I have had an interesting revelation about serial music. For those who don't know what it is, it is a form of music which uses the chromatic scale to form a row of notes to create music. However you must use the entire chromatic scale(12 notes) before repeating it again. I have for fun and games calculate the total amount of note variations that are possible.
First, since there are twelve notes, it is quite simple to find the amount of combinations using the factorial 12!
The factorial of twelve is 479,001,600. Sounds like a lot of combinations doesn't it? I'm not finished.
For each series of tones there is a prime form. This prime form always starts with C, with C meaning 0. And then using a matrix you can find all the other versions of the prime ROW(different from the prime form).
For example, lets say my prime row is (7 4 3 6 1 5 2 e t 0 9 8). For layman's terms, this is G, E, D#, F#, C#, F, D, B, Bb, C, A, G#. Notice that it uses every note in the chromatic scale. The letters t and e in the prime row represent number 10 and 11, but t and e are easier because they don't confuse digits.
Anyways, the prime form of the row is (0 9 8 e 6 t 7 4 2 5 2 1). 0 is always first in the prime row, and then in the second row 0 is the second and so on. Anyways there are 12 of these, so that means that you removed 12 possibilities. Let's hold onto this number.
In continuation, there are retrogrades of the row. this is just the same row backwards. This is another 12.
Then there are inversions of the row. There are 12 of these. Its also complicated to explain how they work so look it up if you don't believe me.
Finally there are 12 retrograde inversions. I.e. inversions of the retrograde. Yay tautology. Anyways that adds another 12.
now we have 48 combination off of the same row. This means that huge number is about to be divided by about 48. How many combinations does that leave us?
That's right. Only 9,979,200. I think it is possible to make 9,979,200 pieces of music. I don't believe I am going to do it, though I expect it is possible using a knowledge of theory and programming. It could be an art statement.
I hope you are all duly impressed and amazed. Thank you very much.
Oh, and bonus points to whoever knows what piece/composer actually wrote the tone row my example is from.