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Transcript of Music-matics
Structure of Music...
Everyone loves music & music is everywhere! People listen to music:
in their cars
Once upon a time, instruments where tuned specifically for the key that the music was to be played in.
A system was created to overcome this...called equal tempering/well tempering.
Math beyond the pitch...
Math of music can also be observed in the notes that music is composed of! Various note lengths (and rests) are equivalent to fractions of a whole:
The Finished Product
But how many people know that there is mathematics in music!
Musical notes are sound waves that can be demonstrated by a sine function!
The amplitude of the wave accounts for how loud the sound is,
higher amplitude=louder sound
Frequency of the wave accounts for the pitch we hear,
higher frequency=higher pitch
. (Shortening a string=lower frequency)
However, a nice sine wave is only achieved from a single note!
As we begin to create music (combine notes), the wave becomes more irregular.
Origin of Sound...
While a note can be visualized as a sine wave, it is important to know why!
Vibration of an object causes alternating pockets of high and low pressure in the air. The faster the vibration, the faster the frequency...
Notes as integers...
The Ancient Greeks were able to draw a connection between integers and musical notes!
Octaves = 2
An octave is when the frequency of a note is
or cut in
Musical 5ths = 3
Resulting from a finding of Pythagoras...if a string producing one note is shortened by 1/3 a new note is created, named a 5th.
His finding resulting in the Circle of 5ths: 12 notes, each the 5th note in the scale of the proceeding note (
the perfect 5th of the other
2nd Octave = 4
If we were to cut in half a already halved string, we would be at a 2nd octave!
Musical 3rd = 5
Similar to a musical 5th, a musical 3rd is produced from a ratio of 5 (decreasing by 1/5 or increasing by 5)!!!
Together, a note from the
, and it's
An example would be...
Do, Mi, So
"Equal tempering is a system for breaking up each octave into
twelve equal semi-tones
. Since each octave represents multiplying the frequency by a factor of ,
each semi-tone represents multiplying the frequency by the
twelfth root of 2
- a number which produces two when twelve copies are all multiplied together. This number is about 1.059463, because twelve copies of 1.059463, all multiplied together, is equal to 2".
"J.S Bach's Well-Tempered Clavier was written in order to demonstrate equal temperament's ability to be played in tune in all twelve major and minor keys"
Which you have been listening to!!!!
Excerpt from Bach's Well-Tempered Clavier
While there may still be many more connections between math and music, this is just a brief look into some of the more important connections!
Thank you, for watching!!
Each measure of the music must reflect the time signature, when all the values of notes and rests are added up!
Time signatures indicate the number of beats per bar. For example:
= 6 eighth note beats in a measure
= 4 quarter note beats in a measure
= 3 quarter note beats in a measure