multiple levels of implication-realisation at the authentic cadence richard parncutt and annemarie...
Post on 20-Dec-2015
220 views
TRANSCRIPT
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
Sys
Mus
Gra
z
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?
Historical accountHistorical account1. Medieval 2-part cadence M6-P8 (e.g. DB-CC)1. Medieval 2-part cadence M6-P8 (e.g. DB-CC)
2. add a third voice2. add a third voice double leading-tone cadence double leading-tone cadence
1414thth Century Ars Nova: Vitry, Machaut Century Ars Nova: Vitry, Machaut
authentic cadence authentic cadence
1515th th Century: Dunstable, Dufay, OckeghemCentury: Dunstable, Dufay, Ockeghem
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)
Implication-realisation theory
fulfilment of expection
= realisation of implication
emotion
Example: melodic gap-fill implication: rising leap realisation: stepwise descentM
eyer
, L. B
. (19
56).
Em
otio
n an
d m
eani
ng in
mus
ic.
Chica
go: U
Chi
cago
Pre
ss.
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))
Authentic cadence V-IAuthentic cadence V-Iimplication-realisation implication-realisation “ultimate” satisfaction? “ultimate” satisfaction?
1.1. Rising semitone (leading tone to tonic)Rising semitone (leading tone to tonic)
2.2. If seventhIf seventhtriad: tension-relaxationtriad: tension-relaxation
3.3. Entire passage Entire passage final triad (Schenker) final triad (Schenker)
4.4. Falling fifth between rootsFalling fifth between roots
1.1. Why do leading tones tend to Why do leading tones tend to riserise by m2? by m2?
2.2. Why Mm7? Why major or minor triad?Why Mm7? Why major or minor triad?
3.3. What aspect of passage? Of final triad? What aspect of passage? Of final triad?
4.4. Why P5? Why fall rather than rise? Why P5? Why fall rather than rise?
1. Origin of the leading tone1. Origin of the leading tonePrevalence of scale steps in Gregorian chant Prevalence of scale steps in Gregorian chant
(Parncutt & Prem, ICMPC 2008)(Parncutt & Prem, ICMPC 2008)
Most prevalent: G and D. C>B, F>E (exception: E as final)Theory: tones are preferred if their harmonics are in diatonic scale
2. Why major and minor triads?2. Why major and minor triads?
19 Tn-types of cardinality 319 Tn-types of cardinality 3after Rahn (1980)after Rahn (1980)
prime form 012 013 014 015 016 024 025 026 027 036 037 048
inversion 023 034 045 056 035 046 047
Most consonant Tn-types of cardinality 3• fourth/fifth (fusion)
• no major/minor second (roughness).
3. Chroma prevalence anticipates 3. Chroma prevalence anticipates chroma saliencechroma salience
Aarden, B. (2003). Dynamic melodic expectancy. PhD dissertation, Ohio State University.
major key minor key
4. Why falling fifth between roots? 4. Why falling fifth between roots?
competing theoriescompeting theories
Common notes or pitchesCommon notes or pitcheschords 1 and 2 have something in commonchords 1 and 2 have something in common
Root newnessRoot newnessroot of chord 2 is not a note in chord 1root of chord 2 is not a note in chord 1
Implication-realisationImplication-realisationimplied pitches* in 1 implied pitches* in 1 real pitches in 2 real pitches in 2
*missing fundamentals*missing fundamentals
Prevalence of diatonic progressions
rising P4
falling P4
rising 3rd
falling 3rd
rising M2
falling M2
total
maj-maj 64 19 0 0 6 2 91maj-min 60 1 2 9 5 0 77min-maj 5 20 1 15 5 3 49
min-min 21 5 0 0 1 0 27
total 150 45 3 24 17 5 244
Eb
erle
in, R
. (1
994
). D
ie E
nts
tehu
ng
der
tona
len
Kla
ngs
ynta
x (p
p. 4
22-
423
). F
rank
furt
: Pe
ter
La
ng.
J. S. Bach 7 chorales; kleine harmonische Labyrinth
Händel Trio sonata Op. 5 No. 5
Mozart Missa brevis KV 65 (Kyrie, Gloria, Agnus Dei)
Beethoven Mass in C (Kyrie, Gloria)
Mendelssohn Motets Op. 78, Nos. 1 & 2
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
P5 M3 m7 M2
pitch relative to root
M2 - - P1 -
P4 P1 - m3 P5
m6 m3 P1 - -
m7 - - - P1
Rank order of salience: P4/m6, M2, m7
Experimental dataExperimental dataParncutt, 1993Parncutt, 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
Physical Physical spectra spectra
and and
calculated calculated experiential experiential
spectraspectra
“Pitch category”: “Pitch category”: 48 = C4, 60 = C5 etc.48 = C4, 60 = C5 etc.
(Parncutt, 1989)(Parncutt, 1989)
Pure tone
Harmonic complex tone
Octave complex tone
Physical Physical spectra spectra
and and
calculated calculated experiential experiential
spectraspectra
“Pitch category”: “Pitch category”: 48 = C4, 60 = C5 etc.48 = C4, 60 = C5 etc.
(Parncutt, 1989)(Parncutt, 1989)
Minor triad
Tristan 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