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 How did people experience consonance and dissonance (C/D) in the Middle Ages? An interdisciplinary question Orientation Humanities Sciences People Music history Music psychology Information Music theory Music computing This is a job for… ystematic musicology! Cognition of Early Polyphony Shoppingverse.de ESF Exploratory Workshop, Graz 2012 Special issue of JIMS ed. Barbara Tillmann & Frans Wiering Preparation of dissonance The dissonant m7 is prepared The dissonant m7 is unprepared Sounds less Sounds more dissonant dissonant Psychological explanations: Stream segregation reduces dissonance (Wright & Bregman, 1987) Roughess depends on relative amplitude (Terhardt,1974) Hypothesis 1 We can learn about C/D from statistical analysis of scores Assumptions: • Consonant sonorities are more prevalent • Composers tend to prepare dissonant sonorities (more so than consonant) head-fi.org Indirect (implicit, unbiased?) measures of C/D Measures of experience of dead participants Hypothesis 2 The C/D of a sonority has three main psychological components: feeds.feedburner.com • Roughness (peripheral) • Harmonicity (central) • Familiarity (central) C/D part 1: Roughness consonance Origin: Inner ear (Helmholtz, Plomp…) Interference between nearby partials (<1CBW) 1.5 1 0.5 dissonance 0 1 2 3 4 5 6 -0.5 Interval class (semitones) -1 -1.5 Huron, D. (1994). Interval-class content in equally tempered pitch-class sets: Common scales exhibit optimum tonal consonance. Music Perception, 11, 289-305. 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. dissonance of P4 is due to harmonicity not roughness www.unc.edu/~chapman3/westernscale.html C/D part 2: Harmonicity Harmonicity or periodicity? Spectral versus temporal representations of complex sounds • 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: 1. Physical attributes of signal 2. Measures of experienced pitch (standard empirical methods) NOT Physiological measures C/D depends on harmonicity in the sense of experienced patterns among experienced partials C/D part 3: Familiarity Scale-step stability is learned from musical experience (Krumhansl & Kessler, 1982) but ultimately depends on pitch-salience profile of tonic triad (Parncutt, 1988, 2011) Krumhansl, C. L., & Kessler, E. J. (1982). Tracing dynamic changes in perceived tonal organization in a spatial representation of musical keys. 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. Sample of music for this study • • • • Representative scores from four centuries Vocal polyphony Mainly sacred, some secular Mainly 4 parts, sometimes 3, 5, 6, or 8 Internet sources • • • • • Kern scores Choral Wiki PMFC (Polyphonic Music of the Fourteenth century) Elvis (Electronic Locator of Vertical Interval Successions) CPDL.org (free choral music) 13th-Century sources Perotin (1150/65 – 1200/25, French) Magnum Liber Organi, Viderunt omnes, Sederunt, Mors Alfonso el Sabio (1221-1284, Spanish) Virgen Santa Maria, Cantigas de Santa Maria Adam de la Halle (1250-1310, French) Fi Maris de vostre Amour, Je muir je muir d'amourete, Li dous regars de ma dame, Hareu li maus d'amer M'ochist, A dieu commant amourete, Dame or sui trais, Amours et ma dame aussi, Or est Baiars en la pasture Hure, A jointes mains vous proi, He Diex quant verrai, Diex comment porroie, Trop desire aveoir, Bonne amourete, Tant con je vivrai Montpellier Codex (1250-1300, Anonymus, French) #66 Mater Dei – Mater Virgo – Eius, #78 Dieus Mout me fet sovent fremir, #158 Mal d'amors presnes m'amie, #319 On parole – A Paris – Frese nouvele, #339 Alle psallite cum luya 14th-Century sources Guillaume de Machaut (1300-1377, French) Messe de 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! dimmi tu, A le sandra lo spirto, Cara mi donna, Quanto piu caro fay, Si dolce non sono Johannes Ciconia (c.1335 or c.1370, French) O felix templum jubila, Petrum Marcellum venetum - O Petre antistes inclite, O Padua, sidus praeclarum, Venetie mundi splendor, Gloria Philippe de Vitry (1291 – 1361, French) Lugentium siccentur, Rex quem metrorum, Virtutibus laudabilis, Vos Qui Admiramini Gratissima virginis species Jacopo da Bologna (1340 - 1386, Italian) Aquila Altera, I Senti Za Como Larcho Damore, In Verde Prato Magister Andreas: Sanctus Egardus: Gloria 15th-Century sources Guillaume Dufay (1397 – 1474, Franco-Flemish) O tres piteulx/Omnes amici, Missa Ave Regina Coelorum, Missa Se la face ay pale, Adieu ces bons Vins John Dunstaple (1390 - 1453) Veni Creator, Descendi in ortum meum, Veni Sancte Spiritus Johannes Ockeghem (1410/30 - 1497) Missa l’homme armé (Kyrie) Jacob Obrecht (1450 - 1505) Parce Domine Heinrich Isaac (1450-1517) A la battaglia, Innsbruck ich muss dich lassen Guillaume le Rouge (1450-1465, Netherlands) Missa Soyez amprantiz, Stella celi (So ys emprentid) Simon de Insula (fl. c.1450–60, English or French) Missa O admirabile 16th-Century sources Orlando de Lassus (1532 - 1594) Matona mia cara, Salve regina mater Giovanni Pierluigi da Palestrina (1514/15 - 1594) Dies sanctificatus, Adoramus Te, Hodie Christus Natus Est, Missa Brevis (Credo), Missa Aeterna Christi munera Josquin Desprez (1450/55 - 1521) Ave Maria, Missa l’homme armé, Salve Regina, Missa Pange lingua, El grillo, Nymphes des Bois a 5, Tulerunt Dominum meum William Byrd (1540 – 1623) Ave verum corpus, Ne irascaris domine Giovanni Gabrieli (1555-1612) O Magnum Mysterium, Plaudite Andrea Gabrieli (1532-1585): Musica tolta da i madrigali di Claudio Monteverdi, e d'altri autori, e fatta spirituale; Bonum est et suaue; Ne confide Counting pc sets: 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” Pitch-class set terminology 6 pc-sets with cardinality 2: • 2-1 = m2, M7, m9 etc. • 2-2 = M2, m7, M9 etc. Intervallic inversion (within octave): capital letters • 2-1A = m2, m9 etc. • 2-1B = M7, M14 etc. Chordal inversion (diff. tone in bass): small letters • 3-11A = minor triad • 3-11Aa = root-position minor triad Dyads 13th-Century sample Plus all transpositions, inversions and compounds unprep prep Centuries: 13 14 15 16 Dyads unprep prep Centuries: 13 14 15 16 2-1 (m2, M7) Both are always dissonant; m2 more so (roughness) unprep prep Centuries: 13 14 15 16 2-2 (M2, m7) both are always dissonant unprep prep Centuries: 13 14 15 16 2-3 (m3, M6) …historical change from dissonant to intermediate …smaller interval (≈1CBWrough) became less dissonant unprep prep Centuries: 13 14 15 16 2-4 (M3, m6) …changed from dissonant to intermediate ……M3 was always more consonant than m6 unprep prep Centuries: 13 14 15 16 2-5 (P4, P5) …P5 always more consonant than P4 …clearly cons; later, unprep. P5 avoided (reduce fusion?) unprep prep Centuries: 13 14 15 16 2-6 (A4, d5) …both clearly diss, but A4 more frequent - can resolve in 2 ways (to M3 or P5); d5 only to M3 (not P4) unprep prep Triads 13th-Century sample Plus all transpositions, inversions and compounds unprep prep Centuries: 13 14 15 16 Triads: Samples from 4 centuries unprep prep 3-1 (012, e.g. CC#D) That‘s a semitone cluster never happened until 20th C. Centuries: 13 14 15 16 3-2 (013, 023, e.g. CDbEb, CDEb) clearly diss; later, unprep. consistently avoided 023 preferably in “root position” unprep prep Centuries: 13 14 15 16 3-3 (014, 034, e.g. CDbE, CD#E) not enough data unprep prep Centuries: 13 14 15 16 3-4 (015, 045. e.g. CDbF, CEF) unprep prep clearly diss; not enough data in 13th later, prep. 3-4Ab & 3-4Ba more common (part of M7 chord) Centuries: 13 14 15 16 3-5 (016, 056, e.g. CDbGb, CFGb) clearly diss; most completely avoided in 16th 3-5Ac & 3-5Bb more common (outer voices span P5) unprep prep Centuries: 13 14 15 16 3-6 (024, e.g. CDE) clearly diss; root position most common (13th: not enough data) unprep prep Centuries: 13 14 15 16 3-7 (025, 035, e.g. CDF, CEbF) clearly diss, but not as diss as other chords earlier, p5 above bass important (3-7Ac, 3-7Bc) later, m7 above bass also important (3-7Ab) m7 chord unprep prep Centuries: 13 14 15 16 3-8 (026, 046, e.g. CDF#, CEF#) clearly diss 3-8Ab: early Mm7 chord unprep prep Centuries: 13 14 15 16 3-9 (027, e.g. CDG sus) clearly diss “sus4” (3-9c) is more common in 13th & 16th (why?) unprep prep Centuries: 13 14 15 16 3-10 (036, e.g. CEbGb dim) clearly diss, but not very diss; 1st inv most cons, as expected; 13th C: too few data unprep prep Centuries: 13 14 15 16 3-11 (037, 047 = min, maj) more major than minor, root position than inversion exception: minor 1st inversion in 14th unprep prep Centuries: 13 14 15 16 3-12 (048, aug) not enough data unprep prep Evidence for 3 components of C/D Roughness • Explains most prevalence data in 13th-16th centuries • Gradually less important irrelevant for modern listeners? (McDermott et al., 2010: McLaughlan et al., sub.) Harmonicity • Explains dissonance of P4, consonance of triads incl. P5, preference for root position triads Familiarity • Moderate dissonances more consonant • Extreme dissonances more avoided (expertise effect?) Acknowledgment Andreas Gaich Student assistant Centre for Systematic Musicology Uni Graz, Austria 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.