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Music Is Math

Nerd Nite Presentation, November 2013

Tiffany Criswell

on 14 November 2013

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Transcript of Music Is Math

Music Is Math
Inner Ear Anatomy
Natural Frequencies
A natural frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. Some of the implications of resonant frequencies are:

1. It is easy to get an object to vibrate at its natural frequencies, hard to get it to vibrate at other frequencies.

2. A vibrating object will "pick out" its natural frequencies from a complex excitation and vibrate at those frequencies, essentially filtering out other frequencies present in the excitation.
Sound through Matter
Sound can move through different media besides air. This is how we can "feel" sound at a super loud show or hear a whole car vibrate from its contained jams.
What Is Sound?
Sometimes this frequency is bad, mmmkay?
Resonant oscillations have been known to cause structural collapses.

In Kansas City in 1981, a hotel walkway collapsed from being vibrated at its natural frequency by dancers during a dance contest. Over 100 people were killed.

Resonant oscillation is why military processions cease marching while crossing bridges. Most bridges can handle marching with ease, but suspension or smaller foot bridges can collapse from resonance.
A wave!

Sound comes from energy moving through a medium (repeating in a nice happy wave shape) within the frequency range audible to the human ear (20 to 20,000 Hz).

Sound can't travel in the absence of matter.
The ear must hear a sound for 15 milliseconds or longer for it to register as a pitch instead of a click.

Human hearing ranges from 20 to 20,000 Hz and from 30 to 100 decibels

Sound waves vibrate tiny bones in our ears. It's gross but cool.
Because someone will ask...
Can an opera singer break a glass with his/her voice?

A metal singer can, yo.

This phenomenon is caused by a singer experimenting until he or she finds a glass's particular natural frequency.
Why does some noise sound like music and some noise sound like... noise?
Harmonic series = series of pure tones in which every overtone frequency is an integral multiple of the fundamental frequency
What about drums and cymbals?
Drums and cymbals have a base frequency, of course, but lack an ordered overtone series.

Our ears hear this as "noise" instead of a musical pitch due to this lack of order, but cymbals can still be "tuned" to have rich nonharmonic overtones.
Why do all instruments sound different?

A subjective term, but technically how two tones of equal loudness and pitch can still sound different. (A guitar and a trumpet sound very different even if playing the same note at the same volume.)

An instrument's timbre depends on the number and relative strength of a tone's partials/overtones.
Magnificent bastard
Simple Ratios
Octave frequency ratio -- 2:1
Perfect 5th -- 3:2
Perfect 4th -- 4:3
Major 3rd -- 5:4

Example: Concert A (440 Hz) and its octave partner above (880Hz) make a delightful 2:1 ratio
Counterpoint: Rules, Rules, Rules
Counterpoint: a complex set of rules that dictated how music was written for hundreds of years, until and including the Baroque era.

Every note has its place and explanation -- no outliers

For Heaven's sake, no tritones*... THE DEVIL'S INTERVAL
(Frequency ratio 45:32)
Music Happens within Narrow Parameters
There are only 24 key signatures in western music.

There is a distinct order of chords within these key signatures (3-6-4-2-5-7-1).

The fact that so many different songs have been written within these narrow parameters is astonishing and rad.
Everything Is a Remix
Within such narrow parameters, patterns and repetitions are inevitable.
Cultural Memory and Repetition
Brains love patterns.

(polio and ice cream)

(shave and a haircut)
"What about Sonic Youth?"
Rhythm and repetition step in where harmonics "fail."

Cultural memory and repetition play enormous roles in music.
Atonal Music Systems
It became popular to write music according to even more strict, often purely mathematical guidelines.

All instruments (in fact, all materials) have their own unique set of natural frequencies.
Anatomy of a sound wave
Hz = [sound] wave cycles per second

Sound is converted into electrical impulses by the cochlea, which are then sent to the brain.
Just like the metal plate in the video, all instruments divide/vibrate into distinct sections while played.
Pitch = the base frequency of a tone
Musical tone = the base frequency plus overtones/harmonics
everythingisaremix.info = amazing source for these occurrences.
Green Day + Pachelbel's Canon in D
Tone row: uses of each tone once before any repeats.


"Also Spake Zarathrustra" by Strauss
Modern Acoustics: Room Tuning
Decay time

Diffusion -- irregular surfaces help mix sound

Certain materials are also used to help take care of aural problems:
Fabric (draperies)

The sound absorption factor of people and chairs are also taken into account.

Textured walls help absorb higher frequencies.

The World's Quietest Room
Aristotle vs. Plato: FACE-OFF
Just as Aristotle had to defend storytelling, so have many composers through the years had to defend secular music.

For many hundreds of years, the "purpose" of music was to inspire people to strive to live up to religious ideals.

Secular music was not recognized by the western musical establishment until the Baroque era--even then, it was controversial.
Remember that sound is turned into electrical impulses and send to the brain.

The brain can pick up on incorrect ratios and can hear that something is "off."
Why do I sound so awesome when I sing in the shower?
Materials (Tile) cause natural:

1) Amplification

2) Reverb

It's not in your mind. You really do sound good.
Piano Strings
Pianos are complex creatures that contain tens of thousands of pounds of string tension.

To make bass strings vibrate slower to produce a lower pitch, they are wrapped in copper or iron wire.

Extra strings are added to the high notes for more volume.
Chandeliers and ornate decor help diffuse and mix sound.
This room is known to cause hallucinations. The longest anyone has ever lasted is 45 minutes.
Air at 0 degrees C = 332 meters/sec
Hydrogen at 0 degrees C = 1,286 meters/sec
Lead = 1,210 meters/sec
Copper = 4,600 meters/sec
Steel = 5,000 meters/sec
Aluminum = 6,320 meters/sec
Diamond = 12,000 meters/sec
Sea water = 1,533 meters/sec

Evelyn Glennie: professional percussionist, deaf, all-around BAMF-type person
Giant, boxy warehouse venues sound sad and are sad.
Harmonic series for the note C
(Piano strings and all stringed instruments are guided by Pythagorean principles.)
He'll be Bach.
... Bueller?
By Tiffany Criswell
A pure tone, lacking overtones, sounds mechanical or "fake" to the ear.

If ordered, a noise sounds musical. If unordered, a noise sounds like noise.
Other popular songs in this key with this chord progression:
"Hook" - Blues Traveler
"Ladies and Gentlemen, We Are Floating in Space" - Spiritualized
"Let It Be" - The Beatles
"Push" - Matchbox 20
"Torn" - Natalie Imbruglia
"With or Without You" - U2
"We're Not Gonna Take It" - Twisted Sister
"Right Here Waiting for You" - Richard Marx
"No Woman, No Cry" - Bob Marley
"Machine Head" - Bush
"I'll C U When U Get There" - Coolio
"I Should Be So Lucky" - Kylie Minogue
"Cryin'" - Aerosmith
"Get Me Away from Here, I'm Dying" - Belle & Sebastian
"Life Goes On" - Tupac
"Fullness of Wind" - Brian Eno
"Go West" - Pet Shop Boys
Question and [Possible] Answer Time!
Choruses! We love them.
*A tritone is an augmented 4th or a diminished 5th
Full transcript