1. Schenkerien prolongation and the emotional connotations of major-minor tonality Schenkerien prolongation and the emotional connotations of major-minor tonality Richard Parncutt University of Graz, Austria ICME3, Jyväskylä Finland, 2013 SysMus Graz

2. Theses 1. A passage of MmT* is perceived as a prolonged background triad 2. This prolonged triad is the origin of “major-minor = happy-sad” *major-minor tonality

3. Questions arising  Does this background triad exist?  Why major=happy and minor=sad? More questions…  Why two triads? Why these two?  Why this specific mapping?  What about Leonard Meyer’s theory?

4. Origins of… …emotion: evolutionary psychology? …MmT:psychohistory?

5. Evolutionary functional origins of emotion Arousal  High: energy available or necessary  Low: energy unavailable or unnecessary Valence  positive: clear situation  safety, confidence  negative: unclear situation  fear or anger

6. Psychohistoric origin of MmT Psychohistoric origin of MmT Five psychohistorical steps 1.Diatonic scales in ancient music 2.Leading tones in medieval polyphony 3.Importance of major and minor triads 4.Implied pitches in these triads 5.No consecutive semitones in scales

7. Major-minor Tonality (MmT) Most music in MmT can be reduced to chord progressions. Most chords correspond to one of these diatonic triads.

8. Origin of pentatonic, diatonic, chromatic scales ethanhein.com Pairs of harmonic complex tones with frequencies or pitches in common  Octave and fifth relations  Circle of fifths Harmonics in common  perceptual similarity

9. Leading tones in early music Leading tones in early music Guillaume de Machaut (1300-1377). Rondeau Ma fin est mon commencement F# tonicizes G - C# tonicizes D

10. Origin of leading tones? Consonance / prevalence of individual tones in chant A B C D E F G Data A B C D E F G Model Data: Counted in the Liber Usualis (DDMAL, Fujiniaga et al., McGill) Model: No. of harmonic pcs (P5, M3, m7, M2) at diatonic scale steps Comparison: df = 5, r = 0.90, p<.01 Finding: C (F) more prevalent than B (E)  origin of leading tone? Cf. Parncutt, R. & Prem, D. (2008 ). The relative prevalence of Medieval modes and the origin of the leading tone (poster). International Conference on Music Perception and Cognition (ICMPC10), Sapporo, Japan, 25-29 August. Based on Bryden, & Hughes (1969). An index of Gregorian chant.

11. Origin of major and minor triads The most consonant sets of 3 pitch classes Include P5  high harmonicity No m2 or M2  low roughness (Parncutt, 1988) Only two chords satisfy this constraint!  Major and minor triads dominate MmT  Our attention is drawn to their difference

12. Missing fundamentals in triads (Parncutt, 1988; Terhardt, 1982) Chord CEG has missing fundamentals at A, F Chord CEbG has missing fundamentals at F, Ab Why? e.g. E and G are harmonics of A Mistuning of a ¼ - ½ tone? No problem in pitch perception Do these missing fundamentals exist?  Empirical evidence E.g. C-major triad goes better with F than F# (Parncutt, 1993) E.g. C-major triad goes better with F than F# (Parncutt, 1993) BUT: can also be explained by musical experience BUT: can also be explained by musical experience  Logical argument Brain tries to locate fundamentals in ambiguous sounds Brain tries to locate fundamentals in ambiguous sounds Perception of missing fundamentals is inevitable Perception of missing fundamentals is inevitable

13. Origin of major and minor scales Compatible with major and minor triads (tonic triads)  Krumhansl’s key profiles as pitch salience profiles of tonic triads Parncutt, 2011 ∆ Krumhansl’s key profiles ▀ calc. pitch salience in tonic triad  evidence that tonic in MmT is a triad, not a tone

14. Avoiding consecutive semitones If there are consecutive semitones in a melody,  middle tone perceived as passing  middle tone not a scale step  no consecutive semitones in (jazz) scales Pressing (1981) Common exceptions: #4-5-b6, #7-8-b9 This can explain why C-major & –minor include D & not Db. Alternative explanations:  Chord V is important. It must have P5 to be consonant.  Use of standard diatonic scales

15. Psychohistoric origin of major and minor scales 1.Diatonic scales in ancient music 2.Importance of major and minor triads  CEG, CEbG 3.Leading tones  CEGB, CEbGB  CEGB, CEbGB 4.Implied pitches in these triads  CEFGAB, CEbFGAbB 5.No consecutive semitones  CDEFGAB, CDEbFGAbB

16. Claim: The tonic in MmT is a triad not a single tone! Corollary: Any passage in MmT is perceived as a prolongation of its tonic triad Any passage in MmT is perceived as a prolongation of its tonic triadEvidence: Qualitative Qualitative Success of Schenkerian approachSuccess of Schenkerian approach Quantitative Quantitative Correlation between pitch salience in tonic triad and stability in scaleCorrelation between pitch salience in tonic triad and stability in scale Transition probabilities in melodiesTransition probabilities in melodies

17. Transition probabilities between scale steps in major-mode melodies (Huron, 2006, 2012) Why is the transition between scale steps 6 and 7 avoided?

18. “Huron’s stereotype” 531531 7 123456 Music theory: Embellishment of tonic triad Arpeggiation Passing notes Neighbor notes Psychological basis: Auditory scene analysis Harmonicity Pitch proximity

19. Pitch range of major-key melodies The lowest scale degree is often 1 or 7. The highest is often 6.

20. A classical example Opening themes of 10 out of 18 Mozart piano sonatas conform to Huron‘s stereotype: KV 279, 280, 281, 283, 284, 310, 331, 332, 333, 545

21. Schenker’s Ursatz “Great music” (Bach, Beethoven, Brahms…) is a prolongation (elaboration, embellishment, Auskomponierung, Auswicklung) of the Ursatz.  The Ursatz (background) prolongs the tonic triad.  The Ursatz is elaborated  middleground  The middleground is elaborated  foreground  The whole piece prolongs the tonic triad

22. Prolongation of prolongation?  Not only “great” music Is all music in Mmt is a prolongation of the tonic triad?  Not only music analysis Does chord prolongation have a psychological basis?

23. Major-minor and valence Major-minor and valence some basic facts   Positive valence happiness, contentment, serenity, grace, tenderness, elation, joy, victory, majesty…   Negative valence sadness, anger, fear, tension, solemnity, lament, tragedy, pathos, mourning, melancholy, frustration, depression, gloom…   Major-minor effect can be overridden by tempo E.g. fast, happy minor or slow, sad major   Applies to tonalities not individual chords A major triad in a minor key can sound sad A minor triad in a major key can sound happy

24. Leonard B. Meyer Emotion and meaning in music (1956)  Minor tonality is more ambiguous Two versions of scale degrees 6 and 7 Two versions of scale degrees 6 and 7 Extreme example: Carmen’s Habanera (“scandalous”: Susan McClary, 2005) Extreme example: Carmen’s Habanera (“scandalous”: Susan McClary, 2005)  Uncertainty  negative emotion measured by information theory measured by information theory

25. Sad speech and music Sad speech and music Huron‘s approach. Some salient stuctural features: 1. Mean pitch is lower than average 2. Smaller pitch intervals between successive syllables 3. Lower sound level 4. Slower My hypothesis:  Only 1 can explain origin of minor-sad  Other are consequences

26. Why is major happy?  Most music is happy (births, weddings, feasts, preparation for war, entertainment, relaxation) not sad (funerals) (births, weddings, feasts, preparation for war, entertainment, relaxation) not sad (funerals)  Most music is major Major keys/chord more common than minor Major keys/chord more common than minor Modulation to relative major; major dominant triadModulation to relative major; major dominant triad Reason: more consonant? (higher harmonicity, less ambiguity)Reason: more consonant? (higher harmonicity, less ambiguity)  Minor keys  the tonal Other  Unhappy music  the Other musical emotion

27. Analogous asymmetries In everyday life and music,  Positive valence is normal  Negative valence is abnormal (emotional Other) In music,  Consonance is normal  Dissonance is abnormal (needs resolution) Consonance includes smoothness, harmonicity, diatonicity, familiarity; major is more consonant

28. Why is minor sad? Why is minor sad? Two theories – competing or complementary? 1. Structural ambiguity (LB Meyer)  Minor: root of tonic and tonic of scale are more ambiguous Is this dynamic (higher-arousal) negativity? afraid, angry, tense, frustrated… 2. Expected pitch in speech (Huron)  Minor: 3rd and 6th scale degrees are lower than expected Is this static (lower-arousal) negativity? sad, solemn, gloomy, melancholy, depressed, lamenting, mourning, tragic, pathetic… In both cases,  association between music and situation/speech  role of duration & prolongation: keys not chords

29. Theses 1. A passage of MmT is perceived as a prolonged background triad. 2. The prolonged triad is the ultimate origin of “major-minor = happy-sad”. Read all about it! Latest issue of Empirical Musicology Review Special thanks to David Huron and Matthew Davis for their study on mean interval size, which inspired this study