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 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
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 (tone height)
• The pitch that you hear is (usually) the
fundamental frequency
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)
Next Time
• Perceiving
Speech