# Math Relate to Music

Topics: Musical notation, Mensural notation, Time signature Pages: 13 (3581 words) Published: February 28, 2013
MATH AND MUSIC
MATH AND MUSIC

Math and Music
Math and music are connected in many ways. Math is seen to be as very precise. Music is often seen as a way to express emotion. They are actually both very closely related together. Music is an expression of scales and notes that are strung together to make sound. Math is the subject of numbers and symbols used to write formulas and equations. At its foundation, music and math are related. In this essay, you will show that math and music are related in many ways. They are more closely related then what they are seen to be. Numbers to beats. Pitch to rhythm.

Rhythm
Math and music’s connection begins with something called rhythm. Music is built on rhythm. Same as how mathematics is based on numbers. Rhythm is made whenever the time range is split into different pieces by some movement or sound. There are many everyday life examples of rhythm the beating of your heart, when waves hit the shore of a beach and the systematic way the traffic light blinks is rhythm. Rhythm measures time so the measure and time signature are created to make rules for a certain piece of music. A piece of music is divided into equal measures. Each measure represents the same amount of time. Each measure gets split into equal shares, or beats.

A time signature has two parts. It resembles a fraction. The top number (numerator) is how many beats in each measure. The bottom number (denominator) indicates tells you which note to count. For example, 4/4 is the most common time signature. The four at the top represents how many beats in that measure (4). The four at the bottom indicates which note to count (in this case, a whole note). Beats are in notes. These represent how long to hold the note for. For example, a quarter note equals one beat.
How many beats in measure, four. (Numerator)
How many beats in measure, four. (Numerator)

Which note to count for, whole note. (Denominator)
Which note to count for, whole note. (Denominator)

Binary Number System
Music is related to math with the binary number system. By following this pattern, one can see how each succeeding power (of two) gives a new note to work with (ex: sixteenth notes, thirty-second notes, sixty-fourth notes, one hundred-twenty-eight notes, and so forth). This pattern is also used for rests. A rest that is a whole rest is equal to a whole note. A half rest is equal to a half note. This pattern continues on. In 4/4 time there is one whole note in a measure, this equals 20=1. Two half notes go in a measure. The binary version of this is 21 = 2 half notes per measure. 4 quarter notes in a measure. The binary version of this is 22=4 quarter notes in a measure. 8 eighth notes go in a measure. The binary version of this is 23=8 eighth in each measure. 16 sixteenth notes fall in each measure. The binary version is 24=16 sixteenth notes in a measure.

Binary Number System is shown above
Adding a ‘dot’ after any note increases the value of the note by one half of the original note value. This also applies to rests.

All of these rests and notes can be a combination of many arrangements to make different rhythms. The only condition it has is that there must the same exact number of beats in every single measure.

A time signature of 4/4 says that every measure, no matter what notes they contain, must equal four beats. The fractional way of saying this is the sum of the fractions that every individualized note represents, must always equal one. This is because 4/4 simplified is “one.” Here are a few examples that will and will not work out.

Another very common time signature is 3/4. The fractional way of saying this 3/4. The quarter note would still get one beat (due to the fact a four is at the bottom) but this time there would only be three beats in a measure. This basically means the total number of beats must be three. These are some examples that...

Bibliography: http://www.goldennumber.net/music/
Math and Music: Harmonious Connections by: Trudi Hammel Garland and Charity Vaughn Kahn