Transcript Physical, experiential and notational representations of

Physical, experiential and
notational representations of
musical works
Richard Parncutt
Centre for Systematic Musicology
Uni Graz, Austria
Deutsche Gesellschaft für Musikpsychologie
Gesellschaft für Musiktheorie
Würzburg, 8-10 October 2010
Paradigm shifts
Physics
classical mechanics  relativity, quantum physics
Biology
creation  evolution
Psychology
behaviorism  cognitivism
Music history
canonic positivism  cultural relativism
Music theory
natural tonality  emancipation of dissonance
Features of paradigm shifts
Old and new paradigms co-exist
• old becomes a “special case”
Shift is triggered by
• failures of old paradigm
• successes of new paradigm
(Kuhn 1968)
Notational monism
A current paradigm in music theory and music psychology
Notation: the music representation
represents our experience?
understanding of musical structure
Alternatives to notational monism
Other possible representations of tonal music
1. Psychoacoustics: running spectrum
2. Theory and psychology: (cognitive) structures
Not adopted by mainstream music theory
limited new insight into tonal structures
• chords, progressions, voice-leading patterns…
• music-theoretic explanations of their nature/origin
“Fatal errors” of notational monism
that could provoke a paradigm shift
Pitch ambiguity of musical tones
• results of pitch-matching experiments
• individual differences
Inaudibility of the notational representation
The musical expertise paradox:
• expert musicians who can’t transcribe
• music students who can’t “train their ears”
Experimental data
Parncutt, 1993
Stimuli in one trial:
A chord of OCTs,
then a single OCT
Listeners rate how well
tone follows chord
Diamonds:
Mean ratings
Squares :
Theoretical predictions
(masking + pattern rec.)
Auditory Ambiguity Test (AAT)
Seither-Preisler et al. (2007)
You will hear 10 tone pairs
In each pair, does the pitch rise or fall?
Write your answers as arrows:
↑ pitch rises
↓ pitch falls
If you wrote this, you are a “fundamental listener“
If the opposite, you are an “overtone listener”
You may also be a “mixed listener”
Auditory Ambiguity Test (AAT)
Seither-Preisler et al. (2007)
rising overtones
5- 10
2- 4
1
1
falling fundamentals
Schneider et al., NY Acad Sci, Vol. 1060, p. 387-395 (2005)
Listening
strategy
depends
on music
experience
and
instrument
fundamental
listeners
overtone
listeners
C-minor triad C4Eb4G4
(i) physical representation
(ii) experiential representation
missing fundamentals
audible partials
Parncutt (1989)
poids (1/n)
Example of template matching in pitch perception

cognitive template

= template match

 = mismatch
 
  
virtual

0pitch
40
36
32
28
24
20
16
12
8
4
0
What is the pitch
interval
(semitones)
of this
bell?
The harmonic series as a
pattern-recognition template
1
weight (1/n)
1
2
3
4
5
6
7 8 9 10
0
40
36
32
28
24
20
16
12
8
4
0
interval (semitones)
Octave generalisation
of the harmonic series template
weight
(Parncutt, 1988)
10
8
6
4
2
0
Five “root-support intervals”
P1
P5
M3
m7
M2
0
1
2
3
4
5
6
7
8
9
10 11
interval class (semitones)
As vector relative to chromatic scale: 10 0 1 0 3 0 0 5 0 0 2 0
Perception of a C-minor triad: Overtones
Physical representation
Experiential representation for “overtone listeners”
C
D
E
F
G
A
B
10
0
1
0
3
0
0
5
0
0
2
0
0
2
0
10
0
1
0
3
0
0
5
0
0
0
5
0
0
2
0
10
0
1
0
3
tot 10 2
6
10
3
3
0
18
0
1
7
3
C
Eb
G
Implications for high-register voicing:
• best tone to double: G (cf. “harmonic dualism”)
• best tones to add: D, Bb ( madd9, m7 chords)
This procedure can be applied to any chord.
Students can do it in a music theory lesson.
Perception of a C-minor triad: Fundamentals
Experiential representation for “fundamental listeners”
C
D
E
F
G
A
B
10
0
2
0
0
5
0
0
3
0
1
0
0
1
0
10
0
2
0
0
5
0
0
3
5
0
0
3
0
1
0
10
0
2
0
0
tot 15 1
2
13
0
8
0
10
8
2
1
3
C
Eb
G
Implications for low-register voicing:
• best tone to double: C ( theory of the root)
• best tones to add: F, Ab ( 7, M7 chords)
This procedure can be applied to any chord.
Students can do it in a music theory lesson.
Theory of consonance/dissonance
and the historical development of Western tonal syntax
Three components:
1. smoothness (lack of roughness)
2. harmonicity
3. familiarity
In chord extension theory:
1. upper extensions minimize roughness
2. lower extensions promote harmonicity
3. history of syntax: stepwise extension
Perceptual extension of triads
added new chords in pop/jazz notation
Triad
CEG
CEbG
Upper extensions
New colors
+B  M7
+D  add9
(not +Bb  7)
Bb  m7
D  m-add9
(not +A  m6)
Lower extensions
New roots
+A  m7
+F  M9 (no 3)
F  9 (no 3)
Ab  M7
CFG
D  7sus
A  9sus, 11
Bb  add6/9 (no 3)
Eb  add6/9 (no 5)
CEbGb
Bb  halfdim7
Ab  7
B, F  7b9
CEG#
(D#, G, B  maj)
Db, F, A  mM7
Perceptual chord extension
Procedure
add notated pitches at non-notated pitches
i.e. “realise” strong harmonics and subharmonics
Rationale
•
•
sounds similar to original (incremental)
promotes consonance
–
–
notes at common harmonics avoid roughness
notes at common subharmonics promote fusion
 Model of evolution of auditory culture?
This is not harmonic dualism!
• triads are not “natural”
• “undertones” do not exist
Alternative theory of triads:
Major and minor are most prevalent
because most consonant:
– perfect fifth/fourth  harmonicity
– no second/seventh  smoothness
Musical aural expertise paradox
Ear training is the art of…
1. ignoring overtones and missing fundamentals
2. recognizing notated intervals
Both skills require years of practice!
• interaction with notation, instrument, sound
• exposure to zillions of sound patterns
• generalisation
Three pitch-time representations
of a piece of music – and what you can explain with them
1. Physical: audible running spectrum
•
timbre, roughness, upper extensions, modal monophony
2. Experiential: Perceived pitches
•
fusion, roots, harmonic function, major-minor tonality
3. Notational: score
•
performance, style, vocabulary, recognition, complexity
The “three worlds” of Karl Popper
The broader context of music representations
1. physical
• environment, body, brain
2. experiential
• sensations, emotions
3. abstract
• knowledge, info, culture
A clear separation of
these “worlds” clarifies
investigations into the
nature and origin of
• human consciousness
• musical structure
How are chords built?
Old paradigm
• stacked thirds
• based on notation
New paradigm
• represent listener’s experience
• reinforce overtones and fundamentals
• promote smoothness and harmonicity
“3 worlds” approach can explain…
• pitch ambiguity
• chord extensions and categories
• musical expertise paradox
Plus (in other research):
•
•
•
•
•
chord and key relationships
origin of major-minor tonality
modal prevalence in chant
why leading tones rise
implied roots of bebop
One world is not enough!