Torment and interpolations

John Stuart Mill makes an argument that there will come a time— if it has not been reached already— when all the great works of music have already been written. He writes:

The octave consists only of five tones and two semi-tones, which can be put together in only a limited number of ways, of which but a small proportion are beautiful: most of these, it seemed to me, must have been already discovered, and there could not be room for a long succession of Mozarts and Webers, to strike out, as these had done, entirely new and surpassingly rich veins of musical beauty.

His idea is that there are only a finite number of notes which can be combined in only a finite number of ways. Many of the ways will be awful. Of those that are not, many have already been discovered and documented by great composers.

Although Mill only addresses instrumental music, we could extend the argument to songs. Any lyrics which can be written down with an alphabet are built from a finite number of letters which can be combined in only a finite number of ways. Many possible lyrics will be bad. Of those that are not, many have already been written— and each new song further reduces the remaining number of unwritten songs. So there will come a time when all of the great songs have been written.

Mill recounts that he was “seriously tormented” by this line of thought, but notably this confession is in his autobiography rather than in one of his philosophical works. He makes light of it in retrospect, offering it as evidence of the dark place he was in rather than suggested it as a real concern. The torment, he writes, was “very characteristic both of my then state, and of the general tone of my mind at this period of my life.”

In order to make it a cause for concern, we would need the additional assumption that running out of tunes would be bad. Mill suggests that “the pleasure of music… fades with familiarity, and requires either to be revived by intermittence, or fed by continual novelty.” For many of us, however, there are favorite songs which can survive being replayed. Even overly-familiar songs can be given new life by a new musician who changes them up. That is part of the fun of covers.

The argument also relies on a questionable assumption of “the exhaustibility of musical combinations.” That is, it requires that the palette of musical materials be sufficiently limited that musicians might explore the whole space of worthwhile combinations. Even if the number of possible songs is finite, it might still be so large that musicians would not write all the good songs even in the lifetime of the whole universe. Moreover, musical performance can offer an uncountable infinity of qualities— in timbre, timing, and expression— such that the same musical passage can offer different rewards when played by different musicians.

Nevertheless, Mill is right that there are only so many ways to put together a finite set of notes and chord progressions. There are only so many ways to combine these in a short sequence like a melody, a chorus, or a bridge. So it is no surprise that many patterns appear in multiple songs. Earlier songs often serve as inspirations for new ones, and songwriters reuse elements from earlier work. Moreover, it is not unheard of for a songwriter to independently hit upon a series of notes that has already been used by someone else.

The industry term for using lyrics or melody from a copyrighted song is interpolation. Unlike a cover or quotation, interpolation need not be deliberate.

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