Presentation on theme: "Richard Parncutt Center for Systematic Musicology"— Presentation transcript:
1 Historical origins of major-minor tonality (MmT) A psychological approach Richard ParncuttCenter for Systematic MusicologyUniversity of Graz, AustriaPresented at Ren Med 2010, Royal Holloway, Egham GB, 5-8 July 2010Refers 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 onmajor & minor triadsmajor & minor keysWhy?In the “West”polyphony, ficta, triads?Beyond the “West”political? psychological?
3 Explaining musical structure the “Why is the sky blue?” approach Explaining musical structure the “Why is the sky blue?” approachMmT: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 tonal syntax: ProcessesHistoryof ideasPerceptualuniversalsDie Entstehung der tonalen Klangsyntax.Eberlein, R. (1994).Frankfurt: Peter Lang.Stylistic or compositional norms(statistical regularities)Music perception(expectations)Rules ofcomposition
5 Music ficta and MmT’s “emergence” a theory focusing on notation Music ficta and MmT’s “emergence” a theory focusing on notationMixolydian 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 Epistemology and approachFavor simpler theories (Ockam)details are important (Dahlhaus)but simpler theories are easier to falsify (Popper)Favor generative theories (Lerdahl)identify underlying principles or axiomsnon-circular arguments, causeeffectFavor interdisciplinarity (CIM, JIMS)relevant knowledge should be consideredmultidisciplinary theories are easier to falsify
7 History of triads 12th 13th 14th 15th Cent 16th 17th History of triads“pretonal”12th2-part counterpoint, discant improvisation13th3- and 4-part ctpt, 3rds & 6ths, imperfect consonances14thArs Nova (Vitry, Machaut)double-leading-tone cadence“emergence” of MmT15thCentDunstable, Dufay, Ockeghemfalling fifth cadence in 3 and 4 partsFauxbourdon: parallel 6/3 triadsFalsobordone: chains of root positions16thPalestrina, Lassusmost sonorities are major and minor triadsfinal fifth replaced by triad; tierce de Picardie17thall final sonorities become triadsseventh chords, clear SDT progressions
8 Historical emergence of triads an educated guess Historical emergence of triads an educated guessCausal relation between the three lines?
9 History of triadic theory History of triadic theoryCenturyIdeaTheorists14thlowest voice governs sonorityTewkesbury (mid 14th), other contrapunctus tracts15thtriad as intervalsTinctoris (1477), Podio (1495), Gafori (1496)16thtriad as sonorityZarlino (1558), Sancta Maria (1565), Avianus (1581)17throot and inversionBurmeister 1606), Harnisch (1608), Lippius (1612), Campion (1618), Crüger (1630)18thimplied rootsRameau (1721)
10 Karl Popper’s “three worlds” and Medieval music perception Karl Popper’s “three worlds” and Medieval music perceptionWorld 1: physical, materialWorld 2: experience, subjectivityWorld 3: knowledge, informationWe need to clearly separate…physics: measured frequencies, durationsexperience: perceived pitches, durationsnotation: symbolic pitches and durations
11 Emergence of Mm triads & tonalities in “Popperian cosmology” World 1 (physics)World 2 (experience)World 3 (knowledge)Represen-tationPerformance (notation)Familiarity(tonal cognition)Conceptualization (verbal cognition)Period14th-16th C.15th-17th C.16th-18th C.Causal chain: Each stage is a pre- or co-requisite for the next
12 What is special about Mm triads? What is special about Mm triads?Frequency ratios?major: 4:5:6 seems okminor: 10:12:15 is not so “simple”Is tuning pure or Pythagorean?Harmonic dualism?overtones existundertones do notroot of C minor is C not G
13 Psychoacoustics of consonance 3 well established psychological factors Roughness (Helmholtz)nearby partials on basilar membraneperipheral physiologyFusion (Stumpf)holistic perception of complex soundsneural processingFamiliarity (Cazden, Tenney)exposure promotes liking
14 pc-set theory and consonance: 19 Tn-types of cardinality 3 after Rahn (1980)prime form012013014015016024025026027036037048inversion023034045056035046047012 = e.g. C-C#-D013 = e.g. C-C#-D#037 = minor triad047 = major triadThe 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 hearfrequencies (World 1), notes (World 3)We hear pitches (World 2)and extrapolate to notes bymusical experiencetheoretic knowledgeWhat about missing fundamentals?e.g. voice on telephoneMm triads have missing fundamentals at 2nd, 4th and 6th above root
16 Missing fundamentals of a major triad notesharmonics(up to C7)missing funda-mentalssome higherC4C5 G5 C6 E6G6 Bb6 C7A3E6 G6 A6 B6E4E5 B5 E6 G#6 B6F3C6 F6 G6 A6G3G4 D5 G5 B5D6 F6 G6 A6 B6D3C6 D6 E6 A6
17 Missing fundamentals of a minor triad notesharmonics(up to C7)missing funda-mentalshigherC4C5 G5 C6 E6G6 Bb6 C7F3C6 Eb6 F6 G6 A6Eb4Eb5 Bb5 Eb6G6 Bb6Ab3C6 Eb6 Bb6G3G4 D5 G5 B5D6 F6 G6 A6 B6D3C6 D6 E6 A6
18 missing funda-mentals Missing fundamentals of a major triad octave generalized model – assuming octave equivalencenotesharmonicsmissing funda-mentalsCC G E Bb DAE G (B)EE B G# D F#FC G (A)GG D B F ADC E (A F#)
19 missing funda-mentals Missing fundamentals of a minor triad octave generalized model – assuming octave equivalencenotesharmonicsmissing funda-mentalsCC 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 Experiment on pitch salience in musical chordsmajor triad 047minor triad 037goodness of fit pc pc Parncutt, R. (1993). Pitch properties of chords of octave-spaced tones.Contemporary Music Review, 9,
21 Krumhansl’s key profiles pc-stability profiles Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological ReviewKrumhansl, C. L., & Kessler, E. J. (1982).
22 Prevalence model of key profiles major keyminor keyAarden, 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 level aClevel bGlevel cElevel dDFABlevel eDbEbF#AbBbhierarchical depth51234Lerdahl, 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 MmT1 Full 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 Review2Parncutt, 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 prevalentImplication for mi-fa:fa ismore commonmore stable origin of leading tone?
27 What is a music psychologist doing at MedRen? Long-term project:history of tonal syntax and perceptionhumanities: music history, music theorysciences: psychology, computingPlanned first step:ESF strategic workshop15-30 speakers, many European countries1-3 days, plenty of discussionfollow-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)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 voicesvoicing GDGB-CCGC avoids parallels
29 Triads in Palestrina: Canticum Canticorum (1583-84), Motet 1 rootmajorminorsusdimtotalC14+3+1=184+7+1=121+0+0=10+0+0=0=31D6+4+0=1018+5+3=268+1+0=9=45Eb2+3+0=5E2+0+0=23+0+0=3F30+5+0=3531+5+0=36G17+1+0=1828+8+1=3747+9+1=57A5+2+0=74+1+0=512+3+0=15Bb29+6+0=3530+6+0=36tot=128=8116+1+0=17each cell: Root position + first inversion + second inversion = total
30 Sonorities in Renaissance polyphony Hierarchy of chord types:major triadminor triadsuspended triaddiminished triadHierarchy of chord positions:root positionfirst inversionsecond inversionPsychological theoryguiding principle is consonancehierarchy 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 Prevalence of 2-chord progressionsEberlein’s sampleJ. S. Bach7 chorales; kleine harmonische LabyrinthHändelTrio sonata Op. 5 No. 5MozartMissa brevis KV 65 (Kyrie, Gloria, Agnus Dei)BeethovenMass in C (Kyrie, Gloria)MendelssohnMotets Op. 78, Nos. 1 & 2Eberlein, R. (1994). Die Entstehung der tonalen Klangsyntax (pp ). Frankfurt: Peter Lang.rising P4falling P4rising 3rdfalling 3rdrising M2falling M2totalmaj-maj64196291maj-min6019577min-maj2015349min-min2127150452417244
33 Wanted! Experts in different European countries Wanted! Experts in different European countriesESF Exploratory Workshop“Evolution of Western tonal syntax”historianstheoristscomputer scientistspsychologists