The term 'functional harmony' derives from Hugo Riemann and, more particularly, from his "Harmony Simplified". Riemann's direct inspiration was Moritz Hauptmann's dialectic description of tonality. Riemann described three abstract functions: the tonic, the dominant (its upper fifth), and the subdominant (its lower fifth). He also considered the minor scale to be the inversion of the major one, so that the dominant was the fifth above the tonic in major, but below the tonic in minor; the subdominant, similarly, was the fifth below the tonic (or the fourth above) in major, and the reverse in minor.