The distinction between music and noise is mathematical form | Hacker News Reader

The distinction between music and noise is mathematical form

physics.info

81 pointscarlos37 comments

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)

The article says "monotonic", not "monophonic". The paragraph discusses pure tones and overtones.

A sine wave, played with dynamics and interesting rhythms, can be just as valid a musical expression as anything else.

The article said monotonic music is boring, not monophonic 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...

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.

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.

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).

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.

Is tonal character the same as timbre?

Yes, I believe they are both terms for frequency spectrum.

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.)

Well put. Take a look at this (one of the first documents regarding futurist "noise" music):

http://en.wikipedia.org/wiki/The_Art_of_Noises

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.

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).

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.

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.

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?

We can define art as some function of popular perception. Then we can treat individual critics' opinions as noisy sensors and get a pretty good idea of whether something is art that way. Then we can throw some ML at the problem :)

"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...

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.

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.

A fiddle is not monotonic.

Indeed. From the end of the third paragraph:

  And don't think that you need more than one instrument
  or more than one voice to make real music. Pretty much
  every musical instrument and every person's voice is a
  source of polytonic sound.

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.

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.

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.

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

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.

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

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

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.

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.

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

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

This discussion seems to ignore purely rhythmic music.

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

"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...). 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.

Reply on news.ycombinator.com