Multiple levels Multiple levels of implication-realisation of implication-realisation at the authentic cadence at the authentic cadence Richard Parncutt and Annemarie Seither-Preisler Richard Parncutt and Annemarie Seither-Preisler University of Graz, Austria University of Graz, Austria Presented at: Music & Emotion, Durham, England, 31 August - 4 September 2009 Presented at: Music & Emotion, Durham, England, 31 August - 4 September 2009 SysMus Graz
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Multiple levels of implication-realisation at the authentic cadence Richard Parncutt and Annemarie Seither-Preisler University of Graz, Austria Presented.
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Multiple levels Multiple levels of implication-realisation of implication-realisation at the authentic cadenceat the authentic cadence
Richard Parncutt and Annemarie Seither-PreislerRichard Parncutt and Annemarie Seither-Preisler
University of Graz, AustriaUniversity of Graz, Austria
Presented at: Music & Emotion, Durham, England, 31 August - 4 September 2009Presented at: Music & Emotion, Durham, England, 31 August - 4 September 2009
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Why is musical syntax like it is?Why is musical syntax like it is?
Can we predict probability distributions of Can we predict probability distributions of pitch-time patterns in a well-defined style? pitch-time patterns in a well-defined style?
...starting from a few “first principles”?...starting from a few “first principles”?• perceptual, cognitive, social, historical...perceptual, cognitive, social, historical...
Whence the authentic cadence?Whence the authentic cadence? Clarification of tonic Clarification of tonic cognitive efficiency cognitive efficiency But why But why thisthis harmony, harmony, thisthis voice leading? voice leading?
Why this change? Why is authentic cadence so stable?Why this change? Why is authentic cadence so stable?
Avoid circular argumentsAvoid circular arguments
Explain by non-musical phenomenaExplain by non-musical phenomena mathematics of frequency ratios (Pythagoras)mathematics of frequency ratios (Pythagoras)
psychophysics of pitch perception (Aristoxenus)psychophysics of pitch perception (Aristoxenus)
Realised implications in tonal musicRealised implications in tonal music
melodic gap-fill, rising leapmelodic gap-fill, rising leapfalling stepfalling step authentic cadence, chains of falling fifthsauthentic cadence, chains of falling fifths rising leading tones, falling appogiaturasrising leading tones, falling appogiaturas thematic repetitionthematic repetition
...and people like it! ...and people like it! (Sloboda, 1991) (Sloboda, 1991)
Thwarted expectationsThwarted expectationsexceptional, but essentialexceptional, but essential
manipulate attention and emotion manipulate attention and emotion create conflict (social metaphor)create conflict (social metaphor)
new expectation of “happy end” (the norm)new expectation of “happy end” (the norm)
ExamplesExamples delayed melodic gap fill delayed melodic gap fill ((baa baa black sheepbaa baa black sheep)) interrupted cadences interrupted cadences (Mozart arias)(Mozart arias) tonic avoidance tonic avoidance (Wagner: (Wagner: TristanTristan))
Assumption: Asymmetry began in 15th Century and grew
Why fourth/fifth intervals?Common notes?
No. of common notes
Non-directional interval between roots
prevalence
0 second low
1 fourth high
2 third medium
3 unison high*
*= sustained chord
Practical constraints on common notesPractical constraints on common notes
Does a “progression” imply same rhythm in Does a “progression” imply same rhythm in each voice? each voice? zero common notes? zero common notes?
Just one common note is better:Just one common note is better: helps perceptual coherencehelps perceptual coherence helps tuning in performancehelps tuning in performance avoids parallel fifthsavoids parallel fifths
Is that why one common note is preferred?Is that why one common note is preferred?Does that in turn explain why fourth/fifths preferred?Does that in turn explain why fourth/fifths preferred?
But what about the cycle of fifths?But what about the cycle of fifths?
Neural net model Neural net model (Bharucha)(Bharucha)
Spontaneous emergence of cycle of fifths from exposure to triads or tonal music?Psychological reality of cycle of fifths?
Interval asymmetry: Root newnessInterval asymmetry: Root newnesse.g. dominant preparation: imply tonic without playing it e.g. dominant preparation: imply tonic without playing it tension tension
Diatonic interval between roots
Preferred direction
Predicted Actual
second -* rising
third falling rising
fourth rising rising
* BUT: 2 rising fourths + rising second = octave
Virtual triangle (Kanizsa, 1955)Reconstruction of foreground object
from elements
Virtual pitch (Terhardt, 1976)Reconstruction of a missing fundamental frequency (F0)
from harmonics
fundamental (F0) overtones
frequency
Virtual objects – Virtual pitchS
PL
Basics of pitch perceptionBasics of pitch perceptionThings that everyone agrees aboutThings that everyone agrees about
Pitches correspond either toPitches correspond either to individual spectral components (spectral)individual spectral components (spectral) harmonic patterns of components (virtual)harmonic patterns of components (virtual)
Pitches vary in saliencePitches vary in salience Predictions of spectral and temporal models Predictions of spectral and temporal models
are about the sameare about the same
Missing fundamentals in major triadsMissing fundamentals in major triads
harmonics above pitch that are present in the chord
P5 M3 m7 M2
pitch relative to root
M2 - - P1 M3
P4 P1 - - P5
M6 M3 - P5 -
m7 - - - P1
Rank order of salience: M6, P4, M2, m7
Missing fundamentals in minor triadsMissing fundamentals in minor triads
harmonics above pitch that are present in the chord
Implication-realisation model of Implication-realisation model of falling fifth progressionsfalling fifth progressions
CEG implies F and ACEG implies F and A in CEG-CFA, implications are realisedin CEG-CFA, implications are realised
CEbG implies F and AbCEbG implies F and Ab in CEbG-CFAb, implications are realisedin CEbG-CFAb, implications are realised
Also explains falling third progressionsAlso explains falling third progressions prevalent because of IRprevalent because of IR less prevalent than fifths because less IRless prevalent than fifths because less IR
Pitch salience and common notesPitch salience and common notes
Consider two chords: C and Am/C Consider two chords: C and Am/C
Prediction: Most salient pitch in both is CPrediction: Most salient pitch in both is C
Chords with 2 common notes are not differentChords with 2 common notes are not differentrelative major-minor (Riemann: relative major-minor (Riemann: parallelparallel))
Fourth progressions > third progressionsFourth progressions > third progressions
Overtone spectrum: Elementary physical dimension
Virtual pitch:
Musical gestalt dimension
2.- 4.
5.- 10.
1.
1.
Individual differences in pitch perceptionAuditory ambiguity test (Seither-Preisler)
Pitch salience and music historyPitch salience and music history
Revised thesis: Revised thesis: Missing fundamentals influence historical development of Missing fundamentals influence historical development of
syntax because syntax because some (not all)some (not all) listeners, performers, listeners, performers, composers perceive themcomposers perceive them
Advantages of virtual pitch approach Advantages of virtual pitch approach pitch commonality - implication-realisationpitch commonality - implication-realisation
Bottom-up: underlying scale not assumedBottom-up: underlying scale not assumed not circularnot circular prevalence of any chromatic progression?prevalence of any chromatic progression?
Same model explains similarity of successive Same model explains similarity of successive tones, chords, keystones, chords, keys
Explain perceptual coherence of progressionExplain perceptual coherence of progression
IR explains why progressions are emotionalIR explains why progressions are emotional
Why is authentic cadence based on a falling fifth between roots?