[Dixielandjazz] Permutations

[Jerry Gordon]

"Crotchet" (as used by Bob) means "quarter note." I get a different
answer than he got, but I don't know how he did his math.

4 measures of quarter-notes, assuming 4/4 time and only 8 possible notes
or a rest, means there are 9-to-the-16th-power possible combinations.
This is 1.85302E15, or, for those not familiar with scientific notation,
1,853,020,000,000,000, which is significantly smaller than Bob's answer
(but still over 7 million years, at one per second). 

This does not include the rhythmic variations that Bill asked about, nor
does it include other time signatures, nor any notes beyond the basic 8.
I don't think we're going to run out of tunes soon.

(As an aside, if we consider 8th notes (semi-crotchets?), then the same 4
measures of 4/4 time yields 9-to-the-32nd-power possible combinations,
which has 15 more zeroes than the number above! And we stil haven't
considered other time signatures or any notes beyond the basic 8, or any
notes other than 1/4, 1/8 and rests.)

Jerry "how high can you count" Gordon


On Tue, 30 Aug 2005 21:47:07 +0000 "Bill Gunter" <jazzboard at hotmail.com>
writes:
> Hi Robert,
> 
> >If you compose four bars each consisting of four straight 
> crotchets, then 
> >there are 184,884,250,000,000,000 possible tunes that can be written,
so 
> I think 
> >it'll be some time before all tunes have been composed.
> 
> I'm not familiar with the term "crotchet" used in this context. Can 
> you 
> explain that a little.
> 
> Do your calculations also include the variations of a melody when 
> you 
> include rhythmic variations?