Help with Drumming/Ryhtym question!!

[drummerneedshelp]

HI

I'm a percussion teacher in Long Beach CA who's in need of an algebraic formula to help me finish my first instructional book. Rythyhm is math after all!

I'm currently writing all of the possible combinations of notes that can be played in a bar of 2/4 time. My question for you is this.

Here are some parameters:
I'm working with 16th notes in 2/4 time. That gives me 8 notes to work with in each bar.

I'm playing 1,2,3 and four note groupings in this bar of 8 notes.

I want to know to maximum amount of permutations that are possible in a bar of 8 notes, using 1, then 2, then 3 and finally four notes per bar.

I've written most of these permutations out already, but I'm looking for a way to see if I've missed any without combing through every exercise.

I know that with 1 note being accented per bar the are 8 possible combinations.
With 2 notes there are up to 28.
With 3 notes as many as 56.
With four notes there are 60 so far.

Here is a visual of what I'm looking at using two not groupings:

1 2 3 4 5 6 7 8
* * * * * * * * (accenting beats 1 and 2)
* *

* * * * * * * * (accenting beats 1 and 3)
*---*

* * * * * * * * (accenting beats 1 and 4)
*-----*

And so on,

So, what is the formula to know how many possibilities there are using 2 accents in a bar that has 8 notes???

THANKS A TON!!!!!!!!!!!!!!!!!!!!!

 

[Opalg]

I know that with 1 note being accented per bar the are 8 possible combinations.
With 2 notes there are up to 28.
With 3 notes as many as 56.
With four notes there are 60 so far.

The number of ways of choosing four elements from a set of eight is 70. So if you have 60 there are still 10 more to find.

The other figures (8 combinations for one note, 28 for two notes, 56 for three notes) are correct. These numbers all come from the eighth row of Pascal's triangle (that's a mathematical triangle, not a percussionist's triangle!). See http://en.wikipedia.org/wiki/Pascal's_triangle.

[If you are writing a book on the subject, I hope you get to spell "rhythm" correctly.]

 

[drummerneedshelp]

Thank you so much!!!

I asked this question on a drumming forum and it almost stared a riot!! Nobody had a clue!! People really could not grasp what what was asking.

Luckily I came to the right forum!!

BTW . . . "rhythm" is one of those words that I always typo for some weird reason -- along with "friend" and "college" (I hear a "d' in there somewhere!!).

Rhythm is the only word I can think of where there is only one vowel ( y) but it's in the middle of the word!

Thanks again!!

 

[ilaggoodly]

erhemm...vowel