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Encyclopedia of Microtonal Music Theory

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diatonic scale

[Joe Monzo]

The essential feature of any diatonic scale is that it uses 7 nominals, each one once and without skipping any. Diatonic scales contain a mixture of whole tones and semitones, and generally feature more whole tones than semitones.

It is important to note that standard Western musical notation is based upon the diatonic scale, in that for purposes of naming the notes, each degree of the diatonic scale is assigned a letter-name in alphabetical order according to ascending pitch -- these are the diatonic scale's nominals. Notes which carry accidentals in addition to the letter-name were originally felt to lie outside the diatonic system.

The primary form of the ancient Greek "diatonic genus" (see #2 below) resulted in a scale which has this ascending L and s pattern:

L s L L s L L

where L = the "whole-tone", s = the semitone, and 5L + 2s = the octave, which gets its name from the fact that 8 diatonic notes span the equivalence-interval with 2:1 ratio.

Later (c.800 AD), medieval European theorists discarded the long Greek names (as in the perfect immutable system), along with the chromatic genus and enharmonic genus, and substituted Roman letters thus:

  L   s   L   L   s   L   L
A   B   C   D   E   F   G   A

The ratio between the logarithmic sizes of the L and s (i.e., the whole-tone and diatonic-semitone, or synonymously the "whole-step" and "half-step") is called the R or Blackwood R value, named after Easley Blackwood, who formulated it in his book The Structure of Recognizable Diatonic Tunings.

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