Historical origins of major-minor tonality (MmT) A psychological approach

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 • major & minor triads • major & minor keys Why? In the “West” • polyphony, ficta, triads? Beyond the “West” • 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 History of ideas Perceptual universals Stylistic or compositional norms (statistical regularities) Eberlein, R. (1994). Die Entstehung der tonalen Klangsyntax. Frankfurt: Peter Lang. Music perception (expectations) Rules of composition

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

7. History of triads

8. Historical emergence of triadsan educated guess Causal relation between the three lines?

9. History of triadic theory

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… • physics: measured frequencies, durations • experience: perceived pitches, durations • notation: symbolic pitches and durations

11. Emergence of Mm triads & tonalities in “Popperian cosmology” Causal chain: Each stage is a pre- or co-requisite for the next

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

13. Psychoacoustics of consonance3 well established psychological factors • Roughness (Helmholtz) • nearby partials on basilar membrane • peripheral physiology • Fusion (Stumpf) • holistic perception of complex sounds • neural processing • Familiarity (Cazden, Tenney) • exposure promotes liking • neural processing

14. pc-set theory and consonance:19 Tn-types of cardinality 3after Rahn (1980) 012 = e.g. C-C#-D 013 = e.g. C-C#-D# 037 = 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 • musical experience • theoretic knowledge What about missing fundamentals? e.g. voice on telephone Mm triads have missing fundamentals at 2nd, 4th and 6th above root

16. Missing fundamentals of a major triad

17. Missing fundamentals of a minor triad

18. Missing fundamentals of a major triadoctave generalized model – assuming octave equivalence

19. Missing fundamentals of a minor triadoctave generalized model – assuming octave equivalence

20. Experiment on pitch salience in musical chords major triad 047 minor triad 037 goodness of fit  pc  pc  Parncutt, R. (1993). Pitch properties of chords of octave-spaced tones. Contemporary Music Review, 9, 35-50.

21. Krumhansl’s key profilespc-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 major key minor key 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?

23. Lerdahl’s “basic pitch space”for the key of C major – after Deutsch & Feroe 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, 503-522.

24. Open triangles: pc stability profile of MmT1Full squares: pc salience profile of tonic triad2 1Krumhansl, C. L., & Kessler, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review 2Parncutt, 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: fais • more common • more stable  origin of leading tone?

27. What is a music psychologist doing at MedRen? Long-term project: history of tonal syntax and perception • humanities: music history, music theory • sciences: psychology, computing Planned first step: ESF strategic workshop • 15-30 speakers, many European countries • 1-3 days, plenty of discussion • follow-up research project *ESF = European Science Foundation (“science” = “Wissenschaft”?)

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

29. Triads in Palestrina: Canticum Canticorum (1583-84), Motet 1 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 (1583-84), Motet 1 number of occurrences

32. Prevalence of 2-chord progressions Eberlein, R. (1994). Die Entstehung der tonalen Klangsyntax (pp. 422-423).Frankfurt: Peter Lang.

33. Wanted! Experts in different European countries • ESF Exploratory Workshop • “Evolution of Western tonal syntax” • historians • theorists • computer scientists • psychologists • parncutt@uni-graz.at