, Brian, "Resonant
Complexity," The Whole Earth Review, 1995, pg. 42]

So given the huge number of serious problems with
B&C's whole system of testing listeners, and given the
large number of multiple independent experiments I
have cited which contadict B&C's results, it's safe
to say that we can go with the experimental results which
are most repeated and also have the fewest methodological
problems. That means the 5 experiments I cited win out.
No one has ever repeated Boomsliter & Creel's experiment
using modern equipment.
So that one experiment conducted by Boomsliter & Creels
seems like a very slender reed to hang your entire
set of ideas about music from...particularly when there
are so many other more solid experiments I have cited,
which have been independently confirmed, and which all
agree in contradicting Boomsliter & Creel.

When I wrote

> However, if Kraig means to point out that string
> players and singers adjust their pitch in complicated ways (not
> according to JI, or any known ET, however) while playing, there's
> plenty of evidence for that.

Kaig replied

"As I stated before the question far exceeds what can be
tested in a laboratory."

But Kraig, the problem with that claim is that you are
essentially saying "my hypothesis is untestable."
An untestable hypothesis is meaningless.
You can't have it both ways. Either the hypothesis posits
real effects in the real world...in which case it can be
tested. Or, you may claim things that have no actual effects
in the real world -- for instance, the so-called "psychic healer"
who claimed he could make "healing energy" flow through the internet.
But could anyone measure the so-called "healing energy"?
Of course not. Since it had no discernible physical
effects, it conveniently couldn't be measured, and his
scam couldn't be detected...or so he thought, until the Attorney
General of the state of Delaware hauled him in an indicted the
alleged psychic healer for interstate wire fraud.

Kraig further averred:

"I just use my ear and can hear these things going on.
According to you all this is the arbitary wandering of
people who can't hear."

No, Kraig, that's not what I said. I said there is
no evidence of any comprehensible plan to these intonational
vaiants, a plan of the kind John deLaubenfels tried to
embody in a computer program.
Notice that I don't claim there isn't some kind of
system to the intonational variants, just that whatever
it might be we don't find it comprehensible.
All that means is that the process by which we select
these intonational variants in real melodies in the real
world is very very V*E*R*Y complex. It's so complex we
can't understand it, even while we're doing it.
The human brain is stupefyingly sophisticated, and
we constantly do things we can't explain. For example,
balancing on one leg. Try to get a robot to do that.
How about riding your bike without touching the handlebars...
most people can do that for maybe a minute or so. Try to
get a computer to control all the variables in that one.
The computer would melt down.
How about catching a fly ball in the outfield? Want
to try to write a computer program to do that? If the
sun's in your eyes? And allyou've got in the input from
2 visual sensors (they're called eyeballs)?
Good luck.
The idea that our intonational variants boil down
to something as cartoonish and trivially simple as B&C's
"extended reference" deeply insults the complexity of
the human brain, in my opinion.

When I cited a quote which pointed out that

> However, there is no generally
> accepted rationale for how it should be done; people have these
> adjustemnts `by ear.' Empirical studies have not, as yet, revealed
> the basis of the practice. But they have demonstrated that no
> explanation in terms of a fixed intervallic scale will match
> the facts;

Kraig Grady responded:

"That is because scientists have little or no understanding
of what goes on in a work of art. They don't know what it is
they are looking at in the first place."

Once again, this boils down to the claim "the hypothesis
is untestable."
But once again, Kraig, you can't have it both ways. EITHER
Boomsliter & Creel's hypothesis involves testable effects, in
which case the other psychoacoustic experiments must be taken
into account, OR Boomsliter & Creel's hypothesis involves
effects which are not testable... In which case B&C's results
are worthless.
If you want to use the language of science, as B&C do
with their mathematics and their statistics, you must use
the methods of science. One or the other. You can't have
it both ways.

When I cited Nicholas Cook's statement that:

> violinists do not play in just intonation, or
> mean-tone intonation, or Pythagorean intonation, any more than
> they play in equal temperament. In other words, they determine
> their intonation in accordance with the individual musical
> context." [Cook, Nicholas. "Music, Imagination, and Culture,"
> Clarendon Press: Oxford, 1990, pg. 236]

Kraig replied:

"If you look at an entire sample that is what you will see
unless you can take into account the intent of the music
at each micropoint."

That seems like a valid point. There needs to be a lot
of work done on this issue. Of course, how do you define
a "micropoint"? Where do you draw the line between phrases
or sections in a melody as performed in the real world so
that we can extract the supposed JI segments as they move
from one extended reference point to another?
We need to have some provable testable way of doing this...
otherwise, the entire hypothesis is unprovable and therefore
unfalisifiable, and consequently all Boomsliter & Creel's
talk about math and difference tones is meaningless.

When I cited a quote which said:

> The audience, which included experienced
> musicians,
> had not noticed them at all." [Zuckerkandl, Victor. "Sound and
> Symbol,"
> Pantheon Books: New York, 1956, pp. 79-81]

Kraig Grady replied

"Of course we don't notice them because they are a part of
the language that has taken thousands of years to build up. It
is subconciously assumed."

The subconscious is always the last refuge of a failed
musical theory, since conveniently enough we can never prove
or disprove the existence of supposed "subsconcious" perceptual
processes.
Once again, Kraig, either B&C's theory can be tested, or
it can't. If it can't (as you try to suggest above by claiming
it's all subconscious), then it uses the language of science
without using the methods of science and is accordingly nothing
more than a musical version of uflology or astrology.

When I cited the quote:

> "This experimental evidence...does not support
> the classical view, still recently promoted by
> Boomsliter and Creel, that harmony is based on
> frequency ratio itself; that the ear might be
> provided with some sort of frequency-ratio detector.
> (..) The experiment does not support the hypothesis
> that the human ear is provided with some sort of
> frequency-ratio detector." [Plomp, R., W. A.
> Wagenaar and A.M.Mimpen, "Musical Interval Recognition
> with Simultaneous Tones," Acustica, Vol. 29, 1973,
> pp. 101-106]

Kraig Grady replied:

"Then where did the major chord come from. People
were adding thirds to chords when all the theory was
telling them it was dissonant."

The major chord in Western music came from culture
and ideology, Kraig. Our major triad was not created
in order to conform to natural laws which arise from
the harmonic series -- just the opposite, a whole
set of superstitions about supposed "natural laws"
in music allegedly arising from the harmonic series
forced us to create the major triad to conform with
all that ideology.
The proof is simple an straightforward. Many
other cultures use harmonic-series instruments,
but none of them (NOT ONE!) ever produced the
major triad. Not even India.
The major triad *only* arose in Western Europe...
because only in Western Europe did the Greek harmonic
series small integer ideology take hold, and force
the development of a whole superstructure of musical
practice based on those Greek superstitions.

More broadly, Kraig's claim that harmony in
Western music occurred by accretion is the old
msuical fairy tale of "the evolution of harmony"
which supposedly occurs by climbing the members
of the harmonic series...first the octave, then
the perfect fifth, then the major third, then the
7th, etc.
This evolutionary myth of Western harmony is
a 19th century supersition. It has been debunked
and no serious musical historian or musicologist
in the West believes in it today:

"In 1885, Alexander John Ellis, the man who
is generlaly regarded as the father of ethno-
musicology, demonstrated that musical scales are
not natural but highly artificial, and that laws
of acoustics may be irrelevant in the human
organization of sound. In spite of his timely
warning, there are still some...who write as if it
were their task to fill in the gaps of musical history
by describing the musical styles of exotic cultures.
Even if they do not say it in so many words, their
techniques of analysis betray affection for an
evolutionary veiew of music. Musical styles cannot
be heard as stages in the evolution of music,
as judged in terms of one particular civilization's
concepts ofmusic. Each style has its own history,
and its present state represents only one stage
of its own development; this may have followed a
separate and unique course, although its surface
patterns may suggest contacts with other styles.
"(..) If our music historian gives the Venda
the credit of producing the heptatonic scale
thesmelves and doesnot assume that they must have
borrowed it from a `higher' culture, I suspect
that he might describe theirmusic as being in a
stage of transition from pentatonic to heptatonic
music -- a fascinating example of musical evolution
in action! The only trouble about such description
is that social and culture evidence contradicts it.
For example, the Venda used a heptatonic xylophone
and petatonic reed pipes long before they adopted
the pentatonic reed pipes of their southern neighbors,
the Pedi, who in turn say they adopted and adapted the
heptatonic reed pipe msuic of the Venda. According
to evolutionary theires of music history,
the Venda should be going backward -- like the Chinese,
who selected a pentaotnic scale for their msuic
although they knew had used `bigger and better' scales!"
[Blacking, John, "How Musical is Man?" University of
Washington Press: Seattle, 1973, pp. 56-57]

The old wive's tale of the supposed "evolution"
of Western harmony is just as mythical and just
as faulty as old wive's tales about the alleged
"evolution" of scales. If we look at the history
of Western music, we find jumps and discontinuous
moves back and forth in harmony -- in the
10th and 11th century, unisons and major seconds.
Then a jump to fauxbourdon. Then a jump up in
complexity to polyphony which allows minor
seconds as passing tones as perfect fourths
and perfect fifths during the high Gothic
period...then a jump back to simplicity with
minor seconds and p4ths strongly discouraged
as harmonic intervals, but majr 3rds encouraged
during the Renaissance.
Then we get 7th chords in the Baroque, but
fewer 7th and dminished and augmented chords
and less chromatic passing tones in the Classical
period. Then dim 7th chords in the late Romantic
period. Then a jump backward to simple intervals
in the early 20th century, with parallel p4ths
allowed in the music of Hindemith and Stravinsky.
Then a jump forward to complex 11th and 13th chords
in jazz by mid 20th century. Then a jump backward
to triadic simlicityin minimalist music circa
the 1960s.
There is no "evolution" of harmony by climbing
the harmonic series. It's a myth.
Music is not a living organism, it doesn't
"evolve." It just changes -- unpredictably.

When I cited a quote which pointed out:

> "An experiment on the perception of melodic
> intervals by musically untrained observers showed
> no evidence for the existence of `natural' categories
> for musical intervals." [Burns, E. M. and W. D. Ward,
> "Categorical Perception--Phenomenon or Epiphenomenon:
> Evidence from experiments in the perception of melodic
> musical intervals," J. Acoust. Soc. Am., Vol. 63, No. 2,
> 1978, pp. 456-468]

Kraig Grady replied:

"Basically all this data does nothing but to say they can't
find any pattern in it. So we are to turn around and become
patternless, wandering amoebae because some overpaid cartmaker
says that is what we are doing."

This is the classic fallacy of argument by extremes.
Either we must go to one extreme or the other, with nothing
in the middle. "If we don't tattoo barcodes on everyone's
forehead, there'll be anarchy in the streets!" No, there
is a broad middle ground between the 2 extremes.
As I pointed out earlier, simlpy because we don't know
what the pattern is doesn't mean we must "turn around and
become patternless."
The obvious conclusion is that we should instead throw
out simplistic baby-math delusions like Boomsliter & Creel's
cartoonish scheme and instead make music using our intuition
and our experience and our emotions.

And when I cited a quote to the effect that:

> "Despite numerological theories going back at least to
> Leibnitz (see Revesz, 1954, p.50), to my knowledge no
> psychologically plausible mechanism has been offered to
> explain how a listener determines that two tones achieve
> or approximate a simple frequency ratio -- particularly
> when the tones are pure sinusoids and are presented only
> successively." [Shephard, Roger, "Structural Representations
> of Musical Pitch," in "The Psychology of Music," ed. Diana
> Deutsch: Academic Press Inc., New York: 1982, pg. 347.]

Kraig Grady responded:

"Gee I can think of a myriad of individuals that tune JI
by ear."

Kraig, music is not the same thing as tuning. If it were,
audiences would go into a concert hall and listen to the
orcehstra tune up and then applaud and leave and congratulate
each other on how beautiful the music was.
No one does that.
Tuning is a completely different process from making music.

Kraig Grady went on to claim:

"according to all this scintific data on the perception of pitch ,
I see none where listeners attempt to produce an ET like 17 or 22. The
result would be far greater discrpancies than you will get from JI
If the tolerance is so great it seems to me that any mood in an ET
could be done with a constant structure of a JI to a close
approximation."

First, the reason there aren't experiments which test listeners
against 17 equal or 22 equal is once again ideology. The JI ideology
is marinated into our culture, soaked into our bones. It's a Western
Europe/America monomania, not found in any other culture.
So of course the listening tests in our culture deal exclusively
with comparing 12 equal to JI -- since the musical ideology of our
culture obseesses over JI. That's my whole point. The ideology
bends and warps our thinking so that we deluded ourselves into
fantasizing that the choice is ONLY between JI or 12. But it isn't.

As for Kraig's claim that "any mood in an ET could be done with
a constant structure of a JI to a close approximation..."
Yes, probably it can, Kraig. But the reverse is equally true.
Any JI limit can be very closely approximated by some sufficiently
large number of equal tones per octave.
So what? All that proves is that at the extremes, JI tunings
can be approximated by ET tunings, and ET tunings can be approximated
by high JI limits.
Every competent musician already knows that. If you push ETs far
enough, you can get 'em to sound like JI's, and if you push the
JI limit high enough you can get it to sound like an ET, and if
you select sufficiently gapped ETs or harmonic series you can
get 'em to sound like any inharmonic series.
All 3 classes of tunings blend into one another at the extremes.

When I pointed out:

> Musicians use various equal divisions
> of the octave for exactly the same reason they use various
> JI tunings...because each tuning has its own remarkable
> musically useful "sound" or "mood" or "sonic fingerprint."

Kraig replied:

"These scales only exist because of the computer and they are the
easiest things to do on them. They are not something that can be tuned
by ear and exstemely difficult with even a monchord."

Kraig, that's just not true. Middle East musicians have been
using 17 equal and 22 equal for quite a while -- longer before
computers appeared on the scene. In Europe, Bonsanquet and
Ogolevets produced many different ETs. Bosanquet had an
harmonium tuned to 22 equal and he discussed it in one of
his articles, while Ogolevets had harmoniums tuned to 17 equal
adn 29 equal. 19 equal was downright common, appearing
starting in 1835 (Joe Monzo has the British pamphlet discussing
19 equal published in that year) and reappearing at regular
intervals. I just came across an article in a Congress of
Musicology in 1911 in which Melchior Sachs dragged a 19-equal
harmonium into the lecture hall and played excerpts from
Bach in 12 equal and 19 equal.
So Kraig, musical use of the ETs has been going on long
long before computers.
Moreover, I don't think you have used a digital synthesizer
very much, because you will quickly discover that on a digital
synth ALL tunings are equally easy to produce. Fire up SCALA
and you can instantly tune your digital synth to any tuning
whether JI or ET or NJ NET. It's equally simple to tune
to any of these systems, Kraig, because in a digital synth
(effectively a dedicated computer) the tunings are just
numbers.
Perhaps you were thinking of analog synthesizers. The
old analog synths were strongly biased toward producing ETs,
because on the old analog synths the reistive ladder used
identical value resistors for each key. Thus you could get
any ET very easily by inserting a pot on the keyboard
as a voltage divider. However, on the old analog synths
you could only get JI pitches by unsoldering and replacing
the resistors for each key, so that made it harder to get
JI.
But Kraig, the old analog synths are long gone. No
synthesizer company manufactures analog synths any more as
MIDI keyboards -- all MIDI keyboards today are digital
synths, and therefore they're all equally easy to tune
to *any* type of intonation, JI or ET or NJ NET.

The claim that ETs are difficult to tune with a
monochord is just not true, Kraig. Ivor Darreg produced
many many different fret charts for guitars, and these
are nothing but ways of marking off a monochord with
4 strings.
All you have to do is mark off the lines on the
monochord (which are very easily calculated, it's
just 1/x where x is the number of equal tones/octave)
and then sound them. It's trivial.

> The claim that "JI is at least a very close
> appoximation to things in nature" is largely false.

"Listen to Tuvans sing. The fact is that then we can
tune it by ear and if it doesn't exist in nature how are
we tuning it!"

Kraig, the Tuvan throat-singers are not operating
exclusively according to the laws of nature. Tuvans
are humans. Humans do what they do because of culture,
not because natural laws force them to behave that
way. Tuvan chosoe to sing in one way, while Balinese
in their kacapi music choose to sing in a completely
different way. Thai vocalists and Vietnamese vocalists
sing a totally different way.
Since we are talking about people, Kraig, their
behavior and their actions and the pitches they produce
are determined by culture, not by the physical laws of
nature.

When I pointed out:

> In nature, essentially ALL vibrating objects produce
> INHARMONIC series of vibrations, forming non-just
> non-equal-tempered tunings. Almost every type of
> vibrating object, whether it is a glass or a spoon
> or a fork or a tire iron or wooden board or a CD
> case or champagne glass or doorknob or a metal
> bracelet or a ceramic tile...ALL of these types
> of vibrating objects produce INHARMONIC series.

Kraig Grady claimed:

"Add resonators at harmonic degrees and you will
percieve a harmonic series."

Kraig, that's just not true. By filing and tweaking
some metal bars you can get vague approximations of
parts of a harmonic series, but there are still plenty
of inharmonic tones.

When I pointed out:

> Only a microscopic minority of exotic and exceptional
> vibrating objects produce HARMONIC series -- namely,
> objects which vibrate in one dimension only. This
> set of vibrating objects is so small that it boils
> down to 2 exotic types *never* found in nature: thin taut
> strings and hollow tubes with tone holes.

Kraig Grady replied:

"Our basic instruments or the ones that human beings
have chosen to make instruments out of."

When you say "our," Kraig youare limiting yourself
to Europe/America.
Throughout the world, most of the musical instruments
used generate inharmonic timbres. Lithophones, metallophones,
drums, xylophones, wood blocks, you name it -- these are
the instruments most cultures in the world use. Almost
anywhere in the third world most of the music is characterized
by cymbals and whirlies and devil chasers and drums and
chimes. Brass instruments and violins are very rare,
guitar-like instruments only slightly less so.

When I wrote:

> As far as dealing with long meters, counting
> does not involve math -- you can count the beats
> in a long meter by beating your fist and after
> a while you will simply get used to the downbeat.

Kraig Grady pointed out:

"In Ethnomusicaology they have a system of measurement
equivalent to cents for rhythms. All the tests find the
same thing it does with pitch. The beats are not equal nor
are the subdivions of even the simpliest of rhythm patterns.
So you should encourge everyone to dispel the even
beat because it doen't exist."

Yes! Exactly!
Thank you for pointing that out, Kraig.
Quantization is death. Kill quantization. They
should take quantization out of every MIDI sequencer,
purge it, destroy it. Mark it with big BIOHAZARD
symbols. Get rid of it. Never use quantization in your
MIDI music, it will destroy everything. A regular beat
is the neutron bomb of music. The music is destroyed
but the notes remain standing. If you have a metronome,
take an axe to it. Burn the bloody thing. Never ever
practice according to a metronome. It will destroy your
musical performance.
Regular even beats are the kiss of death.

When I pointed out:

> Once your muscle memory takes over in musical
> peformance, trying to count makes you stumble and
> fumble. You have to *feel* where the beat is,
> not count your way to it.
> This applies in my experience also with
> complex polyrhythms, which Bill Wesley has taught
> me to produce on his mbira. (Bill can teach anyone
> complex polyrhythms, and quickly too.) Counting gets in
> the way. You have to do it until you feel it. Soon
> you just feel whether the downbeat it...you
> feel the polyrhythm as a single thing, not
> some complicated piece of math.

Kraig Grady claimed:

"You can feel it because we have sinple relationships
ingrained as gestalts. If it wasn't there, how could you
feel it?"

By using the wonderfully sophisticated and complex
blob of goo inside your skull, 90% of whose operations
you are never aware of.
Kraig, we can "feel" when we are in the right position
to catch a fly ball in baseball, but the math is hideously
complex. There are no simple relationships, we "feel"
this stuff and seem to do it "naturally" because our
brains are so fabulously sophisticated.
The entire failure of modern AI and the brick wall
modern vision researchers have hit over the last 30
years proves this. We "feel" it is very "natural" to
recognize a cat from any angle, in any lighting condition...
but no computer can come close to doing it. The math
is so stupefyingly hard the computer would melt down.
We do it because our brains are the end result of
4 billion years of continuous Darwinian melee in which
only the cleverest critters survived.
---------
--mclaren

Boomsliter & Creel

🔗xed@...

🔗Kraig Grady <kraiggrady@...>

🔗nanom3@...