Note Lengths (Duration Ratios)

This section discusses the findings of the Skiptune project with respect to the length, or duration, of notes in tunes spanning the centuries and various genres of music. The length of a note is simply how long it is held, notated throughout this website as “duration.” A more complete description of note durations or duration values can be found on the definitions page, where you can also find the duration values of each kind of note (see the ‘duration’ entry).  For the Skiptune project we define a duration ratio as the duration value of the second note divided by the duration value of the first note.  For instance, a quarter note followed by another quarter note, no matter the pitch change, has a duration ratio of “1” because the quarter notes have the same duration value.

At 82,000 tunes, there are 486 different duration ratios in the Skiptune database.  It is apparent that the number of possible duration ratios is infinite because one could tie an endless number of notes together.  But practically speaking, composers tend to limit themselves to duration ratios that by and large do not extend lower than 1/40 nor exceed 40/1.  That is, one note is almost always less than 40 times longer or shorter than the note next to it.  There are exceptions, of course, but these tend not to be useful or interesting except for their novelty.   Patterns outside these bounds are extremely few in number, so we lose little by limiting our duration ratio analysis to note patterns with duration ratios between 0.025 and 40.

Mathematically, there are 2,561 possible duration ratios between 0.025 and 40.  The Skiptune database contains 486 of those possible duration ratios, or about 19 percent.  That may be surprising at first glance because it’s a rather small percentage of all the possible duration ratios.  However, many of those unused duration ratios are complicated and would have limited use in most compositions.  Take, for instance, the 1.026 duration ratio, which is formed by two successive notes with lengths of 39 and 40 (40/39 = 1.026).  Here’s how that would look in standard notation:

While it’s certainly possible that some composer may find a way to fit this formulation into a composition, it would be contrived and therefore highly unlikely in any piece that would stand the test of time.  We will not be discussing such strained formulations further.  For those interested, here’s the calculation for this duration ratio example, keeping in mind that a sixteenth note has a duration value of 1:  (1 + 8 + 2 + 14 + 14 + 1) / (16 + 16 + 4 + 2 + 1) or 40/39.  Observe that there’s no tie over the two sixteenth notes, which is the demarcation between the first set of notes and the second that form the 1.036 duration ratio.

The pages in this section explore these duration ratios, focusing on those that more common and those that are quite rare. We start off with the big picture: the distribution (that is, the variety) of duration ratios used by composers.