1. 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

2. 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

3. 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)

4. Notational monism A current paradigm in music theory and music psychology Notation: the music representation  represents our experience?  understanding of musical structure

5. 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

6. “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”

7. 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.)

8. 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

9. If you wrote this, you are a “fundamental listener“ If the opposite, you are an “overtone listener” You may also be a “mixed listener”

10. 2- 4 5- 10 1 1 rising overtones falling fundamentals Auditory Ambiguity Test (AAT) Seither-Preisler et al. (2007)

11. Schneider et al., NY Acad Sci, Vol. 1060, p. 387-395 (2005) overtone listeners fundamental listeners Listening strategy depends on music experience and instrument

12. C-minor triad C 4 Eb 4 G 4 (i) physical representation (ii) experiential representation Parncutt (1989) missing fundamentalsaudible partials

13. Example of template matching in pitch perception    cognitive template virtual pitch = template match  = mismatch What is the pitch of this bell?

14. The harmonic series as a pattern-recognition template 1 2 3 4 5 6 7 8 10 9

15. Octave generalisation of the harmonic series template (Parncutt, 1988) m7 Five “root-support intervals” P1 M2 M3 P5 As vector relative to chromatic scale: 10 0 1 0 3 0 0 5 0 0 2 0

16. Perception of a C-minor triad: Overtones Physical representation Experiential representation for “overtone listeners” CDEFGAB C 1001030050020 Eb 0201001030050 G 0050020 0103 tot 1026 330180173 Implications for high-register voicing: best tone to double: G (cf. “harmonic dualism”) best tones to add: D, Bb (  m add9, m 7 chords) This procedure can be applied to any chord. Students can do it in a music theory lesson.

17. Perception of a C-minor triad: Fundamentals Experiential representation for “fundamental listeners” CDEFGAB C 1002005003010 Eb 0101002005003 G 5003010 0200 tot 151213080108213 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.

18. 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

19. Perceptual extension of triads added new chords in pop/jazz notation TriadUpper extensions New colors Lower extensions New roots CEG +B  M7 +D  add9 (not +Bb  7) +A  m7 +F  M9 (no 3) CEbGBb  m7 D  m-add9 (not +A  m6) F  9 (no 3) Ab  M7 CFGD  7sus A  9sus, 11 Bb  add6/9 (no 3) Eb  add6/9 (no 5) CEbGbBb  halfdim7Ab  7 B, F  7b9 CEG#(D#, G, B  maj)Db, F, A  mM7

20. 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?

21. 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

22. 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

23. 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

24. 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

25. 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

26. “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!