Syntax Tonal Music

7/27/2019 Syntax Tonal Music

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10/3/2006 Syntax of tonal music2

Outline of this talk

Background

Introduction to musical phenomena Motivating and characterizing the syntactic nature of

music Notational evidence

Experimental evidence

Theories of Heinrich Schenker Theories of Lehrdal & Jackendoff

Comparison with linguistic theories


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The mental representation of music

What happens when we listen to music?


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Tonal music

European classical music, 1600-1900

Most modern popular music

Highly developed tradition

Lots of materials

Bach

Beethoven

Brahms

Berlin (Irving)

Britney (Spears)

Standard notation

Natural system

Music in a key (Forte & Gilbert 1982)


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Non-tonal music

Atonalism Developed in Vienna, early 20th century

Very short, atmospheric pieces

12-tone composition (Serialism) developed to givestructure to the pieces

Schnberg, Webern, Berg

Compositions highly structured

Very small number of compositional decisions made, then thepiece writes itself

Little perceptual awareness of the organization

Augenmusik


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Other music

Music from other cultures

Divisions of the octave into larger and smallernumbers of pitch classes

The role of harmony generally far less than in

(Western) tonal music

Natural systems


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Musical primitives: pitch

Octaves group pitches into equivalence classes

Each octave subdivided into12 pitch classes

A, A# = B, B, C, C# = D, D, D# = E, E, F, F# = G, G, G# = A

Exact tuning of intervals may vary Octaves are exact, however

Diatonic scales

Two variants Mixture of whole steps (-) and half steps (.)

Major: - - - . - - - .

Minor: - - . - - . - - // - - . - - - - .


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Musical primitives: overtones

Any signal can is equivalent to the sum of sine waves with

frequencies related to each other in simple whole-number ratios

These simple ratios turn out to be musically significant

Observed since Pythagoras

Same intervals in many musical cultures


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Musical primitives: intervals

Distance from one pitch to another

May be absolute Number of half-steps

May be tonal, diatonic interval

Minor third (m3), major third (M3), perfect fourth (P4),

diminished fourth (d4), perfect fifth (P5)

Multiple interpretations of one interval (M3 and d4 both have

the same number of half steps)

Different spellings based on different tonal contexts

One is consonant and the other is dissonant


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Musical primitives: harmony

Conventionally notated with Roman numerals

I = tonic, IV = subdominant, V = dominant

Number based on the root of the chord

Lowercase = minor, Uppercase = major

Associated with specific harmonic expectations

Tonic example:


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Musical primitives: harmony

Dominant example:

Functional harmony Tonic (I) goal, stability, complete

Dominant (V, V7) incomplete, expectation for contination

Harmony is more abstract than chords!


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Musical primitives: voice leading

Diachronic look at musical

context

Where do the individual pitches

lead as the music moves from

one moment to the next?

Complex (perceptual/formal) rules

for determining when an interval

will be perceived harmonically or

as voice movement

?


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Musical primitives: phrases

Music groups into phrases, roughly melodic

Traditional classical melodies have two parts: Antecedent (ending on V)

Consequent (ending on I)

Example: Mozart, Sonata in A major, K. 331, I


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Understanding music

Context

Depending on the surrounding music, a particularinterval, pitch, or harmony can have vastly

different function


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Evidence for hierarchy in music


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What notation tells us about music

History of notation is as long and varied as

the history of music Constants: pitch (vertical, log scale), duration

in time (horizontal, linear)

Some indications of hierarchy in notational

conventions

Ornaments as diacritics


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Notational conventions

Ornaments as diacritics

Aria from the J.S. Bach Goldberg Variations (BWV 988)


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Notional conventions

Hierarchically minor notes notated as grace notes

Grace (small) notes should be played with equallength as the notes they are attached to!

Their smallness indicates their structural value.


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Figured bass structurally unimportant notes

were not even written!

Usually, a melody given, often used in

accompaniment


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Guitar tablature

Indicates chords, inversions Says nothing about

Rhythm

Arpeggiation pattern to

Extremely common in jazz, pop music


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Schenkerian Analysis

An impossibly brief

introduction


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Heinrich Schenker

1868-1935

Viennese music theorist Reactionary against post-tonal

music (ie, music that violated

traditional musical syntax for artistic

effect)

Sought to explicate the genius of

great music, especial German

music


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Schenkerian Analysis: the Ursatz

Ursatz= Fundamental structure

3 forms

All tonal music is really just one of

three melodies.

Fundamental structure is an

elaboration of tonal relationships:

Harmonic

Voice-leading

Tonal relations are not temporal(ie,

not rhythmic and not metrical)


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The Ursatz

Central to Schnkers work is the notion that the

tonic triad, an image of the overtone seriesgenerated by the tonic note, functions as a

matrix As Lerdahl & Jackendoff write the

tonic is in some sense implicit in every

moment of the piece- Schachter1999


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Schenkerian analysis

Three layers Foreground (surface)

Middleground

Background (fundamental structure)

Series of transformations or prolongations Neighbor note

Passing tone Arpeggiation

Register transfer

Composing-out


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Prolongation examples

Take a basic melody

Certain structure-preserving transformations may be

applied:


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Schenkerian analysis

Goal of Schenkerian analysis: recover

underlying structure Explain surface harmonic, voice-leading

phenomena (and problems) in terms of deeper

structure

Analyses are graphical Several levels of abstraction present in one graph


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Schenkerian analysis: example

J.S. Bach Ich bins, ich sollte ben from theMatthus-Passion (BWV 244)

This middle-ground graph shows the relationship of

the surface structure to the fundamental structure


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Hear foreground


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Hear middleground


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Hear background


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L&J: GTTM

Focus on hierarchical dimensions of music

Grouping structure

Break music in motives, phrases, sections Metrical structure

Events in music occur at regular (isochronous) intervals

Hierarchy of strong and weak beats at various levels of abstraction

Time-span reduction

Given metrical and grouping structure assign pitches a hierarchy of

structural importance Prolongational reduction

Assign pitches a hierarchy based on harmonic and melodic (voice-leading) tension (closest aspect to Schenkerian analysis)


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Music theory vs. linguistic theory

Three rule types in GTTM Well-formedness rules

Specify possible SDs

Transformational rules

Fudge the strict hierarchical organization a bit

Preference rules

Given a set of SDs, which ones will be preferred?

The first two establish the SDs for a segment ofmusic

What about preference rules?


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Preference rules

Structural descriptions not sufficient

Ranking various structural descriptions according tocoherence is essential

Grammaticality far less important for music

Almost any passage of music is vastly ambiguous(ie, many possible SDs). Not seemingly the case

with language. According to L&J: musical grammar must be able to

express preference rules among interpretations(absent from generative theories of language)


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Reduction hypothesis

One musical passage can be hear as an elaboration(or variation) of other passages

In some cases, passages may be heard aselaborations of an abstract structure that is neverovertly stated Bach GoldbergVariations (BWV 988)

Aria + 30 variations

Why not 31 separate pieces?

Listeners have intuitive understanding of relativestructural importance of different pitches


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Prolongational rules

Tension and relaxation as fundamental

processes of musical primitives ofharmonic/melodic progress

t r

r t r

r


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Prolongation and reduction

All large-scale strong prolongations are right

branching. All large-scale weak prolongations are left

branching (moving from less consonant to

more consonant)


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Online processing studies

Mireille Besson, Frdrique Fata. 1995. An Event-

Related Potential (ERP) Study of Musical

Expectancy : Comparison of Musicians With

Nonmusicians J. Exp. Psych: HPP.

Maess, B., S. Koelsch, T. Gunter, A. Friederici. 2001.

Musical syntax is processed in Brocas area: anMEG study Nature Neuroscience.


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Maess, et al. 2001

a) unaltered chord

progression

a) Out-of-key chord

(Neopolitan 6th) at 3rd

position

a) Neopolitan at 5th position

*

?


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Maess, et al. 2001


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Maess, et al. 2001

The ability to perceive distances between chords (and keys,respectively) and to expect certain harmonies (and harmonicfunctions) to a higher or lower degree can only rely on arepresentation of the principles of harmonic relatednessdescribed by music theory. These principles, or rules, werereflected in the harmonic expectancies of listeners and may beinterpreted as musical syntax.

The present results indicate that Brocas area and its right-

hemispheric homologue might also be involved in theprocessing of musical syntax, suggesting that these brain areasprocess considerably less domain-specific syntactic informationthan previously believed.


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Interpreting the results

Origins of syntactic representations

Statistical distributions in input?

Possible, but unlikely given rampant experimentation with

alternative compositional formalisms

Three different common continuations for the leading tone,

each with very different expectations satisfied

The leading tone (7) is followed conventionally by the tonic (1)

In compound melody contexts (extremely common), it may bealso followed by the a tone of the dominant chord (2, 4, or 5)

It may moved down to the submediant (6)


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Innateness of musical syntax

Universals in music Isochronous organization extremely common

Stresses tend to be heard as strong beats (stresses never areused to suggest weak beats, except to create a marked context)

Sensitivity to the overtone series

Innateness Tendency to understand music as a hierarchically organized

(events are subject to prolongation) is too abstract to beobservable

Universals Good example of learning without negative evidence: what

could it possibly be? (No, Georgie, you didnt hear that as aconsonant passing tone!)


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What can linguists take home?

Major innovation of L&J: preference rules

Similar in structure to OT constraints Find minimal cost

Used successfully in subsequent cognitivetheories of music, e.g. Temperley (2001)

Unclear implementation/learnability Computational approaches use dynamic programming

Temperley (2001) argues that dynamic programmingprovides an elegant way of describing revisionphenomena, but does not go into any detail


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What can linguists take home?

Preference rules and language (L&J)

Quantifier scope resolution Pragmatics

Gricean implicature encoded as preference rules

Musical acquisition, unlike language

acquisition fails (amusia, arhythmia)


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Music vs. minimalist syntax

What are the interfaces where a derivation

can crash? Primitive operations

Merge

Label/project

Differences The process of merging and label seems to be

interpreted always as one of dominance/subordination


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Mozart, SymphonyNo. 35in D major Haffner

Wagner, Siegfried Idyll

Beethoven, Piano Concerto No. 5Emperor

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10/3/2006 S nta of tonal m sic55

References

Lehrdal & Jackendoff. 1983.A Generative Theory of

TonalMusic. MIT Press.

Forte & Gilbert. 1982. Introduction to Schenkerian

Analysis. W.W. Norton & Company.

Schachter, C. 1999. Unfoldings: Essays in

Schenkerian Analysis

Temperley, D. 2001. The Cognition of BasicMusical

Structures. MIT Press.

Documents

Syntax Tonal Music