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.)
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.”
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
After Terhardt 1979
HOW DOES
PITCH
DEPEND ON
SIGNAL
ENVELOPE?
EFFECT OF INTERFERING SOUNDS
AUDITORY DEMO:) 1000 – Hz TONE + NOISE OF LOWER FREQ.
OCTAVE MATCHING - TWO DIFFERENT OCTAVES?
DEMONSTRATION: WHICH PRESENTATION SOUNDS
MOST IN TUNE?
In München steht ein Hofbräuhaus, eins, zwei gsuffa
Da läuft so manches Wasserl aus, eins, zwei gsuffa . . .
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
VIRTUAL PITCH
DEMO: MASKING SPECTRAL & 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
SEEBECK’S SIREN
IS PITCH DETERMINED BY THE FREQUENCY OR THE PERIOD?
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
REPETITION PITCH
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 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?
ANALYTIC vs SYNTHETIC PITCH
IS THE PITCH OF THE SECOND TONE HIGHER OR LOWER THAN
THE FIRST TONE?
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)
“SHEPARD’S ILLUSION”
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
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)
WHICH RESULTS IN A 431 Hz
•1939: A 440 Hz INTERNATIONAL
STANDARD ADOPTED
TIMBRE
(A MULTIDIMENSIONAL ATTRIBUTE OF SOUND)
DEFINITION (ANSI): “Timbre is that attribute of auditory
sensation in terms of which a listener can judge two
sounds…having the same loudness and pitch as
dissimilar.”
PROPOSED TIMBRE SCALES
Dull______|______Sharp
Dull______|______Brilliant
Compact______|______Scattered
Cold______|______Warm
Full______|______Empty
Pure______|______Rich
Colorful______|______Colorless
(Pratt and Doak, 1976)
(von Bismark, 1974)
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.
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.
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.
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.
EFFECT OF TONE ENVELOPE ON TIMBRE
EFFECT OF ATTACK AND DECAY
EFFECT OF ENVELOPE ON TIMBRE
PIANO NOTES PLAYED FORWARD AND BACKWARD
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
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.
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.
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).
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.