The Nature Behind Math and Music

Birds chirping in the morning or the crashing of waves on the rocks in the ocean helped create some of today’s best-selling music. As some of us may have heard in our Music Appreciation class at Stuyvesant, much of music stems from the natural world and its uniqueness. Sounds of nature often inspire classic albums such as The White Album and the album’s song Blackbird by the rock band The Beatles. But how do the sound of birds chirping, or any sounds of nature, help make music?

The harmonic sounds of the natural environment—such as the music of humpback whales and the song of a variety of bird species—all inspired the structures of human-made music. At the foundational level, whales use pure tones, a sound that consists of one single frequency, which is noticeable in modern symphonic music. Furthermore, our structure in pop music and jazz, for example, can be traced back to the formats of the humpback whales’s music: an initial theme, an elaboration of that theme, and an eventual cycle back to the initial theme.

Humans took nature’s sounds and created specific conventions, styles,  and structures for our music. Modern music includes measurements between two pitches known as intervals, and intervals between two notes are known as octaves. It also includes the waveform height of a sound known as pitch and a physical waveform’s cycle rate measurement known as frequency. All of these definitions stem from mathematics during as early as the fifth century BCE. Famous Greek philosopher Pythagoras of Samos—commonly known as Pythagoras—is mainly known for his invention of the Pythagorean theorem, a fundamental relation between the three sides of a right triangle. However, Pythagoras also understood the arithmetical relationship between pitches. He discovered that a string exactly half the length of another will produce a pitch exactly an octave higher than the other when struck. Furthermore, splitting a string into thirds raises the pitch an octave and a fifth. Splitting the string into fourths further causes the pitch to be higher. Thus,  shorter strings have a higher frequency and a higher pitch. This is known as the overtone series or the harmonic series. However, what makes this series harmonic and thus different from those in nature? 

Harmony is created by using chords or intervals, and it is when at least two notes are played consecutively. Mathematically, harmony is when two pitches vibrate at frequencies with smaller integer ratios in comparison to each other. An example of this is the middle C and the G above it when simultaneously played. They sound concordant and pleasant to the ears due to the fact that the  frequencies of G and C are in a ratio of 3:2. An alternate definition of frequency explains why these ratios sound pleasant. Frequency can also be thought of as the measurement of vibrations (per second) that create sound waves. Our ears are sensitive to sounds between 20 Hz and 20,000 Hz. When two notes between these frequencies are simultaneously played in a ratio, they delight the listener. This is how music is made. To play a specific piece of music, one must play the notes in a certain sequence for a specific amount of time.  

Many people use the delightful sounds of music to motivate themselves while working out, studying, or various other activities, but there are many more benefits to music. Music can increase cognitive function through the use of binaural beats—two different frequencies’ beats that our brain interprets as a unique beat, which can align with your brain waves. You can play, in one ear, music at 120 Hz and, in another ear, music at 110 Hz. There are five main types of brain waves: delta, theta, alpha, beta, and gamma. Every brainwave is associated with a specific kind of activity or thought. For example, delta waves are associated with healing, meditation, and deep sleep, while alpha waves are associated with thought coordination and memory. Theta waves are specifically associated with listening to music, creativity, and intuition. Certain binaural beats can help increase the strength of certain brainwaves. For preoperative patients, binaural beats can help alleviate anxiety and nervousness. Binaural beats can also help increase the brain’s neurological connections, allowing for easier information recall—this can help a student with a test or presentation. Binaural beats in the gamma frequency—which increase cognitive flexibility—allow for more attention to detail, and focus. This could be beneficial for many school subjects such as math, science, or art. However, since listening to music improves memory and recall, these portions of the brain specifically boost remembering mathematical concepts and skills. 

Nature and math helped create the music we love today.  It all comes full circle; the natural sounds that we hear are mathematically in proportion with harmonic music. This harmonic music, such as binaural beats, is beneficial for math skills and other daily activities, creating a complex intersection between music and math.