![]() ![]() ![]() So the number of all sequences of notes that don’t contain a C is For such a sequence there are 12 choices for the first note, 12 choices for the second note, and so on. This means that the number of all sequences of notes isįrom this we need to subtract the sequences that don’t have a C in them. There are 13 choices for what the first note could be (one of C through to C’), 13 choices for the second note, and so on. Suppose we are counting melodies made out of notes (so we’ve already covered and ). Now, writing down all possible combinations of notes and picking out the ones with a C is not a very efficient way of exploring further, so we need an equation that will describe the increase in melodies. So there is a total of 2,197 – 1,728 = 469 three note melodies. There are exactly 2,197 three-note combinations, out of which 1,728 don't contain a C. To count all melodies, all we have to do is to count all sequences of notes than contain a C. Therefore, any melody without a C is a duplicate of a melody that does contain a C. Any melody without a C can always be moved down the scale until its lowest note becomes a C. It turns out that it's easy to find duplicates: they are exactly those sequences of notes that don't have any C in them. We can start by listing all possible combinations of three notes and then crossing out those that are duplicates. The number of three note melodies rises quite sharply, but not so much that they can't also be written out.Ī small extract of the spreadsheet that lists all 2197 three-note combinations with duplicates in grey. Having excluded C' - C' we have a total of 25 exciting two-note melodies! Three note melodies That's why we won't count the unison melody C' – C' - unison was already covered in the first table by C – C. For the purposes of this exercise the melody C – C is identical to D – D or G – G as they are all unison melodies (i.e., they have 0 as their pitch difference). This is because we are only interested in relative pitch, not absolute notes. Now, you might be wondering why combinations like G# - F and E – A are not included. How many two note melodies can be written within an octave? This one is easy and all combinations can be written out: Melodies that go up in pitch 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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