Glossary
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).
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).