PITCH AND TIMBRE

MUSICAL ACOUSTICS

Science of SoundChapter 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 SCALESIF 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

JND DEPENDS ON FREQUENCY,SOUND LEVEL, and DURATION

DIFFERENCE LIMEN OR JUST NOTICEABLEDIFFERENCE (JND)

PITCH OF PURE TONES

PITCH DEPENDENCE ON SOUND LEVEL

After Terhardt 1979

HOW DOES PITCH

DEPEND ONSIGNAL

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 HARMONICS1) HARMONICS BETWEEN 2 AND 62) HARMONICS BETWEEN 5 AND 93) 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 TIMEANALYSIS OF THE SOUND.

CLUES FROM BOTH FREQUENCY AND TIME ANALYSESARE USED TO DETERMINE PITCHLOW FREQUENCY: TIME ANALYSIS IS MORE IMPORTANTHIGH 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 auditorysensation in terms of which a listener can judge twosounds…having the same loudness and pitch as dissimilar.”

PROPOSED TIMBRE SCALES

Dull______|______BrilliantCold______|______WarmPure______|______Rich

(Pratt and Doak, 1976)

Dull______|______Sharp Compact______|______Scattered Full______|______Empty Colorful______|______Colorless

(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 PERIODICWHETHER THE WAVEFORM ENVELOPE IS CONSTANT OR FLUCTUATESWHETHER ANY ASPECT OF SOUND (e.g. SPECTRUM) IS CHANGINGWHAT 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.