

The distinction between music and noise is mathematical form - carlos
http://physics.info/music/

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aufreak3
This is _very_ old thinking (like half a century old) and the folks most
qualified to comment on what is music and what is isn't are those at the
vanguard, the "noise music" folks, the electroacoustic artists.

For one thing, monophonic music can be very rich. The Indian classical
traditions (Hindustani and Carnatic) are both primarily monophonic. The
"monophonic is boring" comment would also insult Bach (ex: suite for solo
cello, which is awesome)

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mvgoogler
The article said mono _tonic_ music is boring, not mono _phonic_ music..

Monotonic means one tone - I.e. a sound that is made up of a single frequency.
About the only time you'll ever here monotonic sounds is from a signal
generator that is producing pure sine waves. The sound is very flat, lacks
character and is, well, boring.

All real instruments, even a tuning fork, produce a multitude of sounds for
each note. The number and intensity of the overtones each instrument is what
makes the instrument sound like it does. Cellos produce rich overtones and are
far from monotonic.

This is all clearly explained in the article. You do, however, have to read
past the first paragraph...

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aufreak3
Apologies for misreading the reframing of "monotonic". I only skimmed the
article 'cos i'm familiar with the domain and the ideas expressed in it. It
doesn't help that the article hijacks a common term in music for the special
purpose of talking about pure sine tones. The rest of my comments hold.

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ecocentrik
This article would probably never be used by anyone as reference for signal
analysis but it does offer a good overview of western harmonic tonality.

I do want to make one correction:

"Did I say music was based on notes? That's not true. Real music is based on
intervals (the ratio of two notes) with high degrees of consonance (shared
harmonics)."

Not true. Real world musical tonality is based on a combination of consonance,
dissonance and noise. We don't just hear the fundamental frequencies and their
harmonic compliments when we listen to a note coming from a musical
instrument. The tonal character of any instrument and hence the tonal
character of music is complimented and equally defined by other factors that
this article is discounting as noise.

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agumonkey
What about time ? the relative ratio of durations and displacement between
sounds is , to me , as important as tonal frequency (well even if at the end
of the day , both are frequencies on different abstraction scales).

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ecocentrik
the article focuses on tonality so I didn't even think to mention rhythm but
you're right, rhythm does have a frequency equivalent which is not always on a
different abstraction scale. 32nd notes in music played at 120bpm have an
audible frequency of 64hz.

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radarsat1
Or it was, anyways, before.. say.. the 1960's.

(Hell, artists were exploring "noise as music" in the 1920's, even earlier...
a century later, and it's really time we stop pretending we can pin down and
define "art" as a mathematical or scientific phenomenon. Art is fundamentally
a _social_ phenomenon, driven specifically by an inherent counter-cultural
attitude, and therefore by definition it naturally evolves beyond any specific
description we attempt to apply to it. By that I mean that art is always
trying to break its own rules. You could argue that _good art_ , what we
consider ground-breaking work, at any point in history, is specifically that
which is not described by previous attempts to define a set of rules.)

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ThomPete
Hmm I don't think that was the point of the article, did you read the entire
article?

The article is not talking about art per se about music or maybe more
precisely about harmony from a technical point of view.

Don't think noise as meaning bad, dissonant or non good.

Instead he says "Music is sound with a discrete structure. Noise is sound with
a continuous structure."

The article isn't trying to make a value judgement here.

It simply talks about tones as a designer would talk about how colors blend
together.

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radarsat1
I guess my point is that at soon as you use the word "music" you are making a
value judgement, particularly if you are categorizing it. Example from the
first paragraph of the article: "Monotonic music is boring." I would consider
this viewpoint at least 50 years out of date. I can find you hundreds of
potential counter-examples, and hundreds of people who will disagree with each
other on the "boring" part. Add to this the fact that it doesn't even _matter_
what hundreds or millions of people think; in "art" popular opinion does not
always line up with the "connaisseurs" or academic thought. More people
probably dislike Phillip Glass than like him, but it doesn't matter: he's
still a world-renowned composer, regardless of what people think of his work.

I understand the viewpoint here, but pointing out mathematical structure in
music / timbre / tonal sounds is not exactly new and we should stop being
amazed everytime a new mathematical feature is discovered, because
fundamentally the rules are _not_ formal, and naturally subject to a large
amount of ambiguity and interpretation. Finding expression of mathematics in
music is sort of akin to astrology--you can find lots of correlations, but at
the end of the day you won't find much causality. Imho a physicist or
mathematician doing "armchair musicology" is just as bad as a musicologist
doing "armchair physics."

The closest we can get, scientifically, is the psycological or psychophysical
viewpoint-- _why_ do certain combinations of harmonics sound a certain way to
us that is distinct from others. This is of course an on-going topic of
research, and it has biological / evolutionary reasons as much as anything.
The mathematics is mostly coincidental, although convenient mathematical
relationships may be enablers (catalysts) to development of perception
mechanisms because they imply convenient forms for decoding mechanics. (e.g.
cochlear membrane as a Fourier transform).

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ThomPete
Sorry but I think you are blowing this way out of proportion. The article is
simply trying to talk about the sound technical term "noise" vs. the technical
term "music".

This is not art critiqe, this is not what you learn in art school. This is
what you learn if you want to be a soundengineer.

So either you haven't read the article at all or you are completely missing
it's point.

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radarsat1
I'm not arguing that the content of the article is incorrect, I'm arguing that
the title and first paragraph of are misleading, and this didn't particularly
encourage me to continue reading. Positioning the words "music" and "noise" as
opposites is fundamentally incorrect. Since the article is about music theory,
the author should know better. Anyways, I'm getting downvoted so I'll just
give up my argument; it's okay for someone to be wrong about music but not
about programming languages or physics. Noted.

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ThomPete
I don't think the title is wrong or for that matter misleading and to be
honest I don't think you thought that either. You just though the article was
about something else.

If you really think the title was misleading then why not say that?

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colomon
"Monotonic music is boring. Real music is polytonic..."

"Ego Trip", MacDara Ó Raghallaigh. An hour of solo fiddle and foot tapping.
Best album I have heard in heard in ages. But then, he occasionally double-
stops, so I guess it's not purely monotonic...

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germano
If it was a computer playing the exact same notes as MacDara Ó Raghallaigh but
with simple sine waves, would it be boring then? The author notes in the first
paragraph that if an instrument is producing overtones then it is being
polytonal, and hence not necessarily boring.

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colomon
Ack, I got so frustrated at the beginning of the paragraph I didn't notice the
author was making up his own definitions of monotonic and polytonic, and
instead assumed he meant monophonic and polyphonic. My bad.

Anyway, I suspect the answer to your question is no, if done properly. That is
to say, I believe if the computer caught all the rhythmic, dynamic, and pitch
subtleties of the music, the music would still be interesting, if perhaps
harder on the ears.

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darkane
_Consonances are sometimes described as being inherently more pleasant to the
ear and dissonances as less pleasant._

This is probably the only article I've read about harmony that properly uses
ambiguity when describing the pleasantness of dissonance. As a (very) long
time, die hard metal head that both appreciates and enjoys the musicality that
dissonance can produce, it irks me whenever someone makes outrageously
definitive claims that it causes physical pain, depression, et cetera.

~~~
baddox
Also, which intervals or chords are interpreted as sounding dissonant is
significantly dependent on culture. There are sounds that were once considered
dissonant in Western music that are no longer.

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yetanotherjosh
The best definition of noise, I think, is sound that interferes with the
transmission of meaning or disrupts the process of interpretation.

It's really that vague, and depends entirely on context and the people and
intentions involved. Any definition that attempts to be more precise is
certainly going to produce counterexamples. Certainly any definition that
tries to define noise in terms of a finite set of identifiable properties of
sound is doomed to fail. And, despite the attempts of this article, you most
certainly cannot define noise as anything other than tonal music. There are
many forms of atonal music, many of which are quite old.

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p4bl0
We have one of the very few research institute dedicated to this kind of
topics in Paris : the IRCAM[1]. They do very interesting and amusing research.
I attended a few talks there and I heard some pretty strange musical stuff,
that I wouldn't have distinguished from noise if I hadn't listened to the talk
before (and even then, I'm 100% sure I didn't get it fully, because I didn't
understand all the math from the talk, and because my ear is not trained
enough).

[1] <http://www.ircam.fr/?L=1>

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dhughes
That was over my head but it did remind me of my sound system engineer career
days (it lasted a week).

All I remember is for some reason odd trans harmonic distortion sounds good
but even trans harmonic distortion doesn't.

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jamesrcole
There's distinctions that you can describe in mathematical terms, but the
notion of 'mathematical form' seems a bit silly to me.

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sporkologist
The difference between art and randomness is... I think this was already dealt
with by John Cage and Jackson Pollock.

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the_cat_kittles
I feel like this is almost like saying "Novels are based on words"- turns
there are some good analytical and physical reasons why we have the words we
do, but that doesn't tell you shit about how to write a novel. I think the
title overstates the scope of the observations within.

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ThomPete
People are generally missing the point of this article. It's not about what
music is, it's no trying to show you how to do music.

It's of interest to those who want to dig deeper into music theory (which does
not teach how to do good music)

There is no value judgement here as such.

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the_cat_kittles
That is true. I think the opening sentences and title maybe frame the
observations in a misleading way in that case.

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sporkologist
This title seems to just be provoking a philosophical ping pong match. Ugh.

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ambler0
This discussion seems to ignore purely rhythmic music.

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ThomPete
it's not about music as such. It's about harmonies.

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fdintino
"The distinction between tonality and noise is mathematical form" doesn't have
the same ring to it, I suppose.

My favorite study of tonal harmony is "Theory of Harmony" by Arnold Schoenberg
(sounds ironic; here's a preview on google books:
<[http://books.google.com/books?id=5Y5MyjbU87oC&lpg=PR3...](http://books.google.com/books?id=5Y5MyjbU87oC&lpg=PR3&pg=PA7#v=onepage&q&f=false>)).
It was the first theory textbook that attempted to teach composition of
harmony without value judgments about what is "correct" or "natural," instead
taking pains at every step to justify itself on first principles. He wrote the
book because he believed his students needed to understand conventional
harmony before they could transcend it. In my mind Schoenberg falls into that
class of visionaries whose legacies are more about their failed predictions
than of their analyses and contributions (Marx shared a similar fate, his own
fault of course). Schoenberg was partially right — nobody in their right mind
argues that ninth chords can't be processed by our feeble minds (jazz is
western canon at this point), or that the tritone will summon demons (well,
maybe some people in Norway still believe that) — but classical harmony hasn't
been completely replaced.

The scientific stuff in Schoenberg's Theory of Harmony is mostly garbage
though. If you're interested in reading more about the modern understanding of
the physical properties of music I'd recommend "Musimathics: The Mathematical
Foundations of Music," and Benson's "Music: A Mathematical Offering." For an
attempt to look at musical structure in terms of its cognition, I enjoyed "The
Cognition of Basic Musical Structures" by David Temperley. It's a bit
speculative, but that's the current state of the field if you're trying to go
beyond the simplest aspects of music.

