Learning music improves math skills because, at some level, all music is math. It’s about time signatures, beats per minute, and formulaic progressions. Performing music, therefore, reinforces parts of the brain used when doing math. Fine motor skills are also improved by playing musical instruments.

If you are thinking of going into the field of music as a teacher, a technician in sound recording, as a producer in the business of music, a composer, or a violinist for the Philharmonic Orchestra, you’ll most likely need to have decent math skills.

From the very beginning, you will see that many of the notes on any given instrument are connected to mathematical equations. You will need to know how they are written in order to play correctly. Whether you sing along with lyrics or play an instrument, mathematics can be found throughout the music. Many musical pieces involve math when it comes to rhythm, notes, and even the instruments themselves.

## How is math used in music?

Music theorists, like experts in other disciplines, use mathematics to develop, express and communicate their ideas. Mathematics can describe many phenomena and concepts in music. Mathematics explains how strings vibrate at certain frequencies, and sound waves are used to describe these mathematical frequencies.

But how is math used exactly in music?

Music uses math mostly for rhythm, notes, patterns, and instruments.  Rhythm is described as how notes are grouped together. For example, two eighth notes would be equal to one, quarter note because there are eight of them in a measure. Notes are also described mathematically.  For example, a perfect fifth is the distance from one note to another that spans seven semitones and an octave (the eighth note) on the chromatic scale (a musical scale of twelve semitones).

Patterns can be found with scales, for example. There are seven notes in the major scale, and there are eight total steps since you begin on the octave. Instruments are based on mathematical equations too. For example, a string bass has four strings that are tuned to E, A, D, and G. These notes are all perfect fifths apart from each other starting at E.

Another use of math in music is from the terms for notes. The A naturals, B flat, and C sharp are all members of a chromatic scale where each note is different by a half step.

In terms of rhythm, the time signature tells you how many beats there will be per measure and what kind of note gets a beat. 4/4 time means that there are four beats per measure and the quarter note gets one beat.

Harmony occurs in music when two pitches vibrate at frequencies in small integer ratios. For instance, the notes of middle C and high C sound good together (concordant) because the latter has TWICE the frequency of the former.

Frequency is the rate of vibrations per second.  For example, the A 440 Hz note has 440 vibrations per second. Frequency can be used to figure out which notes sound good together.  The math for that comes from harmonics and string lengths. For example, two strings that are half as long as each other will produce an octave, four times the frequency.

You will see that math and music go hand in hand when it comes to learning, writing, and playing both. So whether you plan on scoring a movie or dubbing an animation, these skills will be necessary for your success.

Math is one of many reasons why we can’t escape the wonders of music!

#### Math in music examples

Counting, rhythm, scales, intervals, patterns, symbols, harmonies, time signatures, overtones, tone, pitch. The notations of composers and sounds made by musicians are connected to mathematics.

As already expressed, math is used all throughout music in rhythm, scales, and instruments. More detailed examples would be when you see certain notes in music. For example, the key of C consists of only natural notes (A B C D E F G). These notes actually relate to a C major scale which has no sharps or flats in it. The D flat is one half step down from the D natural note and that makes up a different key altogether.

Other examples of math in music would be the use of key signatures and time signatures.

Key signature: there are twelve notes that makeup one octave (A B C D E F G) and only seven different clefs (bass, baritone, tenor, alto, soprano, mezzo-soprano and countertenor). Each clef is split in half and each half has a sharp or flat in it. If you see the key signature at the beginning of sheet music, there will either be no flats or sharps written in it. This changes when different keys are played such as A major and F major.

Time signatures: every bar in a piece of music has two numbers in it separated by a colon. The top number is the number of beats, and the bottom is what kind of note gets a beat. 4/4 time means that there are four beats per bar and the quarter note gets one beat.

What instruments use math in playing?

Instruments that use math in playing come from scales and harmonics. Instruments like the piano, guitar, and drums use scales. The science and mathematics of music (Johnston & Hargreaves, 2012) state that a scale is “a sequence of notes arranged according to the frequency ratios 4:5:6:8.” This means instead of having twelve notes each increasing by a half step, you will have seven and they will increase in fourths and fifths. The guitar and piano use scales where the E string is just tuned to an octave higher than the open E string.  Another instance would be with the drums. A lot of percussion uses perfect fourths, fifths, octaves, etc. to keep the beat.

What are some examples of math in playing an instrument?

An example of math in playing an instrument would be on a piano. When you play certain notes together at the same time, they sound more harmonious than others. This is because there are mathematical equations that dictate which combinations will work and which will not.

An example of math in playing an instrument would be when you are reading sheet music. To play what the notes say, you have to know where they start and end on the staff which will tell you how many beats per measure there are, how long the note gets, etc.

How is math related to singing?

Math is involved with singing because it takes math to figure out which pitches sound good together. An octave is made up of multiple notes and they make the harmony in most songs.

Music is full of math whether you realize it or not, so if your favorite pastime involves listening to music, you might want to look into what went on behind the scenes!