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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. Theses. A passage of MmT * is perceived as a prolonged background triad

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Schenkerien prolongation and the emotional connotations of major-minor tonality

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

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

  3. Questionsarising • 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: evolutionarypsychology? …MmT: psychohistory?

  5. Evolutionaryfunctionaloriginsofemotion Arousal • High: energyavailableornecessary • Low: energyunavailableorunnecessary Valence • positive: clearsituation safety, confidence • negative: unclearsituation fearoranger

  6. PsychohistoricoriginofMmTFivepsychohistoricalsteps • Diatonicscales in ancientmusic • Leadingtones in medievalpolyphony • Importanceofmajorandminortriads • Impliedpitches in thesetriads • Noconsecutivesemitones in scales

  7. Major-minorTonality (MmT) Most musicin MmTcanbereducedtochordprogressions. Most chordscorrespondtooneofthesediatonictriads.

  8. Origin ofpentatonic, diatonic, chromaticscales • Pairs ofharmoniccomplextoneswithfrequenciesorpitches in common • Octave andfifthrelations • Circle offifths ethanhein.com Harmonics in common perceptualsimilarity

  9. Leadingtones in earlymusicGuillaume de Machaut (1300-1377). RondeauMa fin estmon commencementF# tonicizes G - C# tonicizes D

  10. Origin of leading tones?Consonance / prevalence of individual tones in chant Data Model A B C D E F G A B C D E F G Data: Counted in the Liber Usualis(DDMAL, Fujiniagaet al., McGill) Model: No. of harmonicpcs (P5, M3, m7, M2) atdiatonicscalesteps Comparison: df= 5, r = 0.90, p<.01 Finding: C (F) more prevalentthan B (E) origin of leadingtone? 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 ofmajorandminortriads • The mostconsonantsetsof 3 pitchclasses • Include P5  high harmonicity • No m2 or M2 lowroughness • (Parncutt, 1988) • Onlytwochordssatisfythisconstraint! • Major andminortriadsdominateMmT • Ourattentionisdrawntotheirdifference

  12. Missingfundamentals in triads(Parncutt, 1988; Terhardt, 1982) Chord CEG hasmissingfundamentalsat A, F ChordCEbGhasmissingfundamentalsat F, Ab Why? e.g. E and G areharmonicsof A Mistuningof a ¼ - ½ tone? Noproblem in pitchperception Do thesemissingfundamentalsexist? • Empiricalevidence • E.g. C-major triadgoesbetterwith F than F# (Parncutt, 1993) • BUT: can also beexplainedbymusicalexperience • Logical argument • Brain triestolocatefundamentals in ambiguoussounds • Perceptionofmissingfundamentalsisinevitable

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

  14. Avoidingconsecutivesemitones Ifthereareconsecutivesemitones in a melody,  middle tone perceivedaspassing  middle tone not a scalestep  noconsecutivesemitones in (jazz) scales Pressing (1981) Common exceptions: #4-5-b6, #7-8-b9 This canexplainwhy C-major & –minorinclude D & not Db. Alternative explanations: • Chord V isimportant. It must have P5 tobeconsonant. • Useofstandarddiatonicscales

  15. Psychohistoricoriginofmajorandminorscales • Diatonicscales in ancientmusic • Importanceofmajorandminortriads  CEG, CEbG • Leadingtones  CEGB, CEbGB • Impliedpitches in thesetriads  CEFGAB, CEbFGAbB • Noconsecutivesemitones  CDEFGAB, CDEbFGAbB

  16. Claim: The tonic in MmTis a triadnot a singletone! Corollary: • Anypassage in MmTisperceivedas a prolongationofitstonictriad Evidence: • Qualitative • SuccessofSchenkerianapproach • Quantitative • Correlationbetweenpitchsalience in tonictriadandstability in scale • Transition probabilities in melodies

  17. Transition probabilitiesbetweenscalesteps in major-mode melodies(Huron, 2006, 2012) Whyisthetransitionbetweenscalesteps 6 and 7 avoided?

  18. “Huron’s stereotype” 5 3 1 7 1 2 3 4 5 6 • Music theory: Embellishmentoftonictriad • Arpeggiation • Passingnotes • Neighbornotes • Psychological basis: Auditorysceneanalysis • Harmonicity • Pitch proximity

  19. Pitch rangeofmajor-keymelodies The lowestscaledegreeisoften 1 or 7. The highestisoften 6.

  20. A classicalexample Openingthemesof 10 out of 18 Mozart piano sonatasconformtoHuron‘s stereotype: KV 279, 280, 281, 283, 284, 310, 331, 332, 333, 545

  21. Schenker’sUrsatz “Great music” (Bach, Beethoven, Brahms…) is a prolongation (elaboration, embellishment, Auskomponierung, Auswicklung) of the Ursatz. • TheUrsatz (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-minorandvalencesomebasicfacts • 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. MeyerEmotion andmeaning in music(1956) • Minor tonality is more ambiguous • Two versions of scale degrees 6 and 7 • Extreme example: Carmen’s Habanera (“scandalous”: Susan McClary, 2005) • Uncertainty  negative emotion • measured by information theory

  25. SadspeechandmusicHuron‘sapproach. Somesalientstucturalfeatures: • Meanpitchislowerthanaverage • Smallerpitchintervalsbetweensuccessivesyllables • Lowersoundlevel • Slower Myhypothesis: • Only 1 canexplainoriginofminor-sad • Other areconsequences

  26. Whyismajor happy? • Most musicis happy • (births, weddings, feasts, preparationfor war, entertainment, relaxation) not sad (funerals) • Most musicismajor • Major keys/chordmorecommonthanminor • Modulation to relative major; major dominant triad • Reason: moreconsonant? (higherharmonicity, lessambiguity) • Minor keys  the tonal Other • Unhappy music  the Other musical emotion

  27. Analogousasymmetries 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. Whyisminorsad?Twotheories – competingorcomplementary? 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 • A passage of MmT is perceived as a prolonged background triad. • 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

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