Glossary, Involution
   
Glossary
Acoustic
Acoustics
Ancohemitonic

Set Theory

Atonal Theory

Set Theory

Atritonic

Set Theory

Augmented
Avoid Note
Bebop
Blues
Cardinality

Set Theory

Cardinality Equivalence

Set Theory

Cent
Chord
Chord Formula
Chord Type
Chromatic Cluster

Set Theory

Chromatic Scale
Clock Diagram

Set Theory

Cluster-free

Set Theory

Cohemitonic

Set Theory

Common Practice
Compatibility
Complement

Set Theory

Consonance
Diatonic
Diminished
Double Augmented Hexatonic
Double Diminished (Octatonic)
Eleventh
Enharmonic Equivalent
Evenness

Set Theory

Fifth
Forte Number

Set Theory

Fourth
Guitar
Harmonic Major
Harmonic Minor
Harmony
Interval
Interval Class

Set Theory

Interval Content

Set Theory

Inversion
Involution

Set Theory

Jazz
Jazz Theory
Key
Keyboard
Lewin-Quinn FC-components

Set Theory

Limited Transposition

Set Theory

M-Relation

Set Theory

Major
Melody
Minor
Mode
Ninth
Note
OC-Equivalence

Set Theory

OPC-Equivalence

Set Theory

OPTC-Equivalence

Set Theory

OPTIC-Equivalence

Set Theory

OPTIC/K-Equivalence

Set Theory

OTC-Equivalence

Set Theory

Octatonic
Octave
Octave-Equivalence

Set Theory

Other Scales
Parallel Key
Pentatonic
Permutation Equivalence

Set Theory

Piano
Pitch
Pitch Class

Set Theory

Playing Outside
Prime Form

Set Theory

Quartal

Set Theory

Reharmonization
Relative Key
Rhythm
Roman Numeral Function
Root
Scale
Second
Semitone
Set Class

Set Theory

Seventh
Sixth
Slash Chords
Suspended
Symmetry

Set Theory

Tenth
Tertiary
Third
Thirteenth
Tonality
Tonic
Transposition
Triad
Tritone
Tritonic

Set Theory

Tuning Systems
Twelfth
Twelve-tone Equal Temperament
Unison
Voice Leading
Whole Tone
Whole-Tone Scale
Z-Relation

Set Theory



Involution

Glossary

Set Theory

Also called the inverse. (Not to be confused with registral inversion.) Two objects are related by involution when they have the same interval content but in a different order.

The involution of a clock diagram is the mirror image of the clock diagram, so for example major triads and minor triads are related by transposition and involution to other major and minor triads. If the involution of a set class is the same set class, it is symmetric. For example, the diatonic scale is its own involution, so is symmetric.

Tymoczko (2011) mentions that involution preserves the overall feeling of chords, but tends to change the character of melodies more, citing a melody in Bach’s Well-Tempered Clavier that is played “upside-down” the second time it is heard. Outside of twentieth century atonal music, involution is not used so much as a compositional tool as an analytical one.

See also Equivalence Groups.