What are harmonics?

Superposition of two (or more) frequencies yields a complex wave with a fundamental frequency

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 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

• f1= 400 f2 = 800

– (f2 = 2 x f1)…octave

• f1= 400 f2 = 600

– (f2 = 3/2 x f1)…perfect 5th

• f1= 500 f2 = 800

– (f2 = 8/5 x f1)…minor 6th

• f1= 400 f2 = 550

– (f2 = 11/8 x f1)

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

• Consonance seems to decrease with increasing complexity of the ratio of the tones

Music is combinations of intervals played in series (with some rhythm)

• Combination of three different intervals is a chord (major or minor)

• Additional intervals modify the sound of the chord

major minor

3 notes/3 intervals

4 notes/6 intervals (dominant 7)

4 notes/6 intervals (major 7)

Auditory Scene Analysis

• Sounds don’t happen in isolation, they happen in streams of changing frequencies

• How does the system group related auditory events into streams and keep different streams separate?

Auditory Scene Analysis

• Solving this problem is called Auditory Scene Analysis

• One important principle is proximity –in pitch, time, or spatial location

Auditory Scene Analysis

• Effect of proximity:

Pitc

h Do you hear this?

Pitc

h

Or this?

Slow Fast

Auditory Scene Analysis

• Effect of proximity:

Pitc

h

Do you hear this?

Pitc

h

Or this?

closefar

Auditory Scene Analysis

• Effect of proximity:– auditory system groups together events

that happen close together in time and frequency