MATHEMATICS, MUSIC

Simple formula for determining musical royalties

If you’re looking for a useful guide to determine royalty percentages when collaborating with other songwriters, here’s a simple way to calculate a general royalty percentage with respect to musical changes: R=(100e)(bdn)^{-1} where e = total events changed, d = quantity of the unit of metric measurement per bar, b = total number of measures, n = the smallest rhythmic value changed during alteration, and R = the total royalties earned (as a percentage).  Remember, the value for n must be based on the shortest rhythmic value that is changed.

Example:  John writes “Song X,” a 120-measure ballad using a 3/4 meter. Emily collaborates with John and changes 176 events at the nth-note level—in this case, say, sixteenth notes. (This could be 176 sixteenth notes, 88 eighth notes [n = 2], 44 quarter notes [n = 1], 704 thirty-second notes [n = 8], or any combination of such note values, but if we assume the shortest note-value Emily changed was (at least) one sixteenth note, the total amount changed should be based on the sixteenth-note value for n.

Therefore, the total number of musical events—based on the shortest rhythmic value of Emily’s changes—can be calculated as follows: bdn=(120)(3)(4)=1,440. That is, there are 1,440 sixteenth-note events in “Song X,” (bd gives us the total number of musical events with respect to the unit of metric measurement), and Emily will earn the following songwriter’s royalty if she changes 176 (sixteenth-note) musical events: R=100(176)(1,440)^{-1}=.122.

Simple—and pretty convenient if Emily begins clamoring for a 40-60 royalty split based on her efforts.  We could also create a similar algorithm for “chord changes” (based on harmonic rhythm) and even lyrics, but we’ll leave those projects as exercises for the reader.

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