Tone Clock · Binding Partners

Partner hours, live binding, mode networks

ST zero-bindings

Zero-binding of an asymmetrical triad with its inversion yields an ST. The triad’s hour is the partner hour of that ST. V⁴, VIII⁴ and X⁴ have none.

Live binding

Seed from an hour or a custom interval pattern. Original and inversion are superimposed at Binding-0 through Binding-6.

Source

Hour

Form

Starts on

Binding

Binding networks

Tritone, V⁴, VIII⁴ and X⁴ networks and their complements.

About this tool

Binding superimposes a group on its inversion to form a new symmetrical group. Binding-0 (zero-binding) identifies the outer notes; Binding-n enlarges that span. The original and inversion are the binding-partners; their union is the binding-group.

ST zero-bindings — partner hours of the simplest symmetrical tetrads. An ST has at most one partner hour.
Live binding — compute Binding-0…6 for an hour triad or a custom IPF.
Binding networks — documented relations among V⁴, VIII⁴, X⁴, the tritone, and Messiaen modes.