In Music theory, the diatonic major scale (also known as the Guido scale), from the Greek "diatonikos" or "to stretch out", is a fundamental building block of the European-influenced musical tradition. It is sometimes used to refer to all the modes, but is generally used only in reference to the major and minor scales. It contains seven notes to the octave, corresponding to the white keys on a piano, obtained from a chain of six successive fifths in some version of meantone temperament, and resulting in two tetrachords separated by intervals of a whole tone. If our version of meantone is the twelve tone equal temperament the pattern of intervals in semitones will be 2-2-1-2-2-2-1. The major scale begins on the first note and proceeds by steps to the first octave. In solfege, the syllables for each scale degree are "Do-Re-Mi-Fa-Sol-La-Ti-Do".
The natural minor scale can be thought of in two ways, the first is as the relative minor of the major scale, beginning on the sixth degree of the scale and proceeding step by step through the same tetrachords to the first octave of the sixth degree. In solfege "La-Ti-Do-Re-Mi-Fa-Sol." Alternately, the natural minor can be seen as a composite of two different tetrachords of the pattern 2-1-2-2-1-2-2. In solfege "Do-Re-Mé-Fa-Sol-Lé-Té-Do."
Western harmony from the Renaissance up until the late nineteenth century is based upon the diatonic scale and the unique hierarchical relationships created by this system of organizing seven notes. It should be kept in mind that most longer pieces of common practice music change key, but this leads to a hierarchical relationship of diatonic scales in one key with those in another.
These unique relationships are as follows: Only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and that only the diatonic and pentatonic subsets of the 12 tone chromatic set follow these constraints (Balzano, 1980, 1982). The diatonic collection contains each interval class a unique number of times (Browne 1981 cited in Stein 2005, p.49, 49n12). Diatonic set theory describes the following properties: maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity.
- Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1930190808.
- Clough, John (1979). "Aspects of Diatonic Sets", Journal of Music Theory 23: 45-61.
- Balzano, Gerald J. (1980). "The Group Theoretic Description of 12-fold and Microtonal Pitch Systems", Computer Music Journal 4: 66-84.
- Stein, Deborah (2005). Engaging Music: Essays in Music Analysis. New York: Oxford University Press. ISBN 0195170105.
- Browne, Richmond (1981). "Tonal Implications of the Diatonic Set", In Theory Only 5, nos. 1 and 2: 3-21
- Diatonic Scale (http://www.ericweisstein.com/encyclopedias/music/DiatonicScale.html) on Eric Weisstein's Treasure trove of Music