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I have recently discovered Double Harmonic scales and love them. Particularly the major.

I'm having a lot of fun improvising melodies but I can't seem to make any chord progressions that work. It always just ends up being the root chord and the minor chord of the fourth note above the root, which is a tad boring.

I was wondering what the full set of "allowed" chords for each of the Double Harmonic scales is.

PS: I've seen "modes" come up a lot in my searches for information. I know nothing about them.

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As discussed in the other answers, the chords I, II, iv, and V(7b5) are the most usable from within the scale. In addition, don't underestimate the possibilities of harmonizing with chords outside the scale, even though they'll only work with melodies using a part of the scale. For instance, III, borrowed from plain Phrygian, works as a flamenco-style passing chord between iv and II, while vii, also from Phrygian, harmonizes well with a descending melodic line approaching the tonic. All these possibilities can be heard in various renditions of Middle Eastern folk songs, such as "Misirlou":

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    This is the real answer. For music that uses this scale, if you want to use it with chord progressions, you don't stick to only chords that can be built from the notes of the scale – Some_Guy Jun 18 at 16:39
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    (that's also really true for pretty much any scale, but it's especially true for scales like this) – Some_Guy Jun 18 at 16:40
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...chord progressions that work...

If you mean chord progressions that work like basic diatonic harmony like V > I, then you are really just describing the character of this scale: it doesn't fit into common diatonic (major/minor) harmony.

An approach you could try for harmony is build chords in thirds on each scale degree and then exploit the exotic nature of the scale. If we start on A and treat the scale as a major scale with flat scale degrees 2 and 6 the notes are: A, Bb, C#, D, E, F, G#, A. The chords built on thirds (a mix of triads and seventh chords) would be:

A major (I)
Bb major (bII)
C# minor (iii)
D minor (iv)
E dominant seven flat five (V7b5)
F augmented (bVI+)
G# half-diminished with a flat third! (viiø7b3)

Just a few comments before moving on:

  • The chord on G# is weird. It could be spelled as Bb4/2, a Bb dominant seventh chord in third inversion. That's not much easier to deal with, but at least it doesn't have a altered third.
  • Bb-C#-F is possible on Bb. Technically, that isn't built in thirds, because Bb-C# is an augmented second. But, it's equivalent to a Bb minor chord.
  • C#-F-G# is possible on C# where the chord is equivalent to C# major. (You can continue this process on several roots in the scale and build the equivalent of diminished and augmented chords too!)
  • The E7b5 could be inverted and respelled as Bb It+6, a B flat Italian augmented sixth chord.
  • The chord on G# could be inverted and relabeled as Bb Gr+6, a B flat German augmented sixth chord.

Now that we have the chords, we can look for some interesting progressions.

  • You already have I > iv which is a clear diatonic progression.
  • V7b5 > I is a jazzy variation of plain V7 > I.
  • A common chord progression that is lurking here involves the augmented sixth chords, the It+6 and Gr+6 on Bb. Both of those chords can move to A major which is the movement of the standard resolution of the augmented sixth chords. (Normally the resolution is to V, but here it is to I.) So that gives us bII Gr+6 > I or bII It+6 > I.
  • If we use some incomplete chords, we can get bII6 > V > I. In this case we omit the flat five in V. That has the bII6 acting like the N6 Neapolitan chord. Normally that progression would move to a minor i, but here it ends on major I. I think this could also be labeled as N6 > V > I.
  • I > bII or iii > iv which is parallel harmony. Parallel harmony can be used with the diatonic modes, but not these two particular progressions. While you can find two major or minor chords a whole step apart in the diatonic modes, you won't find them a half-step apart.
  • iii > I and iv > bII both are progressions that move by descending third root. These can be found in diatonic harmony and usually are labeled 'weak' progressions.

So there are a few possibilities that hint at diatonic or major/minor harmony and exotic parallelism. You may need to let your ears get acclimated to the different sound of these harmonies. But the point of using this scale is to get new and different sounds. I imagine you may need to try new improv. methods. Someone who can get cookin' on a blues progression - for example - might not be comfortable with the double harmonic. Personally, I am not a skilled improviser, but I've tried to fake my way through improvisation with this scale and generally tried to evoke the feeling of something like a flamenco guitarist.

In A:

iv   > i    = dm    > A
V7b5 > I    = E7b5  > A
bII > V > I = Bb/D > E > A
Gr+6 > I    = Bb7   > A
It+6 > I    = Bb7b5 > A
iii  > I    = c#m   > A 
iv   > bII  = dm    > Bb
bII  > I    = dm    > c#m
iv   > iii  = Bb    > A
  • Trying to understand the chord on G#. If it's diminished (or even half-dim.) its third is flat anyway, isn't it? To get there, the 3rd would need to be sharpened, I think. Tricky! What have I missed? – Tim Dec 12 '18 at 12:53
  • @Tim, yeah that G# chord of the ^7 degree is odd. But, then again, this scale isn't what functional harmony is based on so some weirdness is expected. I figure it's fun to find so chord relationships that are like functional harmony while realizing it really isn't functional. To the point, there isn't a proper dominant chord. – Michael Curtis Dec 12 '18 at 15:22
  • Building triads and seventh chords this was is a bit artificial. Imagine building chords this way from the blues scale. We wouldn't get the basic blues chords! So treating the double harmonic scale this way is experimental. – Michael Curtis Dec 12 '18 at 15:26
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Each of the allowed chords for any mode of a scale is allowed in all of the modes. Only its function would differ.

Here is a list of allowed chords for the 'Double Harmonic' scale and its modes. Note that each chord in the list is transposed to the key of C, while these should be mapped correctly to different keys depending on your mode and the function of the chord in the mode.

Note that only one of each enharmonic equivalent chords is output. If not, the list could get approximately 5 times as big.

Interval Set    Pitch Class Set    Name                  Properties              Quality

0,1,3           1-b9-b3            C-add(b9)             C- add b9 no 5          min5
0,1,4           1-b9-3             Cadd(b9)              C add b9 no 5           Maj5
0,1,7           1-b9-5             Cadd(b9)              C add b9 no 3           Maj5
0,1,11          1-b9-7             CΔ7b9                 CΔ7 b9 no 5 no 3        Maj7
0,2,3           1-9-b3             C-add9                C- add 9 no 5           min5
0,3,5           1-b3-11            C-add11               C- add 11 no 5          min5
0,3,6           1-b3-b5            C°                    C°                      dim5
0,4,5           1-3-11             Cadd11                C add 11 no 5           Maj5
0,4,6           1-3-b5             C(b5)                 C b5                    Maj5
0,4,7           1-3-5              C                     C                       Maj5
0,4,8           1-3-#5             C+                    C+                      Aug5
0,5,7           1-4-5              Csus4                 C sus 4                 Maj5
0,5,8           1-4-#5             C+sus4                C+ sus 4                Aug5
0,5,11          1-4-7              CΔ7sus4               CΔ7 sus 4 no 5          Maj7
0,6,8           1-#11-#5           C+add(#11)            C+ add #11 no 3         Aug5
0,7,8           1-5-b6             Cadd(b6)              C add b6 no 3           Maj5
0,7,9           1-5-6              C6                    C6 no 3                 Maj5
0,8,11          1-#5-7             C+Δ7                  C+Δ7 no 3               AugMaj7
0,1,3,4         1-b9-#9-3          Cadd(b9)add(#9)       C add b9 add #9 no 5    Maj5
0,1,3,7         1-b9-b3-5          C-add(b9)             C- add b9               min5
0,1,4,5         1-b9-3-11          Cadd11add(b9)         C add 11 add b9 no 5    Maj5
0,1,4,6         1-b9-3-b5          C(b5)add(b9)          C b5 add b9             Maj5
0,1,4,7         1-b9-3-5           Cadd(b9)              C add b9                Maj5
0,1,4,11        1-b9-3-7           CΔ7b9                 CΔ7 b9 no 5             Maj7
0,1,5,7         1-b9-4-5           Csus4add(b9)          C sus 4 add b9          Maj5
0,1,5,11        1-b9-4-7           CΔ7b9sus4             CΔ7 b9 sus 4 no 5       Maj7
0,1,7,8         1-b9-5-b6          Cadd(b9)add(b6)       C add b9 add b6 no 3    Maj5
0,1,7,9         1-b9-5-6           C6add(b9)             C6 add b9 no 3          Maj5
0,1,7,11        1-b9-5-7           CΔ7b9                 CΔ7 b9 no 3             Maj7
0,1,8,11        1-b9-#5-7          C+Δ7b9                C+Δ7 b9 no 3            AugMaj7
0,2,3,6         1-9-b3-b5          C°add9                C° add 9                Dim5
0,3,4,6         1-#9-3-b5          C(b5)add(#9)          C b5 add #9             Maj5
0,3,4,7         1-#9-3-5           Cadd(#9)              C add #9                Maj5
0,3,7,9         1-b3-5-6           C-6                   C-6                     min5
0,4,5,7         1-3-11-5           Cadd11                C add 11                Maj5
0,4,5,8         1-3-11-#5          C+add11               C+ add 11               Aug5
0,4,6,7         1-3-#11-5          Cadd(#11)             C add #11               Maj5
0,4,6,10        1-3-b5-b7          C7b5                  C7 b5                   Dom7
0,4,7,8         1-3-5-b6           Cadd(b6)              C add b6                Maj5
0,4,7,9         1-3-5-6            C6                    C6                      Maj5
0,4,7,10        1-3-5-b7           C7                    C7                      Dom7
0,4,7,11        1-3-5-7            CΔ7                   CΔ7                     Maj7
0,5,7,8         1-4-5-b6           Csus4add(b6)          C sus 4 add b6          Maj5
0,5,7,11        1-4-5-7            CΔ7sus4               CΔ7 sus 4               Maj7
0,5,8,11        1-4-#5-7           C+Δ7sus4              C+Δ7 sus 4              AugMaj7
0,1,3,7,9       1-b9-b3-5-6        C-6add(b9)            C-6 add b9              min5
0,1,4,5,7       1-b9-3-11-5        Cadd11add(b9)         C add 11 add b9         Maj5
0,1,4,5,8       1-b9-3-11-#5       C+add11add(b9)        C+ add 11 add b9        Aug5
0,1,4,5,11      1-b9-3-11-7        CΔ11b9                CΔ11 b9 no 5            Maj7
0,1,4,7,8       1-b9-3-5-b6        Cadd(b9)add(b6)       C add b9 add b6         Maj5
0,1,4,7,9       1-b9-3-5-6         C6add(b9)             C6 add b9               Maj5
0,1,4,7,11      1-b9-3-5-7         CΔ7b9                 CΔ7 b9                  Maj7
0,1,4,8,11      1-b9-3-#5-7        C+Δ7b9                C+Δ7 b9                 AugMaj7
0,1,5,7,8       1-b9-4-5-b6        Csus4add(b9)add(b6)   C sus 4 add b9 add b6   Maj5
0,1,5,7,11      1-b9-4-5-7         CΔ7b9sus4             CΔ7 b9 sus 4            Maj7
0,1,5,8,11      1-b9-4-#5-7        C+Δ7b9sus4            C+Δ7 b9 sus 4           AugMaj7
0,1,7,8,11      1-b9-5-b13-7       CΔ7b13b9              CΔ7 b13 b9 no 3         Maj7
0,2,3,6,11      1-9-b3-b5-7        C°Δ9                  C°Δ9                    dimMaj7
0,3,4,6,7       1-#9-3-#11-5       Cadd(#11)add(#9)      C add #11 add #9        Maj5
0,3,4,7,9       1-#9-3-5-6         C6add(#9)             C6 add #9               Maj5
0,4,5,7,8       1-3-11-5-b6        Cadd11add(b6)         C add 11 add b6         Maj5
0,4,5,7,11      1-3-11-5-7         CΔ11                  CΔ7 add 11              Maj7
0,4,6,7,10      1-3-#11-5-b7       C7#11                 C7 #11                  Dom7
0,4,7,8,11      1-3-5-b13-7        CΔ7b13                CΔ7 b13                 Maj7
0,5,7,8,11      1-4-5-b13-7        CΔ7b13sus4            CΔ7 b13 sus 4           Maj7
0,1,4,5,7,8     1-b9-3-11-5-b6     Cadd11add(b9)add(b6)  C add 11 add b9 add b6  Maj5
0,1,4,5,7,11    1-b9-3-11-5-7      CΔ11b9                CΔ11 b9                 Maj7
0,1,4,5,8,11    1-b9-3-11-#5-7     C+Δ11b9               C+Δ11 b9                AugMaj7
0,1,4,7,8,11    1-b9-3-5-b13-7     CΔ7b13b9              CΔ7 b13 b9              Maj7
0,1,5,7,8,11    1-b9-4-5-b13-7     CΔ7b13b9sus4          CΔ7 b13 b9 sus 4        Maj7
0,3,4,6,7,10    1-#9-3-#11-5-b7    C7#11#9               C7 #11 #9               Dom7
0,4,5,7,8,11    1-3-11-5-b13-7     CΔ11b13               CΔ7 b13 add 11          Maj7
0,1,4,5,7,8,11  1-b9-3-11-5-b13-7  CΔ11b13b9             CΔ11 b13 b9             Maj7
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As always it is easiest to analyze these kinds of things in the key of C.

C Db E F G Ab B

produces the following chords: C Db Emi Fmi Gmajb5 Abaug B... this chord is very tough to name correctly. I'm going to say Bdim(dim3).

If we extend to the 7th, you get: Cmaj7 DbMaj7 Emi(dim7)* FmiMa7 G7b5 Abmaj7 Bdim7(dim3).

*This is a spelling oddity. You have to spell this chord this way for functional purposes but it's more realistic that you're going to understand it as an EMi6.

Like most septatonic scales, you're going to be working most with the I, IV and V. Of equal importance in this particular scale is the II. The VI is also fairly useful in this scale, as is the (rather strange) vii. The iii is in a really weird place and doesn't really work as a substitution for the I like it does in diatonic scales, but the fact that as a seventh chord it contains the Db it has some interesting properties.

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    Interestingly, the Byzantine Scale and its modes are widely used in chant of the Greek Orthodox Church, and their use in the Divine Liturgy predates anything resembling modern musical theory and functional harmony by something like 1500 years or more. Except we call the modes 'Tones'. The Tones are rotated with many of the chants over different liturgical calendar Seasons, giving a unique feeling to each, even with the same lyrics-- sometimes with alterations for certain liturgical Seasons. – jdmayfield Mar 5 at 8:52
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Let's take the A double harmonic (major) scale as an example:

A Bb C# D E F G# (A)

We can easily derive its set of allowed chords from here:

  • I: The A chord (A C# E)
  • bII: The Bb chord (Bb D F)
  • iii: The C#m chord (C# E G#)
  • iv: The Dm chord (D F A)
  • Vb5: The E b5 chord (E G# Bb)
  • VIx: The F+ chord (F A C#)
  • vii°b3: The G#° b3 chord (G# Bb D)

As you can tell, the chords for V, VI, and vii are particularly ugly, and I don't recommend using them in full. Using the E and G# to represent V is fine, though.

Part of the attraction of the double harmonic scale for me is the ability to spam the bII chord. I like chord progressions such as I-bII-I here.

Because the double harmonic scale is one note away from the Phrygian Dominant scale (the fifth mode of the harmonic minor scale), I like improvising on the double harmonic scale as if I'm "soloing on the dominant".

As for the double harmonic minor scale, https://en.m.wikipedia.org/wiki/Hungarian_minor_scale says it's the fourth mode of the double harmonic major scale, so take all the bII-like chord symbols and move them down 3 scale degrees (so iv in double harmonic major becomes i in double harmonic minor). Note that the C#m-like chord symbols do not change when this is done--just which bII-like chord symbols they're assigned to.

  • The chord on V is, at least, fairly common in jazz. It is the best dominant chord for when the I-bII relationship exists in the scale because it's necessary in that case to avoid using the natural second. I-3-b5-b7 is also a diminished shape, meaning that for dominant chords with diminished extensions you can start the shape on any degree of the dim7 chord with the same root and end up with appropriate extensions (for G - GBDbF BbDEAb C#E#GB AC#EbG). In short, it's a very useful chord that shows up in a lot of places, especially in jazz. – Fugu Aug 6 '17 at 17:02

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