In the scale above there are two triads which are able to function as tonics: C major and f minor. This gives us two tonally effective modes derived from this prime scale: the double harmonic major and the double harmonic minor.

The double harmonic major scale

The double harmonic major scale and its triads are represented numerically as:

1 	b2 	3 	4 	5 	b6     7      Notes
  	  	  	  	  	  	  	 
1 	b II     iii     iv     V(b5) 	bVI+  b II7   Chords

So if the tonic is C, the scale will consist of the following notes and triads:

c 	db 	e 	f 	g 	ab 	b 	
  	  	  	  	  	  	  	 
C 	Db 	e 	f 	G(b5) 	Ab+ 	Db7

This scale is usually found as a temporary alteration of the standard major scale. But it can be sustained at length because it supports a strong tonic function on the I triad. The melodic deficiencies, and the difficulty of simultaneously avoiding parallel fifths and augmented intervals make this scale difficult to use in a manner consistent with common practice classical. But outside of this stylistic convention it can provide some quite extravagant harmonic progressions and is a fertile source of inspiration.

With two augmented seconds - between b2 and 3 and between b6 and 7 - this scale has a somewhat non-western sound to it. Augmented seconds are common in the musics of North Africa, the Middle East and Eastern Europe, though they were considered unmelodic in common practice classical music.

This scale provides us with the strange, but effective, cadence of III - b II - I.

It also provides the much more common b II aug. 6 - I, whose penult is described in classical theory texts as the German, French or Italian Sixth chord, and in jazz theory texts as the Altered Dominant. In both classical and jazz, this cadence is frequently used as a secondary cadence, resolving to IV or V in the scale (i.e. b V Aug 6 - IV, and b VI aug 6 - V).

The double harmonic minor scale

The double harmonic minor scale and its triads are represented numerically as:

1 	2 	b3 	#4 	5 	b6 	7 	Notes
  	  	  	  	  	  	  	 
1 	II(b5) 	bIII+ 	bVI7 	V 	bVI 	vii 	Chords

c 	d 	eb 	f# 	g 	ab 	b 	
  	  	  	  	  	  	  	 
c 	D(b5) 	Eb+ 	Ab7 	G 	Ab 	b

This scale provides the unique cadence of b VI - VII - I. Of all the scales I have examined this is perhaps the strangest
and certainly the most obscure one. The tonic function of its i triad is very weak and it is easily displaced by its relative double harmonic major scale.It can only be maintained with careful compositional aforethought. This along with its melodic deficiencies make it an extremely rare occurrence. This alone should give the curious composer enough reason to use it now!