How about: invented by God and discovered by Man?
;-)

The "traditional" western 12-tone scale is equal temperament, because of the equal spacing of each frequency along the logarithmic curve you describe. It is actually a compromise scale invented about 300 years ago to allow easy transposition between keys. There are much purer (mathematically) ways of tuning, based on the fourths and fifths, etc., but when an instrument is tuned in that way, it is locked into a very few related keys and sounds awful when playing in other keys.

(Not to mention that the octave can be split into other divisions than twelve, or ignored altogether.)

If you really want to open a can of worms on the subject, here are a few starting points:
http://www.kylegann.com/histune.html
http://www.medieval.org/emfaq/harmony/pyth.html
http://en.wikipedia.org/wiki/Musical_tuning

But back to the original question, I think that God invented/created all of the capabilities of our minds and bodies, and the physics of our world that make sound possible, as the 'raw materials' for us to use to invent instruments and create music to honor him in return. Of course, in our fallen world, music is often not used for that purpose...

Thanks All. I thought it was something like that. I'm fascinated. But if we were going to look at it that way, can't you say that "light bulbs were discovered, not invented"? My definitions:

inventions - light bulb, internet, radio, automobile, cotton gin etc...

Discoveries- laws of thermodynamics, gravity, heisenberg's uncertainty principle etc...

So according to those definitions, was music discovered or invented? Perhaps a little of both since other scales are possible. Who uses a non-western scale, I wonder?

I meant "question", not "questions" - d'oh!

To elaborate a bit more - I say "discovered" in much the way you describe the laws of thermodynamics to have been discovered. There are laws of sound (laws of harmony, for instance) that explain why we like hearing certain sounds together. These are the discoveries. Writing a song is, of course, invention.

By the way, I'm totally fascinated by this topic. In my current (slow) work in progress, the novel I'm writing (did I mention "slow work in progress?") music and the laws behind it play a big part. In one chapter the antagonist (a musical savant) is picturing in his mind the logarithmic spiral of music - in studying this it's been fascinating to me to see how music and it's laws engaged the minds of some of the world's greatest mathematicians throughout history. I was reading a book recently on the topic of the number "e" (another "discovery") and the author of the book delved into the laws of mathematics as they apply to music. Cool stuff.

"Our simplist form of expression"...actually that would be screaming, crying, laughing.

This is a good question Shrode which leads to other questions such as "Was Math invented?" "How about time?";"0

great question shrode.
I guess I see it like this: the standard pleasing harmony was discovered, as they boil down to ratios. The harmonic progressions that we are familiar with in the west -- blues style progressions, cycles of fifths, some chromatic movements, fall out of the mathematics of mod-12 arithmetic, which is important becuase we have 12 notes in our chromatic scale. These too are discovered (but then played with).
Also rhythm was discovered -- we're familiar with taps dripping (or stalactites dripping, for our cave-dwelling ancestors), and hearts beating, the sound of a horse galloping etc. so we have a natural repertoire of rhythms to reproduce and modify.
These are the basic materials of music, like the ingredients of a cake. We invented the process of creaming fat and sugar, folding in egg and flour and baking. Also, we invented the process that transforms harmony and rhythm into music.

Rather like Cos says, the introduction of communication is important and is the motivation behind invention.

This question is interesting from the other direction, what really is the difference between invention and discovery. For example, the examples of the uncertainty principle and the laws of thermo-dynamics I'd say were invented, but the discovery is that the models they describe correspond with the physical world -- the difference is slight, but important to understanding why I think maths is an invention. No maths exists without first inventing a system of axioms.
Bell declared that "God made the natural numbers; all else is the work of man". By natural numbers, he means the positive integers (1, 2, 3, ...) -- that makes zero an invention! (also e, pi etc.). I think that's fair.

Bill said:

"There are laws of sound (laws of harmony, for instance) that explain why we like hearing certain sounds together."

That is partially true, but don't underestimate the influence that culture has on the "we like" aspect of your statement.

Shrode asks:

"Who uses a non-western scale"?

The majority of cultures in history did not use 12-tone equal temperament (the "western scale"). Pythagoras (who invented Pythagorean tuning) would not have found the "western scale" terribly aesthetically pleasing, because of its aforementioned compromises. Authentic music from many parts of the world (most notably in Asia and the Islamic countries) still does not. So, the phrases "the standard pleasing harmony", "in general the one we use is used worldwide", etc., are overstatements, and quite ethnocentric. I don't want to nitpick, but those statements just strike a wrong chord with me. ;)

I'll include the links again, and I could find a few dozen more, if anyone is interested.

http://www.kylegann.com/histune.html
http://www.medieval.org/emfaq/harmony/pyth.html
http://en.wikipedia.org/wiki/Musical_tuning

Also - Jez - it's me, the curmudgeon again . . .

I can agree that perhaps 0 could be said to be "invented" but I take issue with e and pi. Especially when you consider the fact that even with our supercomputers we've never exactly identified these two numbers to all their digits - because they are infinite series' - I maintain that they are discoveries, not inventions. Pi is the discovery of the relationship between radius and circumference in a circle, and e is the discovery of the rate of growth of compounding subjects.

Both of these numbers were primarily discovered through the efforts of dead, white Europeans.

I, of course, apologize profusely for that :-)

---"but those statements just strike a wrong chord with me. ;)"

--"It's getting to tbe point where I can't say anything on this blog without offending someone."

I intended that only as a joke, and I'm not offended at all.

--"I know I shouldn't be, but in a way I'm kind of disheartened."

Please do not be disheartened. I apologize that I overstated my case. This thread just happened to mention a subject I've been interested in for a while. My intention was only to clarify a (rather unimportant, in the grand scheme) point, but I should have done so in a less pompous sounding manner, especially since I am no expert on the subject.

Again, I'm sorry. Keep up the good work.

Schrode, there is a book by Leonard Bernstein, transcribed from the Norton Lectures, called "The Unanswered Question." It would give more insight into this discussion, as it likens the development of music with the science of linguistics. It's an exhausting read, at times, but very rewarding. Here's a few questions to increase the mystery:

Consider a child's taunting melody (I'm better than you are; naah, naah, na-naah, naah). Where did that come from? How is it that every child seems to know this without being taught? And why this melody above others?

Similarly, imagine you are at your front door calling one of your children (BIIIIIIII-LYYYYYYY). You may not realize it, but chances everyone reading this would be chanting a minor third down (C to A on a keyboard, for instance). Why this interval? Why would it sound so strange if you changed it to a fourth? A fifth?

Given the facts of Western tuning that have already been brought up, how can one explain perfect pitch. How do you explain those who can hear any pitch, including a lawn blower, and know that it's a B flat, when "B flat" is not the same today as it was 400 years ago?

One of the marvelous things about music, in my completely objective and unbiased opinion, is the way it defies any logical attempts at explanations. No one knows why Barber's "Adagio for Strings" moves them so much, but they likely will forget to wonder why and only listen in rapt wonderment of inarguable beauty. (If you haven't heard "Adagio," make it your listening project... or watch "Platoon.")

Jez - that's cool you have near-perfect pitch. I have a decent ear for pitch, but nothing out of the ordinary - I am pretty sure I couldn't get within a semitone when guessing.

About the "no perfect circles in nature" arg? I realize this is getting off topic, but what fun :-) - I suppose the key word there is "perfect", but what of the planets, the moon and the sun?

bill -- i can freak people out when I tell them that their guitar is tuned down two and a bit semitones. But part of that is judging from the slack sound of the strings, all kinds of cheats like how it feel when I hum the note. It's not real perfect pitch like some conductors I've worked with have, they show of tuning in timpanies by ear, I couldn't do that. I recognise some keys: G, Ab and D minor have particular colours for me. I'm sure you can get what I have by practicing.

I was rereading J.C. talking about adagio, and I realise I've never asked someone with a really foreign musical heritage what they think of it; that would be interesting. I think pure rhythms, jungle beats and so on definitely communicate across cultures.

When I said "perfect circle" I meant an arc whose distance from a fixed central point does not deviate. Other senses of the word "perfect" are worth discussing, but are not what I meant there. My point is that there are only approximations to this thing we call a circle in the real, concrete world. The circle is a ghost, so it seems natural to me that pi should be somewhat ghostlike too. As the circle is a man-made invention (God did not produce one, as far as we know), then I don't see how He could be mocking us with it. Interesting idea though, planting important values in what really amount to holes in our number system.

I had a conversation once with a friend who dreamed of finding a message from God encoded in the digits of pi. In fact, every finite message conceivable inevitably occurs at some point in the decimal expansion of pi, but I bet you could scare a lot of people with that. Might verge on the blasphemous though.

The orbits of the moon and planets follow elipses, disregarding the small gravitational influence that the planets exert on one another. The circle is an example of an ellipse, but none of the planets follow one.

Jez, have you seen the movie "pi"? It's about this mathematical genius who, at the urging of some Jewish mysticists, starts seeing God's patterns in the fluctuations of the stock market and even in the swirl of cream in his coffee. He eventually goes crazy.
Anyways, it sounds like the stuff you and Bill are talking about. It was a pretty weird and groovy movie.

It was directed by Darren Aranofsky, the dude doing the next Batman movie.

It was directed by Darren Aranofsky, the dude doing the next Batman movie

I don't know Mr. Aranofsky, but I do know Batman. Christopher "Memento" Nolan is doing "Batman Begins". Unless you mean the Batman movie after "Batman Begins", in which case I didn't know they already had a director for that one, or that there were any plans in the works.

Batman Begins starring Christian Bale, Michael Caine, Ken Wantabe, Morgan Freeman and more is due in theaters June 2005. But it's not like I'm looking forward to it or anything. :)

-Shrode

What isthe billionth decimal in the pi?