Yahoo Tuning Groups Ultimate Backup metatuning Writing down a musical score has nothing to do with math

In Message 7131, Joe Monzo claimed:

"even the act of writing down music on
a staff is a mathematical act in that the lines and
spaces of the staff represent discrete quantizations
of the pitch-continuum, and the regular way of notating
rhythm is certainly math-based."

This claim is so foolishly false it's tantamount
to the claim I once heard that "fire is red
because it picks up the color of the sunset."

Joe Monzo's claim about the act of writing
down music being a mathematical act is so obviously
wrong in so many ways, on so many levels,
that it's hard to know where to begin to
debunk a claim so outlandishly incorrect.

Discrete quantizations of the pitch continuum
do not require math to write down or to pereive --
that's known as catregorical perception, Joe,
a phenomenon well known in cognitive psychology.
Catregorical perception is a perception of kind,
and has nothing to do with the perceiver doing
math. Writing down different categories of pitch
also has nothing to do with math -- it's merely a
matter of categorically perceiving an E as sounding
different from an F. That's not math...and, as cognitive
science has shown from studies of categorical
perception, it has absolutely nothing to do
with math.

Moreover, musical scores are based on SHAPE. Look
at the start of medieval Western music notation --
its pure shape. No barlines. No staff lines
except for one line to indicate middle C. No
time signature. Only pure shape, the
neumes.

This is as we would expect, since
cognitive neuroscience experiments
prove that listeners do not bring to mind
melodies as collections of notes but
as gestalt contours.

"At first, the idea of contour being
an important attribute of melody
seems counterintuitive. Contour is a
relatively gross characterization of
a song's identity. However, its utility
has been shown in laboratory experiments.
There is evidence that for melodies we
do not know well (such as melody we
have heard only a few times), the
contour is remembered better than the
actual intervals (Massaro, Kallman and
Kelly 1980). (..) Infants respond to
contour before they respond to melody..."
[Levitin, Daniel J., "Memory For Musical
Attributes," in Music, Cognition and
Computerized Sound: An Introduction To
Psychoacoustics ed. Perry R. Cook,
The MIT Press: Cambridge, 1999, pp.
215-216]

Shapes and contours convey emotion
because the right brain, which processes
shapes, is the brain hemisphere which
is also responsible for emotional
association. The left brian is primarily
responsible for logical rational processing
of hte kind associated with modus ponens
formulations and mathematics. Thus, melodies
carry an emotional charge because theyr
get processes primarily as contours by
the right brain. If Joe Monzo's claim that
"the act of writing down amusical score
is...a mathematical act" then music would
convey no emotion. But music does convey
emotion...precisely because musical scores
primarily convey shapes of melodies, and
because humans perceive melodies as
contonours, not as sets of numbers.

Moreover, because shapes get
processed wholistically they
are processed almost instant-
aneously, whereas numbers must
be processed slowly, bit by bit,
with the left brain hemisphere.
This exlains, for example, why
it takes humans long minutes to
figure out that a complex fraction
is larger than some other complex
fraction, while we can tell at a
glance whether a complex visual figure
filled with solid color is larger
than another complex visual figure.
Similarly we can tell almost instantly
that a contour made from a complex
line is rougher or smoother than
another contour made from another
complex line, while we can tell
almost nothing at all about a set
of integer fractions just by glancing
at 'em. This division between wholistic
emotional processing of sensory input and
step-by-step abstract unemotional processing
of numbers is so basic and so well-defined
in the human brain that the mere fact
anyone could take seriously Joe Monzo's
absurd claim that the step-by-step
abstract conceptual processing of
numbers plays any signfiicant part
in writing or reading a musical score is
a devastating commentary on the gross
ignorance of cognitive neuroscience
and the shocking ignorance of
modern cognitive psychology typical
of the members of the Alternative
Lying List.

We can prove this obvious and
basic fact of human cognition
simply and easily. Which of these
representations of a melody is
more easily recognizable -- the
set of numbers, or the symbols
indicating the shape of the
melody?

13^4/(3*5*7) 5^6/(29*7^2) 23^4/(3*5*11*53) 5^6/(29*7^2)
13^4/(3*5*7)

*
* *
* *

Countless scientific studies have
been done on this subject and they
always show the same result.

Studies also show that when we hear
melodies, our non-mathematical
non-logical right brain hemispheres
light up on PET scans -- the primary
activity in recognizing melodies (unless
we are very very very familiar with
the melody) is right-brain contour
recognition, not activity in the left
mathematically-oriented brain hemisphere.

This also explains why ratio space is
so completely useless for music. It is
just as impossibly difficult to figure
out what pitch a coordinate in ratio
space represents as it is to figure
out what the pitches of those ratios
cited above were. By contrast, it's
easy and near-instantaneous to figure
out which pitches are which, by looking
at the visual shape. Ratio space is
useless, worthless, pointles, valueless,
senseless and perversely foolish because
it completely contradicts the way the
human brain operates where perceiving
music. 50 years of cognitive neuroscience
research completely contradict every
assumption behind the use of ratio space.
This kind of shocking arrogance and
ignorance and icnompetence is typical,
however, for the members of the Alternative
Lying List.

So the claim that musical scores are
based on math or involve any kind of
math for the placement or recognition
of musical pitches is flatly false. It's
entirely a matter of shape and categorical
perception, none of which has anything to
do with math.

What about musical rhythms?

Once again, shape and the visual density
of filled areas is used to denote
rhythms -- not math. The beaming of musical
notes is a matter of pure shape, not numbers.
The entire logic behin multiple beams
on notes is that the eye recognizes
the difference as increased density
of color (black), not by counting the
beams. And in fact it's simple and easy
to prove that too many beams produce
confusion and chaos in performers,
because they must then count the beams.

At an absurdly slow tempo, for example,
it would be necessary to beam notes
with 7 or 8 or 10 or 15 beams to
indicate 1024th notes or 32768th notes,
but no composer does this. The reason
no composer does this is not because
it's impossible to use a very very
slow tempo (metronomose marking 0.00001,
say) and incredibly small note-values.
No composer does this beyond 4 note-
beams because it rapidly becomes impossible
to recognize at a glance how many beams
there are on a note when you get to more
than 4 or so. And this is due to the
well-known subitizing limit on immediate
visual attention, which once again has
been studied exhaustively and cocumented
in detail in cognitive psychology. Beyond
about 4 items, our immediate perception
shifts to "many" because the human brain
has a limited bandwidth for its input
and fo rits short-term perceptual cache
memory.

Barlines and staff lines are clearly not
amthematical since staff lines leave
out important information. If an alien
from Mars looked at staff lines on
a Western musical score, the aline would
conclude we use a 7 tone equal system
A B C D E F G. There is no overt indication
in the staff line system ofnotation that
any of these steps are unequal. That is
not the way a mathematical system works.
That is the way a right-brain-oriented shape-
based system of traditional Western musical
notation works, and it has nothing to
do with math, it's entirely a matter of
foreknowledge on the part of the performer
and composer (where the half-steps are in
the 7 note scale) and visual shape recognition
(is the note head black or white? Is the
note-group beamed or not? ) and categorical
perception (telling E from C).

Barlines totally fail as mathematical
representations, for the size of a measure
of music stretches and shrinks depending
on the number of notes -- this is quite anti-
mathematical, for our perception of time
varies radically. If the barring of measures
truly were "a mathematical act," as Joe Monzo
claims, then writing down measures would be
a simple matter of math: every measure the
same size. But it's not! The size of each
measure varies fluidly, just as our sense of
time varies whil listening, depending on whether
a lot is going on in a measure or very little.
In a musical score full of nothing but whole
notes at a slow tempo each measure is
very short (to conserve manuscript paper)
but to the listener the time passes very
slowly and seems long because almost
nothing is happening. But the tiny
width of the measures gives no
indication of this. Once again, mathematics
fails completely as an analogy for what the
act of writing down a musical score, or of
listening to a piece of music notated in
a musical score.

Clearly, Joe Monzo's claim that math
has a connection with musical notation
fails completely. It is exactly the
opposite of the truth.

The only element of Western musical
notation in which math could even
remotely be said to enter in is
the notation of n-tuplets, and in
time signatures. But a time
signature is a feel, not a number --
anyone who plays music knows that
you cannot "get" how to play a
time signature by doing math,
you must practice it until you
get the feel of the rhythm. This
derives from the well known fact
that musical rhythm is based on
bodily movement -- not on mathematical
operations processed in the
forebrain. If this were not the
case, musicians could perform
complex meters perfectly the
first time just by doing math in
their heads. But they can't.
Musicians must practice and get
the physical _feel_ of a complex
meter before they can perform
it correctly.

Clearly the numerals sometimes used
in Western musical scores are merely
place-keepers, names for feelings or
bodily rhythms, not actual mathematical
symbols -- like the numbers on houses,
these are place markers, not math.
It makes no sense to speak "The
house at 2270 Elm Lane divided by
the house at 1905 Maple Street" just
as it makes no sense to try to do math
based on music, or to try to claim that
the act of writing down a musical score
is mathematical, and for the same obvious
reason. In those rare instances when
numbers are used in music, they're used as
mere names, nothing more than place
markers, like the numbers on a theater
ticket that tell you where to sit, or
the numbers in a parking garage that
let you know where your car is. Many
parking garages dispense with numbers
altogether and instead use other symbols --
in downtown San Diego, one parking garage
symbolizes its levels by using fruits,
and it works just as well as numbers.
Any other symbol could be used other
than 3/4 to indicate a particular rhythmic
feel in music. Thus the numbers are completely
peripheral to a musical score even when use,
since they are nothing more place markers,
not mathematical symbols, and never
representative of mathematical calculations.

Likewise, changing time signatures
are nothing but indicators that the
"feel" changes at certain points.
Instead of putting periodic 3/4
or 4/4 time signatures in a score,
the composer could just as easily
have written the triple time notes
in green and the common time notes
in blue. The only reason composers
don't do that is that it would cost
a fortune to use colored ink in
musical scores.

So in every possible way, Joe Monzo's
claims about musical notation are
just plain wrong. And the evidence
is overwhelming. When a computer
plays a score exactly as written,
it sounds completely wrong --
particularly a jazz score requiring
swing and syncopation. The musical
reality, obvious to any competent
practicing musician and therefore
completely obscure to any of the
know-nothing do-nothing no-music-
all-typing-on-the-internet crackpots
on the ATL, is that musical notes are
never played as proportional
relationships and are never heard
as exact proportional relationships.
When a computer plays half notes that
last precisely twice as long as quarter
notes, musical listeners immediately
hear this as wrong and unmusical. Instead
of being powers of two, the hierarchy of
rhythmic values in Western music is a
complex and non-matheamtical set of
durations -- half notes in real music
never last precisely twice as long
as quarter notes, nor do quarter notes
ever last twice as long as eighth notes,
and so on. According the fantastic delusion
that musical notion is based on math is
the kind of gross fallacy only possible
for someone with virtually no familiarity
with actual music as it is performed
and heard.

If a musical score were based on
mathematics instead of bodily
rhythms and right-brain contour
perception and unspoken rules,
computers would be able to play
scores as written as listeners
would hear them as sounding
correct. Listeners violently
rebel against such computerized
performances. The performances
are heard as repulsive, dead,
cold, inhuman, unmusical, and
as not representing music and
(in many cases) as not even being
music.

Moreover, the process fails in
the other direction too. OCR
scanning of scores produces
many many many errors, and
fails completely on complex
polyphonic scores, or on
modern scores with cross-
bar and cross-stave beaming.
If "the act of writing down
musical scores is a mathematical
act," as Joe Monzo claims, OCR
using math should work perfectly.
It doesn't. In fact, for polyphonic
keyboard music it fails badly.

So Joe Monzo's claim that a
Western musical score is based
on math fails in every possible
way. It is so completely wrong
that it's not even worth
discussing. The fact that Joe
Monzo and Gene "Woolly-Headed
Numerology" Smith made these
absurdly foolish claims about
Western musical scores only
shows that they just are pervasively
uanware of the bulk of modern cognitive
neuroscience and cognitive
psychology and gestalt psychology
and the neurobiological research
of the past 30 years.
---------
--mclaren

Writing down a musical score has nothing to do with math

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