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

ystematic musicology!

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Preparation of dissonance

The dissonant m7 is prepared Sounds less

dissonant

The dissonant m7 is unprepared Sounds more

dissonant

Psychological explanations: Stream segregation reduces dissonance (Wright & Bregman, 1987)Roughess depends on relative amplitude (Terhardt,1974)

Hypothesis 1

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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

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-1

-0.5

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0.5

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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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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

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 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

……M3 was always more consonant than m6

Centuries:

13 1415 16

unprepprep

Centuries:

13 1415 16

2-5 (P4, P5)…P5 always more consonant than P4

…clearly cons; later, unprep. P5 avoided (reduce fusion?)

unprepprep

Centuries:

13 1415 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)

unprepprep

Triads13th-Century sample

unprepprep

Plus all transpositions, inversions and compounds

Triads: Samples from 4 centuriesunprepprep

Centuries:

13 1415 16

3-1 (012, e.g. CC#D)

That‘s a semitone cluster - never happened until 20th C.

3-2 (013, 023, e.g. CDbEb, CDEb)clearly diss; later, unprep. consistently avoided

023 preferably in “root position”

Centuries:

13 1415 16

unprepprep

3-3 (014, 034, e.g. CDbE, CD#E)not enough data

Centuries:

13 1415 16

unprepprep

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.