Download cents

PH 105
Dr. Cecilia Vogel
Lecture 13
OUTLINE
Timbre and graphs:
Time graph
Spectrum graph
Spectrogram
Envelope
scales
units
interval factors
Fourier Analysis
Fourier Synthesis meant from the
spectrum, build the
Fourier Analysis means
from the waveform, find the
Let’s let the computer do it.
This yields a spectrum graph
or ____ graph
Amplitude vs
Pitch and Timbre —Graphs
Dominant influences on pitch and
timbre:
DEMO
Pitch
Timbre
time graph
(p vs t)
find period,
f1=1/T
waveform
spectrum graph find f1*
(A vs f)
spectrum
*f1 might be lowest freq, but might not
*Often overtones are nf1.
Envelope
Envelope is the time variation of the
sound
Often divided into:
attack = initial building up of sound
decay = decrease to sustained level
or to zero, if the sound is not sustained
sustain = sound held fairly steady
release = final decrease of sound to zero
A
D
S
R
ADSR
Attack, decay, and release
Are usually described by the time they last
Sustain
is usually described by the level (amplitude)
But all four may have their own
frequency, spectrum, amplitude, and
duration
Spectrograms
time graphs
show time variation (x-axis is time)
spectrum graphs
show frequencies in spectrum (x-axis is frequency)
Spectrograms
show both
x-axis is time
y-axis is frequency
Amplitude is shown by heaviness of graphing
Bird Song Spectrograms
Top one (a)
three trills
many freq’s — noiselike
Bottom one (b)
first a low tone with
many harmonics
rises and falls slightly
then higher, purer tone
falls slightly
finally lower, more noise-like tone
Octave
If two pitches
the frequency of one is
fundamental similarity in
often leads to
Octaves are further divided
into cents, semitones, whole tones
Logarithmic Frequency
Measures
Unit
Factor
Equivalent
cents
1.000578
semitones
1.0595
100 cents
whole tones
1.1225
2 semitones
200 cents
octaves
2
12 semitones
1200 cents
Cents
One cent interval has a ratio of 1.0006
1 cent above 440Hz is
Can you tell the difference between 440 Hz
and 440.25 Hz?
a jnd is a ratio of 1.005
about 8-9 cents
10 cent above 440Hz is
Can you tell the difference between 440 Hz
and 442.55 Hz? (10 cents)
Cents Calculation
Interval, I, in cents is related to the
1200
I log 2 

I
log R R  inverse log 

log 2
 1200 
Example, an octave has a ratio of
1200
I
log?
log 2
Semitone
An octave is often
each semitone is a factor of
multiply 440 Hz (an A) by
you’ll get about 880 Hz
Keys on a piano are separated by
12 semitones in order is a
Musical Staff
Musical notes are
the x-axis is
the y-axis is
Fig 8.9
Only the notes in spaces are written in.
Notes on lines are letters between.
Short lines indicate where sharp/flat would
be , graphically.
Major Diatonic Scale
Western music uses a ____________ instead.
A major diatonic scale has
(the 8th would be an
The intervals are not all semitones
some are
 whole tone is about a factor of (1.06)2 = 1.12
The intervals in major diatonic scale are

Start with any key on the keyboard.
You’ve played a major diatonic scale.
Example
Key of C (major diatonic scale)
play
 CDEFGAB
C to D is a
C#/Db is between
similarly with
E to F is a

Scale on Piano
 one octave on keyboard
ignore the gray for now
Summary
Envelope — ADSR
equal pitch intervals are equal frequency factors
jnd, cents, semitone, whole tone, octaves
Scales
chromatic, 12 notes, 1 semitone apart
major diatonic, 7 notes, whole and semitone
intervals
Staff