A brief message from your TAs Tine Gulbrandsen Wahab Hanif

Pure Tones are Very Rare in Nature! What are real sounds composed of?

Pure Tones are Very Rare in Nature! What are real sounds composed of? Virtually all sounds are composed of several (or many) frequencies all going at once

Pure Tones are Very Rare in Nature! What are real sounds composed of? Virtually all sounds are composed of several (or many) frequencies all going at once “Extra” frequencies are called harmonics

What are harmonics? position up down imagine a guitar string:

What are harmonics? position up down imagine a guitar string:

What are harmonics? time -> position up down But more than one frequency can “fit” between the end points

What are harmonics? time -> position up down f0f0 f1f1 f2f2 In fact many frequencies can be superposed.

Properties of a Sound Wave A 1 second, 1 Hz sound wave:

Properties of a Sound Wave A 1 second, 2 Hz sound wave:

Properties of a Sound Wave A 1 second, 3 Hz sound wave:

Properties of a Sound Wave What would happen if two or more sound waves were happening at the same time?

Properties of a Sound Wave Sounds superpose (they add together)

Properties of a Sound Wave Sounds superpose (they add together)

Properties of a Sound Wave If most sounds are made of several frequencies, then which sound determines the pitch that you hear?

Properties of a Sound Wave If most sounds are made of several frequencies, then which sound determines the pitch that you hear? Typically you hear the lowest frequency component as the “pitch” of a complex wave

Properties of a Sound Wave The lowest frequency is called the fundamental

The Missing Fundamental Your brain so likes to track the fundamental of a set of harmonics that it will perceptually fill it in even when it is absent missing fundamental

Timbre (pronounced like: Tamber) pure tones are very rare a single note on a musical instrument is a superposition (i.e. several things one on top of the other) of many related frequencies called harmonics Pronounciation of “timbre”

Timbre the characteristic of a particular set of harmonics is called timbre –e.g. the set of harmonics generated when a particular key is pressed on a piano timbre is one reason why we can tell the difference between the same notes played on difference instruments

Timbre Although any musical “note” is a superposition of harmonics, you still hear it as a single pitch (you hear its tone height) The pitch that you hear is (usually) the fundamental frequency (except in the artificial case of the “missing fundamental”)

Musical Intervals in music, notes are played together or in quick succession pairs of notes share a relationship called an interval

Musical Intervals Within each pair, the higher pitch (f2) is some multiple of the lower pitch (f1): –e.g. 200 hz and 400 hz -- f2 is two times f1

Musical Intervals f 1 = 400 f 2 = 800 – (f 2 = 2 x f 1 )…octave f 1 = 400 f 2 = 600 –(f 2 = 3/2 x f 1 )…perfect 5th f 1 = 500 f 2 = 800 –(f 2 = 8/5 x f 1 )…minor 6th f 1 = 400 f 2 = 550 –(f 2 = 11/8 x f 1 ) octave perfect 5th minor 6th not quite a perfect fourth?!

Consonance and Dissonance Consonance is the degree to which two tones played together sound “good” Dissonance is the opposite

Consonance and Disonance Dissonance seems to increase with increasing complexity of the ratio of the tones

Seeing Sound with Spectrograms A spectrogram is a 3D plot of sound Time Frequency

Seeing Sound with Spectrograms A spectrogram is a 3D plot of sound Time Frequency Intensity Intensity is often coded by colour such that red is high and blue is low