Transcript Towards a statistical-perceptual history of western tonal

Towards a
statisticalperceptual history
of western tonalharmonic 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)
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)

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
Interdisciplinarity






Historical musicology
Music performance
History of music theory
Computer science
Music psychology
Music education
Not all in one head!
 Interaction between experts
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
Medieval music perception?
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 polyphony
(missing figure)
From H. van der Werf (1992): Early Western polyphony. In Knighton & Fallows (Eds.)
Music perception
Cross-cultural
Culture-specific aspects
aspects (statistics) (physiology,
psychology)
Evaluate present: More common
sonorities are more
consonance
consonant
Expect that which
Anticipate future: normally follows
expectancies
smoothness
 harmonicity

Some big digital-musical questions…
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 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

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?

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
Background in relevant disciplines…
Music history

Inseparable:
– Evolution of music notation 11th-20th c.
• Increasing specificity
– Evolution of musical syntax 11th-20th c.
• Increasing complexity
Music psychology
Theories of:
– Consonance
– Emotion
– Association
– Expectancy
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
History of music notation…
Medieval chant:
Neume types in Stinson’s SCRIBE
(missing figure)
• Pitches unclear – test in performance?
• Rhythm not defined – omit from analysis
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)
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…
Specificity

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?

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 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?
Tablature
(missing figure)
From F. Wiering (1997), „DARMS extensions for lute tablatures“.
In E. Selfridge-Field (Ed.), Beyond MIDI
Research strategies...
Editorial material

Clearly distinguish original from editorial
material
– Create historically reputable source
– Maintain distinction in statistical analyses
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!
Approach 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…
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

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
Prevalence of two-chord progressions
rising
P4
falling
P4
rising falling
3rd
3rd
rising falling
M2
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 hypothesis
Major-minor tonic is a major or minor triad
 Role of previous familiarity with triads

Example of quantitative test
(a) C major
(b) C minor
K&K82
7
Pmo88
pc-weight/3 (Pmo88)
average rating (K&K82)
7
5
5
3
3
1
1
C
D
E F
G
A
B
-1
chroma
C
D
E F
G
A
B
12
Example of a testable prediction
• Quantify „evolving consciousness of sonority“ in 14th cent. (Fuller, 1986)
• Understand „emergence of tonality“
proportion (%)
100
thirds
triads
final triads
0
1000
1200
1400
year
1600
1800
Project planning…
Project personnel

Main personnel
– Music psychologist
– Music historian
– Computer scientist

Contract personnel
– Coding: Students
– Checking: Musicologists and performers
Project phases
– Representative works from main periods
– Modern performing editions
– Coding
– Statistical analysis
– Psychological theory testing
– Pedagogical applications
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
Problems
Getting a big picture means loss of
detail
 Can‘t average dissimilar styles

– e.g. 12th century English & European
styles