We will tackle this problem by starting with the simplest possible melody - one consisting of two notes - and then building up the melody length one note at a time until we see a pattern that can be turned into a formula. So we can include all of the notes within the octave, including the octave jump (from C to C') as otherwise Over the Rainbow would not count as a melody! The notes are: C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C'. I've not restricted this to just a major or minor scale as many great melodies use accidentals (the black notes in a C major scale). Any of the 13 chromatic notes of the octave can be used.
All melodies should be contained within an octave - C to C' inclusive.For the first section I've discounted rhythm so as to focus only on the permutations of notes.Remember the "old grey whistle test"? If it can be played on a tin whistle - it's a melody. The melodies will be a single stream of notes - no chords, counter-melodies or basslines - just a single line of music.The first thing to do is to lay down some ground rules. So, to counter the fear of there being no new melodies, I thought it would be interesting to examine the number of melodies available to a composer looking at his blank stave to see how many there potentially are.
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