Major locrian scale

In music, the major locrian scale, also called the "locrian major scale", is the scale obtained by sharpening the second and third degrees of the locrian mode. With a tonic of C, it consists of the notes C D E F G♭ A♭ B♭. It can be described as a whole tone scale extending from G♭ to E, with F introduced within the augmented second interval from E to G♭. The scale therefore shares with the locrian mode the property of having a diminished fifth above the tonic.

A version of the major locrian scale is listed as "mode 3" in the French translation of Safi Al-Din's treatise Kitab Al-Adwar. This was a Pythagorean version of the scale.

Aside from this Arabic version, interest in the major locrian is a phenomenon of the twentieth century, but the scale is definable in any meantone system. It is notable as one of the five proper seven-note scales in equal temperament, and as strictly proper in any meantone tuning with fifths flatter than 700 cents. If we take the tonic in the scale given above to be G♭ rather than C, we obtain the "leading whole-tone scale", which with a tonic on C is C D E F♯ G♯ A♯ B; this can equally well be characterized as one of the five proper seven-note scales of equal temperament.

The major locrian scale has only two perfect fifths, but it has in some sense a complete cycle of thirds if one is willing to count a diminished third as a third: four major thirds, two minor thirds and a diminished third making up two octaves. In 12-equal temperament, the diminished third is enharmonically equivalent to a major second, but in other meantone systems it is wider and more nearly like a third.

The major locrian in 12 equal temperament

Howard Hanson in his "Harmonic Materials of Modern Music" devotes several pages to the major locrian, or more precisely to its transpositional set class, a concept Hanson pioneered. He names this transpositional class the "seven-tone impure major second scale", and notes that the various modes of the major locrain can all be defined as the whole tone scale with one additional note, and where that note occurs does not affect the transpositional class. He also notes that the scale has the property that every three-note chord possible in the twelve tone chromatic scale already appears in the major locrian.

Examples are given of the use of this scale by Claude Debussy in his opera Pelléas et Mélisande and Alban Berg in his song Nacht.

References

*Howard Hanson, "Harmonic Materials of Modern Music", Appleton-Century-Crofts, 1960

Further reading

*Rodolfe d'Erlanger, "La Musique Arab", vol. 3, Paul Geunther, 1930
*Vincent Persichetti, "Twentieth-Century Harmony", W. W. Norton & co., 1961