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)
Pronounciation of “timbre”
• 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
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)
major
minor
• Additional intervals modify the sound of
the chord
3 notes/3 intervals
4 notes/6 intervals
(major 7)
4 notes/6 intervals
(dominant 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:
Slow
Fast
Do you hear this?
Or this?
Auditory Scene Analysis
• Effect of proximity:
Do you hear this?
Or this?
far
close
Auditory Scene Analysis
• Effect of proximity:
– auditory system groups together events
that happen close together in time and
frequency