Have you heard this music before?

Question

I don't know much about music but I was wondering...if there are only eight notes in the scale, and three octaves for each; factoring in sharps, flats and all the different chord combinations, should'nt we have heard every musical combination possible?

- So you're saying that if I sing the alphabet song and hold the notes longer, it's a different song?

Answer 1

Even if you account for all of the possibilites for a single note, including how long it was held, which keys were involved, and so on, which itself would be a large number, you'd then have to raise that to a large power derived from the number of notes in a composition. And what about having several instruments? We're not even close. I'll bet we've barely scratched the surface, actually. Then again, many of the unplayed combinations probably aren't very appealing :)

Answer 2

What you are talking about is like the "free group on the set of musical notes."
What is the free group of a set?

One way is to view it as "words" formed by "letters." Let's say that there is only one note, and we can call it "a." Then the possible "songs" or "words" we can make are 0 (the silent song, or unsong), a, aa, aaa, aaaa, . . . and so on. Therefore with only 1 note, we can actually make an infinite number of songs (and thus have not heard them all). Since we have many more notes, we end up with a set of songs of an amazing size.

So can we have possibly heard every musical combination? In reality, no we haven't.

On a mathematical note: The reason this isn't a free group is because songs don't have inverses, and thus prevent the set from forming a group.

Answer 3

And not just the length of the note, but also the number of notes.

Theoretically, you could have a musical piece of infinite length, and also, composers also utilize silence. The length of the silence also will have a factor.

Regards,

Mysstere

Answer 4

No, you forgot the length each note is held.