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Double harmonic scale
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The double harmonic major scale[1] is a musical scale with a flattened second and sixth degree. This scale is enharmonic to the Mayamalavagowla raga, Bhairav raga, Byzantine scale, Arabic scale (Hijaz Kar),[1][2] and Gypsy major scale.[3] It can be likened to a gypsy scale because of the diminished step between the 1st and 2nd degrees. Arabic scale may also refer to any Arabic mode, the simplest of which, however, to Westerners, resembles the double harmonic major scale.[4]
Details
[edit]The sequence of steps comprising the double harmonic scale is :
- half, augmented second, half, whole, half, augmented second, half
Or, in relation to the tonic note
- minor second, major third, perfect fourth and fifth, minor sixth, major seventh, octave
However, this scale is commonly represented with the first and last half step each being represented with quarter tones:[citation needed]
The non-quarter tone form is identical, in terms of notes, to the North Indian Thaat named Bhairav and the South Indian (Carnatic) Melakarta named Mayamalavagowla.
The double harmonic scale is arrived at by either:
- lowering both the second and sixth of the Ionian mode by a semitone.
- lowering the second note and raising the third note of the harmonic minor scale by one semitone.
- raising the seventh of the Phrygian dominant scale (a mode of the harmonic minor scale) by a semitone. The Phrygian dominant in turn is produced by raising the third of the diatonic Phrygian mode (a mode of the major scale) by a semitone.
- raising the third of the neapolitan minor scale by a semitone.
- lowering the second note of the harmonic major scale by a semitone.
- combining the lower half of the Phrygian dominant scale with the upper half of harmonic minor.[1]
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.
There is a variation of the double harmonic major scale called Double Harmonic Majorb7, which is also the fifth mode of the harmonic minor scale. This variation is sometimes confused with the double harmonic major scale because many sources refer to it simply as "double harmonic major" without indicating the "b7" sign. The primary difference between these two scales is the seventh degree, with the double harmonic majorb7 scale having a flat seventh (♭7) and the Double Harmonic Major having a natural seventh (7).
The scale contains a built-in tritone substitution, a dominant seventh chord a half step above the root, with strong harmonic movement towards the tonic chord.
The double harmonic scale is not commonly 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 double harmonic major 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.[5] 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.[citation needed]. Opeth used this scale in their song "Bleak" from the album Blackwater Park. It is also used by Hans Zimmer in his score for Dune.
Symmetry and balance
[edit]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.
Because it features symmetry, its steps form a palindrome. Using the letters T = tone, S = semitone and M = minor third, we can give the seven steps of the scale as SMSTSMS. This string of letters reads the same backwards. In comparison, among the modes of the major scale, the Dorian mode is a palindrome.
Whenever a scale is a palindrome, or has a mode which is palindromic, reflections of that scale generate modes of that same scale (usually chromatically transposed to another root). Thus any reflection of double harmonic gives rise to a class of pitches which contain a double harmonic scale, just like (thanks to the palindromic Dorian) any reflection of the major scale around any point gives rise to a class of pitches which contain the major scale. However, the major scale itself (Ionian mode), in contrast to the double harmonic major, is not a palindrome; its reflection around its root gives rise to a Phrygian mode. The double harmonic major is its own reflection around the root, itself being the palindromic mode.
The double harmonic 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 on a circle (whose full circumference represents an octave), their average position (or "centre of mass") is the centre of the circle.[6]
Tetrads
[edit]The main chords of the double harmonic major are:

I7M bII7M iii6 iv7M V7(b5) bVI7M(#5) viisus2add13(b5)
There are other possibilities of tetrad:
I7M(#5) bII7 bii7M bii7 bii7(b5) III6 iv° V6(b5) bvi°
Modes
[edit]Like all heptatonic (seven-pitch) 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:[7]
Mode Name of scale Degrees 1 Double harmonic major 1 ♭2 3 4 5 ♭6 7 8 2 Lydian ♯2 ♯6 1 ♯2 3 ♯4 5 ♯6 7 8 3 Ultraphrygian 1 ♭2 ♭3 ♭4 5 ♭6
78 4 Hungarian/Gypsy minor 1 2 ♭3 ♯4 5 ♭6 7 8 5 Oriental 1 ♭2 3 4 ♭5 6 ♭7 8 6 Ionian ♯2 ♯5 1 ♯2 3 4 ♯5 6 7 8 7 Locrian
3
71 ♭2
34 ♭5 ♭6
78
Related scales
[edit]Some of the closest existing scales to the double harmonic major scale are the Phrygian dominant scale, the fifth mode of the harmonic minor scale, as they are alike save for the Phrygian dominant's flattened seventh degree. The harmonic major scale (also known as major flat 6 and Ionian flat 6) is identical to the standard major scale aside from the sixth scale degree being flattened by a semitone, differing from the double harmonic major in having a natural second degree.
See also
[edit]References
[edit]- ^ a b c Stetina, Troy (1999). The Ultimate Scale Book, p. 59. ISBN 0-7935-9788-9.
- ^ Christiansen, Mike (2003). Mel Bay Complete Guitar Scale Dictionary, p. 43. ISBN 0-7866-6994-2.
- ^ Jonathan Bellman, The "Style hongrois" in the Music of Western Europe (Boston: Northeastern University Press Archived 2011-01-15 at the Wayback Machine, 1993): 120. ISBN 1-55553-169-5.
- ^ "R. G. Kiesewetter's 'Die Musik der Araber': A Pioneering Ethnomusicological Study of Arabic Writings on Music", p. 12. Philip V. Bohlman. Asian Music, vol. 18, no. 1. (Autumn–Winter, 1986), pp. 164–196.
- ^ Elie Robert Schmitz, Virgil Thomson (1966). The Piano Works of Claude Debussy, p. 28. ISBN 0-486-21567-9.
- ^ 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
- ^ Patrice, "Acheter une guitare électrique – Zoom pour ne pas se tromper[failed verification] Archived June 18, 2015, at the Wayback Machine" 23 May 2016 (accessed 9 October 2016).
Further reading
[edit]- Hewitt, Michael. 2013. Musical Scales of the World. The Note Tree. ISBN 978-0957547001.
External links
[edit]Double harmonic scale
View on GrokipediaDefinition and Construction
Interval Structure
The double harmonic scale is a heptatonic scale characterized by the interval pattern of one semitone, minor third, one semitone, major second, one semitone, minor third, and one semitone, expressed numerically as 1-3-1-2-1-3-1 in semitones.[5][6] This structure can also be denoted using step sizes as H (half step), W+H (whole step plus half step), H, W, H, W+H, H, where H represents a semitone and W a whole tone.[6] It is constructed by altering the major scale through the flattening of the second and sixth scale degrees, resulting in the pitch classes 1, ♭2, 3, 4, 5, ♭6, 7.[5] For example, in the key of C, the scale consists of the notes C, D♭, E, F, G, A♭, B.[5]Names and Notations
The double harmonic scale is known by several names reflecting its cross-cultural adoption in various musical traditions. In Western music theory, it is primarily termed the double harmonic scale or double harmonic major scale, emphasizing the presence of two augmented seconds in its structure. This nomenclature highlights its derivation from the major scale with alterations to the second and sixth degrees. It is also referred to as the Byzantine scale, a name derived from its association with Byzantine chant and Greek folk music traditions. In Arabic musical systems, the scale corresponds to the Hijaz Kar (or Hijazkar) maqam, the most prevalent variant of the Hijaz maqam, where it is constructed from the Hijaz jins on the tonic followed by the Nikriz jins on the fourth degree. The Gypsy major scale is another common designation, particularly in the context of Eastern European Romani music, underscoring its exotic, emotive quality in violin and guitar traditions. Regional variants further illustrate its nomenclature diversity. The term double harmonics occasionally appears in Western pedagogical materials to denote the scale's dual augmented intervals. These names trace back to the scale's integration into Ottoman and Arabic theoretical frameworks during the 19th century, where makam systems formalized such structures, though the specific "double harmonic" label emerged in Western analysis during the 20th century as ethnomusicology documented non-Western scales. Notation for the double harmonic scale typically employs flats to indicate the lowered second and sixth degrees relative to the major scale, as in the C double harmonic: C–D♭–E–F–G–A♭–B–C. Alternative notations may use sharps in certain transpositions to align with key signatures or enharmonic equivalents; for instance, the D double harmonic can be written as D–E♭–F♯–G–A–B♭–C♯–D to facilitate reading in contexts with fewer accidentals. Due to its two augmented seconds, the scale lacks a fixed position in the circle of fifths, which organizes diatonic keys, and is instead treated as an exotic or synthetic mode outside standard tonal hierarchies. To avoid confusion, the double harmonic scale is distinct from the harmonic minor scale, which alters the seventh degree of the natural minor rather than modifying the major scale's second and sixth degrees.Theoretical Properties
Symmetry and Balance
The double harmonic scale demonstrates a high degree of internal symmetry through its palindromic interval pattern of 1-3-1-2-1-3-1 semitones (minor second, augmented second, minor second, major second, minor second, augmented second, minor second), which remains identical when reversed. This structure creates reflectional symmetry centered on the root note, often described as radial symmetry, where the scale's design mirrors itself around the central axis at pitch class 0. Such symmetry contributes to the scale's balanced and exotic sonic profile, distinguishing it from asymmetric Western scales.[7][8] In pitch-class set theory, the double harmonic scale is represented by the set class 7-22, with prime form {0,1,4,5,7,8,11}. Its interval vector <4,2,4,5,4,2> reveals a balanced distribution of interval classes: four minor seconds, two major seconds, four minor thirds, five major thirds, four perfect fourths, and two tritones. This even spread of smaller and larger intervals enhances the scale's equilibrium, with the augmented seconds positioned symmetrically to frame clusters of semitones and the single whole tone providing central stability. The scale's center of gravity distance measures 0, confirming perfect axial balance around the root without deviation.[7][9] Visually, an interval diagram of the scale—plotting cumulative semitones from the root—highlights its palindromic elements, forming a symmetric waveform that peaks evenly between the augmented seconds while the semitones create tight clusters at the edges and center. In contrast to the diatonic scale (set class 7-35, interval vector <443434>), which exhibits no such reflectional symmetry and evolved from just intonation adaptations in Western music, the double harmonic scale's properties stem from modal traditions emphasizing inherent balance over tempered equality.[7][9]Tetrachords
The double harmonic scale is constructed from two disjunct tetrachords that form its foundational structure. The lower tetrachord spans the first four degrees (1, ♭2, 3, 4) and corresponds to the hijaz tetrachord, featuring the interval pattern of a half step (H), augmented second (A2), and half step (H).[10] The upper tetrachord covers the remaining degrees (5, ♭6, 7, 8=1) and aligns with the harmonic minor tetrachord transposed to the fifth degree, exhibiting intervals of a half step (H), augmented second (A2), and half step (H). Both the lower and upper tetrachords are hijaz jins (H-A2-H), making the scale a union of two hijaz tetrachords connected disjunctly by a whole tone.[11][12] These tetrachords are connected disjunctly by a whole tone interval between the fourth and fifth degrees, creating an overall span of an octave without overlap.[12] This arrangement generates the complete double harmonic scale through the union of two hijaz tetrachords, emphasizing the scale's characteristic augmented seconds in both segments.[11] In theoretical terms, the hijaz tetrachord's pattern (H, A2, H) imparts an exotic, tense quality often associated with Middle Eastern modalities, while the upper tetrachord's (H, A2, H) mirrors the ascending structure found in the harmonic minor scale's upper portion. This tetrachord-based construction is rooted in Arabic maqam theory, where short melodic segments known as jins (tetrachords or similar) serve as modular building blocks for larger maqamat, such as Hijaz Kar, which directly corresponds to the double harmonic scale.[12]Modes
The Seven Modes
The double harmonic scale, with its defining interval structure of half, augmented second, half, whole, half, augmented second, and half steps, yields seven rotational modes, each beginning on successive degrees of the scale. These modes preserve the scale's exotic, tense character through the presence of augmented seconds but vary in their overall tonality, from major-like to highly dissonant. While analogous names drawn from the major scale modes (Ionian, Dorian, etc.) are sometimes applied for familiarity, many have distinct traditional or theoretical designations reflecting their unique properties. The modes are detailed below, showing the starting degree relative to the parent scale (assuming root as 1), the sequence of degrees in the parent scale, the interval formula relative to the mode's own tonic, and notable alternative names.[3]| Mode Number | Analogous Name | Starting Degree | Degree Sequence | Relative Interval Formula | Common Alternative Name(s) |
|---|---|---|---|---|---|
| 1 | Ionian double harmonic | 1 | 1, ♭2, 3, 4, 5, ♭6, 7 | 1, ♭2, 3, 4, 5, ♭6, 7 | Double harmonic major, Byzantine |
| 2 | Dorian double harmonic | ♭2 | ♭2, 3, 4, 5, ♭6, 7, 1 | 1, ♯2, 3, ♯4, 5, ♯6, 7 | Lydian ♯2 ♯6, Hungarian major |
| 3 | Phrygian double harmonic | 3 | 3, 4, 5, ♭6, 7, 1, ♭2 | 1, ♭2, ♭3, ♭4, 5, ♭6, ♭♭7 | Ultraphrygian |
| 4 | Lydian double harmonic | 4 | 4, 5, ♭6, 7, 1, ♭2, 3 | 1, 2, ♭3, ♯4, 5, ♭6, 7 | Hungarian minor, Gypsy minor |
| 5 | Mixolydian double harmonic | 5 | 5, ♭6, 7, 1, ♭2, 3, 4 | 1, ♭2, 3, 4, ♭5, 6, ♭7 | Oriental |
| 6 | Aeolian double harmonic | ♭6 | ♭6, 7, 1, ♭2, 3, 4, 5 | 1, ♯2, 3, 4, ♯5, 6, 7 | Ionian ♯2 ♯5 |
| 7 | Locrian double harmonic | 7 | 7, 1, ♭2, 3, 4, 5, ♭6 | 1, ♭2, ♭♭3, 4, ♭5, ♭6, ♭♭7 | Locrian ♭♭3 ♭♭7 |


