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
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Estimating historical changes in consonance by counting prepared and unprepared dissonances in musical scores Richard Parncutt and Fabio Kaiser Centre.
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Estimating historical changes in consonance by counting prepared and
unprepared dissonances in musical scores
Richard Parncutt and Fabio KaiserCentre for Systematic Musicology, University of Graz, Austria
Craig SappCCARH, Department of Music, Stanford University
Internat. Conference on Music Perception and CognitionThessaloniki, 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
Cognition of Early PolyphonyESF Exploratory Workshop, Graz 2012Special issue of JIMS ed. Barbara Tillmann & Frans Wiering
We can learn about C/D from statistical analysis of scores
Indirect (implicit, unbiased?) measures of C/D Measures of experience of dead participants
Assumptions:• Consonant sonorities are more prevalent• Composers tend to prepare dissonant
sonorities (more so than consonant)
Hypothesis 2
The C/D of a sonority has three main psychological components:• Roughness (peripheral)• Harmonicity (central)• Familiarity (central)
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C/D part 1: Roughness Origin: Inner ear (Helmholtz, Plomp…)
Interference between nearby partials (<1CBW)
1 2 3 4 5 6
-1.5
-1
-0.5
0
0.5
1
1.5
Interval class (semitones)
Huron, D. (1994). Interval-class content in equally tempered pitch-class sets: Common scales exhibit optimum tonal consonance. Music Perception, 11, 289-305.
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C/D part 2: Harmonicity
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
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an3/westernscale.htm
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Harmonicity or periodicity?Spectral versus temporal representations of complex sounds
• Mathematically equivalent• Both present at different places on auditory pathwaysWhich 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 signal2. Measures of experienced pitch (standard empirical methods)NOT Physiological measures
C/D depends on harmonicity in the sense ofexperienced patterns among experienced partials
C/D part 3: FamiliarityScale-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 sourcesPerotin (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 sourcesGuillaume 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: SanctusEgardus: Gloria
15th-Century sourcesGuillaume 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
Simon de Insula (fl. c.1450–60, English or French)Missa O admirabile
16th-Century sourcesOrlando 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
Dyads13th-Century sample
unprepprep
Plus all transpositions, inversions and compounds
Dyads unprepprep
Centuries:
13 1415 16
2-1 (m2, M7)Both are always dissonant; m2 more so (roughness)
Centuries:
13 1415 16
unprepprep
2-2 (M2, m7)both are always dissonant
Centuries:
13 1415 16
unprepprep
2-3 (m3, M6)…historical change from dissonant to intermediate
…smaller interval (≈1CBWrough) became less dissonant
Centuries:
13 1415 16
unprepprep
2-4 (M3, m6)…changed from dissonant to intermediate
3-4 (015, 045. e.g. CDbF, CEF)clearly diss; not enough data in 13th
later, prep. 3-4Ab & 3-4Ba more common (part of M7 chord)
Centuries:
13 1415 16
unprepprep
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)
Centuries:
13 1415 16
unprepprep
3-6 (024, e.g. CDE)clearly diss; root position most common
(13th: not enough data)
Centuries:
13 1415 16
unprepprep
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
Centuries:
13 1415 16
unprepprep
3-8 (026, 046, e.g. CDF#, CEF#)clearly diss
3-8Ab: early Mm7 chord
Centuries:
13 1415 16
unprepprep
3-9 (027, e.g. CDG sus)clearly diss
“sus4” (3-9c) is more common in 13th & 16th (why?)
Centuries:
13 1415 16
unprepprep
3-10 (036, e.g. CEbGb dim)clearly diss, but not very diss; 1st inv most cons, as expected;
13th C: too few data
Centuries:
13 1415 16
unprepprep
3-11 (037, 047 = min, maj)more major than minor, root position than inversion
exception: minor 1st inversion in 14th
Centuries:
13 1415 16
unprepprep
3-12 (048, aug)not enough data
Centuries:
13 1415 16
unprepprep
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 GaichStudent assistantCentre for Systematic MusicologyUni 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.