Pitch in tonal and nontonal music

Tonal: A hierarchy named by letter names and keys

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nontonal: No hierarchy. The pitches are now numbers


Tonality vs. Atonality

Tonal: interaction with harmony and voice leading- hierarchies and tendencies

Non-tonal: still important, but no pitch language- intervalic construction super important

Pitch names in non-tonal music


Interval class: numbers

No scales, no hierarchies


a non-tonal motive

Set of intervals that serve as motific value

Irregular meters
not having a steady beat/no hierarchy of beats
Notes with added values
Term coined by Messiaen, involves “cramming an extra subdivision such as an etra 16th to a beat”
Mixed Meter
A variety of adjacent measures with changing meters
complex/composite meter

Several “numerators” over a single “denominator”

Example 8+5/8

different parts of music occur in contrasting meter 
Metric/tempo regulation
Immediate change in temp by reinterpretting an equivilent note value

Ametric Music


No sense of meter (as we know it) exists- as if totally absent- whether no meter is readable or written meter is not percievable
How we hear texture

Determined by:




Tone color

New Textures
Layered textures, new “single line,” and timbral explorations
New perception of the “single Line”

Extreme registral shifts

changing timbres

changing dynamics

varying articulations

New Timbres

New combinations of instruments

New techniques

Old models
Still used in the 20th century. Includes sonatas, symphonies, string quartet, theme and variations, etc.
Arch Form
Formal Symmetry between the movements of a piece: Fast sonata, scherzo/trio, slow ABA, Scherzo/trio, fast sonata
Transformations of old forms
may lengthen or shorten pieces while using traditional formal structures
New Possibilities

Collage: juxtaposing and layering musical textures and matierials

Continuous variation: thematic materials appear once and new materials are developed

Numbering Pitch Classes
Numbered 1-11 by half steps
Fixed vs. Movable 0

Fixed: C=0 always

Movable: changes depending on scenario

Interval Numbers
Subtract lower pitch class from the higher one to get interval
Interval Class
Includes interval and all its likes: including its complement and all compound intervals

Pitch-Class set


a group of disparate pitch classes

repeated notes don’t count

Pitch class set sizes

between 1 and 12 pitch classes;

Usually between 3 and 10

pitch class set with 3 pitches
pitch class set containing 4 pitches
pitch class set with 5 pitches
pitch class set containing 6 pitch classes
pitch class set containing 8 pitches
a pitch class set containing 7 pitches
Move each pitch class up the given interval
replace each interval with its complement

Lowest Ordering

(normal order, best normal order)

Standard name for a pitch-class set… like root position
Interval Class Vector
Shows the intervalic content of a pitch class-set
Inversionally symmetrical set
pitch class set that retains pitch classes when inverted
A smaller set derived from a larger set
2 sets that share an interval class vector
Forte Number

categorizes sets according to idiosyncrasies

contains 3 pieces of info

Number of pitches in a set

categorized number and

possibly a z indicating that it has a z relation to another set


(in pitch class set theory)

The presentation of all 12 pitch classes
Pitch-class regions
serves as like a scale in traditional theory
Diatonic Scale

PCS based on fifths

(traditional diatonic scale without implied hierarchies)



all twelve pitches presenting more than one row using combinatoriality
derived set
a trichord, heptachord or other pattern from which a row is derived