Glossary, Prime Form
   
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



Prime Form

Glossary

Set Theory

A prime form is a transposable, numerical representation of a clock diagram, reduced to its lowest (numerical) form, and where t and e mean ten and eleven in base twelve. Prime forms collect up two or more transpositions (usually twelve) into a single object.

See Grouping Clocks for a tutorial with animations and examples.

In the case of the diatonic scale, its prime form is (013568t). If we start on the note B and simply count on the keyboard (including black and white keys) we get B = 0, C = 1, skip D, D = 3, skip E, E = 5, F = 6, skip F#, G = 8, skip A, A = “t”, skip B, and back to the note B = 0, yielding (unordered) BCDEFGA or the C diatonic collection.

Harmonious elides the distinction between the prime form of a set class and its involution, usually denoted by square brackets. Here we treat the prime forms of involutions as distinct entities, but Allen Forte’s set classes combine them into a single set class (which we still group with the Forte numbers he assigned them).