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