Any mathematicians among us? 2009-07-25 08:20 am 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? Quote Selected
Re: Any mathematicians among us? Reply #1 – 2009-07-25 09:52 am 216 = 65,536316 = 43,046,721 Quote Selected
Re: Any mathematicians among us? Reply #2 – 2009-07-25 10:12 am 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 possibilitiesThe third note, in turn, doubles the number of possibilities of the two previous: 2 x 2 x 2 = 8I'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) = 65536Add 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 Quote Selected
Re: Any mathematicians among us? Reply #3 – 2009-07-25 07:56 pm Thank you both very much. This makes sense to me. Quote Selected