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95:(literally "five-step" in a mixture of Latin and German) transposed a triad by a perfect fifth, transforming C major into G major (up) or F major (down). A Wechsel inverted a triad according to the Riemann's theory of dualism, mapping a major triad to a minor triad. 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. Riemann's theory of transformations formed the basis for
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In the 1880s, Riemann proposed a system of transformations that related triads directly to each other. Riemann's system had two classes of transformations: "Schritt" and "Wechsel". A Schritt transposed one triad into another, moving it a certain number of scale steps. For example, the "Quintschritt"
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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 melodic minor scale shown has the same order of half steps and whole steps as the ascending major
46:(1849–1919). His theoretical writings cover many topics, including musical logic, notation, harmony, melody, phraseology, the history of music theory, etc. More particularly, the term
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