Schenkerien prolongation and the

emotional connotations of major-minor tonality

Richard ParncuttUniversity of Graz, Austria

ICME3, Jyväskylä Finland, 2013SysMus Graz

Theses

1. A passage of MmT* is perceived as a prolonged background triad

2. This prolonged triad is the origin of “major-minor = happy-sad”

*major-minor tonality

Questions arising

Does this background triad exist? Why major=happy and minor=sad?

More questions… Why two triads? Why these two? Why this specific mapping? What about Leonard Meyer’s theory?

Origins of…

…emotion:

evolutionary psychology?

…MmT:

psychohistory?

Evolutionary functional origins of emotion

Arousal High: energy available or necessary Low: energy unavailable or unnecessary

Valence positive: clear situation safety, confidence negative: unclear situation fear or anger

Psychohistoric origin of MmTFive psychohistorical steps

1. Diatonic scales in ancient music

2. Leading tones in medieval polyphony

3. Importance of major and minor triads

4. Implied pitches in these triads

5. No consecutive semitones in scales

Major-minor Tonality (MmT)

Most music in MmT can be reduced to chord progressions.Most chords correspond to one of these diatonic triads.

Origin of pentatonic, diatonic, chromatic scales

etha

nhei

n.co

m

Pairs of harmonic complex tones with frequencies or pitches in common Octave and fifth relationsCircle of fifths

Harmonics in common perceptual similarity

Leading tones in early musicGuillaume de Machaut (1300-1377). Rondeau Ma fin est mon commencement

F# tonicizes G - C# tonicizes D

Origin of leading tones?Consonance / prevalence of individual tones in chant

1 2 3 4 5 6 70

10000

20000

30000

40000

50000

60000

70000

A B C D E F G

1 2 3 4 5 6 70

1

2

3

4

5

Data

A B C D E F G

Model

Data: Counted in the Liber Usualis (DDMAL, Fujiniaga et al., McGill)Model: No. of harmonic pcs (P5, M3, m7, M2) at diatonic scale steps Comparison: df = 5, r = 0.90, p<.01

Finding: C (F) more prevalent than B (E) origin of leading tone?

Cf. Parncutt, R. & Prem, D. (2008 ). The relative prevalence of Medieval modes and the origin of the leading tone (poster). International Conference on Music

Perception and Cognition (ICMPC10), Sapporo, Japan, 25-29 August.Based on Bryden, & Hughes (1969). An index of Gregorian chant.

Origin of major and minor triads

The most consonant sets of 3 pitch classes• Include P5 high harmonicity

• No m2 or M2 low roughness(Parncutt, 1988)

Only two chords satisfy this constraint!Major and minor triads dominate MmTOur attention is drawn to their difference

Missing fundamentals in triads(Parncutt, 1988; Terhardt, 1982)

Chord CEG has missing fundamentals at A, F

Chord CEbG has missing fundamentals at F, Ab

Why? e.g. E and G are harmonics of AMistuning of a ¼ - ½ tone? No problem in pitch perception

Do these missing fundamentals exist? Empirical evidence

E.g. C-major triad goes better with F than F# (Parncutt, 1993) BUT: can also be explained by musical experience

Logical argument Brain tries to locate fundamentals in ambiguous sounds Perception of missing fundamentals is inevitable

Origin of major and minor scalesCompatible with major and minor triads (tonic triads)

Krumhansl’s key profiles as pitch salience profiles of tonic triadsParncutt, 2011

∆ Krumhansl’s key profiles ▀ calc. pitch salience in tonic triadevidence that tonic in MmT is a triad, not a tone

Avoiding consecutive semitones

If there are consecutive semitones in a melody, middle tone perceived as passing

middle tone not a scale step

no consecutive semitones in (jazz) scalesPressing (1981)

Common exceptions: #4-5-b6, #7-8-b9

This can explain why C-major & –minor include D & not Db. Alternative explanations: Chord V is important. It must have P5 to be consonant. Use of standard diatonic scales

Psychohistoric origin of major and minor scales

1. Diatonic scales in ancient music

2. Importance of major and minor triads CEG, CEbG

3. Leading tones CEGB, CEbGB

4. Implied pitches in these triads CEFGAB, CEbFGAbB

5. No consecutive semitones CDEFGAB, CDEbFGAbB

Claim: The tonic in MmT is a triad not a single tone!

Corollary: Any passage in MmT is perceived

as a prolongation of its tonic triad

Evidence: Qualitative

• Success of Schenkerian approach Quantitative

• Correlation between pitch salience in tonic triad and stability in scale

• Transition probabilities in melodies

Transition probabilities between scale steps in major-mode melodies

(Huron, 2006, 2012)

Why is the transition between scale steps 6 and 7 avoided?

“Huron’s stereotype”

531

7 1 2 3 4 5 6

Music theory: Embellishment of tonic triad• Arpeggiation

• Passing notes• Neighbor notes

Psychological basis: Auditory scene analysis• Harmonicity

• Pitch proximity

Pitch range of major-key melodies

The lowest scale

degree is often 1 or 7.

The highest is often

6.

A classical example Opening themes of 10 out of 18 Mozart piano sonatas conform to Huron‘s stereotype:

KV 279, 280, 281, 283, 284, 310, 331, 332, 333, 545

Schenker’s Ursatz

“Great music” (Bach, Beethoven, Brahms…) is a prolongation (elaboration, embellishment, Auskomponierung, Auswicklung) of the Ursatz.

The Ursatz (background) prolongs the tonic triad. The Ursatz is elaborated middleground The middleground is elaborated foreground

The whole piece prolongs the tonic triad

Prolongation of prolongation?

Not only “great” musicIs all music in Mmt is a prolongation of the tonic triad?

Not only music analysisDoes chord prolongation have a psychological basis?

Major-minor and valencesome basic facts

Positive valence happiness, contentment, serenity, grace, tenderness, elation, joy,

victory, majesty…

Negative valence sadness, anger, fear, tension, solemnity, lament, tragedy, pathos,

mourning, melancholy, frustration, depression, gloom…

Major-minor effect can be overridden by tempo E.g. fast, happy minor or slow, sad major

Applies to tonalities not individual chords A major triad in a minor key can sound sad A minor triad in a major key can sound happy

Leonard B. MeyerEmotion and meaning in music (1956)

Minor tonality is more ambiguous Two versions of scale degrees 6 and 7 Extreme example: Carmen’s Habanera

(“scandalous”: Susan McClary, 2005)

Uncertainty negative emotion measured by information theory

Sad speech and musicHuron‘s approach. Some salient stuctural features:

1. Mean pitch is lower than average

2. Smaller pitch intervals between successive syllables

3. Lower sound level

4. Slower

My hypothesis: Only 1 can explain origin of minor-sad Other are consequences

Why is major happy? Most music is happy

(births, weddings, feasts, preparation for war, entertainment, relaxation) not sad (funerals)

Most music is major Major keys/chord more common than minor

• Modulation to relative major; major dominant triad• Reason: more consonant? (higher harmonicity, less ambiguity)

Minor keys the tonal Other Unhappy music the Other musical emotion

Analogous asymmetries

In everyday life and music, Positive valence is normal Negative valence is abnormal (emotional Other)

In music, Consonance is normal Dissonance is abnormal (needs resolution)

Consonance includes smoothness, harmonicity, diatonicity, familiarity; major is more consonant

Why is minor sad?Two theories – competing or complementary?

1. Structural ambiguity (LB Meyer) Minor: root of tonic and tonic of scale are more ambiguous

Is this dynamic (higher-arousal) negativity? afraid, angry, tense, frustrated…

2. Expected pitch in speech (Huron) Minor: 3rd and 6th scale degrees are lower than expected

Is this static (lower-arousal) negativity? sad, solemn, gloomy, melancholy, depressed, lamenting, mourning, tragic, pathetic…

In both cases, association between music and situation/speech role of duration & prolongation: keys not chords

Theses

1. A passage of MmT is perceived as a prolonged background triad.

2. The prolonged triad is the ultimate origin of “major-minor = happy-sad”.

Read all about it!

Latest issue of Empirical Musicology ReviewSpecial thanks to David Huron and Matthew Davis for their study on mean interval size, which inspired this study