How is music different than other sounds?

Factual Questions
21

I learned this at school, our computers teacher was a trombonist.

In western scales, a semitone can be calculated using the twelfth root of two ( approximately equal to 1.0594631, thanks Wikipedia!) so, for example, “concert A” is a sound at 440Hz, and the B-flat above it can be calculated as

440 x 12th root of two = 466.16Hz

(Sorry, I have no fancy LaTex skills for formatting)

Later edit: I should have read the whole thread before responding. I had added a little about Indonesian gamelan music (which sounds very discordant to me, but still follows mathematical rules) which seems to have been covered above.

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23

Mathematical whole-number ratios make harmony. The universe is essentially made of math. In Classical learning, music was classified as a branch of mathematics.

I’m asked “Why do power ballads sound so appealing?” I answered: Power ballads use time-tested chord changes and melodic contours that have not been updated since Franz Schubert, so the hearer easily slips into a receptive comfort zone. Then the “power” instrumentation and dynamics energize the emotions.

Rhythm is life itself. Our heartbeat, breath, steps, work, our every living moment is suffused with rhythm. Rhythmic music jibes with our very existence.

24

I did not say anything at all, really, about gamelan music, except that the scale may sound unusual if your frame of reference is classical Western music.

An interesting point, though, is that even though the equally tempered 12-tone scale in use can be derived through mathematics— this was worked out by Isaac Newton, among others— it still delivers dissonances in its chords, major thirds being the main example of being audibly (though not way) off.

25

Reiterating a bit.
Whilst there is a huge body of work deriving the frequencies of notes in scales, none of it speaks to human perception. Our ears cannot perform arithmetic. The work of Helmholtz is based upon roughness arising from ratios, but it admits a lot of valid scales that don’t fit things like the equally tempered scale or other intonations of the diatonic scale.
More interesting again, his initial work implicitly assumes that partials are precise integer multiples. This isn’t always true. (Helmholtz knew this.)
Bowed instruments have pure integer partials due to the phenomenon of mode locking. Struck or plucked strings do not, and the partials are intrinsically out of tune with the fundamental. Wind instruments can have a whole raft of problems including inharmonicity of partials. Bells and other struck percussion is even worse with wildly off integer partials. Helmholtz’s analysis can be applied to these problems as well, and it leads to different scales. Scales that are interestingly much the same as the scales used in those musical cultures that use these instruments. Such as Gamelan.

Whilst deriving a scale from a small set of integer ratios looks appealing, when it comes to human perception of consonant notes, it is more a coincidence that stems from the physics of the western culture of music’s choice of instruments.

Music most certainly changes as one learns. The wider and more interesting the music the wider the music you will enjoy. Jazz can be bewildering at first. Once get it, a world opens up. Other genres and musical styles are the same. It isn’t an intellectual question but one of your ears opening up. There are some deep questions here.

An anecdote I love to retell. Years ago I was at a post concert dinner and sat next to the guest conductor. We were talking about Mahler. He told me his time in Germany studying under one of the great conductors. When it came to Mahler the great conductor was quite clear. “Nicht für Kinder”. You needed an adults life experience and musical experience to truly appreciate it.

26

Frequencies are important. But I think it has more to do with time. Or more precisely, time intervals.

27

Time is what stops everything happening at once.

A pure rhythm based work is quite possible. Steve Reich’s Clapping music as an example.
A pure melodic or harmonic piece without rhythm is equally possible. Much ambient music fits that.

Music does have extent in time and something needs to happen.

Some experimental music cuts this back to extraordinary small amounts. Yves Klein’s The Monotone Symphony being perhaps the most extreme. Although I would regard that as performance art rather actual music. Drone music is on the edge here, but popular in some circles. Or controversial offerings such as Metal Machine Music.

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But that (apparently admittedly arbitrary) definition still expects or assumes that music is made of notes. Cage and others understood that it doesn’t have to be, and that’s kind of the point of 4’ 33" . You don’t need notes, and any abstract sounds you decide to use are just fine.

I’d argue that the brain is processing sound constantly, and it is only your experience is what makes it affect you in a certain way.

And well, some musicians will take Metal Machine Music and kind of make it a basis of their entire style. I’ll happily admit that the first few times I heard Merzbow their work took me completely off guard, even though I was acquainted with the Lou Reed record. By the time I actually digested Pulse Demon, I understood why my cousin named her dog after them. I wouldn’t say I listen to it for comfort, that’s not what that music is for.

29

How is it different from other sounds? Other sounds don’t turn into earworms that you end up listening to for the next day or two. Or three.

30

Wow. Thank you!

31

Keep in mind that consonance/dissonance is determined by variable factors, such as societal convention. In the Middle Ages, only an octave, later the open fifth, was considered consonant. I can only wonder what the monks who sang organum would think about some modern jazz harmony; even a simple major triad was considered unlistenable back then.

32

I guess you guys aren’t ready for that yet. But your kids are gonna - actually, never mind.

33

This is probably in some of the linked articles, but it’s worth noting that there’s a condition called musical anhedonia where some people don’t experience music as different from other sounds.

34

Schoenberg, writing in the 1920s, states quite clearly that “What today is remote can tomorrow be close at hand; it is all a matter of whether one can get closer. And the evolution of music has followed this course: it has drawn into the stock of artistic resource more and more of the harmonic possibilities inherent in the tone”, and moreover that “the expressions ‘consonance’ and ‘dissonance’, which signify an antithesis, are false” and “the evolution of harmony will, in a short time, prove the inadequacy of this classification.”

Why did he use those rules and definitions, which I have quoted, then? As he explains, he was writing a harmony textbook for students, and it was not the place to introduce new terminology nor to present a scientific theory of tones (he says that even if the overtone theory is false that is irrelevant to his textbook, which does not concern itself with the scientific basis).

I doubt that the average working musician follows mathematical or scientific rules when composing their music; they know the rules they have been taught and what the genre is supposed to sound like, and the brain can follow those rules even unconsciously. So the jazz musician is thinking in the language of jazz, and the medieval composer is using a different (though not utterly unrelated, in this example) musical language.

35

Typical jazz textbook on improvisation spends an inordinate amount of time on the circle of fifths and the relationships of chords. Most of this can be turned into a concise mathematical formulation. Musicians often seem to be expected to learn this stuff by rote. Or more often they learn a subset that they like and that subset informs their style and sound. They are also expected to be able to recognise a lot of this by ear.
But improvisation won’t work if you are thinking about the rules. You don’t have the brain space to play in the moment and also worry about harmonising a chord or what to play next. Which is why playing to known chord changes is so useful. Everyone knows where they are going, with enough room to explore.

In classical theory there are a lot of rules of harmony that stem from much the same ideas, albeit from a more constrained pallet.

Just how much you distinguish rules from mathematics is a bit open. Musicians wouldn’t recognise, say, a group, within the rules; a mathematician would instantly.

If you look at one of the seminal textbooks on orchestral arrangement, Principles of Orchestration by Rimsky-Korsakov, he spends the first chapter on Helmoltz’s work. Understanding the nature of sound, harmony and timbre from a scientific rather than rote learnt basis. This strikes to the core of the question of noise versus music.

Not that noise isn’t valid thing in music. Tim Hecker, Ben Frost, Lustmord, and a legion more. All the way up to soundscapes of a wall of harsh noise. Done right and you still have a story arc in sound and emotional energy.

So I remain unconvinced that music is captured in simple mathematics in a useful manner.

Something I think music does have some common ground with is humour. The structure of a joke or other humorous story has an arc that isn’t wildly different to the structure of a musical passage.

Where one sees a tiny relationship to mathematics is catastrophe theory, in so far as tension and release, setup and punchline might be captured as a mathematical catastrophe. Again it isn’t clear this is useful, but as an aid to making sense of what happens it is at least interesting. One needs a metric for tension, something that is likely peculiarly difficult. Some things are simple.

The rule of three in a musical phrase pattern. Phrase, recapitulation, variation. The building block of much improvisation, and the base structure of the simple joke.

An Englishman, a Scotsman and a viola player walk into a bar. The Englishman says, “a gin and tonic please”, the Scotsman says, “a scotch with water on the side”, and the viola player looks around and says, “I’m terribly sorry but I appear to be in the wrong joke”.

36

Another point that I learned about is the theory of optimal complexity of music. In short, we enjoy music most when it both surprises us and rewards our expectation. This point is different for every person for every genre, but basically, you hear a piece of music, and your enjoyment of it is highest when the surprising moments and moments of fulfilled expectation are in balance. For instance, in a 12 bar blues, you “know” what the next chord is going to be, but if you can basically predict every single musical element, the piece with bore you fairly quickly, wheras if it’s completely unpredicable, you won’t enjoy it either, since you cannot make heads or tails of it.

By studying (or listening to) music, you can shift your place on this inverted u-curve, and both become bored with music that’s now too “easy”, and appreciate music that used to go over your head before.

37

This book, This is Your Brain on Music: Understanding a Human Obsession by Daniel Levitin, might help you.

I read it about ten years ago and found it really interesting. Here’s a description in Wikipedia: This Is Your Brain on Music - Wikipedia.

38

Atonal jazz evokes for me the aphorism “too many scales, not enough music.” Atonal jazz sounds like jazz, it seems like jazz, but lacks the musicality that we associate with jazz. It lacks the human connection. I suppose arguments can be made that this is all culturally determined, but so what? If you can’t pat your foot to it, and you can’t hum it, it has no natural connection to human endeavors. We naturally feel rhythm, and we are accustomed, at least in Western music, to consonance. I know it’s unfashionable to contend this but if it doesn’t swing, it isn’t jazz. It may fall under the large rubric of “music” because it has many of the elements of music, but it also lacks the essential elements that make it jazz.

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OTOH, not everyone feels this way about it. If someone else gets enjoyment from it, it is music.

A colleague of mine is a very accomplished jazz artist, and has taught at tertiary level as well as being an internationally recognised performer. There are parts of jazz he hates. But he won’t call it not jazz. As he very incitefully observed to me once - “Jazz is a way of making music.” That is it. It doesn’t need to swing to be jazz. That is called “Swing era Jazz”. The manner in which jazz is created is what sets it apart. There is a common thread of exploring the boundaries of harmony that runs though a lot of jazz, (and is the component that seems to have inspired some early 20th century classical composers) but it isn’t a given either.

Atonalism is always a divisive subject. We had an entire generation of modern composers immersed in it. Not all by choice. A deliberate attempt to create atonal music, where rules of harmony and melody are explicitly broken is a bit of a curious beast. (As I snidely wrote earlier, sometime music to be appreciated on the printed page rather than heard.)

I remember attending John Addam’s El Niño opera a decade odd ago. It left me cold. And I generally adore his work. I went with a colleague, and he was raving about it after the performance. Was it music? Of course it was. I have the opera on CD. It never gets played. Perhaps one day it will click with me. Experience suggests that one day it could. So I still have it.

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Is 4’ 33" by John Cage music?