Week 1.2 Some Math

Last Session Elements of Music Structured/Designed Sound Some pleasant – bells, most musical instruments Some nasty – whip Some intermediate - drums Rhythm (time) Tones (Not defined, though) Loudness (not actually listed, nor defined) Pleasurable ???? Message ???? We listened to some interesting samples of music. We will be listening to much more.

Bone Flute – Music is older than I am! 40,000 years or more Neanderthal

Where did instruments come from???

What does this mean?

Lightening Takes time to get to you or you are in big trouble. Speed = distance/time What is distance? What is time?

Sound --- A “disturbance”

Important Definitions Length or Distance How “far” something moves or travels. Measured against some agreed upon standard. Length Standard .. The Gorf 1 2 3 4 1/8 = 4 1/8 Gorfs Unknown Length

The real standard: The Meter

Systems of Units SI Units …. Meters, Seconds, Newtons/Kilograms English System ….. Feet/yards, seconds, pounds/poundals

More Important Definitions TIME The subjective “distance” between two EVENTS. It needs to be objective … ie measurable and reproducible. Original Clock – The Earth’s Rotation “It is two days journey” Today’s Clocks – “He ran the race in 4 hours, 2 minutes and 21.85 seconds”

Things that “tick” at some rate The planet … once a day The Pendulum .. Depends on a number of things; Parameters: Mounting Length Weight, whatever that is.

We will discuss this “g-thing” when we In case you care We will discuss this “g-thing” when we get to acceleration.

Sun Clock

Water Clocks

And so on … Rolex (~$10K) Atomic Clock (NASA) $ megabucks

The music clock: the Metronome 112 quarter notes per minute. Tempo Kind of Pendulum

We hear music (and other noise) in our ears. Sound

And you didn’t even know that you have one! Sound pushes against your Tympanic Membrane

Better View

Inside your head d D To Brain

A graph … what does it all mean? time (seconds) 2 distance (meters) 1 100 50 snail rabbit

Another Graph .. a biggy! -1.5 -1 -0.5 0.5 1 1.5 5 10 15 20 25 0.5 1 1.5 5 10 15 20 25 Time (seconds) disturbance

Important Definitions The PERIOD, T is the time it takes to go from one condition to the next time that exact condition is repeated. The frequency, the number of oscillations per second, is given by:

Siren … a scientific instrument

The Graph

Bottles on the wall …

Resonance (later) Loudness Rotational Speed (Turns/second)

Helmholtz Resonators

Helmholtz’s Results Note from Middle C Frequency C 264 D 297 E 330 F 352 G 396 A 440 B 496

Next ... Fun with Strings