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### How Many Melodies Are There?

From a practical standpoint, you are correct - there should be more eliminations for "equal" rhythms, etc; not to mention questions of practicality, aesthetics, etc.
On the other hand, melodies can have much more than 10 notes, and each additional note increases the possible number of melodies exponentially - literally!
A somewhat similar example, which I also find mind-boggling: a normal human being is capable of producing over 8.3 million genetically unique offspring (ie, we have 23 pairs of chromosomes, and each egg/sperm cell gets 1 chromosome from each pair *at random*; so 23 pairs/sets, 2 possibilities from each one)
This gives us 2^23, which = 8,388,608.
This mean that with ONE man/woman couple, there are more than 70.3 TRILLION different possibilities for each of their offsprings' genetic makeup. (8,388,608^2 = 70,368,744,177,664). Of course we don't produce nearly this many children, females don't even produce close to 8.3 million egg cells. But per individual and couple, those numbers ARE what's *possible*.