1. MUSICAL ACOUSTICS
PITCH AND TIMBRE
Science of Sound
Chapter 7

2. 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.)

3. DEPENDENCE OF SUBJECTIVE QUALITIES OF SOUND ON PHYSICAL PARAMETERS

4. 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.”

5. FREQUENCY DISCRIMINATION
DIFFERENCE LIMEN OR JUST NOTICEABLE
DIFFERENCE (JND)
JND DEPENDS
ON FREQUENCY,
SOUND LEVEL,
and DURATION

6. 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 Hz.

7. 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)
Indicate by pointing if the second tone appears higher or lower in pitch than the first one (or the same pitch).
12 Dependence of pitch on intensity Tr 27,28

8. HOW DOES PITCH DEPEND ON SIGNAL ENVELOPE?

9. EFFECT OF INTERFERING SOUNDS
AUDITORY DEMO:) 1000–Hz TONE + NOISE OF LOWER FREQ.
14 Influence of masking noise on pitch, Track 30

10. OCTAVE MATCHING
A 500-Hz tone alternates with a comparison tone on increasing frequency. Which pair sounds like a “correct” octave?
(Raise your hand when you hear a “correct” octave)
15 Octave matching, Track 31

11. 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.

12. OCTAVE MATCHING - TWO DIFFERENT OCTAVES?

13. DEMONSTRATION: WHICH PRESENTATION SOUNDS MOST IN TUNE?
16 Stretched and compressed scales Track 32

14. 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

15. 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

16. VIRTUAL PITCH
20, 21 Virtual pitch, Tracks 37, 38, 39

17. VIRTUAL PITCH
DEMO: MASKING SPECTRAL & VIRTUAL PITCH
22, Tracks 40-42

18. VIRTUAL PITCH DEMO: VIRTUAL PITCH WITH RANDOM HARMONICS
HARMONICS BETWEEN 2 AND 6
HARMONICS BETWEEN 5 AND 9
3) HARMONICS BETWEEN 8 AND 12
23 Tracks 43-45

19. 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

20. 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

21. 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  750 Hz (disregard steady 1000 Hz tone)
25 Analytic vs Synthetic Pitch, Track48

22. SEEBECK’S SIREN IS PITCH DETERMINED BY THE FREQUENCY OR THE PERIOD?

23. 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

24. REPETITION PITCH

25. REPETITION PITCH
26 Scale with repetition pitch, Tracks 49-51

26. CIRCULARITY IN PITCH JUDGMENT “SHEPARD’S ILLUSION”
27 Circularity in pitch judgment, Track 52

27. CIRCULARITY IN PITCH JUDGMENT “SHEPARD’S ILLUSION”
27 Circularity in pitch judgment, Track 52

28. 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.

29. PITCH STANDARDS •Early organs had A’s tuned from 374 to 567 Hz
•Handel’s tuning fork vibrated at 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.

30. Assignment for Monday, February 2
Hearing curve plots due
Loudness scaling curves due
Re-read Chapter 7

31. TIMBRE
Chapter 7 Science of Sound

32. 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.”

33. DEPENDENCE OF SUBJECTIVE QUALITIES OF SOUND ON PHYSICAL PARAMETERS

34. 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.

35. 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)

36. 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.

37. SPECTRAL (FOURIER) ANALYSIS

38. 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

39. 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

40. EFFECT OF TONE ENVELOPE ON TIMBRE
EFFECT OF ATTACK AND DECAY

41. TIMBRE DURING ATTACK OF A NOTE
WAVEFORM OF ATTACK TRANSIENT SPECTRUM OF FIRST 5 PARTIALS
(KEELER, 1972)

42. EFFECT OF ENVELOPE ON TIMBRE PIANO NOTES PLAYED FORWARD AND BACKWARD
29 Effect of tone envelope on timbre, Tracks 54-56

43. EFFECT OF ENVELOPE ON TIMBRE PIANO NOTES PLAYED FORWARD AND BACKWARD
THE SPECTRUM IS THE SAME; THE TIMBRE IS NOT

44. 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

45. 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.

46. 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.

47. 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).

48. 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.

49. 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

50. Assignment for Wednesday Exercises 1-12 (p. 172) Read Chapter 8