Pattern Recognition Algorithm/Technique

Question

Background

I apologize for the music-based question, but the details don't really mean all that much. I'm sequentially going through a midi file and I'm looking for an efficient way to find a pattern in the data to find something called a tuplet. See image below:

The tuplets have the numbers (3 or 6) over top of them. I need to know at which position they begin in the data file. The numbers below the notes are the values you would see sequentially in the data file. Just in case you can't decipher the data below, here it is:

1, 2, 2.3333, 2.6666, 3, 3.5, 3.6666, 3.83333, 4, 4.1666, 4.3333, 4.5, 4.6666, 4.8333,
5, 6.3333, 6.6666, 7.1666, 7.3333, 7.5, 7.6666, 7.8333, 8, 8.1666, 8.333, 8.5, 8.6666.

• The first tuplet begins at position 2 and the difference between the position of notes is 0.3333 (repeating)
• The second tuplet begins at position 3.5 and the difference between the position of notes is 0.1666 (repeating)

The main issue is that in the note, unlike the image below, position 7 will not be noted in the data file because the data only file only lists note locations. The icon that you see in that location is called a rest, which is not notated in the data file.

Question

How can I find an efficient method to find the start of each tuplet? Is there some sort of recursive method?

Answer 1

I don't think you need any recursion for this.

The normal note values can only be represented by fractions of the beat of the type a / 2^b . The tuplets can be arbitrary fractions, but mostly I've seen something like triplets, quintuplets or (in your case sextuplets).

So the simplest way would be to compute the length of every note (maybe the time difference between two MIDI events? Or the length is stored explicitly in MIDI? I'm not that familiar with the format) and compute the rational representation of this length.

Every group of notes with a denominator that is not a power of two belongs to such a tuplet. To group the notes together, I would recommend the following approach (assuming that all notes of a tuplet have the same value):

• Factorize the denominator into a power of two a and the rest b (eg a * b = 4 * 5 )
• Initialize an empty tuplet of size b
• For every note compute the distance to the beginning of the tuplet and store the note at the corresponding position, inserting rests if necessary. The length of the tuplet can be computed by taking the minimum length l of all notes in the tuplet, so greedily adding them until the end of these notes exceeds a distance of l * b from the beginning of the tuplet
  This way, you base the tuplet on the minimum note length and add all notes that fit into it.