Math seems to be one of those subject that finds itself in pretty much every aspect of art. From geometric art, to the circle of fifths, to even help determing how much support a truss needs so that it can sustain several actors/dancers running back and forth onstage.

By far the most interesting to me, is its influence in music. Music theory has everything to do with math. The first to discover the relation between math and music was Pythagoras of Samos. To Pythagoras ratios were everything and in music, ratios play a big role. In Greek music at the time, each octave only had 5 notes. Pythagoras noted that each note in an octave was simply a fraction of a string. For example, if you had a string that played the note A, if you only allowed ¾ of the string to vibrate upon being plucked you would get approximately the note D, if 4/5 of the string vibrated then you’d get C, and so on.

Later on, we got 12 note scales because followers of Pythagoras started applying this notion to other notes.

Math and physics can also answer other questions in music. For example, why if a flute and a violin play the same note, do they sound different? Answer: harmonics. Music is made of sound. Sound is made up of repeating sound waves. In physics, harmonics are waves at proportional frequencies, and inversely, at proportional amplitudes. If we were to play an “A” we not only hear the 440hz tone, but also the 880hz, 1320hz, 1760hz, and so on until the frequencies get too low or high for us to hear them.

Many classical composers are said to have incorporated math in their music. For example, Beethoven’s Fifth Symphony is based on the “golden mean”. That is, the ratio between the sum of two quatities and the larger quantity is equal to the ration between the large quantity and the smaller quantity. This is actually a constant (1.618033988….) usually denoted by the Greek letter phi, Φ. Another piece that is said to have been influenced by math is Bartok’s “Music for Strings, Percussion, and Celesta” in which Bartok structured his music using the Fibonacci sequence in the first movement.

Here is a link to Bartok’s piece Music for Strings, Percussion and Celesta , and Beethoven’s Fifth Symphony.

Furthermore there is also the relationship between learning math and music commonly referred to as the Mozart effect. It is said that if a child is exposed early on to early classical music, then it will lead to better performance on tests including spatial visualization and abstract reasoning, plus they tend to excel in subjects like math and science. Now where this is true or not, I am not sure, but it is definitely something to look into.