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Estimating historical changes in consonance by counting prepared and unprepared dissonances in musical scores

Estimating historical changes in consonance by counting prepared and unprepared dissonances in musical scores . Richard Parncutt and Fabio Kaiser Centre for Systematic Musicology, University of Graz, Austria Craig Sapp CCARH , Department of Music, Stanford University

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Estimating historical changes in consonance by counting prepared and unprepared dissonances in musical scores

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  1. Estimating historical changes in consonance by counting prepared and unprepared dissonances in musical scores Richard Parncutt and Fabio Kaiser Centre for Systematic Musicology, University of Graz, Austria Craig Sapp CCARH, Department of Music, Stanford University Internat. Conference on Music Perception and Cognition Thessaloniki, Greece 23-30 July 2012 SysMus Graz

  2. Howdidpeopleexperienceconsonanceanddissonance (C/D) in theMiddle Ages?An interdisciplinaryquestion This is a job for… ystematic musicology! • Cognition of Early Polyphony • ESF Exploratory Workshop, Graz 2012 • Special issueofJIMS • ed. Barbara Tillmann & Frans Wiering Shoppingverse.de

  3. Preparationofdissonance The dissonant m7 isprepared  Sounds less dissonant The dissonant m7 isunprepared  Sounds more dissonant Psychological explanations: Stream segregationreducesdissonance (Wright & Bregman, 1987) Roughessdepends on relative amplitude (Terhardt,1974)

  4. Hypothesis 1 Wecanlearnabout C/D fromstatisticalanalysisofscores • Assumptions: • Consonantsonoritiesaremoreprevalent • Composers tendtoprepare dissonant sonorities (more so thanconsonant) head-fi.org • Indirect(implicit, unbiased?) measuresofC/D • Measuresofexperienceofdeadparticipants

  5. Hypothesis 2 The C/D of a sonorityhasthreemainpsychologicalcomponents: • Roughness (peripheral) • Harmonicity (central) • Familiarity (central) feeds.feedburner.com

  6. C/D part 1: RoughnessOrigin: Innerear (Helmholtz, Plomp…)Interferencebetweennearbypartials (<1CBW) dissonanceconsonance Huron, D. (1994). Interval-class content in equally tempered pitch-class sets: Common scales exhibit optimum tonal consonance. Music Perception, 11, 289-305.

  7. C/D part 2: Harmonicity www.unc.edu/~chapman3/westernscale.html • The harmonicity of an interval or chord • “Harmonic”= “Similar to harmonic series” • No standard quantitative formulation • Seems to explain why… • Major triad more consonant/frequent than minor • Triads/dyads in root position more cons/freq than inversion • E.g. dissonanceof P4 is due toharmonicity not roughness

  8. Harmonicityorperiodicity?Spectral versus temporal representationsofcomplexsounds • Mathematically equivalent • Both present at different places on auditory pathways Which correspond to conscious experience? (How?) • Mind-body problem is unsolved! Careful scientific approach: Don’t jump to conclusions! Focus on parameters whose relationship to conscious experience has been clarified by previous research: • Physical attributes of signal • Measures of experienced pitch (standard empirical methods) NOT Physiological measures  C/D depends on harmonicity in the sense of experienced patterns among experienced partials

  9. C/D part 3: FamiliarityScale-stepstabilityislearnedfrommusicalexperience (Krumhansl & Kessler, 1982)but ultimatelydepends on pitch-salienceprofileoftonictriad (Parncutt, 1988, 2011) Krumhansl, C. L., & Kessler, E. J. (1982). Tracingdynamicchanges in perceived tonal organization in a spatialrepresentationofmusicalkeys. Psychol Rev, 89, 334-368. Parncutt, R. (2011). The tonic as triad: Key profiles as pitch salience profiles of tonic triads. Music Perception, 28, 333-365.

  10. Sample ofmusicforthisstudy • Representative scores from four centuries • Vocal polyphony • Mainly sacred, some secular • Mainly 4 parts, sometimes 3, 5, 6, or 8

  11. Internet sources • Kern scores • Choral Wiki • PMFC (Polyphonic Music of the Fourteenth century) • Elvis (Electronic Locator of Vertical Interval Successions) • CPDL.org (freechoralmusic)

  12. 13th-Century sources Perotin (1150/65 – 1200/25, French) Magnum Liber Organi, Videruntomnes, Sederunt, Mors Alfonso el Sabio(1221-1284, Spanish) VirgenSanta Maria, Cantigas de Santa Maria Adam de la Halle (1250-1310, French) Fi Maris de vostreAmour, Je muir je muird'amourete, Li dousregars de ma dame, Hareuli mausd'amerM'ochist, A dieucommantamourete, Dame or sui trais, Amours et ma dame aussi, Or estBaiars en la pasture Hure, A jointes mains vousproi, He Diex quant verrai, Diexcomment porroie, Trop desire aveoir, Bonne amourete, Tant con je vivrai Montpellier Codex (1250-1300, Anonymus, French) #66 Mater Dei – Mater Virgo – Eius, #78 DieusMout me fetsoventfremir, #158 Mal d'amorspresnesm'amie, #319 On parole – A Paris – Fresenouvele, #339 Allepsallite cum luya

  13. 14th-Century sources Guillaume de Machaut(1300-1377, French) Messede nostre dame (Kyrie and Gloria), Hoquetus David, Comment puet on mieus dire, De toutes Flours Landini, Francesco (1325-1397, Italian) madrigal from Squarcialupi Codex, Deh! dimmitu, A le sandra lo spirto, Cara mi donna, Quantopiucarofay, Si dolce non sono Johannes Ciconia(c.1335 or c.1370, French) O felixtemplumjubila, PetrumMarcellumvenetum- O Petreantistesinclite, O Padua, siduspraeclarum, Venetiemundi splendor, Gloria Philippe de Vitry(1291 – 1361, French) Lugentiumsiccentur, Rex quemmetrorum, Virtutibuslaudabilis, Vos Qui AdmiraminiGratissimavirginis species Jacopo da Bologna (1340 - 1386, Italian) Aquila Altera, I SentiZa Como LarchoDamore, In Verde Prato Magister Andreas: Sanctus Egardus: Gloria

  14. 15th-Century sources Guillaume Dufay (1397 – 1474, Franco-Flemish) O trespiteulx/Omnesamici, Missa Ave Regina Coelorum, MissaSe la face ay pale, Adieu cesbonsVins John Dunstaple(1390 - 1453) Veni Creator, Descendiin ortummeum, VeniSancteSpiritus Johannes Ockeghem(1410/30 - 1497) Missal’hommearmé (Kyrie) Jacob Obrecht(1450 - 1505) ParceDomine Heinrich Isaac (1450-1517) A la battaglia, Innsbruck ich muss dichlassen Guillaume le Rouge (1450-1465, Netherlands) MissaSoyezamprantiz, Stella celi (So ysemprentid) Simon de Insula (fl. c.1450–60, English or French) MissaO admirabile

  15. 16th-Century sources Orlando de Lassus(1532 - 1594) Matonamiacara, Salve reginamater Giovanni Pierluigi da Palestrina(1514/15 - 1594) Dies sanctificatus, AdoramusTe, HodieChristusNatusEst, MissaBrevis (Credo), MissaAeterna Christi munera JosquinDesprez(1450/55 - 1521) Ave Maria, Missal’hommearmé, Salve Regina, MissaPangelingua, El grillo, Nymphesdes Bois a 5, TuleruntDominummeum William Byrd (1540 – 1623) Ave verumcorpus, Ne irascarisdomine Giovanni Gabrieli(1555-1612) O Magnum Mysterium, Plaudite Andrea Gabrieli(1532-1585): Musicatolta da imadrigali di Claudio Monteverdi, e d'altriautori, e fattaspirituale; Bonumest et suaue; Ne confide

  16. Countingpcsets: Procedure No. of voices varies from 1 to 8 At every onset in any voice: count number of pcs in vertical sonority • If 2: count a “dyad” • If 3: count a “triad”

  17. Pitch-classsetterminology 6 pc-sets withcardinality 2: • 2-1 = m2, M7, m9 etc. • 2-2 = M2, m7, M9 etc. Intervallicinversion (withinoctave): capitalletters • 2-1A = m2, m9 etc. • 2-1B = M7, M14 etc. Chordalinversion (diff. tone in bass): smallletters • 3-11A = minortriad • 3-11Aa = root-position minortriad

  18. unprep prep Dyads13th-Century sample Plus all transpositions, inversionsandcompounds

  19. Centuries: 13 14 15 16 unprep prep Dyads

  20. Centuries: 13 14 15 16 unprep prep 2-1 (m2, M7)Botharealways dissonant; m2 more so (roughness)

  21. Centuries: 13 14 15 16 unprep prep 2-2 (M2, m7)both are always dissonant

  22. Centuries: 13 14 15 16 unprep prep 2-3 (m3, M6)…historicalchangefrom dissonant to intermediate…smallerinterval (≈1CBWrough) becameless dissonant

  23. Centuries: 13 14 15 16 unprep prep 2-4 (M3, m6)…changedfrom dissonant to intermediate……M3 was alwaysmoreconsonantthan m6

  24. Centuries: 13 14 15 16 unprep prep 2-5 (P4, P5)…P5 always more consonant than P4…clearly cons; later, unprep. P5 avoided (reduce fusion?)

  25. Centuries: 13 14 15 16 unprep prep 2-6 (A4, d5)…bothclearlydiss, but A4 more frequent - can resolve in 2 ways (to M3 or P5); d5 only to M3 (not P4)

  26. unprep prep Triads13th-Century sample Plus all transpositions, inversionsandcompounds

  27. Centuries: 13 14 15 16 unprep prep Triads:Samples from 4 centuries

  28. 3-1 (012, e.g. CC#D) That‘s a semitonecluster - neverhappeneduntil 20th C.

  29. Centuries: 13 14 15 16 unprep prep 3-2 (013, 023, e.g. CDbEb, CDEb)clearly diss; later, unprep. consistently avoided023 preferably in “root position”

  30. Centuries: 13 14 15 16 unprep prep 3-3 (014, 034, e.g. CDbE, CD#E)not enoughdata

  31. Centuries: 13 14 15 16 unprep prep 3-4 (015, 045. e.g. CDbF, CEF)clearlydiss; not enoughdata in 13thlater, prep. 3-4Ab & 3-4Ba morecommon (partof M7 chord)

  32. Centuries: 13 14 15 16 unprep prep 3-5 (016, 056, e.g. CDbGb, CFGb)clearlydiss; mostcompletelyavoided in 16th3-5Ac & 3-5Bb morecommon (outervoices span P5)

  33. Centuries: 13 14 15 16 unprep prep 3-6 (024, e.g. CDE)clearlydiss; rootpositionmostcommon(13th: not enoughdata)

  34. Centuries: 13 14 15 16 unprep prep 3-7 (025, 035, e.g. CDF, CEbF)clearlydiss, but not asdissasotherchordsearlier, p5 above bass important (3-7Ac, 3-7Bc)later, m7 above bass also important (3-7Ab)  m7 chord

  35. Centuries: 13 14 15 16 unprep prep 3-8 (026, 046, e.g. CDF#, CEF#)clearlydiss3-8Ab: early Mm7 chord

  36. Centuries: 13 14 15 16 unprep prep 3-9 (027, e.g. CDG sus)clearly diss“sus4” (3-9c) is more common in 13th & 16th (why?)

  37. Centuries: 13 14 15 16 unprep prep 3-10 (036, e.g. CEbGbdim)clearlydiss, but not verydiss; 1st invmostcons, asexpected; 13th C: toofewdata

  38. Centuries: 13 14 15 16 unprep prep 3-11 (037, 047 = min, maj)moremajorthanminor, rootpositionthaninversionexception: minor 1st inversion in 14th

  39. Centuries: 13 14 15 16 unprep prep 3-12 (048, aug)not enoughdata

  40. Evidencefor 3 componentsof C/D Roughness • Explainsmostprevalencedata in 13th-16th centuries • Graduallylessimportant  irrelevant for modern listeners? (McDermott et al., 2010: McLaughlan et al., sub.) Harmonicity • Explainsdissonanceof P4, consonanceoftriads incl. P5, preferenceforrootpositiontriads Familiarity • Moderate dissonances  moreconsonant • Extreme dissonances  moreavoided(expertiseeffect?)

  41. Acknowledgment Andreas Gaich Student assistant CentreforSystematicMusicology Uni Graz, Austria

  42. Literature Fazio, R. H., & Olson, M. A. (2003). Implicit measures in social cognition research: Their meaning and use. Annual Review of Psychology, 54, 297-327. McDermott, J. H., Lehr, A. J., & Oxenham, A. J. (2010). Individual differences reveal the basis of consonance. Current Biology, 20, 1035–1041. McLachlan, N. M., Marco, D. J. T. & Wilson, S. J. Consonance and pitch. Under review. Parncutt, R., & Hair, G. (2011). Consonance and dissonance in theory and psychology: Disentangling dissonant dichotomies. Journal of Interdisciplinary Music Studies, 5 (2), 119-166.

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