Mathematics of Music

I feel it is safe to say that all people enjoy at least some genre of music, and I personally find music to be one of the most pleasurable sensations we are given in life. However, few people truly understand the direct correlation between mathematics and music. Music is an excellent example of how the human brain can receive a wide range of frequencies and interpret them from both objective and subjective points of view. Putting aside an individual’s specific tastes, most people can agree upon the need for certain harmony and musical theory to exist in order for the sound to be considered pleasing to the ear. But what is it that determines whether a music piece is amazingly beautiful or absolutely awful? The answer lies within the mathematical language of sound and harmony. The music of nature first serenaded humans, but it didn’t take long for man to learn how to produce every sound imaginable. Pythagoras was the first to really apply his knowledge of sacred mathematics and ratios to the art of music. For any stringed instrument, the position at which the string is pushed down determines the note produced by the different frequencies. For each depressed string, the ratio at which the string is divided governs how well the sound is to the ear. By recording every different ratio and its respected sound, Pythagoras was able to find the most delightful ratios and create the Diatonic Scale. Pythagoras was fixated on the Golden Ratio and the Fibonacci Numbers and wanted to see how they behaved in the musical spectrum. Not surprisingly, the perfect ratios yielded the most beautiful notes and chords in the entire scale. For these reasons, many musicians including Beethoven, Mozart, Chopin, and Schubert implemented the Fibonacci ratios into some of their entire compositions. Even the timing and measures at which the different instrumental sections such as strings, percussion, and cellos entered the symphony were deliberately based on the Fibonacci intervals. Next posts, I will continue discussing the fundamentals of mathematics that create the frequencies we perceive as musical harmony.