Diatonic functional harmony
Diatonic functional harmony is the functional harmony based on the diatonic scale as well as that of similar MV3 and MV4 scales such as both Nicetone and Classitone in the 5-limit.
Basis of tonal harmony
Psychological basis
The very fundamental of tonal harmony seems to be the expectation of instability–stability, a near-universal human psychological characteristic. We thus speak of tonal tension, with high level of tonal tension corresponding to a sense of imperfection and a greater desire to go elsewhere, and vice versa. The core idea may be used to derive various harmonic functions. A common 20th-century pedagogy has tonic, dominant, and predominant identified, for example.
Harmonic and melodic causes
On a closer look, part of each function can be said to be caused by harmony, others by melody. Harmonically, it is the root motion of each individual chord constituting clear connections in terms of just intonation ratios. Melodically, it is the voice leading gestures. This article focuses on the harmonic facet.
Tonic
The tonic the first and most important of the three primary functions of diatonic functional harmony. It typically serves as one, or often more, of the following — the primary tonal center, the main resolution tone, one of the most common initiating events of a piece, the most important melodic and or harmonic anchor in tonal music, the generator of other tones either harmonically or subharmonically, and or a discourager against the usage of other microtonally nearby pitches.
Dominant
Generated by the tonic as the first 3-limit interval and indeed the first nontonic note in the "majoresque" direction, the dominant is the second of the three primary functions of diatonic functional harmony, and, as its name suggests, is the most important nontonic function. The harmonic basis of this function comes from both its strong connection to the tonic and its drastic contrast to it, since no other ratio is as simple and as contrastive. It typically serves as one, or often more, of the following — a primary creator of instability in the "majoresque" direction that requires the tonic for resolution, the second most important melodic and or harmonic anchor after the tonic, a generator of many of the "majoresque" notes in a diatonic MOS, and or a discourager against the usage of other microtonally nearby pitches.
Subdominant and Superdominant
In octave equivalent tonal systems built from the low pitches to the high pitches, the subdominant is the third of the three primary functions and is the second most important nontonic function after the dominant. The harmonic basis of this function comes from both its strong connection to the tonic and its drastic contrast to it, albeit in the opposite direction from the dominant. It typically serves as one, or often more, of the following — a primary creator of instability in the "minoresque" direction that can either be intensified with the dominant or resolved with the tonic, the third most important melodic and or harmonic anchor after the tonic and the dominant, a generator of many of the "minoresque" notes in a diatonic MOS, and or a discourager against the usage of other microtonally nearby pitches.
In octave equivalent tonal systems built from the high pitches to the low pitches, the superdominant takes over the usual roles of the subdominant, and in fact, in microtonal theories derived from Aura's work, the subdominant and the superdominant are combined into the serviant (alternatively spelled servient) function, since both the subdominant and the superdominant are considered to be generated by the tonic as the first 3-limit interval and indeed the first nontonic note in the "minoresque" direction.
Supervicinant and Subvicinant
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Mediant, Submediant and Supermediant
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