I would appreciate some help for my son-in-law please. We both figure there is a mathematical formula for the two problems I describe here. However, my two sons-in-law couldn't agree on a formula for a drumming problem.
Is there is a formula that will count the number of combinations of accented and unaccented notes in a bar of sixteenth notes where each sixteenth not may be either:
-Unaccented
-Accented
For example:
AUUU UUUU UUUU UUUU / UAUU UUUU UUUU UUUU / UUAU UUUU UUUU UUUU/ and so on all the way to AAAA AAAA AAAA AAAA / can be done manually, but there must be a formula.
Next, we'd like to know how the formula would change if a ghost note is added to the mix, so you now have three possible articulations for each note.
It's beyond me. Help please?
216 = 65,536
316 = 43,046,721
By way of explanation what Rick just said:
The first note can have 2 states (accented and unaccented), and thus creates 2 possibilities.
The second note, also having two states, doubles that number: 2 x 2 = 4 possibilities
The third note, in turn, doubles the number of possibilities of the two previous: 2 x 2 x 2 = 8
I'm sure you see the pattern emerging now...
The final 16th note: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = (2 to the power 16) = 65536
Add a three state possibility for every note, and every added note triples the number of possibilities:
3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = more than you'll care to count.
Regards,
Alvatrus
Thank you both very much. This makes sense to me.