Canada's Homeschool

Music is a wonderful learning tool that is motivational, fun and helps with memorization through rhythm, rhyming and repetition. My own children and students have memorized many facts - including math through music.

Let’s first review the basic elements of music - rhythm, melody, harmony, timbre and texture.
Rhythm is the placement of the sounds in time – the length of the notes and the duration between the notes. The beat refers to a steady pulse or rhythm. And the beats are grouped into measures or bars.

Melody is a string of notes with a particular pitch and duration that stands out. The pitch is how high or low a note is or in other words, the position of a tone in the musical scale designated by a letter. This pitch is determined by the frequency of vibrations (i.e., number of cycles in a second) and is measured in hertz (Hz).

Harmony is the result of more than one pitch of note playing at the same time.

Timbre is the different sounds that can be noticed between different instruments playing the same note (for example a flute versus clarinet or even two different clarinets). Timbre is created because each note from a musical instrument is actually a complex wave containing more than one frequency.

Texture puts all of the pieces together. This describes how much is going on at any given moment (i.e., thick or thin, single or interweaving melodies, complex or simple rhythmic patterns).

Rhythm and Patterns are easy to see and feel! Musical notation is comprised of fractions – whole note, half note, quarter note, eighth note etcetera. Patterns of these notes are grouped into different measures or bars that are given a time signature. The time signature is like a fraction of which the numerator is the number of beats per measure and the denominator represents the type of note getting one beat. The arrangement of the rhythm in a repetitive pattern of strong and weak beats provides for the meter of the music.

Frequency and Pitch the musical scale we use today evolved in part from mathematics. As early as the 5th century BC, Pythagoras who was obsessed with ratios became one of the first mathematicians to make a connection with music. The ancient Greek octave had only 5 notes and the kitharas, a type of harp had 6 strings. Pythagoras noticed that each note was a fraction of the string used to create the first note.

Today’s scale is made up of 12 notes (the seven notes plus their corresponding sharps or flats).
So how did we get the 12 note scale?  Over time followers of Pythagoras played around with different ratios. Around the time of Bach, the full scale was created by using the ratio of an irrational number (2 to the 1/12th power or approximately 1.0594630943593...).
Each successive note can be found by multiplying this number (i.e., A= 440 Hz;   A#=440 x 1.059 = 466.16 Hz;  B=466.16 x 1.059 = 493.88 Hz). If you continue on, you will also notice that each octave is exactly twice the size of the previous octave. (110 Hz, 220Hz, 440Hz, 880Hz, 1760Hz).

With the “tempered scale,” composers had the ability to make beautiful music in varying keys. They also learned that different notes sounded good together – thus discovering harmonics where you can find even more math!

I will leave harmonics and tuning theory for your own research. However keep in mind while you are listening to your favourite song in the background, that your favourite subject – MATH, had a big role in its creation! <>

 Math Resources:

Music and Math Lesson Plan
http://cnx.org/content/m11638/latest/

Music and Mathematics Q & A
http://mathforum.org/library/drmath/sets/select/dm_music_math.html 

Wikipedia
http://en.wikipedia.org/wiki/Music_and_mathematics