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Words and Music
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We have half a million words to choose from; it's easy to see how permutations for book writing is virtually infinite but musically, there are only 8 notes, 12 including the black notes, in an octave. Only about 3 octaves are commonly used in songs so 36 notes. Okay for a ball park figure, say 50 notes. Though some combinations would sound ridiculous.. So how are so many different melodies possible and when will we run out of possibilities for a new tune?
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For more on marking an answer as the "Best Answer", please visit our FAQ.Luckily enough for us musicians music isn't an exact science in the way your question looks at it. You have to add in Tempo, Rhythm and Key to the equation as well as just the actual notes played, there are many songs which share very similar melody lines but sound very different due to being played in totally different genres. As to the last part of your question when will we run out of new tunes......Unless we run out of original songwriters and music purely becomes a medium for cover versions and rip-offs by DJ's nicking bits from loads of different records just to make a pastiche then I hope we'll be ok for a good few years yet.
You also have to take into account the instrument or combination of instruments the notes are played on obviously a tune played by the Royal Philharmonic will sound different to a similar or same sequence of notes played by Napalm Death. Interestingly Pete Waterman claims he has been nicking tunes from classical composers for years!