Interval Frequencies

The table below, reflecting the database at 66,000 tunes, shows how many times intervals occur in the database in four different ways:

1. The column headed “Patt Count” counts the intervals in all the two-pattern pairs of notes found in the database.

2. “# Tunes” is the number of tunes containing the relevant interval.

3. “Count (No Duplicates)” counts an interval just one time per tune, but counts the interval every time it is used with a different duration in the tune.

4. “Count (with Duplicates)” counts an interval every time it appears, including duplicates.

Each row represents a different interval.  Negative intervals move down in pitch (the top half of the table) and positive intervals move up in pitch (the bottom half of the table).  The “0” (unison) row indicates no change in pitch.  Here are a few observations about what this table suggests:

1. Major second intervals (MIDI value of plus or minus 2) are the most common intervals used by composers across all genres and across all centuries.  You can see this for yourself by scrolling down the table to the “-2” and “2” rows toward the middle.  Roughly 96 percent of all tunes have a major second interval going down (midi value -2) in pitch and 94 percent of all tunes have a major second interval going up (midi value +2).   There’s quite a large overlap between the two subsets of tunes; that is, a lot of tunes have both a minor and major second interval.   Before beginning the Skiptune project, we had expected unison (no pitch change, or a midi value of zero) to be the most common interval, but unison intervals are used in only 86 percent of all tunes.  When we include repeated intervals within a tune (Count, No Duplicates) and look at all intervals no matter how many times repeated (Count with Duplicates), we find that again major seconds are the most common interval.

2.  The most uncommon  interval within an octave is the major 7th (MIDI value of +/- 11) as each can only be found in two percent of the tunes. Augmented fourths (MIDI value of +/- 6) are next, each occurring run roughly six to seven  percent of the tunes.

3. The biggest difference in the frequency of an interval going up in pitch versus going down in pitch is the perfect fourth (MIDI value of -5). When counting the number of tunes with perfect fourths going down in pitch, we find that 54 percent of the tunes have such an interval, whereas 70 percent have perfect fourths going up in pitch. However, this difference, as it does for other intervals, melts away when counting every instance of the interval, including repeats. For a graphical examination of this question see the Intervals Distribution page on this website.

Interval Counting (Comprehensive) for All Tunes