Rarity and Duration Value Differences

Relationship Between Rare Patterns and Their Duration Values

This page summarizes the analysis suggesting that the more common a pattern, the more likely it is made up of two notes whose duration values are near each other.  Likewise, rarer two-note patterns tend to consist of notes whose individual duration values are far apart from each other numerically.  Another way of saying this is that the more common a pattern is, generally speaking, the more likely its duration ratio approaches “1”.   For example, a quarter note followed by a quarter note has a duration ratio of “1” because each note has the same duration value, and patterns with duration ratios of “1′ are indeed highly common.  Likewise, a pattern with a duration ratio of, say, 40 means that the second note is 40 times longer than the first note, and we would expect that pattern to be rarely used in a melody.  This analysis is confined to the subset of patterns that are surprisingly rare, defined and discussed here.

While it is common sense that rare patterns would be formed with notes whose duration values were far apart from each other, it is nevertheless good to check that common sense with the evidence.  The following table was constructed when there were 52000 tunes in the database (February 2021).

Rarer Patterns Have Duration Ratios Further from the Number 1 Than More Common Patterns

The above table shows that the average difference between the numerator and the denominator of duration ratios in extremely rare patterns in this subset is 17.  For rare and somewhat rare patterns in the same subset, the average difference is 11 and 13, respectively.  So while it is true that extremely rare duration ratios have extreme differences between the numerator and denominator that forms them, it is not the case that progression toward “one” is uniform.  The difference between the numerator and the denominator goes down as we move from extremely rare to rare, but then back up a bit as we move into the somewhat rare category.

For completeness, we show in the following tables the various duration ratios in each of the extremely rare, rare, and somewhat rare subset of surprisingly rare patterns.  For examples of each of these patterns or duration ratios, click on extremely rare, rare, or somewhat rare.