Towards a statistical-perceptual history of western tonal-harmonic syntax

1. Towards a statistical-perceptual history of western tonal-harmonic syntax To reduce the size of this file, several figures have been removed Richard Parncutt University of Graz Digital Resources in the Humanities Lancaster, September 2005

2. Aims (1) Why is Western tonal-harmonic syntax like it is – and not completely different? Solution: Digital history of musical style as: • Statistical description of scores • Psychological description of perception

3. Aims (2) • Music history: • Revive interest in syntax through digital history • Test claims about history of syntax • Document European musical heritage • Music performance: • Improve performing editions • Music theory and analysis: • Statistical, quantitative basis • Nature and origin of tonalities • Music psychology: • Nature vs. nurture, physiology vs. culture • Music education: • New computer tools

4. Interdisciplinarity • Historical musicology • Music performance • History of music theory • Computer science • Music psychology • Music education Not all in one head!  Interaction between experts

5. Definitions Musical pattern • Pitch-time pattern Musical element • Small, categorically perceived pattern, e.g. melodic fragment, chord Musical syntax • Pattern of probabilities that elements occur in relations to configurations of other elements Musical style • Syntax plus associations

6. Medieval music perception?

7. Psychological approach Experimental subjects no longer available… but some things never change • Music perception • Syntax (consonance, expectancies) • Semantics (emotions, associations) • Syntactic aspect depends on: • Statistical properties of music • Perceptual „universals“

8. Example: Early polyphony (missing figure) From H. van der Werf (1992): Early Western polyphony. In Knighton & Fallows (Eds.)

9. Music perception

10. Some big digital-musical questions…

11. What is musical style? • Pop, country, jazz, baroque, romantic…? • Easy to recognize by ear? • Not only syntax but also associations  Hard to model! (ISMIR)

12. Major-minor tonality • Music perceived in a major or minor key • „Emerged“ in Europe in 15th-17th cent. • Now dominates world music • Hard to model (Music perception) even though purely syntactic

13. Musical memory • Typical person knows c. 1000 songs • Each is a complex structure of sounds, patterns and associations • Hard to model (cognitive psychology: memory map?) • Key to understanding non-musical memory?

14. History of musical syntax • Specific innovations at specific times, e.g. • double-leading tone cadence in 14th cent. • unprepared seventh in Monteverdi • Triggered by • Compositional trial and error? • When is culture “ready”? • History of ideas? • Politics and sociology? • Physiology of consonance? • Hard to model

15. Background in relevant disciplines…

16. Music history • Inseparable: • Evolution of music notation 11th-20th c. • Increasing specificity • Evolution of musical syntax 11th-20th c. • Increasing complexity

17. Music psychology Theories of: • Consonance • Emotion • Association • Expectancy

18. History of music theory • As history of ideas and terms • Not necessarily of syntax • Loose relation to musical practice • Time lag • triads in 16th-century music • this talk • Implication: • separate from history of syntax

19. History of music notation…

20. Medieval chant:Neume types in Stinson’s SCRIBE (missing figure) • Pitches unclear – test in performance? • Rhythm not defined – omit from analysis

21. Musica ficta (1) • Renaissance concept • Modern practical definition: • introduce accidentals (sharps and flats) to old scores following historical rules • Rationale: • approach cadences correctly • sharpen leading tone • prefer consonances • avoid tritone

22. Musica ficta (2) Basis in medieval theory: • Hexachord do re mi fa so la • Semitone only at mi - fa • Modulations between hexachords: common tones • Origin of modern accidentals • mi …  sharp # • fa …  flat b (missing figure)

23. Transcription problems…

24. Specificity • Notation becomes increasingly specific:

25. Which code? • Generally, encoding methods depend on: • Musical syntax • Envisaged scholarly applications • We need a standard for many styles  flexible e.g. Humdrum not DARMS • Problem: not user friendly

26. Ambiguity of musica ficta • Competing principles • Leading tone versus consonance • Interpreting accidentals, e.g. • F marked mi, implying F-G is mi-fa • F#-G or F-Gb? • Repetitions of tones and patterns • For how long does the accidental apply?

27. Tablature (missing figure) From F. Wiering (1997), „DARMS extensions for lute tablatures“. In E. Selfridge-Field (Ed.), Beyond MIDI

28. Research strategies...

29. Editorial material • Clearly distinguish original from editorial material • Create historically reputable source • Maintain distinction in statistical analyses

30. Transcription • Transcribe all pitches into chromatic scale • Problem: varying specificity • Ignore rhythm • Preserve only order of events, focus on pitch • Ignore text and social/political context • One thing at a time!

31. Approach to musica ficta • Assumption: • chromatic scale since ancient Greece • Problem: • Microtonality in history of music theory • Solution: • Chromatic scale as pitch categories

32. Examples of data and theories…

33. Example of data Eberlein‘s (1994) sample (1700-1850): • J. S. Bach: 7 Chorales • Händel: Trio sonata Op. 5 No. 5 • Mozart: Missa brevis KV 65 • Beethoven: Mass in C • Mendelssohn: Motets Op. 78

34. Results: Prevalence of individual sonorities Ranking: • major triad • minor triad • major-minor (dominant) seventh • diminished seventh • minor added sixth chord • triad with suspended fourth • minor seventh • diminished triad

35. Prevalence of two-chord progressions

36. Example of a hypothesis • Major-minor tonic is a major or minor triad • Role of previous familiarity with triads

37. Example of quantitative test

38. Example of a testable prediction • Quantify „evolving consciousness of sonority“ in 14th cent. (Fuller, 1986) • Understand „emergence of tonality“

39. Project planning…

40. Project personnel • Main personnel • Music psychologist • Music historian • Computer scientist • Contract personnel • Coding: Students • Checking: Musicologists and performers

41. Project phases • Representative works from main periods • Modern performing editions • Coding • Statistical analysis • Psychological theory testing • Pedagogical applications

42. Implications • Music history: • Digital history changes thinking • Music theory: • Pitch structures better defined and understood • Music analysis: • Statistical claims about syntax become testable • Music psychology: • Stops neglecting historical context

43. Problems • Getting a big picture means loss of detail • Can‘t average dissimilar styles • e.g. 12th century English & European styles