The Math State Test is only a week away! We know music spurs brain development, increases test scores, and improves social emotional skills. Math is also another subject that is linked to music. Famous mathematician, Albert Einstein stated, “If ... I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music.” In music, we start with simple math: counting beats by nodding our head or figuring out the numerical value of how long to hold a half note (2 beats), and then we move on to the fractional relationship of notes and their frequency. For instance:

“It was observed that when a frequency is multiplied by 2, the note stays the same. For example, the A (440 Hz) multiplied by 2 = 880 Hz is also an A, but just one octave above. If the goal was to lower one octave, it would be enough just dividing by 2. We can conclude then, that a note and its respective note have a relation of ½.

Let’s return to Ancient Greece. There was a man called Pythagoras that made really important discoveries to Mathematics (and music). Related to the math above, he discovered “playing” with a stretched string. Imagine a stretched string tied in its extremities. When we touch this string, it vibrates (look the drawing below):

Pythagoras decided to divide this string in two parts and touched each extremity again. The sound that was produced was the same, but higher (because it was the same note one octave above):

“It was observed that when a frequency is multiplied by 2, the note stays the same. For example, the A (440 Hz) multiplied by 2 = 880 Hz is also an A, but just one octave above. If the goal was to lower one octave, it would be enough just dividing by 2. We can conclude then, that a note and its respective note have a relation of ½.

Let’s return to Ancient Greece. There was a man called Pythagoras that made really important discoveries to Mathematics (and music). Related to the math above, he discovered “playing” with a stretched string. Imagine a stretched string tied in its extremities. When we touch this string, it vibrates (look the drawing below):

Pythagoras decided to divide this string in two parts and touched each extremity again. The sound that was produced was the same, but higher (because it was the same note one octave above):

Pythagoras didn’t stop there. He decided to experience how it would be the sound if the string was divided in 3 parts:

He noticed that a new sound appeared; different from the previous one. This time, it wasn’t the same note one octave above, but a different note, that was supposed to receive another name. This sound, besides being different, worked well with the previous one, creating a pleasant harmony to the ear, because these divisions showed here have Mathematics relations 1/2 and 2/3 (our brain likes well defined logic relations).

Thus, he continued doing subdivisions and combining the sounds mathematically creating scales that, later, stimulated the creation of musical instruments that could play this scales. The tritone interval, for example, was obtained in a relation 32/45, a complex and inaccurate relation, factor that makes our brain to consider this sound unstable and tense. In the course of time, the notes were receiving the names we know today.”

There is much more to music than just pretty sounds- there are deep mathematical processes happening when we listen or play music. And luckily, your student is experiencing this multiple times a week. For more interesting music and math descriptions, this website was the reference for this newsletter.

He noticed that a new sound appeared; different from the previous one. This time, it wasn’t the same note one octave above, but a different note, that was supposed to receive another name. This sound, besides being different, worked well with the previous one, creating a pleasant harmony to the ear, because these divisions showed here have Mathematics relations 1/2 and 2/3 (our brain likes well defined logic relations).

Thus, he continued doing subdivisions and combining the sounds mathematically creating scales that, later, stimulated the creation of musical instruments that could play this scales. The tritone interval, for example, was obtained in a relation 32/45, a complex and inaccurate relation, factor that makes our brain to consider this sound unstable and tense. In the course of time, the notes were receiving the names we know today.”

There is much more to music than just pretty sounds- there are deep mathematical processes happening when we listen or play music. And luckily, your student is experiencing this multiple times a week. For more interesting music and math descriptions, this website was the reference for this newsletter.