b-flat major leading scale g major scale submediant

And most 20th-ct theorists rejected tonal dualism in favor of a monist theory based on fifth motion in one direction only. They didn't, because undertones don't exist. The world of the lower fifth was a perfect inversion of the world of the upper fifth, and by this logic, influential theorists (Hugo Riemann, for example) assumed that acousticians would soon discover a series of undertones (C-F-Bb-Eb etc.) to match the overtone series. The problem that immediately arose was how literal to make this 'mirroring'? Some theorists argued that the two balanced triads should really be C major (CEG) and F minor (C-Ab-F), because if F is the lower fifth, then its triad should be created downward from C using the same sequence of intervals (M3, m3) that got you from the tonic to the upper fifth. In order to do that, they constructed a dualist system: that is, for a tonic note, C, they imagined a balanced, dual system of fifths, one above (C-G) and one below (C-F), and then filled in the fifths to create the tonic (CEG) and subdominant (FAC) triads. Rockin' Cowboy's answer above recapitulates a whole line of 19th-ct attempts to derive the basic functions of tonal music from the major triad (which at least one theorist called the 'Chord of Nature' because of the way it follows the overtone series).

The way the major and minor thirds fall is because of the interval order that is used to distinguish a major scale: C-D, 2 semitones D-E, 2 semitones E-F, 1 semitone F-G, 2 semitones G-A, 2 semitones A-B, 2 semitones B-C, 1 semitone. Triad on B: B-D, minor 3rd B-F, diminished 5th - diminished triad Triad on A: A-C, minor 3rd A-E, perfect 5th - minor triad Triad on G: G-B, major 3rd G-D, perfect 5th - major triad Triad on F: F-A, major 3rd F-C, perfect 5th - major triad Triad on E: E-G, minor 3rd E-B, perfect 5th - minor triad Triad on D: D-F, minor 3rd D-A, perfect 5th - minor triad Let's look at it, eh? Triad on C: C-E, major 3rd C-G, perfect 5th - major triad In a major scale, it happens that diatonic major triads (i.e., those built with members of the scale) are found on I, IV & V. The definition of a major triad in canonical form (in practice it can be spaced out in terms of octaves, inverted and its members doubled, obviously, hence 'canonical') is not 1-3-5 in terms of major scale degrees it is 4 semitones (a major third) and 7 semitones (a perfect fifth) from a given root, any given root.

B-flat major leading scale g major scale submediant