@agitato said:
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
Thank you for sharing this. I was not aware of these numbers. And they do not seem to include a calculation for note durantion (rhythm). I am no mathematician or physicist, so I have no idea how to include duration. Perhaps you could help us. If we also say every one of the 8 notes of the diatonic scale can have a rythmic value of whole note, half note, quarter note, eigth note or sixteenth note, or any of those values as a triplet, how would that alter the calculation?
Yes I assumed all notes are the same length.
If we want to include whole, 1/4, 1/8, and 1/16th notes, keeping it still an 8 note melody, we now have 12 x 4 = 48 notes to pick from. So now the calculation is 48!/(48-8)! = 15 trillion. (there is a simpler way to look at this. There are empty 8 slots, and we have 48 apples. The first slot can be filled with any of the 48 apples, second with any of the remaining 47, third with 46, and so on. So we have 48*47*46*45*44*43*42*41 ways of filling the 8 slots, which comes to 15 trillion)
So you can make 15 trillion 8-note melodies with chromatic notes and note lenghts from whole to 16th. Of course many of these will be redundant. For example, if all 8 notes are the same duration, changing from quarter to whole is simply like playing the same melody faster! But if I am not wrong that is only the case for 12 x 4 = 48 melodies.
So that still leaves us with 15 trillion - 48 melodies, which makes the same difference as a turtle peeing in the atlantic ocean. Note that I have left out rests. (John cage will pick all 8 as rest notes. so he wont care about this discussion. LOL)
I still believe there will be many redundancies, but if we can use even 1 millionth of these, it leaves us with a biliion combinations.
Not bad to be a composer!
Anand