A ‘unique pattern‘ is a series of notes that occurs only once in the Skiptune database of melodies. Although the number of possible unique patterns is finite, it is an extremely large number. Some patterns are just highly unlikely to be used in a melody or tune because they are virtually unsingable or unplayable. For instance, four whole notes tied together followed by a 1/128th note would be unlikely in a musical composition. If we consider just known two-note patterns, we can calculate that there are over a googol possible tunes or melodies. (A googol is a 1 followed by 100 zeroes and as an English word pre-existed, and is unrelated to, the famous search engine.) That’s more tunes than atoms in the visible universe, and it’s more tunes than the number of possible chess games. We won’t be running out of songs anytime soon, even if most of those patterns will never be used in a tune.
How Many Two-Note Patterns Can There Be?
How many theoretical unique two-note patterns are there? With 82,000 tunes, we have found 486 distinct duration ratios and 85 different intervals (pitch changes). The number of possible pitch changes is technically higher–a piano spans seven octaves–but the vast majority (all but a handful) of intervals are within 3-1/2 octaves, which equates to 85 intervals. We constrain the pitch changes to 85 to save computing time and storage while encompassing the vast majority of intervals.
Multiplying those together, we calculate that so far there are around 41,310 possible two-note patterns. Of those, 4,651 different two-note patterns exist in songs, tunes, or melodies that have stood the test of time and are in the database. In other words, all the tunes entered in our database only use 11 percent of the possible two-note patterns. Admittedly, many of these patterns will never be used because their intervals are so large that they are too unwieldly to fit into a melody, or because the duration ratios are so unusual that they would be hard to work into a tune, or both. See this histogram of duration ratios plotted against intervals for more information about which patterns are used.
Growth Rate of New Patterns Slowing
As we add new tunes to the Skiptune database, the rate of discovered patterns is quite slow, roughly 20 new two-note pattern for every 1000 new tunes entered. Even lower is the rate of growth of unique patterns, which is under 10 per 1000 new tunes. Of the 4,277 two-note patterns in the database, 1,392 are unique (used in only one melody in the database).
Both the rate of adding new two-note patterns and the rate of adding unique two-note patterns are strongly affected by the era in which the tunes were written. Tunes written since 1920 add more new two-note patterns and unique two-note patterns at a much faster rate than those written in previous eras. We enter music from all musical eras on a rotating basis, entering 100 new melodies at a time from a given era before moving on to another era.
Over time, as new tunes are added from all musical eras, we expect the number of new two-note patterns to continue to grow slowly and eventually decelerate. We also expect the number of unique two-note patterns to eventually fall, though that hasn’t happened reliably yet at 82,000 tunes. That’s because while each new two-note pattern we add is unique when first entered, that uniqueness may not persist. Eventually, the number of unique two-note patterns must at least level off and likely start declining. Indeed, we have had the experience of adding 100 new tunes, finding a few new two-note patterns, but decreasing the number of unique two-note patterns. In those cases, we happened to have added tunes that repeated previously catalogued unique two-note patterns.