Mathematics, Music and the Military

It is safe to say that mathematics is not universally loved.  It shares many of its unappealing characteristics with an infantry regiment, uncompromising rules, unquestioned orders, dull repetitions and enforced discipline, leaving no room for individuality and personality.  Put at the end of a spectrum of expressions of character, on the other end we would find creativity, individuality, the free, breathing human soul.

To those who share this view I present a paradox.  In music, the most fragile and soulful moments, the most delicate sighs of a loving heart, music described as divine is often produced by the dullest, repetitive, most militaristic and mathematical means.  This implies that our soul, or our subconscious, or whatever it is we want to call that which generates feeling within us from vibrations in air pressure, ties these two apparently different human expressions closely together.

Example 1:  If we think of fragile, delicate music, what better example than the music written by Chopin, for example his prelude No. 15, Opus 28.  Listening to it without any analytical ambition we find behind a thoughtful character first cautious anxiety with a glimpse of hope, followed by utter despair.  If we however analyse the structure of that piece we find that it moves around the note A-flat, which is played throughout the piece in evenly spaced short intervals, like the footsteps of soldiers.  And what could be less creative, duller, simpler than stubbornly playing one and the same note repeatedly throughout an entire piece, surrounded by the simplest of decoration.  Yet the effect is sublime.

Example 2:  Beethoven’s Adagio Sostenuto from the Piano Sonata No. 14., named misleadingly after moonlight, is one of his most intimate, silent and contemplative pieces.  In terms of structure it is at the same time one of the dullest, repetitive and simplest pieces he ever wrote, consisting of long harmonic chords for the left hand, shorter equally unimaginative chords for the right hand, split in individual notes, and some notes hanging over it that in itself could hardly be called a melody.

The reverse argument can equally be made.  Musicians opposed to structure have developed types of so called free music such as free jazz that deliberately avoid structure, repetition and harmony.  The results typically do not invite contemplative and intimate sentiment.

The effect of music may result to a great deal from its abstraction that has no equal in nature, we might say that music is a state of rather low entropy.  The sublime effect of music is partly produced by a brain that is confronted with more abstraction than it is made to expect anywhere.  Order, repetition, harmony in music add to that, essentially.  Even if the effects of music differ from the effects of a marching regiments, the means can resemble, surprisingly especially in the most delicate musical moments.