Its concept is similar to Schillinger's manifolds. 180 degrees, etc., until the cycle is complete. Two such devices permit triangulation and will pinpoint the exact location. Once this general principle is grasped more complex manifold signals readily fall into place. We see the logic of this for scales, diads, triads and sevenths.
Cadences are no exception.
Until about 1900 classic cadences predominated in music as did classical mechanics in mathematics. Each era is confined within the limits of its mathematical or musical systems. In the classical mechanics, Euclidian and Newtonian systems prevail, triangular measurement dominating this system. In classical music, harmonic triads prevail. After 1900 quantum theory envelopes all science with a 4th dimensional parameter being added to the classical system.