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Towards a Towards a statistical-statistical-perceptual history perceptual history of western tonal-of western tonal-harmonic syntaxharmonic syntax
Richard Parncutt
University of Graz
Digital Resources in the Humanities Lancaster, September 2005
To reduce the size of this file, several figures have been removed
Aims (1)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
Aims (2)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
InterdisciplinarityInterdisciplinarity
Historical musicology Music performance History of music theory Computer science Music psychology Music education
Not all in one head! Interaction between experts
DefinitionsDefinitions
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
Medieval music perception?Medieval music perception?
Psychological approach 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“
Example: Early polyphonyExample: Early polyphony
From H. van der Werf (1992): Early Western polyphony. In Knighton & Fallows (Eds.)
(missing figure)
Music perceptionMusic perception
Culture-specific aspects (statistics)
Cross-cultural aspects (physiology, psychology)
Evaluate present: consonance
More common sonorities are more consonant
smoothness harmonicity
Anticipate future: expectancies
Expect that which normally follows
Some big digital-musical questions…Some big digital-musical questions…
What is musical style?What is musical style?
Pop, country, jazz, baroque, romantic…?Easy to recognize by ear?Not only syntax but also associations
Hard to model! (ISMIR)
Major-minor tonalityMajor-minor tonality
Music perceived in a major or minor key„Emerged“ in Europe in 15th-17th cent.Now dominates world musicHard to model (Music perception) even
though purely syntactic
Musical memoryMusical memory
Typical person knows c. 1000 songsEach is a complex structure of sounds,
patterns and associationsHard to model (cognitive psychology:
memory map?)Key to understanding non-musical
memory?
History of musical syntaxHistory 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
Background in relevant disciplines…Background in relevant disciplines…
Music historyMusic history
Inseparable:– Evolution of music notation 11th-20th c.
• Increasing specificity
– Evolution of musical syntax 11th-20th c.• Increasing complexity
Music psychologyMusic psychology
Theories of:– Consonance– Emotion– Association– Expectancy
History of music theoryHistory 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
History of music notation…History of music notation…
Medieval chant:Medieval chant:Neume types in Stinson’s SCRIBENeume types in Stinson’s SCRIBE
• Pitches unclear – test in performance?• Rhythm not defined – omit from analysis
(missing figure)
Musica ficta (1)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
Musica ficta (2)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)
Transcription problems…Transcription problems…
SpecificitySpecificity
Notation becomes increasingly specific:
Chant (from 9th cent., neumes)
pitch and rhythm unclear
Mensural notation
(13th cent.)
pitch and rhythm clearer but ambiguous
14th cent. rhythm clearer, more complex (note shapes, values)
Renaissance,
musica ficta
both rhythm and pitch can still be ambiguous
Which code?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
Ambiguity of musica fictaAmbiguity 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?
TablatureTablature
From F. Wiering (1997), „DARMS extensions for lute tablatures“. In E. Selfridge-Field (Ed.), Beyond MIDI
(missing figure)
Research strategies...Research strategies...
Editorial materialEditorial material
Clearly distinguish original from editorial material– Create historically reputable source– Maintain distinction in statistical analyses
TranscriptionTranscription
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!
Approach to musica fictaApproach to musica ficta
Assumption: – chromatic scale since ancient Greece
Problem: – Microtonality in history of music theory
Solution: – Chromatic scale as pitch categories
Examples of data and theories…Examples of data and theories…
Example of dataExample of data
Eberlein‘s (1994) sample (1700-1850):
J. S. Bach: 7 ChoralesHändel: Trio sonata Op. 5 No. 5Mozart: Missa brevis KV 65 Beethoven: Mass in C Mendelssohn: Motets Op. 78
Results: Prevalence of individual sonoritiesResults: 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
Prevalence of two-chord progressionsPrevalence of two-chord progressions
rising P4
falling P4
rising 3rd
falling 3rd
rising M2
falling M2
total
maj-maj 64 19 0 0 6 2 91
maj-min 60 1 2 9 5 0 77
min-maj 5 20 1 15 5 3 49
min-min 21 5 0 0 1 0 27
total 150 45 3 24 17 5 244
Example of a hypothesisExample of a hypothesis
Major-minor tonic is a major or minor triadRole of previous familiarity with triads
Example of quantitative testExample of quantitative test
1
3
5
7
chroma
(a) C major
Pmo88
K&K82
C D E F G A B
1
3
5
7
-1 1 2
(b) C minor
avera
ge r
ati
ng
(K
&K
82
)
pc-
weig
ht/
3 (
Pm
o8
8)
C D E F G A B
Example of a testable predictionExample of a testable prediction
0
100
1000 1200 1400 1600 1800
year
pro
po
rtio
n (
%)
thirds
triads
final triads
• Quantify „evolving consciousness of sonority“ in 14th cent. (Fuller, 1986)• Understand „emergence of tonality“
Project planning…Project planning…
Project personnelProject personnel
Main personnel– Music psychologist– Music historian– Computer scientist
Contract personnel – Coding: Students– Checking: Musicologists and performers
Project phasesProject phases
– Representative works from main periods– Modern performing editions– Coding– Statistical analysis– Psychological theory testing– Pedagogical applications
Implications 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
ProblemsProblems
Getting a big picture means loss of detail
Can‘t average dissimilar styles – e.g. 12th century English & European
styles