The double harmonic major scale, also known as the Byzantine scale or Gypsy major scale, is characterized by its distinctive, exotic sound due to its unique interval structure. It’s often used in Middle Eastern, Eastern European, and some flamenco music. The scale has a formula that includes two augmented seconds, giving it a particularly dramatic and exotic flavor.

Construction of Double Harmonic Major:

The double harmonic major scale is built using the following interval pattern:

• Half step

• Augmented second

• Half step

• Whole step

• Half step

• Augmented second

• Whole step

Modes of the Double Harmonic Major Scale:

Here are the seven modes of the double harmonic major scale, each starting from a different degree of the scale:

1. Double Harmonic Major (Ionian ♯2 ♯6)

   • Pattern: Half, Augmented second, Half, Whole, Half, Augmented second, Whole

   • Example: C Double Harmonic Major (C, D♭, E, F, G, A♭, B, C)

   • Sound: Exotic and dramatic, with both augmented seconds and a major third.

2. Locrian ♮2 ♯6

   • Pattern: Augmented second, Half, Whole, Half, Augmented second, Whole, Whole

   • Example: D♭ Locrian ♮2 ♯6 (D♭, E, F, G♭, A, B♭, C♭, D♭)

   • Sound: Dissonant and unstable with a natural 2nd and raised 6th.

3. Ionian ♯2 (Phrygian ♯6)

   • Pattern: Augmented second, Half, Whole, Whole, Half, Whole, Whole

   • Example: E Phrygian ♯6 (E, F, G♯, A, B, C, D, E)

   • Sound: Exotic with a raised 6th, giving it a unique blend of Phrygian and major qualities.

4. Lydian ♯2 (Lydian ♯2 ♯6)

   • Pattern: Augmented second, Whole, Whole, Whole, Half, Whole, Half

   • Example: F Lydian ♯2 (F, G♯, A♯, B, C, D, E, F)

   • Sound: Bright and ethereal with both a raised 2nd and 4th.

5. Mixolydian ♯2 ♯6

   • Pattern: Augmented second, Whole, Whole, Half, Whole, Whole, Half

   • Example: G Mixolydian ♯2 (G, A♯, B, C, D, E, F♯, G)

   • Sound: Major with a raised 2nd and 6th, giving it a bluesy and exotic quality.

6. Aeolian ♯2 (Aeolian ♯6)

   • Pattern: Augmented second, Half, Whole, Whole, Half, Whole, Whole

   • Example: A Aeolian ♯2 (A, B♭, C♯, D, E, F♯, G, A)

   • Sound: Dark with an exotic twist due to the raised 2nd.

7. Altered Scale (Super Locrian, Diminished Whole-Tone)

   • Pattern: Half, Whole, Half, Whole, Whole, Whole, Whole

   • Example: B Altered (B, C, D, E♭, F, G, A, B)

   • Sound: Extremely tense and dissonant, with a flat 2nd, 3rd, 4th, 5th, and 7th, and a sharp 4th (♯4).

Summary

• Double Harmonic Major: Exotic and dramatic with augmented seconds.

• Locrian ♮2 ♯6: Dissonant with a natural 2nd and raised 6th.

• Ionian ♯2 (Phrygian ♯6): Exotic with a raised 6th.

• Lydian ♯2 (Lydian ♯2 ♯6): Bright with raised 2nd and 4th.

• Mixolydian ♯2 ♯6: Major with raised 2nd and 6th.

• Aeolian ♯2: Dark with raised 2nd.

• Altered Scale (Super Locrian): Highly dissonant and tense.

These modes provide a range of exotic and dramatic colors, useful for creating music that needs to evoke a sense of the mystical or the unusual.