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

Locrian mode

The Locrian mode is either a musical mode or simply a diatonic scale. Although the term occurs in several classical authors on music theory, including Cleonides and Athenaeus , there is no warrant for the modern usage of Locrian as equivalent to Glarean's Hyperaeolian mode, in either classical,...

. 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 diminished third

Diminished third

In classical music from Western culture, a diminished third is the musical interval produced by narrowing a minor third by a chromatic semitone. For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A to C, and from A to C are diminished thirds,...

 interval from E to G♭. The scale therefore shares with the Locrian mode the property of having a diminished fifth above the tonic.

In English, Arabian scale may refer to what is known as the major Locrian scale. 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

Pythagorean tuning

Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...

 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

Meantone temperament

Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...

 system. It is notable as one of the five proper

Rothenberg propriety

In music, Rothenberg propriety denotes an important concept in the general theory of scales which was introduced by David Rothenberg in a seminal series of papers in 1978. The concept was independently discovered in a more restricted context by Gerald Balzano, who termed it coherence...

 seven-note scales in equal temperament

Equal temperament

An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...

, and as strictly proper in any meantone tuning with fifths flatter than 700 cents

Cent (music)

The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...

. 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 is the 5th mode of the Neapolitan scale, which may be used in conjunction with the Neapolitan chord

Neapolitan chord

In music theory, a Neapolitan chord is a major chord built on the lowered second scale degree. It most commonly occurs in first inversion so that it is notated either as II6 or N6 and normally referred to as a Neapolitan sixth chord...

, but is not limited to it. This scale is also known as melodic minor ♭2. Its modes and corresponding seventh chords are:

1. melodic minor ♭2; Cmin/maj7
2. leading whole-tone; D♭maj7(#5)
3. Lydian augmented dominant (♯5, ♭7); E♭7(#5)
4. Lydian Dominant b6; F7
5. major Locrian; G7(b5)
6. Locrian ♮2 ♭4; Am7♭5 or A7+5
7. Locrian ♭♭3; i.e., T, ♭2, ♭♭3, ♭4, ♭5, ♭6, ♭7; Bmaj7+5

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

Diminished third

In classical music from Western culture, a diminished third is the musical interval produced by narrowing a minor third by a chromatic semitone. For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A to C, and from A to C are diminished thirds,...

 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

Howard Hanson

Howard Harold Hanson was an American composer, conductor, educator, music theorist, and champion of American classical music. As director for 40 years of the Eastman School of Music, he built a high-quality school and provided opportunities for commissioning and performing American music...

 in his Harmonic Materials of Modern Music devotes several pages to the major Locrian, or more precisely to its transpositional set class

Set theory (music)

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte , drawing...

, 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 Locrian can all be defined as the whole tone scale

Whole tone scale

In music, a whole tone scale is a scale in which each note is separated from its neighbors by the interval of a whole step. There are only two complementary whole tone scales, both six-note or hexatonic scales:...

 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

Claude Debussy

Claude-Achille Debussy was a French composer. Along with Maurice Ravel, he was one of the most prominent figures working within the field of impressionist music, though he himself intensely disliked the term when applied to his compositions...

 in his opera Pelléas et Mélisande

Pelléas et Mélisande (opera)

Pelléas et Mélisande is an opera in five acts with music by Claude Debussy. The French libretto was adapted from Maurice Maeterlinck's Symbolist play Pelléas et Mélisande...

 and Alban Berg

Alban Berg

Alban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique.-Early life:Berg was born in...

 in his song Nacht

Seven Early Songs (Berg)

The Seven Early Songs , , are early compositions of Alban Berg, written while he was under the tutelage of Arnold Schoenberg. They are an interesting synthesis combining Berg's heritage of pre-Schoenberg song writing with the rigour and undeniable influence of Schoenberg...

.

Further reading

• Howard Hanson, Harmonic Materials of Modern Music, Appleton-Century-Crofts, 1960.
• Rodolfe d'Erlanger, La Musique Arab, vol. 3, Paul Geunther, 1930
• Vincent Persichetti, Twentieth-Century Harmony, W. W. Norton & co., 1961