btw being a physicist, I thought I might add a bit of math info regarding the number of possible melodies, which some here might already know about.
Even if we take a diatonic scale with an 8-note melody or theme, choosen out of 12 chromatic notes with no repetitions, the number of possible combinations are 12!/(12-8)! = 19 million. (the ! refers to the factorial function)
That means even without note repetitions there are 19 million possible diatonic melodies. But of course most of these will not sound pleasant. But even if 1/100th of these are good, we have 200,000 melodies. Now imagine if we add 7 note or 6 note or 5 note melodies, allso variations in rhythm.
There is much room for new music!
Anand
anand, being a physicist myself I have to correct you there 😉: the minimal number of 8-note melodies is 12^8 (taking a melody as an ordered set with repetitions - see guy’s first masterpiece 😃), which is already nearly half a billion. as you point out this does not take into account that notes can have different lengths … as well as different velocities, being played with different articulations, dynamics, vibrato—and changing some of these additional properties you can easily mess up any good melody.
so the odds to find a good melody by chance should be far less than hitting the jackpot. but the amazing examples in this thread (which I enjoyed very much!) show that music is not math and that all these extremely talented people here definitively know what they are doing 😊.
Hi Kai
I had stated that my calculation assumed no repetitions. You are right that it is 12^8 (or roughly 1 billion) with repetitions, which makes sense. But I like to exclude repetitions since a melody like C C C C C C C C is obviously not interesting. And this is for only one note length and I never intended to include any variations in expression and articulation or dynamics. One could go crazy with this calculation and I am not that interested. This was just for a rough idea.
I did not intend to suggest that music is math (oh please, lets not get side tracked here!) but posted that with the idea that someone might be curious about the number of combinations possible.
The traditions of classical music composition have found ways to teach us how to narrow down this amazingly complex "landscape" of tonal possibilities into beautiful melodies without ever knowing math. It is fascinating to me that a computer algorithm that churns out melodies will probably take a million years to write a melody like Tchaikovsky or Mozart that can move us emotionally. How does the human brain achieve it? Fascinating.
Cheers
Anand