Starting Information:

a) 2 octaves=14 notes (white keys scale).

14!= 87,178,291,200. Or, 87 billion possible14-note melodies (with NO rhythmic variations and no note repeated).
With notes repeatable, it's 11,112,006,825,560,ooo (or 11,ooo trillion)!
Many more if we can have shorter than 14 note melodies (or longer).
b) Now, include note durations. Minimum available: Eleven.
14 x 11= or, (number of notes times the possible durations of each note) =154 choices.
Calculating154^14 (i.e., 154 times itself 14 times) = Number of melodies with varying durations of melody notes, i.e., WITH a rhythm, or:
= 4,220 [+27 more zeros] -- which is a number too large to have a name, sometimes called googillion by astronomers, or (my term), Godzillion.
Again, HUGE numbers more if we count melodies shorter or longer than 14 notes, or melodies with non-scale tones ("blue notes," et al).
Imagine: AT LEAST 4 thousand godzillion 14-note melodies still available to be written!! And probably thousands of times more than that. Gadzooks!!
This is NOT COUNTING black notes (sharps & flats) NOR the various possibilities for harmonizing the 14-note melodies.
Now: The number of 14-note melodies with varying durations of melody notes, i.e., WITH a rhythm AND allowing the melodies to include about 10% sharps & flats:
= 801,000 [+27 more zeros], or, 800 thousand godzillion! 200 times more! ...Still NOT counting harmony choices or longer or shorter melodies.
But enough!
With all things included, EVEN discounting 99% of them sounding awful, the number, even reduced to a conservative 8,000 godzillion, probably exceeds the number of atoms in the universe [give or take 6 or 7 atoms].
Bob Fink & Mike Finley
Origin of Music
Neanderthal Flute
Role of Drone/counterpoint in origin of harmony
All art © Greenwich / Bob Fink March 1999
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