This was quite the question!
Let's consider one-finger songs...melodies that can be played with
just one finger on a piano, one note at a time.
There are 88 keys to choose from. Each key can be played in say, 10
ways (whole note, half note, stacatto, etc ... I told you, one needs
to make assumptions for these sorts of things).
So, there are then 88 x 10 = 880 ways to start a one-finger song on the piano.
Similarly, there are 880 options for the second note, which means that
there are 880 x 880 = 774,400 combinations for just the first two
For the third note, another 880 options, and so on.
Let's say (another assumption) that a typical song is 100 notes long.
Then there are 880 raised to the 100th power note combinations, which
is roughly equal to 10 ^ 294 (10 raised to the 294th power).
This represents the number of possible one-finger piano melodies with
a length of 100 notes.
This number is ridiculously large. For comparison, the universe is
estimated to be about 10 ^ 17 seconds old.
Even writing millions of one-finger songs per second since the
beginnning of time, one would not yet even be close to exhausting the
number of possible songs that could be written.
Obviously, once we add notes in combination (chords, rhythym, back
melody, and so on), the numbers grow much, much larger. So much so,
that there is no real end to the number of tunes than can be written.
Just as obviously, not all the combinations would be recognized as
melodic. In fact, most of the combinations would not be very pleasing
to listen to, I'm sure. However, what is or isn't a melody is a
matter of taste, which varies from person to person, and which goes
through considerable cultural change over time.
However, even if only one in a million note combinations is a viable
melody by some sort of definition, then there is still, for all
purposes, an endless number of tunes waiting to be written.
I trust this information fully answers your question.
However, please don't rate this answer until you have everything you
need. If you would like any additional information, just post a
Request for Clarification to let me know how I can assist you further,
and I'm at your service.
All the best,
search strategy -- Searched my own small supply (about 10 ^ 10) of brain cells.
Clarification of Answer by
02 Oct 2005 17:44 PDT
Yes, I agree with your math, though I can't say I agree with all of
your assumptions. But that probably doesn't matter much. In this
sort of exercise, the important thing is articulating what assumptions
are being made. Then, others are free to do exactly what you did --
rewrite the assumptions to suit their own sensibilities, and then
re-do the math.
A lot of music borrows riffs from existing tunes. This has always
been true, but is especially so these days in a lot of hip-hop and
other popular music.
So...does the new song with borrowed riffs count as a new tune, or an
old tune? To me, it's a new song, since it has a lot of individual
riffs mixed together in a new and unique way. But if that's the case,
then there's a lot more than just 10 or 20 or 40 notes involved, so
I'd be tempted to stick with my 100-note number.
However, that's just an individual judgement. As I said, I think the
numbers you came up with are readily defensible.
But in the final analysis, it's still an awfully big number anyway you
look at it.
There are plenty of tunes yet to be written, I'm sure.
All the best,