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Richard Parncutt, Andreas Fuchs, Andreas Gaich , Fabio Kaiser

The perceptual history of consonance and dissonance Counting vertical pitch-class sets in vocal polyphony. Richard Parncutt, Andreas Fuchs, Andreas Gaich , Fabio Kaiser Centre for Systematic Musicology, University of Graz, Austria. Medieval and Renaissance Music Conference

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Richard Parncutt, Andreas Fuchs, Andreas Gaich , Fabio Kaiser

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  1. The perceptual history ofconsonance and dissonanceCounting vertical pitch-class sets in vocal polyphony Richard Parncutt, Andreas Fuchs, Andreas Gaich, Fabio Kaiser Centre for Systematic Musicology, University of Graz, Austria Medieval and Renaissance Music Conference University of Birmingham, 3-6 July 2014 SysMus Graz

  2. Abstract How were consonance and dissonance perceived in early polyphony? We are complementing existing theory by counting vertical sets of three pitch classes. Our sample includes works attributed to Perotin, Savio, Halle (13th century); Machaut, Landini, Ciconia, Magister Andreas (14th); Dufay, Dunstable, Ockeghem, Obrecht, Isaac, Le Rouge, de Insula (15th); Lassus, Palestrina, Desprez, Byrd, Gabrieli (16th). We use electronic scores available in the internet; we have not systematically addressed ficta. With the Humdrum Toolkit we count unprepared sonorities (tones beginning simultaneously) and prepared sonorities (one or more ties). As expected, the most consonant pc-sets in the 14th-16th centuries correspond to today’s major, minor, suspended and diminished triads in that order, plus 025/035 (e.g. CDF, DFG). With time, major and minor became relatively more common. Suspended  (057) and 025/035 were common in the 13th. The data allow us to test psychological models of consonance and dissonance based on smoothness (lack of beating), harmonicity (similarity to harmonic series), diatonicness (scale belongingness) and evenness (spacing around chroma cycle). All four predictions correlate with mean results for the 13th-14th century, but only roughness and harmonicity correlate with 15th and 16h separately, consistent with gradually increasingly sensitivity to roughness and harmonicity.

  3. Consonance and dissonance (C/D) in earlymusicAn interdisciplinaryquestion!

  4. Perotin: Mors“Gm/A”: unprepared! pcset: GABbD

  5. Perotin: VideruntOmnes“Cadd9/G” pcset: CDEG

  6. Perotin: VideruntOmnes“C7/G” – unprepared! pcset: EGBbC

  7. Alfonso el Sabio:Santa Maria, strela do dia“D7/C” – unprepared! pcset: F#ACD

  8. Alfonso el Sabio: Santa Maria, strela do diaD/E ... ??? ... E7/sus4 ... D7sus/C ... ??? pcsets: DEF#A ABD ABDE GACD EGA

  9. Dissonant sonorities in earlymusicHowshouldweapproachthem? • Are pc-set labels appropriate? • Are dissonances accidental or deliberate? • Are they products of voice-leading rules? • Should we look at individual examples or do statistics? • Is frequency of occurrence (prevalence) a useful measure of their consonance?

  10. Why do statisticalanalysis? • Assumptions: • “Consonant” sonorities are more prevalent • Composers are more likely to “prepare” dissonant than consonant sonorities •  Two indirect measures of C/D

  11. Preparationofdissonance prepared less dissonant unprepared more dissonant Psychological explanations Stream segregationreducesdissonance (Wright & Bregman, 1987) Roughessdepends on relative amplitude (Terhardt,1974)

  12. Pitch-classsets – Tn-typesJohn Rahn(1980): Basic atonal theory Intervallic inversion 037= minor; 047 = major • same pc-set “3-11” • different Tn-types“3-11A”, “3-11B” There are… 19 Tn-sets of cardinality 3 (012, 013...) 43? Tn-sets of cardinality 4 (0123, 0124...) Familiar examples 036 = dim, 048 = aug, 027 = sus (=702=057) 025/035: no name

  13. All Tn-typesofcardinality 3

  14. Whatis the C/D ofa Tn-set?Threeapproximatemeasures • Consensus amongmusictheorists (past and present) • Prevalence in musicalscores • Psychological predictions Here, wetest 3bycomparingpredictionswith 2.

  15. Psychological theoriesof C/Dofsonorities (vertical C/D) Roughness Peripheral (ear); innate (Helmholtz, Plomp…) Harmonicity (fusion) Central (brain); partly learned (Stumpf, Terhardt…) Familiarity Completely learned (Cazden, Krumhansl…) Diatonicity Diatonic scale is “overlearned” (Deutsch…)

  16. The intervalvectorInterval-based C/D models Minor and minor triads have the same interval vector: <001110> i.e. both chords have: 0 m2s, 0 M2s, 1 m3s, 1M3s, 1 P4s, 0 TTs (plus intervallic inversions) Assumption The C/D of a pc-set depends approximately on its interval vector (cf. interval-based Renaissance theory)

  17. RoughnessA measureof C/D?

  18. C/D ofintervalclassesconvergentevidencefrom different sources

  19. HarmonicityA measureof C/D?

  20. DiatonicityA measureof C/D? • Possiblejustifications: • Notation: Practicallimitationsofdiatonicnotationsystem • Psychology: Deepfamiliarityofdiatonicscalesinceantiquity

  21. Music database • Vocal polyphony • Mainly sacred, some secular • Mainly 4 parts; sometimes 3, 5, 6, or 8 Sources • Kern scores • CPDL (Choral Public Domain Library) • Elvis (Electronic Locator of Vertical Interval Successions) • PMFC (Polyphonic Music of the Fourteenth Century) • musicalion.com • IMSLP.org

  22. “Composers” in database 13th century Perotin (1150/65-1200/25, French) Alfonso el Sabio(1221-1284, Spanish) Adam de la Halle (1250-1310, French) Montpellier Codex (1250-1300, French) 14th century Guillaume de Machaut(1300-1377, French) Landini, Francesco (1325-1397, Italian) Johannes Ciconia(c.1335 or c.1370, French) Philippe de Vitry(1291-1361, French) Jacopo da Bologna (1340-1386, Italian) Egardus(fl.c. 1370 – after 1400, Flemish)

  23. Composers in database 15th century Guillaume Dufay (1397-1474, Franco-Flemish) John Dunstaple(1390-1453, English) Johannes Ockeghem(1410/30-1497, Franco-Flemish) Jacob Obrecht(1450-1505, Flemish) Heinrich Isaac (1450-1517, Franco-Flemish) Guillaume le Rouge (fl. 1450-1465, Netherlands) Simon de Insula (fl. c.1450-60, English or French) 16th century Orlando de Lassus(1532-1594) Giovanni Pierluigi da Palestrina (1514/15-1594) JosquinDesprez(1450/55-1521) William Byrd (1540-1623) Giovanni Gabrieli(1555-1612) Andrea Gabrieli(1532-1585)

  24. Composers in database 17th century ClaudioMonteverdi (1567-1643) Heinrich Schütz (1585-1672) Adriano Banchieri(1568-1634) GirolamoFrescobaldi(1583-1643) RuggeroGiovannelli(1560-1625) 18th century Johann Joseph Fux (1660-1741) Georg Philipp Telemann (1681-1767) Johann Sebastian Bach (1685-1750) Georg Friedrich Händel (1685-1759) Giovanni Battista Pergolesi(1710-1736) Niccolo Jommelli(1714-1736) Christof Willibald Gluck (1714-1787) Carl Philipp Emanuel Bach (1714-1788) Johann Friedrich Doles (1715-1797) Joseph Haydn (1732-1809) Dmitri StepanowitchBortniansky (1751-1825) Wolfgang Amadeus Mozart (1756-1791)

  25. Composers in database 19th century Ludwig van Beethoven (1770-1827) Franz Schubert (1797-1828) Felix Mendelssohn Bartholdy (1809-1847) Robert Schumann (1810-1856) Charles Gounod (1818-1893) Anton Bruckner (1824-1896) Robert Lowry(1826-1899) Johannes Brahms (1833-1897) Josef Gabriel Rheinberger(1839-1901) Peter Iljitsch Tschaikowsky (1840-1893) Antonin Dvorak (1841-1904) Nikolai Rimski-Korsakow (1844-1908)

  26. 13th-C sample in database • Adam de la Halle • Fi Maris de vostre Amour • Je muir je muir d'amourete • Li dousregars de ma dame • Hareu li maus d'amer M'ochist • A dieu commantamouretes • 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 desireaveoir • Bonne amourete • Tant con je vivrai Perotin • Magnum Liber Organi • Videruntomnes • Sederunt • Mors Montpellier Codex • #66 Mater Dei – Mater Virgo – Eius • #78 Dieus Mout me fetsoventfremir • #158 Mal d'amorspresnes m'amie • #319 On parole – A Paris – Fresenouvele • #339 Allepsallite cum luya

  27. 14th-C sample in database • Johannes Ciconia • O felixtemplumjubila • Petrum Marcellum venetum • O Padua, sidus praeclarum • Venetiemundisplendor • Gloria • Philippe de Vitry • Lugentiumsiccentur • Rex quem metrorum • Virtutibuslaudabilis • Vos Qui AdmiraminiGratissimavirginis • Magister Andreas • Sanctus • Egardus • Gloria • Solage • Fumeux fume par fumee Guillaume de Machaut • Messe de nostre dame (Kyrie, Gloria) • Hoquetus David • Comment puet on mieux dire • De toutes Flours Francesco Landini • Squarcialupi Codex: madrigal • Deh! dimmitu • A le sandralospirto • Cara mi donna • Quanto piu carofay • Si dolce non sono Jacopo da Bologna • Aquila Altera • I Senti ZaComoLarchoDamore • In Verde Prato

  28. Size ofdatabase in eachcentury

  29. Counting “chords”: Method Database in Kern format Analyse using Humdrum Toolkit (Huron) Count Tn-types of cardinality 3 and 4 Distinguish prepared from unprepared sonorities Correlate counts with model predictions

  30. All trichords 1200-1900“Cases“: all trichords and tetrachordsNext slides: onlythe top tentrichords

  31. The main 10 trichordsin 13th-C vocal polyphonyignoring register, “inversion”, spacing, doubling... Tn-type

  32. All tetrachords 1300-1900“Cases”: all trichords and tetrachordsNext slides: only the top ten

  33. The maintetrachords, 13th century

  34. Trichordsbefore 1600

  35. Trichords after 1600

  36. Tetrachords before 1600

  37. Tetrachords after 1600 Nb 17th-C sample ismissing 1672-1700

  38. Whichis the best C/Dmodel? • Predict C/D using different models • Comparewithprevalencedata • Whichmodelperformsbetter? • Implicationsforhistoryof C/D?

  39. Whichintervalclassdetermines C/D?Correlationcoefficient between predictions and prevalence UNpreparedtrichords and tetrachords • Winner: ic 1 (m2/M7)  Roughness • Runner-up: ic5 (P4/P5)  Harmonicity

  40. ComparisonofroughnessmodelsCorrelation between predictions and prevalence UNpreparedtrichords • Roughnessisgenerally a goodpredictor • Winner: Huronmodel (the addedcomplexityhelps)

  41. ComparisonofroughnessmodelsCorrelationbetween predictions and prevalence Preparedtrichords Conclusion: asbefore

  42. ComparisonofroughnessmodelsCorrelationbetween predictions and prevalence: tetrachords

  43. ComparisonofharmonicitymodelsCorrelationbetween predictions and prevalence UNpreparedtrichords Again, the more complex models are better

  44. ComparisonofharmonicitymodelsCorrelationbetween predictions and prevalence Preparedtrichords Again, the more complex models are better

  45. ComparisonofpitchclaritymodelsCorrelationbetween predictions and prevalence: trichords All 3 measure the “peakedness” of the pc-salience profile (Parncutt, 1988). “Salience”: salience of most salient pc “Root ambiguity”: defined in Parncutt (1988) “Entropy”: equation from statistical mechanics.

  46. ComparisonofpitchclaritymodelsCorrelationbetween predictions and prevalence: tetrachords UNprepared Prepared

  47. ComparisonofbestmodelsCorrelationbetween predictions and prevalence. trichords In 13th C, all 3 are important. Later, roughness and harmonicity are equally important; diatonicity becomes irrelevant

  48. ComparisonofbestmodelsCorrelationbetween predictions and prevalence: tetrachords More complex, here diatonicity is the best predictor. These are new calculations, we need to check them.

  49. Specificconclusions Main sonorities • 13th C prepared: 027, 037, 047, 035, 025, … 0247, 0257, 0358, 0357 • 14th-16th: more 047 and 037, less diversity • 13th…16th: More unprepared dissonances Roughness and harmonicity • Explainprevalenceoftriads in 13th-16th C  prefer 5ths & avoid 2nds  major/minor Familiarity • Moderate dissonances  morecommon • Extreme dissonances  lesscommon

  50. General conclusions Verticalor horizontal? Prevalenceofsonorities in multi-voiced western musicisdeterminedmainlybyvertical C/D!  not byvoice-leadingrules? Psychological C/D-concepts Vertical C/D isdeterminedmainlyby 3 factors: roughness, harmonicity, familiarity Future research Toexplain C/D, weneedhumanities & sciences: • historyofmusictheory • psychological and statisticalstudies

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