I am not a musician…music is a wonderful mystery to me. I’ve heard it said that music is actually a kind of math or is mathematically determined or something along those lines.
Which leads me to wonder…is music something we actually invented, or did we discover it?
I vote for “discovered”. Music is an artefact of the way we perceive sound and time. If a particular frequency is prominent in a sound, we perceive it as a note. If we hear several notes simultaneously or in succession, and the frequencies of those notes are in certain pleasing ratios, we hear music. Since it is possible for such sounds to produced by natural processes, music was already there, waiting to be discovered by suitable minds.
I would say it is partially discovered, partially invented, and partially developed within us as well.
There are certain parts of music that certainly have a mathematical relationship. This wikipedia article gives a lot of detail about it: Music and mathematics - Wikipedia
Music is an art, not a science, though. Exactly how you put these various mathematical relationships together to form music takes some creativity, and there isn’t any one way to do it. Hence, music was invented.
Over time, our inventions have altered what we think of as pleasing. 7th chords, for example, are common today, but sounded bad to folks a few hundred years ago. Part of what we like is based on what we are exposed to and how our musical tastes develop.
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As a mathematician who used to play music (it was a toss up as to which was to be my major in college), I hear this too. I think it’s a bunch of baloney, however, especially because the claim is always as indefinite as yours.
The idea that music and math are closely related is very, very old in the west. Western music theory can be traced back to the work De institutione musica libri quinque by Boethius, written in the sixth century CE. Boethius’ work though, is based on a philosophical tradition going back to Pythagoras. This quote by the late Greek philosopher Proclus sums up the theory nicely:
The practice of music has essentially nothing in common with the practice of mathematics. However, there is a very old and very rich tradition of thinking of musical theory as deeply linked to mathematics.
As for the origin of music, one theory championed by scientists like Steven Mithen in his book The Singing Neanderthals is that music and language evolved together and that musical expression is a fundamental human trait rooted in genetics. If that is the case, then it was neither invented nor discovered. Not anymore than was your hand invented or discovered.
Particular theories of music, however, were both invented and discovered. They were discovered because some rules describe acoustic and hard-wired perceptual properties. For example, the harmonic series, which is of central importance to western music theory, is a description of a physical phenomenon; it is not arbitrary. On the other hand, many other aspects of musical theory are arbitrary, and those elements of style can be thought of as having been “invented”.
jovan: You are correct of course. It is also the case that stuff like “music is actually a kind of math or is mathematically determined” is baloney.
It depends how it’s put. In my opinion, I think the line of thought that goes: “someone found fractal patterns in Jackson Pollock’s paintings, this is proof of how great they are” is in fact pretty much baloney. It is baloney because you can find mathematical patterns in anything. Hence, the value of a particular work cannot derive from the mere presence of these patterns.
This leads to the Pythagorean position, which some musician still adhere to: the universe is mathematically determined, and hence, so is music. Music can be, and often is non-representational. A Bach fugue (to take a tired example) does not stand for anything, hence it is pure form, and hence it is a “mathematical object”, in the same sense that a circle or a torus is one.
For the record, when I was in high school I wanted to punch anyone who pulled that “music is really math” line. I hated math. Ironically, it was ultimately music and acoustics that made me appreciate mathematics.
How about a third word, “evolved?” Music progresses by roughly the same process as biological evolution. New musical ideas are always being experimented with: some are successful, and others die out. Limitless diversity is culled by popularity.
The same is true for literature. The modern novel was neither “discovered” nor “invented,” but evolved over a long period of time. Science fiction is a benevolent mutation…
I am a mediocre musician with no math or science background, but it has always seemed to me that music in its most basic form springs from the behavior of a vibrating string (or column of air). Left to its own devices, a vibrating string will produce a harmonic series, a progression of tones which we find pleasing. I recall that when I first discovered this (in high school, I think, when my guitar teacher explained the physics that allowed me to produce a “harmonic” tone by touching a vibrating guitar string), I believed that music was indeed discovered, that it was lurking in the fabric of the universe to be perceived by us. As I grew more aware of the complex nature of music and how it has evolved over time (differently in various cultures), my understanding changed. I now view the harmonic series as analogous to (as an example) iron ore. It may well have been waiting to be discovered, but it required the hand of invention to hammer it into all the things it could become.