Diatonic and Chromatic - Diatonic Scales

Diatonic Scales

Medieval theorists defined scales in terms of the Greek tetrachords. The gamut was the series of pitches from which all the Medieval "scales" (or modes, strictly) are notionally derived, and it may be thought of as constructed in a certain way from diatonic tetrachords. The origin of the word gamut is explained at the article Hexachord; here the word is used in one of the available senses: the all-encompassing gamut as described by Guido d'Arezzo (which includes all of the modes).

The intervals from one note to the next in this Medieval gamut are all tones or semitones, recurring in a certain pattern with five tones (T) and two semitones (S) in any given octave. The semitones are separated as much as they can be, between alternating groups of three tones and two tones. Here are the intervals for a random string of ascending notes (starting with F, in fact) from the gamut:

... –T–T–T–S–T–T–S–T–T–T–S–T– ...

And here are the intervals for one random ascending octave (the seven intervals separating the eight notes A–B–C–D–E–F–G–A, in fact) from the gamut:

T–S–T–T–S–T–T

In its most strict definition, therefore, a diatonic scale is one that may be derived from the pitches represented in successive white keys of the piano (or a transposition thereof): the modern equivalent of the gamut. (For simplicity, throughout this article equal temperament tuning is assumed unless otherwise noted.) This would include the major scale, and the natural minor scale (same as the descending form of the melodic minor), but not the old ecclesiastical church modes, most of which included both versions of the "variable" note B♮/B♭.