A question for the math minded.

Greetings I have a math question. It can apply to anything but in this case it is to musical notes........If I took 3 musical notes..........What would the number of possibilities I could create with the 3 notes.........What area of math does one use to come up with the answer...................If one added a 4th note how many more possibilities would this add...............................I sincerely appreciate any attention this posting gets. Thanks, Jazzlover

That is combinations and permutations. here is website so you can calculate them.
Math webpage

For your first question of 3 notes. I'd assume you can repeat the any of the 3 notes and the order matters so it's a permutation with repetition. So, 3 x 3 x 3 = 27 different ways to play 3 notes.

4 x 4 x 4 x 4 = 256 ways to play 4 notes.

Now, if you took 4 notes but only wanted to play a 3 note riff: 4 x 4 x 4 = 64 ways

3 notes to play a 4 note riff: 3 x 3 x 3 x 3 = 81 ways

Great answer Thank you very much..........you made my subscription pay off with your accurate and right on answer. Jazzlover

Not to add anything mathematical to this discussion, but I saw a feature on TCM how "they" (some guys) took 6 musical notes and created an intro piece which is used before a movie is aired, using just those 6 notes. Interesting.

I can name that song in . . . 2 notes!! (lol)


Just to add to Snidely’s post above, if a note cannot be repeated, meaning that each note must be played once and only once, but order still matters, the number of permutations is significantly smaller:

3 notes: 6 possibilities
abc
acb
bac
bca
cab
cba


By similar analysis, 4 notes: 24 possibilities



Edit:
By the way, I’m seeing a pattern here. If n notes cannot be repeated but each must be played once, and order matters, the number of possible permutations appears to be n! (n factorial).

2 notes: 2! = 1x2 = 2 possibilities
3 notes: 3! = 1x2x3 = 6 possibilities
4 notes: 4! = 1x2x3x4 = 24 possibilities
5 notes: 5! = 1x2x3x4x5 = 120 possibilities
6 notes: 6! = 1x2x3x4x5x6 = 720 possibilities

And so on. I know I’m boring the shit out of everyone, but I’m kind of a math geek and I couldn’t help myself. Sorry.

Thank you all I am you have helped me more than you know.......I like to figure out riddles when I practice and these comments have opened the heavens for me ......Thanks
If you are curious ......Go to www.bobwinett.com
I am generous in providing 3 tunes start to finish from my CD for all to listen too.
Getting ready to do a new one and plan on taking a different direction.
A Happy and Healthy New year to all................And I will say Thank You again.

Hey Jazz. As a musician myself, I'm asking myself questions like:
'How many measures are you going to use in order to combine those notes?'
'Are time signatures an influencing factor?'
'Are repeated notes, or phrases taken into consideration?'
'Are chord combinations with 3 or 4 (or more) notes in the mix, or just melodic combinations?'
Sometimes I overthink this stuff.

Would be cool to hear your stuff.

Chuck

Chafro See PM