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Historical origins of major-minor tonality (MmT) A psychological approach Richard Parncutt Center for Systematic Musicology University of Graz, Austria.

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Presentation on theme: "Historical origins of major-minor tonality (MmT) A psychological approach Richard Parncutt Center for Systematic Musicology University of Graz, Austria."— Presentation transcript:

1 Historical origins of major-minor tonality (MmT) A psychological approach Richard Parncutt Center for Systematic Musicology University of Graz, Austria Presented at Ren Med 2010, Royal Holloway, Egham GB, 5-8 July 2010 Refers to the following article in press in Music Perception: The tonic as triad: Key profiles as pitch salience profiles of tonic triads

2 Explaining MmT’s hegemony Like it or lump it... most music heard today is based on n major & minor triads n major & minor keys Why? In the “West” n polyphony, ficta, triads? Beyond the “West” n political? psychological?

3 Explaining musical structure the “Why is the sky blue?” approach MmT: Why is it like it is? And not quite different? (Eberlein, 1994) Early music: Why did certain structures and patterns emerge in one century and disappear again in another?

4 History of tonal syntax: Processes Perceptual universals Music perception (expectations) Stylistic or compositional norms (statistical regularities) History of ideas Rules of composition Eberlein, R. (1994). Die Entstehung der tonalen Klangsyntax. Frankfurt: Peter Lang.

5 Music ficta and MmT’s “emergence” a theory focusing on notation Mixolydian  major, Dorian  minor, usw. Musica ficta can explain the scale steps in major/minor keys. But it cannot explain their relative stability

6 Epistemology and approach n Favor simpler theories (Ockam) u details are important (Dahlhaus) u but simpler theories are easier to falsify (Popper) n Favor generative theories (Lerdahl) u identify underlying principles or axioms u non-circular arguments, cause  effect n Favor interdisciplinarity (CIM, JIMS) u relevant knowledge should be considered u multidisciplinary theories are easier to falsify

7 History of triads “pretonal” 12th n 2-part counterpoint, discant improvisation 13th n 3- and 4-part ctpt, 3rds & 6ths, imperfect consonances 14th n Ars Nova (Vitry, Machaut) n double-leading-tone cadence “emergence” of MmT 15th Cent n Dunstable, Dufay, Ockeghem n falling fifth cadence in 3 and 4 parts n Fauxbourdon: parallel 6/3 triads n Falsobordone: chains of root positions 16th Cent n Palestrina, Lassus n most sonorities are major and minor triads n final fifth replaced by triad; tierce de Picardie 17th Cent n all final sonorities become triads n seventh chords, clear SDT progressions

8 Historical emergence of triads an educated guess Causal relation between the three lines?

9 History of triadic theory Century IdeaTheorists 14th lowest voice governs sonority Tewkesbury (mid 14th), other contrapunctus tracts 15th triad as intervals Tinctoris (1477), Podio (1495), Gafori (1496) 16th triad as sonority Zarlino (1558), Sancta Maria (1565), Avianus (1581) 17th root and inversion Burmeister 1606), Harnisch (1608), Lippius (1612), Campion (1618), Crüger (1630) 18th implied roots Rameau (1721)

10 Karl Popper’s “three worlds” and Medieval music perception World 1: physical, material World 2: experience, subjectivity World 3: knowledge, information We need to clearly separate… 1. physics: measured frequencies, durations 2. experience: perceived pitches, durations 3. notation: symbolic pitches and durations

11 Emergence of Mm triads & tonalities in “Popperian cosmology” World 1 (physics) World 2 (experience) World 3 (knowledge) Represen- tation Performance (notation) Familiarity (tonal cognition) Conceptualization (verbal cognition) Period14 th -16 th C.15 th -17 th C.16th-18 th C. Causal chain: Each stage is a pre- or co-requisite for the next

12 What is special about Mm triads? n Frequency ratios? u major: 4:5:6 seems ok u minor: 10:12:15 is not so “simple” u Is tuning pure or Pythagorean? n Harmonic dualism? u overtones exist u undertones do not u root of C minor is C not G

13 Psychoacoustics of consonance 3 well established psychological factors n Roughness (Helmholtz) u nearby partials on basilar membrane u peripheral physiology n Fusion (Stumpf) u holistic perception of complex sounds u neural processing n Familiarity (Cazden, Tenney) u exposure promotes liking u neural processing

14 pc-set theory and consonance: 19 Tn-types of cardinality 3 after Rahn (1980) 012 = e.g. C-C#-D 013 = e.g. C-C#-D# prime form inversion = minor triad 047 = major triad The major and minor triads are by far the most consonant Tn-types of cardinality 3. Only they have a P4 or P5 (fusion) and no M2 or m2 (roughness).

15 Why is ear training so difficult? We do not hear frequencies (World 1), notes (World 3) We hear pitches (World 2) and extrapolate to notes by u musical experience u theoretic knowledge What about missing fundamentals? e.g. voice on telephone Mm triads have missing fundamentals at 2 nd, 4 th and 6 th above root

16 Missing fundamentals of a major triad notes harmonics (up to C7) missing funda- mentals some higher harmonics C4 C5 G5 C6 E6 G6 Bb6 C7 A3 E6 G6 A6 B E4E5 B5 E6 G#6 B6F3 C6 F6 G6 A G3 G4 D5 G5 B5 D6 F6 G6 A6 B6 D3 C6 D6 E6 A

17 Missing fundamentals of a minor triad notes harmonics (up to C7) missing funda- mentals higher harmonics C4 C5 G5 C6 E6 G6 Bb6 C7 F3 C6 Eb6 F6 G6 A Eb4 Eb5 Bb5 Eb6 G6 Bb6 Ab3 C6 Eb6 Bb G3 G4 D5 G5 B5 D6 F6 G6 A6 B6 D3 C6 D6 E6 A

18 Missing fundamentals of a major triad octave generalized model – assuming octave equivalence notesharmonics missing funda- mentals harmonics CC G E Bb DAE G (B) EE B G# D F#FC G (A) GG D B F ADC E (A F#)

19 Missing fundamentals of a minor triad octave generalized model – assuming octave equivalence notesharmonics missing funda- mentals harmonics CC G E Bb DFC Eb G (A) EbEb Bb G Db FAbC Eb (Bb) GG D B F ADC (D A E)

20 Experiment on pitch salience in musical chords major triad 047minor triad 037 pc  goodness of fit  Parncutt, R. (1993). Pitch properties of chords of octave-spaced tones. Contemporary Music Review, 9,

21 Krumhansl’s key profiles pc-stability profiles Krumhansl, C. L., & Kessler, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review

22 Prevalence model of key profiles Aarden, B. (2003). Dynamic melodic expectancy. PhD dissertation, Ohio State University. Why is G more prevalent that C in C major - but C is more stable ? major keyminor key

23 Lerdahl’s “basic pitch space” for the key of C major – after Deutsch & Feroe level aC level bCG level cCEG level dCDEFGAB level eCDbDEbEFF#GAbABbB hierarchical depth Lerdahl, E. (2001). Tonal pitch space (p. 47). New York: Oxford. Deutsch, D., & Feroe, J. (1981) The internal representation of pitch sequences in tonal music. Psychological Review, 88,

24 Open triangles: pc stability profile of MmT 1 Full squares: pc salience profile of tonic triad 2 1 Krumhansl, C. L., & Kessler, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review 2 Parncutt, R. (1988). Revision of Terhardt's psychoacoustical model of the root(s) of a musical chord. Music Perception

25 Prevalence of pitches in Gregorian chant B (11) is the least frequent tone at any position. Source of data: Bryden, J. R., & Hughes, D. G. (1969). An index of Gregorian chant. Cambridge, MA: Harvard University Press.).

26 Chant: Why are some pitches more common than others? Theory: Tones whose harmonics correspond to diatonic scale steps are more consonant  preferred  more prevalent Implication for mi-fa: fa is n more common n more stable  origin of leading tone?

27 What is a music psychologist doing at MedRen? Long-term project: history of tonal syntax and perception u humanities: music history, music theory u sciences: psychology, computing Planned first step: ESF strategic workshop u speakers, many European countries u 1-3 days, plenty of discussion u follow-up research project *ESF = European Science Foundation (“science” = “Wissenschaft”?)

28 Double leading-tone cadence prevalence of cadence and contexts in different periods? Origin: two-part cadences (12th Century) u major sixth  octave; major third  fifth; etc.  double-leading-tone cadence (14th) u two intervallic resolutions simultaneously  falling-fifth cadence (16th) u transition from 3 to 4 voices u voicing GDGB-CCGC avoids parallels

29 Triads in Palestrina: Canticum Canticorum ( ), Motet 1 rootmajorminorsusdimtotal C14+3+1= = =10+0+0= =31 D6+4+0= = =90+0+0= =45 Eb2+3+0=50+0+0= =5 E0+0+0=01+0+0=10+0+0=02+0+0=23+0+0=3 F30+5+0= =01+0+0=10+0+0= =36 G17+1+0= = =20+0+0= =57 A5+2+0=74+1+0=53+0+0=30+0+0= =15 Bb29+6+0= =01+0+0=10+0+0= =36 tot = = = =2 each cell: Root position + first inversion + second inversion = total

30 Sonorities in Renaissance polyphony Hierarchy of chord types: major triad minor triad suspended triad diminished triad Hierarchy of chord positions: root position first inversion second inversion Psychological theory guiding principle is consonance hierarchy of psychoacoustic components: fusion (brain; perception of complex tones) smoothness (inner ear; frequency analysis)

31 Triads in Palestrina: Canticum Canticorum ( ), Motet 1 number of occurrences

32 Prevalence of 2-chord progressions rising P4 falling P4 rising 3rd falling 3rd rising M2 falling M2 total maj-maj maj-min min-maj min-min total Eberlein, R. (1994). Die Entstehung der tonalen Klangsyntax (pp ). Frankfurt: Peter Lang. Eberlein’s sample J. S. Bach7 chorales; kleine harmonische Labyrinth HändelTrio sonata Op. 5 No. 5 MozartMissa brevis KV 65 (Kyrie, Gloria, Agnus Dei) BeethovenMass in C (Kyrie, Gloria) MendelssohnMotets Op. 78, Nos. 1 & 2

33 Wanted! Experts in different European countries ESF Exploratory Workshop “Evolution of Western tonal syntax” historians theorists computer scientists psychologists


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