Pitch and Music
Pitch
• Pitch is the subjective perception of
frequency
Period - amount of time for one cycle
Frequency - number of
cycles per second
(1/Period)
Air Pressure
time ->
Pitch
• Pure Tones - are sounds with only
one frequency
f = 400 hz
f = 800 hz
Tone Height
• Tone Height is our impression of how
high or low a sound is
• but there’s something more to our
impression of how something sounds
than just its tone height…
Chroma
• Tone Chroma is the subjective
impression of what a tone sounds like
• Notes that have the same Chroma
sound similar
500 Hz
400 hz
800 Hz
Chroma
• Tones that have the same Chroma are
octaves apart
Chroma
• chroma is best represented as
a helix
• chroma repeats every octave
• tones with the same chroma
are above or below each other
on a helix
Chroma
• Tones that are octaves apart have the
same chroma
• one octave is a doubling in frequency
Chroma
• frequency is determined (in part) by
location of stimulation on the basilar
membrane
Chroma
• frequency is determined (in part) by
location of stimulation on the basilar
membrane
• but that relationship is not linear (it’s
logarithmic)
Chroma
• doublings of
frequency map
to equal
spacing on the
basilar
membrane
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?
imagine a guitar string:
up
position
down
What are harmonics?
imagine a guitar string:
up
position
down
What are harmonics?
But more than one frequency can “fit” between the end points
up
position
time ->
down
What are harmonics?
In fact many frequencies can be superposed.
up
f0
f2
position
time ->
down
f1
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)
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 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
• 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
• Dissonance
seems to
increase
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 timing proximity:
Slow
Fast
Auditory Scene Analysis
• Effect of timing proximity:
Slow
Fast
Do you hear this?
Or this?
Auditory Scene Analysis
• Effect of pitch proximity:
far
close
Auditory Scene Analysis
• Effect of pitch 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