Transcript pitch and timbre

MUSICAL ACOUSTICS
PITCH AND
TIMBRE
Science of Sound
Chapter 7
PITCH
“That attribute of auditory sensation in terms of
which sounds may be ordered on a scale
extending from low to high.” (ANSI)
The basic unit in most musical scales is the
octave. In music, the octave is divided in
different ways (In Western music it is generally
divided into 12 semitones).
PYTHAGORAS DISCOVERS THE OCTAVE (ca. 600 B.C.)
DEPENDENCE OF SUBJECTIVE QUALITIES
OF SOUND ON PHYSICAL PARAMETERS
PSYCHOACOUSTICAL PITCH SCALES
If a listener hears a 4000-Hz tone followed by one of low frequency, a tone
of about 1000 Hz would likely be selected as having a pitch “half way
between them.”
FREQUENCY
DISCRIMINATION
DIFFERENCE
LIMEN OR JUST
NOTICEABLE
DIFFERENCE
(JND)
JND DEPENDS
ON FREQUENCY,
SOUND LEVEL,
and DURATION
PITCH OF PURE TONES
PITCH DEPENDENCE ON SOUND LEVEL
Stevens (1935) found shifts in pitch as large as two semitones when
the sound level increased from 40 to 90 dB.
Terhardt (1974) found
individual shifts as large as
this, but averaging over a
group of individuals made
them much smaller.
Rossing and Houtsma (1986) found a monotonic decrease in pitch
with intensity over the frequency range 200-3200 Hz.
PITCH OF PURE TONES
PITCH DEPENDENCE ON SOUND LEVEL
Demonstration 12 uses 500-ms tone bursts having frequencies of
200, 500, 1000, 3000, and 4000 Hz.
Six pairs of tones are presented at each frequency, with the
frequency of the second tone having a level 30 dB higher than the
first one (which is 5 dB above the 200-Hz calibration tone)
12 Dependence of pitch on intensity Tr 27,28
Indicate by pointing if the second tone appears higher or lower in
pitch than the first one (or the same pitch).
HOW DOES
PITCH
DEPEND ON
SIGNAL
ENVELOPE?
EFFECT OF INTERFERING SOUNDS
AUDITORY DEMO:) 1000–Hz TONE + NOISE OF LOWER FREQ.
14 Influence of masking noise on pitch, Track 30
OCTAVE MATCHING
A 500-Hz tone alternates with a comparison tone on
increasing frequency. Which pair sounds like a
“correct” octave?
15 Octave matching, Track 31
(Raise your hand when you hear a “correct” octave)
OCTAVE MATCHING
A 500-Hz tone alternates with a comparison tone on
increasing frequency. Which pair sounds like a
“correct” octave?
The comparison tone frequencies were
985, 990, 995, 1000, 1005, 1010, 1015, 1020, 1025, 1030,
and 1035 Hz.
OCTAVE MATCHING - TWO DIFFERENT OCTAVES?
DEMONSTRATION: WHICH PRESENTATION SOUNDS
MOST IN TUNE?
16 Stretched and compressed scales Track 32
DEMONSTRATION: WHICH PRESENTATION SOUNDS
MOST IN TUNE?
In München steht ein Hofbräuhaus, eins, zwei gsuffa
Da läuft so manches Wasserl aus, eins, zwei gsuffa . . .
16 Stretched and compressed scales, Track 32
DEMONSTRATION: WHICH PRESENTATION SOUNDS
MOST IN TUNE?
In München steht ein Hofbräuhaus, eins, zwei gsuffa
Da läuft so manches Wasserl aus, eins, zwei gsuffa . .
FIRST: BASS IN C, MELODY IN B
SECOND: BASS IN C, MELODY IN C#
THIRD: BASS IN C, MELODY IN C
VIRTUAL PITCH
20, 21 Virtual pitch, Tracks 37, 38, 39
VIRTUAL PITCH
DEMO: MASKING SPECTRAL & VIRTUAL PITCH
22, Tracks 40-42
VIRTUAL PITCH
DEMO: VIRTUAL PITCH WITH RANDOM HARMONICS
1) HARMONICS BETWEEN 2 AND 6
2) HARMONICS BETWEEN 5 AND 9
3) HARMONICS BETWEEN 8 AND 12
23 Tracks 43-45
STRIKE NOTE OF A CHIME
In orchestra chimes (tubular bells) the strike note
lies between 2ND and 3RD PARTIALS. The pitch is
usually identified as the missing fundamental of the
4TH, 5TH, and 6TH partials, which have frequencies
nearly in the ratio 2:3:4.
A few listeners identify the chime strike note as
coinciding with the 4TH partial (an octave higher).
In which octave do you hear it?
24 Strike note of a chime, Tracks 46, 47
ANALYTIC vs SYNTHETIC PITCH
Is the pitch of the second tone higher or lower
than the first tone?
Please indicate by pointing upward or downward.
25 Analytic vs Synthetic Pitch, Track48
ANALYTIC vs SYNTHETIC PITCH
Is the pitch of the second tone higher or lower
than the first tone?
800, 1000 Hz  750, 1000 Hz
Synthetic: 200  250 Hz
Analytic 800  750 Hz (disregard steady 1000 Hz
tone)
25 Analytic vs Synthetic Pitch, Track48
SEEBECK’S SIREN
IS PITCH DETERMINED BY THE FREQUENCY OR THE PERIOD?
THEORIES OF PITCH
PLACE THEORY: Vibrations of different frequencies
excite different resonant areas on the basilar membrane.
PERIODICITY THEORY: The ear performs a TIME
analysis of the sound.
Clues from both frequency and time analyses are used to
determine pitch
LOW FREQUENCY: Time analysis is more important
HIGH FREQUENCY: Frequency analysis is more important.
MODERN THEORIES:
•Optimum processor theory
•Virtual pitch
•Pattern transformation theory
REPETITION PITCH
REPETITION PITCH
26 Scale with repetition pitch, Tracks 49-51
CIRCULARITY IN PITCH JUDGMENT
“SHEPARD’S ILLUSION”
27 Circularity in pitch judgment, Track 52
CIRCULARITY IN PITCH JUDGMENT
“SHEPARD’S ILLUSION”
27 Circularity in pitch judgment, Track 52
ABSOLUTE PITCH
(Incorrectly called “perfect pitch”)
Ability to identify pitch without a reference tone; a
rare trait.
More common among speakers of “tone languages”
(such as Chinese).
Reference may change with time in some persons.
PITCH STANDARDS
•Early organs had A’s tuned from 374 to
567 Hz
•Handel’s tuning fork vibrated at 422.5 Hz
•1859: A 435 Hz adopted by French
government
•C 256 (powers of two) results in
A 431 Hz
•1939: A 440 Hz international standard
adopted.
Assignment for Monday, February 2
Hearing curve plots due
Loudness scaling curves due
Re-read Chapter 7
TIMBRE
Chapter 7 Science of Sound
WHAT IS TIMBRE?
The American National Standards defines it;
“TIMBRE IS THAT ATTRIBUTE OF AUDITORY
SENSATION IN TERMS OF WHICH A LISTENER CAN
JUDGE TWO SOUNDS SIMILARLY PRESENTED AND
HAVING THE SAME LOUDNESS AND PITCH AS
DISSIMILAR.”
DEPENDENCE OF SUBJECTIVE QUALITIES
OF SOUND ON PHYSICAL PARAMETERS
TIMBRE PERCEPTION
It is likely that the total number of dimensions required to characterize
timbre might approach the number of critical bands (about 37). For most
sounds, however, fewer dimensions would suffice.
SCHOUTEN (1968) suggested that timbre recognition may depend on
factors such as:
●Whether the sound is periodic
●Whether the waveform envelope is constant or fluctuates
●Whether any aspect of the sound (e.g. spectrum) is changing
●What the preceding and following sounds are like.
PATTERSON (1995) found that ramped and damped sounds had different
timbres, pointing out the important role of temporal envelope in timbre
perception.
A MULTIDIMENSIONAL ATTRIBUTE OF SOUND
Timbre can be described as a multidimensional attribute
of sound. It is impossible to construct a single
subjective scale of timbre of the type used for loudness
(sones) and pitch (mels), for example.
Pratt and Doak (1976)
von Bismarck (1974)
A HYBRID MODEL OF TIMBRE
A hybrid model of timbre, which integrates the concepts
of COLOR and TEXTURE of sound, was developed at
CCRMA by Hiroko Terasawa and Jonathan Berger (see
JASA 124, 2448 (2008)). The “color” of sound is
described in terms of an instantaneous spectral
envelope, while the “texture” of a sound describes the
temporal nature of the sound as the sequential changes
in color with an arbitrary time scale.
SPECTRAL
(FOURIER)
ANALYSIS
EFFECT OF SPECTRUM ON TIMBRE
DEMONSTRATION: Tones of two musical instruments are
presented, beginning with the fundamental and adding
partials one at a time.
Raise your hand when you recognize the instrument and
note the number of partials required for your identification.
28 Effect of spectrum on timbre, Track 53
CHANGE IN TIMBRE WITH TRANSPOSITION
High and low tones from a musical instrument
normally do not have the same relative spectra.
DEMONSTRATION: A 3-octave scale is played on a
bassoon, followed by a 3-octave scale synthesized
by temporal stretching of the highest note to
obtain the desired pitches. Except for the highest
note, the tones do not sound as played on the
bassoon.
30 Change in timbre with transposition, Track 57
EFFECT OF TONE ENVELOPE ON TIMBRE
EFFECT OF ATTACK AND DECAY
TIMBRE DURING ATTACK OF A NOTE
WAVEFORM OF ATTACK TRANSIENT SPECTRUM OF FIRST 5 PARTIALS
(KEELER, 1972)
EFFECT OF ENVELOPE ON TIMBRE
PIANO NOTES PLAYED FORWARD AND BACKWARD
29 Effect of tone envelope on timbre, Tracks 54-56
EFFECT OF ENVELOPE ON TIMBRE
PIANO NOTES PLAYED FORWARD AND BACKWARD
THE SPECTRUM IS THE SAME; THE TIMBRE IS NOT
TONES AND TUNING WITH STRETCHED PARTIALS
DEMONSTRATION: FIRST A SYNTHESIZED 4-PART BACH CHORALE IS PLAYED
THEN THE SAME CHORALE IS PLAYED WITH BOTH THE MELODIC AND
HARMONIC SCALES STRETCHED LOGARITHMICALLY IN SUCH A WAY THAT THE
OCTAVE RATIO IS 2.1 TO 1
NOW THE SAME PIECE WITH ONLY THE MELODIC SCALE STRETCHED
FINALLY THE SAME PIECE WITH ONLY THE PARTIALS OF EACH VOICE
STRETCHED
31 Tones and tuning with stretched partials, Track 58-61
TRISTIMULUS DIAGRAMS
Timbre can be represented on a tristimulus diagram similar to that
used to represent color. Three dimensions x, y, and z are selected
such that x + y = z. x represents the strength of the high-frequency
partials, y represents those of mid-frequency, and z represents those
near the fundamental.
VIBRATO
Vibrato is defined by the National Standards Institute as
“a family of tonal effects in music that depend on
periodic variations of one or more characteristics in the
sound wave.”
Frequency vibrato, amplitude vibrato, and phase vibrato
are widely used in musical performance. In practice, it is
unusual to have frequency vibrato (fm) without amplitude
vibrato (am).
The rate and depth of vibrato are important contributors
to timbre. Performers typically select a vibrato rate of
about 7 Hz.
BLEND OF COMPLEX TONES
Our auditory system has the ability to listen complex sounds in different
modes. When we listen analytically, we hear the different partials
separately. When we listen synthetically (or holistically), we focus on the
whole sound and pay less attention to the individual partials.
A tone with several harmonic partials, whose frequencies and relative
amplitudes remain steady, is generally heard as a single complex tone even
if the total intensity changes. However, when one of the partials is turned on
and off, it stands out clearly.
Demonstration 1 Cancelled harmonics Track 1
The same is true if one of its harmonics is given a vibrato (i.e., its
amplitude, frequency, or phase is modulated at a slow rate).
TONE OR CHORD?
Erickson (1975) points out that
a complex sound can be heard
as a CHORD, a single tone
(with timbre); a SINGLE TONE
(with TIMBRE); or as an
UNPITCHED SOUND.
Transformation from a chord
to a sound, for example, is
illustrated by the music of
Edgar Varese.
EFFECT OF ECHOES
In most rooms, reflections occur from the walls, ceiling,
and floor. These are not “heard” as echoes unless the
room is large. By recording the sound and playing the
recording backwards, however, these reflections become
apparent and have a large effect on the timbre.
DEMONSTRATION: This is done: 1) in an anechoic room;
2) in a conference room; and 3) in a very reverberant
room.
35 Effect of echoes Track 70
Assignment for Wednesday
Exercises 1-12 (p. 172)
Read Chapter 8