Download Perception and Psychoacoustics of Tuning

Perception and
Psychoacoustics of
Tuning
Emery Schubert
ARC Australian Research Fellow
School of Music and Music Education
University of New South Wales, Australia
[email protected]
Richard Parncutt
Professor of Systematic Musicology
Department of Musicology
University of Graz, Austria
[email protected]
Aim
• To describe some psychological and
psychophysical issues concerned with the
perception of pitch and tuning.
– Pitch and Virtual Pitch
– Roughness and Critical Band
– Just noticeable difference in and categorical
perception of pitch
• Psychological questions in tuning
Vibration -> Pitch Perception
• Many sounds (including vowels in speech and
musical tones) consist of repeating wave patterns
• When the rate of these repeating patterns is less
than around 12 repetitions per second (Hertz), they
are perceived in the realms of rhythmic pulse,
ornaments (trills) or vibrato.
• If the rate is increased to above 20 (20 Hertz - Hz)
the vibrations fuse into a single percept that is
referred to as pitch.
• Repetition rates of up to around 15,000Hz can still
be perceived as pitch by most people.
Frequency ->
Pitch Perception
• Frequency of vibration
can be mapped onto pitch
perception.
Source: Joe Wolfe, Music Acoustics Group,
School of Physics, University of New South
Wales:
www.phys.unsw.edu.au/~jw/graphics/notes.GIF
QuickTime™ and a
TIFF (LZW) decompressor
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are needed to s ee this pic ture.
Spectograms for 4 tones at D4
(293Hz) and 1 at D5 (587Hz)
Source: Campbell
& Greated, 1987
1762.02Hz
Dark regions indicate
frequencies at which
high energy is emitted
1468.35Hz
1174.68Hz
Lowest
QuickTime™
and a
harmonic
TIFF (LZW) decompressor
are needed to seedetermines
this picture.
587.34Hz
pitch
881.01Hz
293.67Hz
Square + 8ve
French horn
Sawtooth
Square
Sine wave
Time ------>
TIFF (LZW) decompressor
are needed to see this picture.
Spectograms for 4 tones at D4
(293Hz) and 1 at D5 (587Hz)
Source: Campbell
& Greated, 1987
1762.02Hz
Dark regions indicate
frequencies at which
high energy is emitted
1468.35Hz
1174.68Hz
Does
QuickTime™
and a
lowest
TIFF (LZW) decompressor
are needed to seeharmonic
this picture.
587.34Hz
determine
pitch?
881.01Hz
293.67Hz
Horn D4
Square
Wave D5
Time ------>
Horn D4
with F0
taken out!
If fundamental is missing, the brain extracts it ‘virtual pitch’
~B2
~B3
~B4
These are
spectral plots,
which are like
spectograms
turned on
their side.
Fastl, H. & Stoll, G. Scaling of pitch strength,
Hearing Research 1(1979): 293-301
Missing Fundamental
Summary - Pitch and Virtual Pitch Perception
• Most instruments produce harmonically related
‘partials’ or ‘harmonics’.
• The lowest of these partials is called the
fundamental (F0) and usually determines the
perceived pitch.
• Other components contribute to the timbre of the
tone (whether it sounds like a sine wave, square
wave, French horn, human voiced vowel …)
• Virtual pitch perceived if fundamental[F0] is
missing but some harmonically related partials are
present. Suggests higher order processing.
Hearing anatomy &
function
• Outer Ear: Sound Collection
• Middle Ear: Mechanical
Transducer
• Inner Ear (Cochlea):
– Frequency to position (fourier
analysis)
– Mechanical vibration to nerve
impulse
• Auditory Nerve, Brain, Mind
– Pitch & Timbre Sensation
– Right-Left synthesis
– Sound Identification (danger,
music, speech)
focus on cochlear
Cochlea: Conversion of mechanical
vibrations to nerve impulses
•
•
•
•
Fluid filled tube, divided in half longitudinally by Basilar Membrane.
Sound vibrations in fluid cause the basilar membrane to vibrate.
The Basilar Membrane is tapered in width and in thickness along 3.5 cm length.
Basilar Membrane, Tension and density change with position:
– Narrow, stiff near Oval Window. Large and floppy at Helicotrema
– Simple sound oscillations produce localized vibration
Low Frequencies near Helicotrema.
High Frequencies near Oval Window.
Hair cells are stimulated
in the corresponding frequency
region, sending impulses to the brain.
What does cochlear do when two
nearby frequencies are presented?
• When a region of the cochlear is stimulated by a
frequency, nearby (topological and, therefore,
frequency) areas are inhibited, making the effect
of other incoming, nearby frequencies not behave
in a simple linear fashion.
• For the case of two sine waves (single harmonic)
tones f1 and f2, the following can be noted as the
frequency of the two start to separate further:
Perception of close frequencies separating
Increasing Difference in Frequency
f2 - f1 (Hz)
As f2 is increased in frequency:
Critical
Band
0
Sound ‘in-tune’
~0.5-3
Beating heard. Pitch of f1 and f2 cannot be
distinguished. Frequency perceived as the
average of the two.
~4-10
Vibrato like effect.
~20-300
(~ minor 3rd)
Perceived as rough (dissonant). The effect is
starting frequency dependent. The region of
roughness encompasses a larger musical
interval for two low frequency tones, than it
does for two high frequency tones. Difference
(‘tartini’) tones may be heard.
Most
salient
at
0.250.33
>~m3
Separate pitches, perceived as consonant
>1
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Play
f1 = 1000Hz (constant)
1kHz Sweep Demonstration
5 10 15 20 25 30 35 40 45
f2 = 1-2kHz (sweep)
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Critical bands
• How well can the hearing system discriminate between
individual frequency components?
• Whether or not two components that are of similar
amplitude and close together in frequency can be
discriminated depends on the extent to which the basilar
membrane displacements due to each of the two
components are clearly separated or not.
Just noticeable difference (JND)
• Just noticeable difference (JND)
for pitch as a function of
frequency for four different
loudness levels
• For a considerable portion of
the auditory range, humans can
discriminate between two tones
that differ in frequency by 3 Hz
or less.
Increments of 1Hz
from 200 to 210Hz
200, 205, 200, 210Hz
Increments of 1Hz from
2000 to 2010Hz
2000, 2005, 2000, 2010Hz
Other Variables affecting JND
• The degree of sensitivity to frequency changes, or
frequency resolution capability, depends on the
frequency, intensity, and duration of the tone in
question.
• It varies greatly from person to person, is a
function of musical training.
• It is also dependent on the method of measurement
employed (e.g. making a choice between two,
versus adjusting).
Tervaniemi, M. et al. (2005). Pitch discrimination accuracy in musicians vs
nonmusicians: an event-related potetial and behavioral study. Exp Brain Res, 161, 1-10
Compare JND with Tuning Systems
• Difference between intonation and tuning
– Intonation: e.g. singing, string quartet
– Tuning: e.g. piano, guitar
• Theoretical tuning systems
– Pure: M3 = 5:4 = 386 cents
– Pythagorean: M3 = 81:64 = 408 cents
– Equal tempered: M3 = 400 cents
• Perfect pure tuning is impossible!
– E.g. M2 + P5 ≠ M6! (9/8 x 3/2 ≠ 5/3)
• Tuning of real musical instruments
– Piano: stretched equal tempered (M3 = 405 cents?)
Intonation and categorical perception
When is a tone “in tune”? Two different ranges:
• Category width corresponding to scale step:
+ 50 cents
• In-tune (within category) range:
+ 10-30 cents
There are 1200 cents in an
octave. An equal-tempered
semitone has 100 cents.
Role of context:
• Both category width and in-tune range are smaller when
–
–
–
–
slower music (longer tones)
less vibrato
more familiar tuning
more exact tuning
• See also categorical colour perception.
Higher level cognition
• physiological basis for learning
• neural networks (Bharucha)
• mental represention (e.g. represention of a tuning
system) emerges (learned through exposure)
• e.g. 17th century expectation of hunting
horn.
• Which one (natural or tempered)?
Answer:
Introduction from Cantin’s La Grande Messe de Saint-Hubert
Performed by Münchner Parforcehorn-Bläser (on original hunting horns)
Concluding remarks:
Future research on microtonal music/perception
Perception of microtonal music
• Effect of computer-contolled tuning deviations on composer’s
and listener’s evaluations
• Expressive tuning versus microtonality
Tuning feedback by computer interface
• Can performers get used to it? (c.f. horn example)
• Does their intonation improve faster with feedback?
• What is the most accurate performance with/without AP?
…
Thank you!
Perception and
Psychoacoustics of Tuning
Emery Schubert
ARC Australian Research Fellow
School of Music and Music Education
University of New South Wales, Australia
[email protected]
Richard Parncutt
Professor of Systematic Musicology
Department of Musicology
University of Graz, Austria
[email protected]