PITCH AND TIMBRE

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PITCH AND TIMBRE

• MUSICAL ACOUSTICS

Science of Sound Chapter 7
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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.)
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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.
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FREQUENCY DISCRIMINATION
DIFFERENCE LIMEN OR JUST NOTICEABLE DIFFERENCE
(JND)
JND DEPENDS ON FREQUENCY, SOUND LEVEL, and
DURATION
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PITCH OF PURE TONESPITCH DEPENDENCE ON SOUND
LEVEL
After Terhardt 1979
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HOW DOES PITCH DEPEND ONSIGNAL ENVELOPE?
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EFFECT OF INTERFERING SOUNDS
AUDITORY DEMO) 1000 Hz TONE NOISE OF LOWER
FREQ.
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OCTAVE MATCHING - TWO DIFFERENT OCTAVES?
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DEMONSTRATION WHICH PRESENTATION SOUNDS MOST IN
TUNE? In München steht ein Hofbräuhaus, eins,
zwei gsuffa Da läuft so manches Wasserl aus,
eins, zwei gsuffa . . .
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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
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VIRTUAL PITCH
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VIRTUAL PITCH
DEMO MASKING SPECTRAL VIRTUAL PITCH

• DEMO VIRTUAL PITCH WITH RANDOM HARMONICS
• HARMONICS BETWEEN 2 AND 6
• HARMONICS BETWEEN 5 AND 9
• 3) HARMONICS BETWEEN 8 AND 12

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SEEBECKS SIRENIS PITCH DETERMINED BY THE
FREQUENCY OR THE PERIOD?
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THEORIES OF PITCH
PLACE THEORY VIBRATIONS OF DIFFERENT
FREQUENCIES EXCITE 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 THEORY
• PATTERN TRANSFORMATION THEORY

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REPETITION PITCH
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STRIKE NOTE OF A CHIME
IN ORCHESTRA CHIMES (TUBULAR BELLS) THE STRIKE
NOTE LIES BETWEEN THE 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 234.
A FEW LISTENERS IDENTIFY THE CHIME STRIKE NOTE
AS COINCIDING WITH THE 4TH PARTIAL (AN OCTAVE
HIGHER). In which octave do you hear it?
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ANALYTIC vs SYNTHETIC PITCH
IS THE PITCH OF THE SECOND TONE HIGHER OR LOWER
THAN THE FIRST TONE?
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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)
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SHEPARDS ILLUSION
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ABSOLUTE PITCH

• ABILITY TO RECOGNIZE AND DEFINE THE PITCH OF A
  TONE 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

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PITCH STANDARDS
EARLY ORGANS HAD As TUNED FROM 374 TO 567
Hz HANDELS TUNING FORK VIBRATED AT 422.5
Hz 1859 A 435 Hz ADOPTED BY FRENCH
GOVERNMENT C 256 (POWERS OF TWO) WHICH
RESULTS IN A 431 Hz 1939 A 440 Hz
INTERNATIONAL STANDARD ADOPTED
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TIMBRE
(A MULTIDIMENSIONAL ATTRIBUTE OF SOUND)
DEFINITION (ANSI) Timbre is that attribute of
auditory sensation in terms of which a listener
can judge two soundshaving the same loudness and
pitch as dissimilar.
PROPOSED TIMBRE SCALES
Dull____________Sharp
Compact____________Scattered
Full____________Empty Colorful____________Colo
rless (von Bismark,
1974)
Dull____________Brilliant Cold____________Warm
Pure____________Rich (Pratt and Doak,
1976)
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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 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.
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A HYBRID MODEL OF TIMBRE
A HYBRID MODEL OF TIMBRE, WHICH INTEGRATES THE
CONCEPTS OF COLOR AND TEXTURE OF SOUND, HAS BEEN
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.
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SPECTRAL (FOURIER) ANALYSIS
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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.
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CHANGE IN TIMBRE WITH TRANSPOSITION
HIGH AND LOW TONES FROM A MUSICAL INSTRUMENT
NORMALLY DO NOT HAVE THE SAME RELATIVE
SPECTRUM. 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.
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EFFECT OF TONE ENVELOPE ON TIMBRE
EFFECT OF
ATTACK AND DECAY
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EFFECT OF ENVELOPE ON TIMBREPIANO NOTES PLAYED
FORWARD AND BACKWARD
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EFFECT OF ENVELOPE ON TIMBRE PIANO NOTES PLAYED
FORWARD AND BACKWARD
THE SPECTRUM IS THE SAME THE TIMBRE IS NOT
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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
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TRISTIMULUS DIAGRAMS
TIMBRE CAN BE REPRESENTED ON A TRISTIMULUS
DIAGRAM SIMILAR TO THAT USED RO REPRESENT COLOR.
THREE DIMENTIONS x, y, and z ARE SELECTED, SUCH
THAT x y z.
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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 VI BRATO
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.
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BLEND OF COMPLEX TONES
OUR AUDITORY SYSTEM HAS THE ABILITY TO LISTEN TO
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 PLAY 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 . 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).
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TONE OR CHORD?
ERICKSON (1975) POINTS OUT THAT A COMPLEX SOUND
CAN BE HEARD AS A CHORD 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.