Transcript Grouping mechanisms in music. - Jacobs University Mathematics

Auditory scene
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
– Music provides us with a complex, rapidly
changing acoustic spectrum, often derived
from the superposition of sounds from
many different sources.
– Our auditory system has the task of
analyzing this spectrum as to reconstruct the
originating sound events.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Two mechanisms
– The first is a fast, involuntary process of
auditory grouping
– The second involves using schemas to guide
the grouping and listening process. Schemas
are higher-level hypotheses or expectations
based upon our knowledge of familiar
sound.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Grouping
– Dimensions along which grouping
principles operate: frequency, amplitude,
temporal position, spatial location, timbre
– Principles that govern grouping along these
dimensions
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Principles of auditory grouping
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Similarity of timbre
Similarity of pitch
Temporal proximity
Good continuation
Location
Onset and offset
Experience
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
– The Gestalt approach to perceptual organization:
How elements are grouped: Goldstein, pp. 148 –
156
– Auditory scene analysis: Identifying sound
sources: Goldstein, pp. 395 – 401
– CWE, 245 – 247, 411 – 417
– Shepard, R. Stream segregation and ambiguity in
audition. In: Cook, Chapter 10
– Deutsch, D. Grouping mechanisms in music. In:
D.Deutsch (Ed), The Psychology of Music,
(1999), Chapter 9
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of similarity
Similar things appear to be grouped
together.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of similarity
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of similarity
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of similarity
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Similarity of timbre
– Sounds that have the same timbre are often
produced by the same source.
– This principle means that we tend to group
stimuli that sound similar together.
– If pairs are alternately similar and dissimilar
in timbre, they will group by similarity.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Similarity of timbre
Auditory stream segregation
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Example
Grouping by timbral similarity: trumpet
tones alternating with a vocal tone and a
steel drum sound.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Similarity of pitch
– Sounds with similar frequencies are often
produced by the same source.
– Imagine tones with different pitch. Those
tones close in pitch will become grouped by
similarity.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Example
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3.
4.
5.
6.
7.
8.
High and low pitch played in succession; easy to follow
as single line
High-low-high pattern repeated ever faster until there are
two streams of pitch
Slow alternation between a minor second apart. Note
that it is easy to think of the sound as a single line
Same as 3., but the interval is wider
Same interval as 3., but faster
Same interval as 4., but faster
Same as 3., even faster. Do you here one or two lines?
Same as 4., even faster. Do you here one or two lines?
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Composers in the Baroque period (1600 – 1750)
knew that if a single instrument plays notes that
alternate rapidly between high and low tones, with
the high notes perceived as being played by one
instrument and the low notes as being played by
another. This effect, which has been called implied
polyphony or compound melodic line, is an
example of auditory stream segregation.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Example of Gestalt
grouping and stream
segregation
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Similarity of pitch
J.S.Bach, Cello Suite I, Prelude
A.Diederich– International University Bremen – USC – MMM – Spring 2005
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Law of proximity or nearness
Things that are near to each other appear to
be grouped together.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of proximity or nearness
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of proximity or nearness
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Left: Competition between grouping by proximity (columns)
and grouping by similarity ( rows)
Right: Demonstration of active grouping when multiple
possibility are available
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Temporal proximity
– Sounds that occur in rapid progression tend
to be produced by the same source.
– Grouping a set of tones so that some are
closer together than others are perceived as
belonging together.
– If steps are large and rapid (e.g., on a
diatonic scale), melodies are not perceived
as a stream but segregate into separate
entities.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Example
Yodeling: The singer alternates between the
head and chest voice modes of production,
and the leaps are large and rapid. The high
note and low notes of yodeling are often
perceived as two separate streams.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Interleaving two melodies
– Another example that illustrates this phenomenon
involves interleaving two melodies so that the
notes of each melody alternate.
– If the relative range of the melodies is such that
the interleaved patterns contain small leaps, the
individual melodies are not recognized.
– As one of the melodies are transposed so that it is
farther and farther from each other, a point it
reached when both melodies are recognized.
– The connection from one tone to the next is a
function of proximity.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Overlapped melodies
cannot be separated even
though they alternate in
time.
Separating in pitch allows
the two melodies to be
easily identified.
Different timbre
or volume
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Example
1. Melodies just seen
2. Same as in 1., increasing distance between
melodies each time
3. Separation by volume
4. Separation by timbre
5. Two new melodies, increasing distance
6. Separation by volume
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7. Separation by timbre
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of good continuation
Points that, when connected, result in
straight or smoothly curving lines are seen
as belonging together, and the lines tend to
be seen in such a way as to follow the
smoothest path.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Law of good continuation
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Good continuation
– Sounds that stay constant or that change
smoothly are often produced by the same
source.
– Sound stimuli with the same frequency or
smoothly changing frequencies are
perceived as continuous even if they are
interrupted by another stimulus.
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Good continuation
a) Albinez
b) Perceived as two
separate streams
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
Example
1. Sinusoid going up and down in pitch with
pauses at the top
2. Gaps in previous example are filled with noise.
Now the sine wave sounds continuous, but is
just obscured by the noise burst.
3. Musical example with gaps
4. Musical example with gaps filled by noise.
Track 5
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A.Diederich– International University Bremen – USC – MMM – Spring 2005
– http://www.ece.uvic.ca/~aupward/p/demos.
htm
– http://www.psych.mcgill.ca/labs/auditory/bregmancd.html
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A.Diederich– International University Bremen – USC – MMM – Spring 2005