Riemannian theory

Riemann's "dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists.

The term "dualism" refers to the emphasis on the inversional relationship between major and minor, with minor triads being considered "upside down" versions of major triads; this "harmonic dualism" (harmonic polarity) is what produces the change-in-direction described above.

[7] In the 1880s, Riemann proposed a system of transformations that related triads directly to each other.

[7] A Schritt transposed one triad into another, moving it a certain number of scale steps.

For example, Seitenwechsel ("die Seiten wechseln" translates as "to exchange sides") mapped a triad on to its parallel minor or major, transforming C major to C minor and conversely.

Illustration of Riemann's "dualist" system: minor as upside down major. Half steps are indicated by slur marks, other notes are separated by whole steps. The descending C melodic minor scale shown has the same order of half steps and whole steps as the ascending C major scale.