Double harmonic scale
In music, the double harmonic major scale is a scale whose gaps may sound "exotic" to Western listeners. This is also known as the Arabic, Gypsy major, and Byzantine scale. It can be likened to a gypsy scale because of the augmented step between the 2nd and 3rd degrees. Arabic scale may also refer to any Arabic mode, the simplest of which, however, to Westerners, resembles the double harmonic major scale.
The sequence of steps comprising the double harmonic scale is:
Or, in relation to the tonic note:
- minor 2nd, major 3rd, perfect 4th and 5th, minor 6th, major 7th.
However, this scale is commonly represented with the first and last half step each being represented as a quarter tone. The non-quarter tone form ( Play (help·info)) is identical to the North Indian Thaat named Bhairav and the South Indian (Carnatic) Melakarta named Mayamalavagowla.
The double harmonic scale is arrived at by either:
- raising the seventh of the Phrygian dominant scale, (a mode of the harmonic minor scale), by a semitone.
- raising the seventh and third of the Phrygian mode, (a mode of the Major Scale), by a semitone.
- lowering both the sixth and second of a major scale by a semitone.
- lowering the 2nd note of a harmonic major scale by a semitone.
- combining the lower half of phrygian dominant with the upper half of harmonic minor.
It is referred to as the "double harmonic" scale because it contains two harmonic tetrads featuring augmented seconds. By contrast both the harmonic major and harmonic minor scales contain only one augmented second, located between their sixth and seventh degrees.
The double harmonic scale is uncommonly used in classical music from Western culture, as it does not closely follow any of the basic musical modes, nor is it easily derived from them. It also does not easily fit into common Western chord progressions such as the authentic cadence. This is because it is mostly used as a modal scale, not intended for much movement through chord progressions. The Arabic scale (in the key of E) was used in Nikolas Roubanis's "Misirlou", and in the Bacchanale from the opera Samson and Delilah by Saint-Saëns. Claude Debussy used the scale in "Soirée dans Grenade", "La Puerta del Vino", and "Sérénade interrompue" to evoke Spanish flamenco music or Moorish heritage. In popular music, Ritchie Blackmore of Deep Purple and Rainbow used the scale in pieces such as "Gates of Babylon" and "Stargazer". The Miles Davis jazz standard "Nardis" also makes use of the double harmonic.
Symmetry and balance
The double harmonic scale features radial symmetry, or symmetry around its root, or center note. Breaking up the three note chromaticism and removing this symmetry by sharpening the 2nd or flattening the 7th note respectively by one semitone yields the harmonic major and Phrygian Dominant mode of the harmonic minor scales respectively, each of which, unlike the double harmonic minor scale, has a full diminished chord backbone.
This scale (and its modes like the Hungarian minor scale) is the only seven-note scale (in 12-tone equal temperament) that is perfectly balanced; this means that when its pitches are represented as points in a circle (whose full circumference represents an octave), their average position (or "centre of mass") is the centre of the circle.
Like most heptatonic (seven pitches in the octave) scales, the double harmonic scale has a mode for each of its individual scale degrees. The most commonly known of these modes is the 4th mode, the Hungarian minor scale, most similar to the harmonic minor scale with a raised 4th degree. The modes are as follows:
- Tonic mode - Double harmonic major
- 2nd mode - Lydian ♯2 ♯6
- 3rd mode - Ultraphrygian
- 4th mode - Hungarian minor
- 5th mode - Oriental
- 6th mode - Ionian augmented ♯2
- 7th mode - Locrian 3 7
Relationship to Phrygian major (Jewish scale)
The nearest other existing scale to the double harmonic scale is the Phrygian dominant scale. The double harmonic scale may be made from a Phrygian dominant scale by sharpening its 7th degree.
- Minor gypsy scale
- Ukrainian Dorian scale
- Arabic music
- Byzantine music
- Tritone substitution
- Neapolitan chord
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- It can be verified in 36:38 minutes of the video
- Milne, A.J., Bulger, D., Herff, S.A. Sethares, W.A. "Perfect balance: A novel principle for the construction of musical scales and meters", Mathematics and Computation in Music (Lecture Notes in Computer Science, Vol. 9110, pp. 97–108) Heidelberg: Springer. ISBN 978-3-319-20602-8
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