Longest Unique Patterns

As of January 2026 and with 82,000 tunes in the Skiptune database, 281 tunes (0.3 percent of the database) require a minimum of 13 notes to uniquely distinguish each from all the other tunes in the database.  Another way of saying this is that 99.7 percent of tunes require a dozen or fewer notes to identify them.  (For a breakdown of how many notes are needed to identify tunes, see this pie chart).  These tunes are shown 20 at a time in the list below (you can see more using the tools included in the table).  We are curious about tunes requiring many notes to identify them, and most can be explained easily.

Most of the tunes in the table are centuries-old melodies that have evolved over time into families of tunes.  The similarities within a family of tunes sometimes require a longer series of notes to distinguish them because they have so many melodic phrases in common.

To explore tunes requiring a long pattern to identify them uniquely,  we present an example below, one of many from nearly four centuries ago.  Such tunes have a few things in common:  1)  They are all old tunes or derived from old tunes.  2)  The tunes tend to have short intervals (seconds or thirds).  Short intervals tend to be common and their use usually signals a longer series of notes is needed to identify the tunes uniquely.  3) Few notes are tied together, resulting in many more common duration ratios.  4) Some tunes have different lyrics that cause slight variations in the melody.

A good example of such a tune is the second strain of Jack’s Health, of which there are four versions published, respectively, in 1679, 1686, 1703, and 1721 from John Playford’s Dancing Master (DM).  They are reproduced below.

The 1686 version provides an example of why a tune might need a long series of notes to identify it. The notes circled in red at the left comprise the shortest pattern that uniquely identifies this tune from all others in the database, a total of 15 notes.  By comparing this encircled string with the variations below, it is easy to see that if you shorten the pattern by just one note, all the other versions contain that shortened pattern, rendering the pattern unable to uniquely identify just one tune.

The version from 1679 differs from the 1686 version at the end of the first measure and the beginning of the second measure.  Observe that the second half of this strain is identical in the 1686, 1679, and 1703 versions.  However, only four notes, encircled, are needed to uniquely identify this tune, a much shorter pattern than for the 1686 version above.

The only difference between the 1686 version and the 1703 version, shown at the left, is the “C” at the end of the first line, sharpened in the 1703 version (circled in red).  The shortest pattern requited to uniquely identify this tune is 10 notes long, encircled.

The 1721 version also has the “C” sharpened at the end of the first line.  But in addition, the 1721 version has a slightly modified bottom line that makes it different from all the other three versions.  The encircled six notes form the shortest pattern that uniquely identifies this tune from all others in the database.

There are dozens of examples of such tunes in the database, many of which are from John Playford’s Dancing Master series.  Some of the differences in the many variations of the tunes in Playford’s publication may be corrections, but we don’t know that for sure.  Consequently, unless the variation involves a musical transition, such as a first ending to a repeat, we include them all in the database.