Surprisingly Rare Patterns

Perhaps the most surprising finding of this research is how some two-note patterns that appear as though they might be common are rarely used by composers of any genre. While it’s easy to find rare patterns made with a multiple set of tied notes (there are a couple hundred of those), all the instances here can be formed in at least one way by a single pair of tied notes either followed by or preceded by a single note. (Remember that for the purposes of our research a two-note pattern can consist of three or more notes if some of them are tied to produce the sound of two notes to the ear). In a few rare cases, the pattern is even simpler–a single note followed by another single note.

The importance of “surprisingly rare patterns” is its relationship to the exploration of new melodies. In the never-ending search for new tunes, composers inevitably reach for note combinations that sound fresh, or at least rarely used. To a composer who wants to be on the cutting edge of music composition, certainly with respect to melody, the identification of rarely used patterns provides a set of clues as to where to look for new sounds. As artificial intelligence spreads into the musical space, it will also try to find the balance between ear-jarring new patterns and the banality of all the familiar, common ones.

Elsewhere we examined the distribution of duration ratios and found that composers heavily rely on a dozen or two duration ratios and only occasionally use a rare one. Of the roughly 2,560 duration ratios possible in theory, we have counted 486 of them used by composers thus far over time. However, 25 of those duration ratios are used 99 percent of the time. The remaining 460 or so duration ratios are candidates for the “surprisingly rare” category.

The definition of “surprisingly rare” is necessarily arbitrary because it depends on the subjective meaning of “surprising.” For our purposes, we have defined “surprisingly rare patterns” as those with the following characteristics:

Can be formed with one or two ties.
Found in fewer than 100 tunes in the Skiptune database.
Have fewer than 25 pitch changes that are within plus or minus an octave (+/- 12 MIDI values from 0)
Appear easily formed in the sense that it seems composers ought to have used more of them than they have (admittedly subjective).

The first criterion forces us to reject those patterns that can only be formed with a lot of ties and therefore do not look as though they should be common. Note that the requirement is that it is possible for the pattern to be formed with one or two ties, not that all instances of the pattern occur with one or two ties. In other words, if the duration ratio can be formed simply, we examine it even if some instances are formed with complicated note durations and ties. The second criterion roughly corresponds with the point where patterns have fallen to only one-half of one percent (0.5 percent) of the instances (see Fig. 1 in our discussion of duration ratio distributions). The third criterion considers how many intervals are used with a specific duration ratio. Limiting ourselves to an octave in either direction, there are 25 possible intervals. The fewer of these used for a given duration ratio, the more likely it is for us to include it in the “rarely used” category. The last item is in the eye of the beholder and is admittedly subjective. Still, that experience of seeing a pattern and feeling surprised that we haven’t seen it much is palpable. Composers trying to create a new melody would do well to examine surprisingly rare patterns when crafting a new melody.

After applying the above criteria, we are left with just 45 or so duration ratios that qualify as “surprisingly rare” when used in two-note patterns. We have documented them here in two categories:

Somewhat rarely used: 30 – 99 tunes
Extremely rarely used: 29 tunes or fewer

These surprisingly rare patterns were found when the database had 82,000 tunes in early 2026. While we expect some of these patterns to become less rare as we enter more music, that will happen at quite a slow rate. These patterns are either just not favored by composers or for some reason are hard to work into melodies.

Examining the duration ratios in the “somewhat rare” and “extremely rare” categories, we find that in general the rarer a duration ratio is, the more likely it is far from “one”. In other words, the individual duration values of the two notes involved are far apart from each other numerically. The further a duration ratio deviates from unison (“1”), the rarer it likely is. That is discussed more in Rarity and Duration Value Differences.