Historical origins of major-minor tonality (MmT) A psychological approach 11.04.2017 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

Explaining MmT’s hegemony 11.04.2017 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?

Explaining musical structure the “Why is the sky blue?” approach 11.04.2017 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?

History of tonal syntax: Processes 11.04.2017 History of tonal syntax: Processes History of ideas Perceptual universals Die Entstehung der tonalen Klangsyntax. Eberlein, R. (1994). Frankfurt: Peter Lang. Stylistic or compositional norms (statistical regularities) Music perception (expectations) Rules of composition

Music ficta and MmT’s “emergence” a theory focusing on notation 11.04.2017 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

Epistemology and approach 11.04.2017 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

History of triads 12th 13th 14th 15th Cent 16th 17th 11.04.2017 History of triads “pretonal” 12th 2-part counterpoint, discant improvisation 13th 3- and 4-part ctpt, 3rds & 6ths, imperfect consonances 14th Ars Nova (Vitry, Machaut) double-leading-tone cadence “emergence” of MmT 15th Cent Dunstable, Dufay, Ockeghem falling fifth cadence in 3 and 4 parts Fauxbourdon: parallel 6/3 triads Falsobordone: chains of root positions 16th Palestrina, Lassus most sonorities are major and minor triads final fifth replaced by triad; tierce de Picardie 17th all final sonorities become triads seventh chords, clear SDT progressions

Historical emergence of triads an educated guess 11.04.2017 Historical emergence of triads an educated guess Causal relation between the three lines?

History of triadic theory 11.04.2017 History of triadic theory Century Idea Theorists 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)

Karl Popper’s “three worlds” and Medieval music perception 11.04.2017 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

Emergence of Mm triads & tonalities in “Popperian cosmology” 11.04.2017 World 1 (physics) World 2 (experience) World 3 (knowledge) Represen-tation Performance (notation) Familiarity (tonal cognition) Conceptualization (verbal cognition) Period 14th-16th C. 15th-17th C. 16th-18th C. Causal chain: Each stage is a pre- or co-requisite for the next

What is special about Mm triads? 11.04.2017 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

Psychoacoustics of consonance 3 well established psychological factors 11.04.2017 Roughness (Helmholtz) nearby partials on basilar membrane peripheral physiology Fusion (Stumpf) holistic perception of complex sounds neural processing Familiarity (Cazden, Tenney) exposure promotes liking

11.04.2017 pc-set theory and consonance: 19 Tn-types of cardinality 3 after Rahn (1980) prime form 012 013 014 015 016 024 025 026 027 036 037 048 inversion 023 034 045 056 035 046 047 012 = 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).

Why is ear training so difficult? 11.04.2017 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

Missing fundamentals of a major triad 11.04.2017 notes harmonics (up to C7) missing funda-mentals some higher C4 C5 G5 C6 E6 G6 Bb6 C7 A3 E6 G6 A6 B6 6 7 8 9 E4 E5 B5 E6 G#6 B6 F3 C6 F6 G6 A6 6 8 9 10 G3 G4 D5 G5 B5 D6 F6 G6 A6 B6 D3 C6 D6 E6 A6 7 8 9 12

Missing fundamentals of a minor triad 11.04.2017 notes harmonics (up to C7) missing funda-mentals higher C4 C5 G5 C6 E6 G6 Bb6 C7 F3 C6 Eb6 F6 G6 A6 6 7 8 9 10 Eb4 Eb5 Bb5 Eb6 G6 Bb6 Ab3 C6 Eb6 Bb6 5 6 9 G3 G4 D5 G5 B5 D6 F6 G6 A6 B6 D3 C6 D6 E6 A6 7 8 9 12

missing funda-mentals Missing fundamentals of a major triad octave generalized model – assuming octave equivalence 11.04.2017 notes harmonics missing funda-mentals C C G E Bb D A E G (B) E E B G# D F# F C G (A) G G D B F A D C E (A F#)

missing funda-mentals Missing fundamentals of a minor triad octave generalized model – assuming octave equivalence 11.04.2017 notes harmonics missing funda-mentals C C G E Bb D F C Eb G (A) Eb Eb Bb G Db F Ab C Eb (Bb) G G D B F A D C (D A E)

Experiment on pitch salience in musical chords 11.04.2017 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.

Krumhansl’s key profiles pc-stability profiles 11.04.2017 Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review Krumhansl, C. L., & Kessler, E. J. (1982).

Prevalence model of key profiles 11.04.2017 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?

Lerdahl’s “basic pitch space” for the key of C major – after Deutsch & Feroe 11.04.2017 level a C level b G level c E level d D F A B level e Db Eb F# Ab Bb hierarchical depth 5 1 2 3 4 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.

Open triangles: pc stability profile of MmT1 Full squares: pc salience profile of tonic triad2 11.04.2017 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

Prevalence of pitches in Gregorian chant 11.04.2017 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.).

Chant: Why are some pitches more common than others? 11.04.2017 Theory: Tones whose harmonics correspond to diatonic scale steps are more consonant  preferred  more prevalent Implication for mi-fa: fa is more common more stable  origin of leading tone?

What is a music psychologist doing at MedRen? 11.04.2017 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”?)

11.04.2017 Double leading-tone cadence prevalence 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

Triads in Palestrina: Canticum Canticorum (1583-84), Motet 1 11.04.2017 root major minor sus dim total C 14+3+1=18 4+7+1=12 1+0+0=1 0+0+0=0 19+10+2=31 D 6+4+0=10 18+5+3=26 8+1+0=9 32+10+3=45 Eb 2+3+0=5 E 2+0+0=2 3+0+0=3 F 30+5+0=35 31+5+0=36 G 17+1+0=18 28+8+1=37 47+9+1=57 A 5+2+0=7 4+1+0=5 12+3+0=15 Bb 29+6+0=35 30+6+0=36 tot 103+24+1=128 55+21+5=81 16+1+0=17 each cell: Root position + first inversion + second inversion = total

Sonorities in Renaissance polyphony 11.04.2017 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)

Triads in Palestrina: Canticum Canticorum (1583-84), Motet 1 11.04.2017 number of occurrences

Prevalence of 2-chord progressions 11.04.2017 Prevalence of 2-chord progressions Eberlein’s sample J. S. Bach 7 chorales; kleine harmonische Labyrinth Händel Trio sonata Op. 5 No. 5 Mozart Missa brevis KV 65 (Kyrie, Gloria, Agnus Dei) Beethoven Mass in C (Kyrie, Gloria) Mendelssohn Motets Op. 78, Nos. 1 & 2 Eberlein, R. (1994). Die Entstehung der tonalen Klangsyntax (pp. 422-423). Frankfurt: Peter Lang. rising P4 falling P4 rising 3rd falling 3rd rising M2 falling M2 total maj-maj 64 19 6 2 91 maj-min 60 1 9 5 77 min-maj 20 15 3 49 min-min 21 27 150 45 24 17 244

Wanted! Experts in different European countries 11.04.2017 Wanted! Experts in different European countries ESF Exploratory Workshop “Evolution of Western tonal syntax” historians theorists computer scientists psychologists parncutt@uni-graz.at