Neo-Rimsky-Korsakovian Space

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A diagram of a Neo-Rimsky-Korsakovian Space, with every possible mode organized by brightness and stability

Nikolai Rimsky-Korsakov considered four scales to be the "basis of harmony": the natural minor and major, and the harmonic minor and major.

A Neo-Rimsky-Korsakovian space (abbreviated NeRK) is the basis of almost all heptatonic harmony within modality. Initially posited by Russian composer Nikolai Rimsky-Korsakov, since Fizzheads consider the natural minor scale to be the Aeolian major mode, the natural minor scale is thus replaced with the melodic minor scale. This replacement creates four distinct parent scale quadrants defined by the combinations of absence or presence of a ♭3 or a ♭6 in the parent scale.

An individual NeRK yields 28 total scales that cover almost any possible heptatonic color in common practice. 12 different NeRKs exist within 12-tone equal temperament, one for each root note.

Notable exceptions

Melodic minor ♯5

In his book Modal Jazz Composition & Harmony, Vol. 1, Ron Miller presents a unique heptatonic scale, the melodic minor ♯5, that doesn't exist in any NeRK. Two of the most common modes of this scale are Mixolydian ♯9 and Palamidian ♮13. However, these colors can be derived from an octatonic scale, or "close enough" with one of the modes in a NeRK, such as Palamidian or Adonian respectively.

Neapolitan

The Neapolitan major and minor scales are the melodic and harmonic minor scales respectively but with a ♭9. Two of the most common modes of Neapolitan major are Arcadian♭13 and major Locrian. Both are "close enough" to a whole-tone scale for these to be unnecessary.

Non-heptatonic scales

Scales such as octatonic scales, bebop scales, whole-tone scales, etc. that contain more or less than seven notes fall out of the scope of a NeRK.