Making Exotic Scales with Familiar Arpeggios
Struck by a bout of insomnia, I decided to figure out all the 7-note scales that can be made by combining a pair of common triad or seventh arpeggios, one at the root and one somewhere else. Here are the results.
The idea is that when playing over a harmony we can superimpose another familiar sound to create "tension" notes; in jazz it goes back to Charlie Parker, but you can hear nineteenth century composers doing something similar too.
The approach is useful in practice for two reasons. First, we often find ourselves playing over these conventional harmonies, and when we do it's nice to have the notes of the chord available in the scale. Second, we know (or ought to know) our basic arpeggios very well, so these are easy to think of, find and play when improvising. Yet when combined they can produce some very exotic sounds, as this post demonstrates. This approach can also suggest ideas for chord substitutions, if you're into that.
The arpeggios I used were:
| Abbreviation | Spelling | Example with root "A" |
| Maj | 1, 3, 5 | A C# E |
| Min | 1, b3, 5 | A C E |
| Dim | 1, b3, b5 | A C Eb |
| Aug | 1, 3, #5 | A C# F |
| Maj7 | 1, 3, 5, 7 | A C# E G# |
| 7 | 1, 3, 5, b7 | A C# E G |
| mMaj7 | 1, b3, 5, 7 | A C E, G# |
| m7 | 1, b3, 5, b7 | A C E, G |
| m7b5 | 1, b3, b5, b7 | A C Eb, G |
| dim7 | 1, b3, b5, bb7 | A C Eb, Gb |
As an example, "7 + IIm7" means play the dominant seventh chord at the root and the minor seventh built on the second. In the key of C this would mean C7 and Dm7. In terms of notes this would give you C, E, G, Bb (the C7 arpeggio) plus D, F, A, C (the Dm7). Putting these in order gives C, D, E, F, G, A, Bb, which is C Mixolydian, a mode of the Major Scale.
With one exception I've listed the possibilities by modal group -- that is, under "Major Scale" are all the modes of the Major Scale. The spelling of the specific mode is given as well. All the modes can be found in the free ebook Arpeggio and Scale Resources along with analysis, guitar diagrams etc.
It would certainly be interesting to repeat this analysis for scales with different numbers of notes, and for other pitch structures. The below, though, is probably enough to be going on with. Those who want to explore these ideas further might find my free ebook Spectral Analysis of Scales helpful.
Fair warning: this is a long post with a lot of "data" in it. I've mostly put it together for my own reference, and I don't expect many people to find it exciting in itself. To use it, pick one idea and try to apply it musically.
Common Scales
There are lots of ways to make the commonest scales out of common arpeggios; this isn't really surprising, given that the two are closely related to one another.
Major Scale
| 7 + IIm7: 1, 2, 3, 4, 5, 6, b7, |
| 7 + bVIIMaj7: 1, 2, 3, 4, 5, 6, b7, |
| 7 + IIMin: 1, 2, 3, 4, 5, 6, b7, |
| m7 + bVII7: 1, 2, b3, 4, 5, b6, b7, |
| m7 + IIm7: 1, 2, b3, 4, 5, 6, b7, |
| m7 + bVIIm7: 1, b2, b3, 4, 5, b6, b7, |
| m7 + IIDim: 1, 2, b3, 4, 5, b6, b7, |
| m7 + bIIMaj7: 1, b2, b3, 4, 5, b6, b7, |
| m7 + bVIIMaj7: 1, 2, b3, 4, 5, 6, b7, |
| m7 + bIIMaj: 1, b2, b3, 4, 5, b6, b7, |
| m7 + IIMin: 1, 2, b3, 4, 5, 6, b7, |
| m7 + IIm7b5: 1, 2, b3, 4, 5, b6, b7, |
| Dim + bVIIm7: 1, b2, b3, 4, b5, b6, b7, |
| Maj7 + II7: 1, 2, 3, b5, 5, 6, 7, |
| Maj7 + IIm7: 1, 2, 3, 4, 5, 6, 7, |
| Maj7 + VIIm7: 1, 2, 3, b5, 5, 6, 7, |
| Maj7 + IIMaj: 1, 2, 3, b5, 5, 6, 7, |
| Maj7 + IIMin: 1, 2, 3, 4, 5, 6, 7, |
| Maj7 + VIIm7b5: 1, 2, 3, 4, 5, 6, 7, |
| Maj + VIIm7: 1, 2, 3, b5, 5, 6, 7, |
| Maj + bVIIMaj7: 1, 2, 3, 4, 5, 6, b7, |
| Maj + VIIm7b5: 1, 2, 3, 4, 5, 6, 7, |
| Min + bVII7: 1, 2, b3, 4, 5, b6, b7, |
| Min + bVIIm7: 1, b2, b3, 4, 5, b6, b7, |
| Min + bVIIMaj7: 1, 2, b3, 4, 5, 6, b7, |
| m7b5 + bVIIm7: 1, b2, b3, 4, b5, b6, b7, |
| m7b5 + bIIMaj7: 1, b2, b3, 4, b5, b6, b7, |
| m7b5 + bIIMaj: 1, b2, b3, 4, b5, b6, b7, |
Harmonic Minor
| mMaj7 + IIdim7: 1, 2, b3, 4, 5, b6, 7, |
| mMaj7 + IVdim7: 1, 2, b3, 4, 5, b6, 7, |
| mMaj7 + bVIdim7: 1, 2, b3, 4, 5, b6, 7, |
| mMaj7 + VIIdim7: 1, 2, b3, 4, 5, b6, 7, |
| mMaj7 + IIDim: 1, 2, b3, 4, 5, b6, 7, |
| mMaj7 + IIm7b5: 1, 2, b3, 4, 5, b6, 7, |
| mMaj7 + bVm7b5: 1, b3, 3, b5, 5, 6, 7, |
| dim7 + bIImMaj7: 1, b2, b3, 3, b5, b6, 6, |
| dim7 + IIImMaj7: 1, b3, 3, b5, 5, 6, 7, |
| dim7 + VmMaj7: 1, 2, b3, b5, 5, 6, b7, |
| dim7 + bVIImMaj7: 1, b2, b3, 4, b5, 6, b7, |
| dim7 + bIIIMaj7: 1, 2, b3, b5, 5, 6, b7, |
| dim7 + bVMaj7: 1, b2, b3, 4, b5, 6, b7, |
| dim7 + VIMaj7: 1, b2, b3, 3, b5, b6, 6, |
| dim7 + bIIMin: 1, b2, b3, 3, b5, b6, 6, |
| dim7 + IIIMin: 1, b3, 3, b5, 5, 6, 7, |
| dim7 + VMin: 1, 2, b3, b5, 5, 6, b7, |
| dim7 + bVIIMin: 1, b2, b3, 4, b5, 6, b7, |
| 7 + bVIIm7: 1, b2, 3, 4, 5, b6, b7, |
| 7 + bIIMaj7: 1, b2, 3, 4, 5, b6, b7, |
| 7 + bIIMaj: 1, b2, 3, 4, 5, b6, b7, |
| m7 + II7: 1, 2, b3, b5, 5, 6, b7, |
| m7 + IIMaj: 1, 2, b3, b5, 5, 6, b7, |
| Dim + bVIImMaj7: 1, b2, b3, 4, b5, 6, b7, |
| Dim + VIMaj7: 1, b2, b3, 3, b5, b6, 6, |
| Maj7 + bIIIdim7: 1, b3, 3, b5, 5, 6, 7, |
| Maj7 + bVdim7: 1, b3, 3, b5, 5, 6, 7, |
| Maj7 + VIdim7: 1, b3, 3, b5, 5, 6, 7, |
| Maj7 + VII7: 1, b3, 3, b5, 5, 6, 7, |
| Maj7 + bIIIDim: 1, b3, 3, b5, 5, 6, 7, |
| Maj + VII7: 1, b3, 3, b5, 5, 6, 7, |
| Maj + bVIIm7: 1, b2, 3, 4, 5, b6, b7, |
| Aug + bIIIm7b5: 1, b2, b3, 3, b5, b6, 6, |
| Aug + Vm7b5: 1, b2, 3, 4, 5, b6, b7, |
| Aug + VIIm7b5: 1, 2, 3, 4, b6, 6, 7, |
| Min + IIdim7: 1, 2, b3, 4, 5, b6, 7, |
| Min + IVdim7: 1, 2, b3, 4, 5, b6, 7, |
| Min + bVIdim7: 1, 2, b3, 4, 5, b6, 7, |
| Min + VIIdim7: 1, 2, b3, 4, 5, b6, 7, |
| m7b5 + bVmMaj7: 1, b2, b3, 4, b5, 6, b7, |
| m7b5 + bVIImMaj7: 1, b2, b3, 4, b5, 6, b7, |
| m7b5 + bIIAug: 1, b2, b3, 4, b5, 6, b7, |
| m7b5 + IVAug: 1, b2, b3, 4, b5, 6, b7, |
| m7b5 + VIAug: 1, b2, b3, 4, b5, 6, b7, |
Melodic Minor
| mMaj7 + IIm7: 1, 2, b3, 4, 5, 6, 7, |
| mMaj7 + IIMin: 1, 2, b3, 4, 5, 6, 7, |
| mMaj7 + VIIm7b5: 1, 2, b3, 4, 5, 6, 7, |
| 7 + II7: 1, 2, 3, b5, 5, 6, b7, |
| 7 + bVII7: 1, 2, 3, 4, 5, b6, b7, |
| 7 + IIDim: 1, 2, 3, 4, 5, b6, b7, |
| 7 + IIMaj: 1, 2, 3, b5, 5, 6, b7, |
| 7 + IIm7b5: 1, 2, 3, 4, 5, b6, b7, |
| m7 + bVIImMaj7: 1, b2, b3, 4, 5, 6, b7, |
| m7 + bIIAug: 1, b2, b3, 4, 5, 6, b7, |
| m7 + IVAug: 1, b2, b3, 4, 5, 6, b7, |
| m7 + VIAug: 1, b2, b3, 4, 5, 6, b7, |
| Dim + bVII7: 1, 2, b3, 4, b5, b6, b7, |
| Dim + bVIIm7b5: 1, b2, b3, 3, b5, b6, b7, |
| Maj + bVII7: 1, 2, 3, 4, 5, b6, b7, |
| Aug + bIIIm7: 1, b2, b3, 3, b5, b6, b7, |
| Aug + Vm7: 1, 2, 3, 4, 5, b6, b7, |
| Aug + VIIm7: 1, 2, 3, b5, b6, 6, 7, |
| Min + bVIImMaj7: 1, b2, b3, 4, 5, 6, b7, |
| Min + VIIm7b5: 1, 2, b3, 4, 5, 6, 7, |
| m7b5 + bIImMaj7: 1, b2, b3, 3, b5, b6, b7, |
| m7b5 + bVII7: 1, 2, b3, 4, b5, b6, b7, |
| m7b5 + IIDim: 1, 2, b3, 4, b5, b6, b7, |
| m7b5 + bIIMin: 1, b2, b3, 3, b5, b6, b7, |
| m7b5 + IIm7b5: 1, 2, b3, 4, b5, b6, b7, |
| m7b5 + bVIIm7b5: 1, b2, b3, 3, b5, b6, b7, |
Moderately Exotic Scales
This section contains four modal groups that, while uncommon, are far from unheard-of. Harmonic Major is often referred to as the "missing" fourth member of the common scale family; this can be overstated, but look how similar this table is to the three above, and how much longer it is than any of the others.
Harmonic Major
| mMaj7 + II7: 1, 2, b3, b5, 5, 6, 7, |
| mMaj7 + VIIm7: 1, 2, b3, b5, 5, 6, 7, |
| mMaj7 + IIMaj: 1, 2, b3, b5, 5, 6, 7, |
| dim7 + bIIMaj7: 1, b2, b3, 4, b5, b6, 6, |
| dim7 + IIIMaj7: 1, b3, 3, b5, b6, 6, 7, |
| dim7 + VMaj7: 1, 2, b3, b5, 5, 6, 7, |
| dim7 + bVIIMaj7: 1, 2, b3, 4, b5, 6, b7, |
| dim7 + bIIMaj: 1, b2, b3, 4, b5, b6, 6, |
| dim7 + IIIMaj: 1, b3, 3, b5, b6, 6, 7, |
| dim7 + VMaj: 1, 2, b3, b5, 5, 6, 7, |
| dim7 + bVIIMaj: 1, 2, b3, 4, b5, 6, b7, |
| 7 + bVIImMaj7: 1, b2, 3, 4, 5, 6, b7, |
| 7 + bIIAug: 1, b2, 3, 4, 5, 6, b7, |
| 7 + IVAug: 1, b2, 3, 4, 5, 6, b7, |
| 7 + VIAug: 1, b2, 3, 4, 5, 6, b7, |
| m7 + bIImMaj7: 1, b2, b3, 3, 5, b6, b7, |
| m7 + bIIMin: 1, b2, b3, 3, 5, b6, b7, |
| m7 + bVIIm7b5: 1, b2, b3, 3, 5, b6, b7, |
| Dim + bVIIMaj7: 1, 2, b3, 4, b5, 6, b7, |
| Maj7 + IIdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj7 + IVdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj7 + bVIdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj7 + VIIdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj7 + IIDim: 1, 2, 3, 4, 5, b6, 7, |
| Maj7 + IIm7b5: 1, 2, 3, 4, 5, b6, 7, |
| Maj + bVIImMaj7: 1, b2, 3, 4, 5, 6, b7, |
| Maj + IIdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj + IVdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj + bVIdim7: 1, 2, 3, 4, 5, b6, 7, |
| Maj + VIIdim7: 1, 2, 3, 4, 5, b6, 7, |
| Aug + bIII7: 1, b2, b3, 3, 5, b6, b7, |
| Aug + V7: 1, 2, 3, 4, 5, b6, 7, |
| Aug + VII7: 1, b3, 3, b5, b6, 6, 7, |
| Min + VIIm7: 1, 2, b3, b5, 5, 6, 7, |
| Min + bVIIm7b5: 1, b2, b3, 3, 5, b6, b7, |
| m7b5 + IIm7: 1, 2, b3, 4, b5, 6, b7, |
| m7b5 + bVIIMaj7: 1, 2, b3, 4, b5, 6, b7, |
| m7b5 + IIMin: 1, 2, b3, 4, b5, 6, b7, |
Neapolitan
| mMaj7 + bIIAug: 1, b2, b3, 4, 5, 6, 7, |
| mMaj7 + IVAug: 1, b2, b3, 4, 5, 6, 7, |
| mMaj7 + VIAug: 1, b2, b3, 4, 5, 6, 7, |
| Aug + bIIImMaj7: 1, 2, b3, 3, b5, b6, b7, |
| Aug + VmMaj7: 1, 2, 3, b5, 5, b6, b7, |
| Aug + VIImMaj7: 1, 2, 3, b5, b6, b7, 7, |
Double Harmonic
| mMaj7 + bVIm7b5: 1, 2, b3, b5, 5, b6, 7, |
| 7 + VIIMaj7: 1, b3, 3, b5, 5, b7, 7, |
| 7 + VIIMaj: 1, b3, 3, b5, 5, b7, 7, |
| Maj7 + bII7: 1, b2, 3, 4, 5, b6, 7, |
| Maj7 + bIIMaj7: 1, b2, 3, 4, 5, b6, 7, |
| Maj7 + VIIMaj7: 1, b3, 3, b5, 5, b7, 7, |
| Maj7 + bIIMaj: 1, b2, 3, 4, 5, b6, 7, |
| Maj7 + bIIIMin: 1, b3, 3, b5, 5, b7, 7, |
| Maj + bII7: 1, b2, 3, 4, 5, b6, 7, |
| Maj + VIIMaj7: 1, b3, 3, b5, 5, b7, 7, |
| Min + VIMaj7: 1, b2, b3, 3, 5, b6, 6, |
| Min + bVIm7b5: 1, 2, b3, b5, 5, b6, 7, |
| m7b5 + IIImMaj7: 1, b3, 3, b5, 5, b7, 7, |
| m7b5 + IIIMin: 1, b3, 3, b5, 5, b7, 7, |
Nasikabhushani (sometimes called Hungarian Major)
| dim7 + IIIDim: 1, b3, 3, b5, 5, 6, b7, |
| 7 + bIIIdim7: 1, b3, 3, b5, 5, 6, b7, |
| 7 + bVdim7: 1, b3, 3, b5, 5, 6, b7, |
| 7 + VIdim7: 1, b3, 3, b5, 5, 6, b7, |
| 7 + bIIIDim: 1, b3, 3, b5, 5, 6, b7, |
| m7 + bVm7b5: 1, b3, 3, b5, 5, 6, b7, |
| m7b5 + VIm7: 1, b3, 3, b5, 5, 6, b7, |
Very Exotic Scales
The last list in this section contains a mixture of scales that contain more than two consecutive semitones and so aren't in my book. There may, of course, still be usable sounds to be had from them.
The first two are remarkable for being very rarely-heard scales that offer quite a lot of possibilities for arpeggio superimposition, which suggests on paper that they would be worth further attention.
Neetimati
| mMaj7 + bIIImMaj7: 1, 2, b3, b5, 5, b7, 7, |
| mMaj7 + VmMaj7: 1, 2, b3, b5, 5, b7, 7, |
| mMaj7 + VIImMaj7: 1, 2, b3, b5, 5, b7, 7, |
| mMaj7 + IIAug: 1, 2, b3, b5, 5, b7, 7, |
| mMaj7 + bVAug: 1, 2, b3, b5, 5, b7, 7, |
| mMaj7 + bVIIAug: 1, 2, b3, b5, 5, b7, 7, |
| m7 + VIImMaj7: 1, 2, b3, b5, 5, b7, 7, |
| m7 + VMaj7: 1, 2, b3, b5, 5, b7, 7, |
| m7 + VIIMin: 1, 2, b3, b5, 5, b7, 7, |
| Min + VIImMaj7: 1, 2, b3, b5, 5, b7, 7, |
| m7b5 + VMaj7: 1, 2, b3, b5, 5, b7, 7, |
| m7b5 + VMaj: 1, 2, b3, b5, 5, b7, 7, |
Chitrambari
| 7 + VIImMaj7: 1, 2, 3, b5, 5, b7, 7, |
| 7 + VMaj7: 1, 2, 3, b5, 5, b7, 7, |
| 7 + VIIMin: 1, 2, 3, b5, 5, b7, 7, |
| Maj7 + VmMaj7: 1, 2, 3, b5, 5, b7, 7, |
| Maj7 + VIImMaj7: 1, 2, 3, b5, 5, b7, 7, |
| Maj7 + IIAug: 1, 2, 3, b5, 5, b7, 7, |
| Maj7 + bVAug: 1, 2, 3, b5, 5, b7, 7, |
| Maj7 + bVIIAug: 1, 2, 3, b5, 5, b7, 7, |
| Maj + VIImMaj7: 1, 2, 3, b5, 5, b7, 7, |
b 7maj + natural 7maj
| m7b5 + VIIDim: 1, 2, b3, 4, b5, b7, 7, |
Vishwambari
| Maj7 + bV7: 1, b2, 3, b5, 5, b7, 7, |
| Maj7 + bVMaj: 1, b2, 3, b5, 5, b7, 7, |
Mixolydian #2 ##4 #5
| m7 + VImMaj7: 1, b3, 3, 5, b6, 6, b7, |
Double Sharp #2
| m7 + VII7: 1, b3, b5, 5, 6, b7, 7, |
Locrian bb6 bb7
| Min + bVmMaj7: 1, b2, b3, 4, b5, 5, 6, |
Susdim Dominant
| m7 + bVIm7: 1, b3, b5, 5, b6, b7, 7, |
| m7b5 + bVImMaj7: 1, b3, b5, 5, b6, b7, 7, |
Neetimati #5
| m7b5 + bVIDim: 1, 2, b3, b5, b6, b7, 7, |
| m7b5 + bVIm7b5: 1, 2, b3, b5, b6, b7, 7, |
Locrian Blues
| m7 + bVMaj7: 1, b2, b3, 4, b5, 5, b7, |
| Dim + Vm7b5: 1, b2, b3, 4, b5, 5, b7, |
| Min + bVMaj7: 1, b2, b3, 4, b5, 5, b7, |
| m7b5 + Vm7b5: 1, b2, b3, 4, b5, 5, b7, |
1maj + 7maj + b2
| Dim + bIIm7b5: 1, b2, b3, 3, b5, 5, 7, |
Phrygian b5
| Aug + bVMaj7: 1, b2, 3, 4, b5, b6, b7, |
Phrygian Major b5 bb6
| 7 + bVMaj7: 1, b2, 3, 4, b5, 5, b7, |
| Maj + bVMaj7: 1, b2, 3, 4, b5, 5, b7, |
Dorian b5 bb6
| Dim + Vm7: 1, 2, b3, 4, b5, 5, b7, |
| m7b5 + Vm7: 1, 2, b3, 4, b5, 5, b7, |
Super Locrian natural 6
| dim7 + bV7: 1, b2, b3, 3, b5, 6, b7, |
| dim7 + bVIIDim: 1, b2, b3, 3, b5, 6, b7, |
| m7b5 + bVm7: 1, b2, b3, 3, b5, 6, b7, |
| m7b5 + VIMaj: 1, b2, b3, 3, b5, 6, b7, |
Gayakapriya
| 7 + bVImMaj7: 1, b3, 3, 5, b6, b7, 7, |
| 7 + IIIMaj7: 1, b3, 3, 5, b6, b7, 7, |
| 7 + bVIMin: 1, b3, 3, 5, b6, b7, 7, |
| m7 + IIIMaj7: 1, b3, 3, 5, b6, b7, 7, |
| m7 + IIIMaj: 1, b3, 3, 5, b6, b7, 7, |
b 2min + 2min
| Aug + IImMaj7: 1, b2, 2, 3, 4, b6, 6, |
Super Locrian natural 7
| Dim + bIIm7: 1, b2, b3, 3, b5, b6, 7, |
Suvarnangi
| mMaj7 + bVMin: 1, b2, b3, b5, 5, 6, 7, |
| mMaj7 + bIIIm7b5: 1, b2, b3, b5, 5, 6, 7, |
Semidominant Augmented
| 7 + III7: 1, 2, 3, 5, b6, b7, 7, |
| 7 + bVIDim: 1, 2, 3, 5, b6, b7, 7, |
Locrian Double-Flat Major
| Maj + IIMaj7: 1, b2, 2, 3, b5, 5, 6, |
Harmonic Minor b5
| Dim + IIdim7: 1, 2, b3, 4, b5, b6, 7, |
| Dim + IVdim7: 1, 2, b3, 4, b5, b6, 7, |
| Dim + bVIdim7: 1, 2, b3, 4, b5, b6, 7, |
| Dim + VIIdim7: 1, 2, b3, 4, b5, b6, 7, |
Natakapriya b4
| m7 + VI7: 1, b2, b3, 3, 5, 6, b7, |
| m7 + VIMaj: 1, b2, b3, 3, 5, 6, b7, |
Mixolydian #2 b5
| m7b5 + IVMaj7: 1, b3, 3, 4, b5, 6, b7, |
Chakravakam #5
| Aug + bVIImMaj7: 1, b2, 3, 4, b6, 6, b7, |
Gamanashrama
| Maj7 + bVm7: 1, b2, 3, b5, 5, 6, 7, |
| Maj7 + bVMin: 1, b2, 3, b5, 5, 6, 7, |
Superaugmented ##4
| m7 + IVDim: 1, b3, 4, 5, b6, b7, 7, |
| m7 + IVm7b5: 1, b3, 4, 5, b6, b7, 7, |
Rupavati
| mMaj7 + bVIIMin: 1, b2, b3, 4, 5, b7, 7, |
| mMaj7 + Vm7b5: 1, b2, b3, 4, 5, b7, 7, |
Superaugmented natural3
| Aug + VIIMaj7: 1, b3, 3, b5, b6, b7, 7, |
| m7b5 + IIIMaj7: 1, b3, 3, b5, b6, b7, 7, |
| m7b5 + IIIMaj: 1, b3, 3, b5, b6, b7, 7, |
Superdiminished Major
| Aug + IIMaj7: 1, b2, 2, 3, b5, b6, 6, |
5maj + b 6maj
| m7 + bVIDim: 1, 2, b3, 5, b6, b7, 7, |
Superaugmented ##2 ##4
| 7 + IVDim: 1, 3, 4, 5, b6, b7, 7, |
1maj + 7maj
| Dim + IIIm7: 1, 2, b3, 3, b5, 5, 7, |
Aeolian b 4
| Aug + bIIIMaj7: 1, 2, b3, 3, 5, b6, b7, |
Latangi
| Maj7 + bVIm7b5: 1, 2, 3, b5, 5, b6, 7, |
| Maj + bVIm7b5: 1, 2, 3, b5, 5, b6, 7, |
| Aug + VMaj7: 1, 2, 3, b5, 5, b6, 7, |
Susdim Major
| dim7 + IVDim: 1, b3, 4, b5, b6, 6, 7, |
| dim7 + IVm7b5: 1, b3, 4, b5, b6, 6, 7, |
Dhenuka
| mMaj7 + bII7: 1, b2, b3, 4, 5, b6, 7, |
| mMaj7 + bIIMaj7: 1, b2, b3, 4, 5, b6, 7, |
| mMaj7 + bIIMaj: 1, b2, b3, 4, 5, b6, 7, |
| Min + bII7: 1, b2, b3, 4, 5, b6, 7, |
Superaugmented
| m7b5 + IVDim: 1, b3, 4, b5, b6, b7, 7, |
| m7b5 + IVm7b5: 1, b3, 4, b5, b6, b7, 7, |
Locrian natural 7
| Dim + bII7: 1, b2, b3, 4, b5, b6, 7, |
Jyoti Swarupini
| 7 + bVI7: 1, b3, 3, b5, 5, b6, b7, |
Hatakambari
| Maj7 + bVIIMin: 1, b2, 3, 4, 5, b7, 7, |
| Maj7 + Vm7b5: 1, b2, 3, 4, 5, b7, 7, |
Ionian b2 (Suryakantam)
| Maj7 + bIIAug: 1, b2, 3, 4, 5, 6, 7, |
| Maj7 + IVAug: 1, b2, 3, 4, 5, 6, 7, |
| Maj7 + VIAug: 1, b2, 3, 4, 5, 6, 7, |
Varunapriya b4
| mMaj7 + IIIm7b5: 1, 2, b3, 3, 5, b7, 7, |
| m7 + IIIm7: 1, 2, b3, 3, 5, b7, 7, |
| Maj7 + bIIIMaj7: 1, 2, b3, 3, 5, b7, 7, |
Ionian #6 (Naganandini)
| 7 + V7: 1, 2, 3, 4, 5, b7, 7, |
| 7 + VIIDim: 1, 2, 3, 4, 5, b7, 7, |
| Maj7 + Vm7: 1, 2, 3, 4, 5, b7, 7, |
| Maj7 + bVIIMaj: 1, 2, 3, 4, 5, b7, 7, |
Divyamani
| mMaj7 + bIIIm7: 1, b2, b3, b5, 5, b7, 7, |
| mMaj7 + bVMaj: 1, b2, b3, b5, 5, b7, 7, |
Gayakapriya b5
| Aug + bVmMaj7: 1, b2, 3, 4, b5, b6, 6, |
Phrygian Double-Flat
| Maj + IImMaj7: 1, b2, 2, 3, 4, 5, 6, |
Ultra Locrian bb7
| dim7 + VI7: 1, b2, b3, 3, b5, 5, 6, |
| dim7 + bIIDim: 1, b2, b3, 3, b5, 5, 6, |
| Dim + VI7: 1, b2, b3, 3, b5, 5, 6, |
| Maj + bIIIm7b5: 1, b2, b3, 3, b5, 5, 6, |
| Min + bVm7: 1, b2, b3, 3, b5, 5, 6, |
Jhankaradhvani b5
| dim7 + IIDim: 1, 2, b3, 4, b5, b6, 6, |
| dim7 + IIm7b5: 1, 2, b3, 4, b5, b6, 6, |
Dhatuvardani
| Maj7 + bVI7: 1, b3, 3, b5, 5, b6, 7, |
| Maj7 + bVIm7: 1, b3, 3, b5, 5, b6, 7, |
| Maj + bVIm7: 1, b3, 3, b5, 5, b6, 7, |
Melodic Minor b4
| mMaj7 + VI7: 1, b2, b3, 3, 5, 6, 7, |
| mMaj7 + VIMaj: 1, b2, b3, 3, 5, 6, 7, |
Melodic Minor b5
| dim7 + VIIDim: 1, 2, b3, 4, b5, 6, 7, |
| dim7 + VIIm7b5: 1, 2, b3, 4, b5, 6, 7, |
| Dim + VIIm7b5: 1, 2, b3, 4, b5, 6, 7, |
Augmented #2 ##4
| mMaj7 + VImMaj7: 1, b3, 3, 5, b6, 6, 7, |
Ragavardhini
| 7 + IVm7: 1, b3, 3, 4, 5, b6, b7, |
| m7 + IVmMaj7: 1, b3, 3, 4, 5, b6, b7, |
Augmented b2 ##4 #6
| 7 + bIIm7: 1, b2, 3, 5, b6, b7, 7, |
| Maj7 + bVIIm7b5: 1, b2, 3, 5, b6, b7, 7, |
Phrygian bb3 bb4 natural6
| m7b5 + IIMaj7: 1, b2, 2, b3, b5, 6, b7, |
Ramapriya
| 7 + bVm7: 1, b2, 3, b5, 5, 6, b7, |
| 7 + bVMin: 1, b2, 3, b5, 5, 6, b7, |
Dhenuka b4
| mMaj7 + bIImMaj7: 1, b2, b3, 3, 5, b6, 7, |
| mMaj7 + bIIm7: 1, b2, b3, 3, 5, b6, 7, |
| mMaj7 + bIIMin: 1, b2, b3, 3, 5, b6, 7, |
| Min + bIIm7: 1, b2, b3, 3, 5, b6, 7, |
Shadvidamargini
| dim7 + bIII7: 1, b2, b3, b5, 5, 6, b7, |
| dim7 + VDim: 1, b2, b3, b5, 5, 6, b7, |
| m7 + bVMin: 1, b2, b3, b5, 5, 6, b7, |
| m7 + bIIIm7b5: 1, b2, b3, b5, 5, 6, b7, |
Semidiminished
| Dim + III7: 1, 2, b3, 3, b5, b6, 7, |
Double Flat b5
| Min + IIMaj7: 1, b2, 2, b3, b5, 5, 6, |
Lydian Dominant #2#5
| m7b5 + VImMaj7: 1, b3, 3, b5, b6, 6, b7, |
Mixolydian #5
| Aug + bVIIMaj7: 1, 2, 3, 4, b6, 6, b7, |
Phrygian Semiaugmented
| Maj7 + VIMaj7: 1, b2, 3, 5, b6, 6, 7, |
Ionian #2 (Sulini)
| mMaj7 + IVMaj7: 1, b3, 3, 4, 5, 6, 7, |
| Maj7 + IV7: 1, b3, 3, 4, 5, 6, 7, |
Harmonic Minor #6 (Varunapriya)
| mMaj7 + Vm7: 1, 2, b3, 4, 5, b7, 7, |
| mMaj7 + bVIIMaj: 1, 2, b3, 4, 5, b7, 7, |
| m7 + V7: 1, 2, b3, 4, 5, b7, 7, |
| m7 + VIIDim: 1, 2, b3, 4, 5, b7, 7, |
Vagadheeswari
| 7 + IV7: 1, b3, 3, 4, 5, 6, b7, |
| m7 + IVMaj7: 1, b3, 3, 4, 5, 6, b7, |
Gangeyabhushani
| mMaj7 + IVmMaj7: 1, b3, 3, 4, 5, b6, 7, |
| Maj7 + IVm7: 1, b3, 3, 4, 5, b6, 7, |
| Maj7 + IVm7b5: 1, b3, 3, 4, 5, b6, 7, |
| Maj + IVm7b5: 1, b3, 3, 4, 5, b6, 7, |
Harmonic Minor b5 bb6
| Dim + V7: 1, 2, b3, 4, b5, 5, 7, |
Mixolydian #2 b5 b6
| m7b5 + IVmMaj7: 1, b3, 3, 4, b5, b6, b7, |
Locrian natural3 bb6 bb7
| Maj + bVmMaj7: 1, b2, 3, 4, b5, 5, 6, |
Harmonic Minor b 4
| mMaj7 + III7: 1, 2, b3, 3, 5, b6, 7, |
| Min + III7: 1, 2, b3, 3, 5, b6, 7, |
Ultra Locrian
| Min + IImMaj7: 1, b2, 2, b3, 4, 5, 6, |
Lydian b5
| dim7 + bVIDim: 1, 2, b3, b5, b6, 6, 7, |
| dim7 + bVIm7b5: 1, 2, b3, b5, b6, 6, 7, |
Super Locrian bb6
| 7 + bIIIm7: 1, b2, b3, 3, b5, 5, b7, |
| m7 + bV7: 1, b2, b3, 3, b5, 5, b7, |
| Dim + bIIdim7: 1, b2, b3, 3, b5, 5, b7, |
| Dim + IIIdim7: 1, b2, b3, 3, b5, 5, b7, |
| Dim + Vdim7: 1, b2, b3, 3, b5, 5, b7, |
| Dim + bVIIdim7: 1, b2, b3, 3, b5, 5, b7, |
| Maj + bIIIm7: 1, b2, b3, 3, b5, 5, b7, |
| Min + bV7: 1, b2, b3, 3, b5, 5, b7, |
| m7b5 + bIIdim7: 1, b2, b3, 3, b5, 5, b7, |
| m7b5 + IIIdim7: 1, b2, b3, 3, b5, 5, b7, |
| m7b5 + Vdim7: 1, b2, b3, 3, b5, 5, b7, |
| m7b5 + bVIIdim7: 1, b2, b3, 3, b5, 5, b7, |
| m7b5 + bIIDim: 1, b2, b3, 3, b5, 5, b7, |
Super Locrian natural2 bb6
| 7 + bIIImMaj7: 1, 2, b3, 3, b5, 5, b7, |
| Dim + IIIm7b5: 1, 2, b3, 3, b5, 5, b7, |
| Maj + bIIImMaj7: 1, 2, b3, 3, b5, 5, b7, |
| m7b5 + IIIm7b5: 1, 2, b3, 3, b5, 5, b7, |
Those Belonging to the Emperor
| mMaj7 + bIIdim7: 1, b2, b3, 3, 5, b7, 7, |
| mMaj7 + IIIdim7: 1, b2, b3, 3, 5, b7, 7, |
| mMaj7 + Vdim7: 1, b2, b3, 3, 5, b7, 7, |
| mMaj7 + bVIIdim7: 1, b2, b3, 3, 5, b7, 7, |
| mMaj7 + bVIIDim: 1, b2, b3, 3, 5, b7, 7, |
| dim7 + IImMaj7: 1, b2, 2, b3, 4, b5, 6, |
| dim7 + IVmMaj7: 1, b3, 3, 4, b5, b6, 6, |
| dim7 + bVImMaj7: 1, b3, b5, 5, b6, 6, 7, |
| dim7 + VIImMaj7: 1, 2, b3, b5, 6, b7, 7, |
| 7 + VIMaj7: 1, b2, 3, 5, b6, 6, b7, |
| m7 + bIIm7b5: 1, b2, b3, 3, 5, b7, 7, |
| Dim + IImMaj7: 1, b2, 2, b3, 4, b5, 6, |
| Maj7 + bIII7: 1, b2, b3, 3, 5, b7, 7, |
| m7b5 + VIIm7: 1, 2, b3, b5, 6, b7, 7, |
Octatonics
As a bonus, and because it's still to early to get up, I ran the same analysis for eight-note scales. Of course to get eight notes we must have a pair of seventh arpeggios that share no common notes. I expected to find hardly any of these and was pleasantly surprised by the results. I hardly ever use octatonics (except our old friends the Half-Whole and Whole-Half) so there's some stuff here to look into.
Many of the names of these scales in my book are already based on arpeggios they contain, but in some cases this analysis has pointed to simpler versions than I'd noticed by just looking at them really hard.
Double Chromatic IV
| Maj7 + bVMaj7: 1, b2, 3, 4, b5, 5, b7, 7, |
Half-Whole
| dim7 + bIIdim7: 1, b2, b3, 3, b5, 5, 6, b7, |
| dim7 + IIIdim7: 1, b2, b3, 3, b5, 5, 6, b7, |
| dim7 + Vdim7: 1, b2, b3, 3, b5, 5, 6, b7, |
| dim7 + bVIIdim7: 1, b2, b3, 3, b5, 5, 6, b7, |
| 7 + bIIIm7b5: 1, b2, b3, 3, b5, 5, 6, b7, |
| m7 + bVm7: 1, b2, b3, 3, b5, 5, 6, b7, |
| m7b5 + VI7: 1, b2, b3, 3, b5, 5, 6, b7, |
Minor Pentatonic + 3maj
| 7 + IVm7b5: 1, b3, 3, 4, 5, b6, b7, 7, |
4m7b5 + b5min
| dim7 + bII7: 1, b2, b3, 4, b5, b6, 6, 7, |
1dim + 3dom
| dim7 + III7: 1, 2, b3, 3, b5, b6, 6, 7, |
Sarasangi Add b2
| mMaj7 + bV7: 1, b2, b3, 3, b5, 5, b7, 7, |
| 7 + bVmMaj7: 1, b2, 3, 4, b5, 5, 6, b7, |
| m7 + VIMaj7: 1, b2, b3, 3, 5, b6, 6, b7, |
| Maj7 + bIIIm7: 1, b2, b3, 3, b5, 5, b7, 7, |
| m7b5 + bIIm7b5: 1, b2, b3, 3, b5, 5, b7, 7, |
| m7b5 + VIIm7b5: 1, 2, b3, 4, b5, 6, b7, 7, |
1m7b5 + 3dom
| m7b5 + III7: 1, 2, b3, 3, b5, b6, b7, 7, |
1dom + #5maj + 7maj
| 7 + bVIm7: 1, b3, 3, b5, 5, b6, b7, 7, |
1maj + 2aug + 7maj
| Maj7 + bIIImMaj7: 1, 2, b3, 3, b5, 5, b7, 7, |
| m7b5 + IIIm7: 1, 2, b3, 3, b5, 5, b7, 7, |
1min + b 7maj + 7maj
| m7b5 + V7: 1, 2, b3, 4, b5, 5, b7, 7, |
Harmonic Minor Add #4
| 7 + bII7: 1, b2, 3, 4, 5, b6, b7, 7, |
| 7 + VII7: 1, b3, 3, b5, 5, 6, b7, 7, |
| m7 + IIMaj7: 1, b2, 2, b3, b5, 5, 6, b7, |
| Maj7 + bVIIm7: 1, b2, 3, 4, 5, b6, b7, 7, |
Lydian Add #2
| dim7 + IIIm7: 1, 2, b3, 3, b5, 5, 6, 7, |
Ionian b5 Add b7
| mMaj7 + bVMaj7: 1, b2, b3, 4, b5, 5, b7, 7, |
| Maj7 + bVmMaj7: 1, b2, 3, 4, b5, 5, 6, 7, |
Major Add b7
| 7 + VIIm7b5: 1, 2, 3, 4, 5, 6, b7, 7, |
| Maj7 + IIMaj7: 1, b2, 2, 3, b5, 5, 6, 7, |
| Maj7 + bVIIMaj7: 1, 2, 3, 4, 5, 6, b7, 7, |
| m7b5 + bII7: 1, b2, b3, 4, b5, b6, b7, 7, |
Locrian Add natural 6
| dim7 + bVIIm7: 1, b2, b3, 4, b5, b6, 6, b7, |
1maj + 2maj + b3min
| dim7 + IIIm7b5: 1, 2, b3, 3, b5, 5, 6, b7, |
1dim + b 7maj + 7dim
| m7b5 + IIdim7: 1, 2, b3, 4, b5, b6, b7, 7, |
| m7b5 + IVdim7: 1, 2, b3, 4, b5, b6, b7, 7, |
| m7b5 + bVIdim7: 1, 2, b3, 4, b5, b6, b7, 7, |
| m7b5 + VIIdim7: 1, 2, b3, 4, b5, b6, b7, 7, |
1m7 + 7m6
| m7 + bVIm7b5: 1, 2, b3, b5, 5, b6, b7, 7, |
Major Add #2
| mMaj7 + bVIIm7: 1, b2, b3, 4, 5, b6, b7, 7, |
| 7 + VIIm7: 1, 2, 3, b5, 5, 6, b7, 7, |
| m7 + IImMaj7: 1, b2, 2, b3, 4, 5, 6, b7, |
| m7 + bII7: 1, b2, b3, 4, 5, b6, b7, 7, |
1min + b 2aug + b 3min
| dim7 + Vm7b5: 1, b2, b3, 4, b5, 5, 6, b7, |
| m7 + bVmMaj7: 1, b2, b3, 4, b5, 5, 6, b7, |
3m7b5 + 4dim
| 7 + IIdim7: 1, 2, 3, 4, 5, b6, b7, 7, |
| 7 + IVdim7: 1, 2, 3, 4, 5, b6, b7, 7, |
| 7 + bVIdim7: 1, 2, 3, 4, 5, b6, b7, 7, |
| 7 + VIIdim7: 1, 2, 3, 4, 5, b6, b7, 7, |
| Maj7 + bVII7: 1, 2, 3, 4, 5, b6, b7, 7, |
Dorian Add #4
| dim7 + Vm7: 1, 2, b3, 4, b5, 5, 6, b7, |
Common Minor Pentatonic + 7dom
| dim7 + V7: 1, 2, b3, 4, b5, 5, 6, 7, |
1min + b 2aug + 7maj
| mMaj7 + bVmMaj7: 1, b2, b3, 4, b5, 5, 6, 7, |
Sarasangi Add #2
| mMaj7 + bVIIm7b5: 1, b2, b3, 3, 5, b6, b7, 7, |
| m7 + bIIm7: 1, b2, b3, 3, 5, b6, b7, 7, |
| m7 + VIIm7: 1, 2, b3, b5, 5, 6, b7, 7, |
| m7b5 + IImMaj7: 1, b2, 2, b3, 4, b5, 6, b7, |
1dim + b 7^m7b5
| dim7 + bVIIm7b5: 1, b2, b3, 3, b5, b6, 6, b7, |
| m7b5 + VIMaj7: 1, b2, b3, 3, b5, b6, 6, b7, |
Aeolian Add natural 7
| mMaj7 + bVII7: 1, 2, b3, 4, 5, b6, b7, 7, |
| m7 + IIdim7: 1, 2, b3, 4, 5, b6, b7, 7, |
| m7 + IVdim7: 1, 2, b3, 4, 5, b6, b7, 7, |
| m7 + bVIdim7: 1, 2, b3, 4, 5, b6, b7, 7, |
| m7 + VIIdim7: 1, 2, b3, 4, 5, b6, b7, 7, |
b 3dim + b 7dom
| dim7 + bVII7: 1, 2, b3, 4, b5, b6, 6, b7, |
Whole-Half
| dim7 + IIdim7: 1, 2, b3, 4, b5, b6, 6, 7, |
| dim7 + IVdim7: 1, 2, b3, 4, b5, b6, 6, 7, |
| dim7 + bVIdim7: 1, 2, b3, 4, b5, b6, 6, 7, |
| dim7 + VIIdim7: 1, 2, b3, 4, b5, b6, 6, 7, |
1maj + b6maj + 6maj
| mMaj7 + VIMaj7: 1, b2, b3, 3, 5, b6, 6, 7, |
# 4m7 + 5min
| 7 + IIMaj7: 1, b2, 2, 3, b5, 5, 6, b7, |
1maj + 6maj + 7maj
| mMaj7 + bVm7: 1, b2, b3, 3, b5, 5, 6, 7, |
| dim7 + bIIm7b5: 1, b2, b3, 3, b5, 5, 6, 7, |
| Maj7 + bIIIm7b5: 1, b2, b3, 3, b5, 5, 6, 7, |
Major Add b2
| mMaj7 + bVIIMaj7: 1, 2, b3, 4, 5, 6, b7, 7, |
| m7 + VIIm7b5: 1, 2, b3, 4, 5, 6, b7, 7, |
| Maj7 + IImMaj7: 1, b2, 2, 3, 4, 5, 6, 7, |
| m7b5 + bIIm7: 1, b2, b3, 3, b5, b6, b7, 7, |
b 2m7 + b 5^{\circ}
| dim7 + bIIm7: 1, b2, b3, 3, b5, b6, 6, 7, |
Mixolydian Add b2
| 7 + IImMaj7: 1, b2, 2, 3, 4, 5, 6, b7, |
1maj + 5min + b 6min
| m7 + III7: 1, 2, b3, 3, 5, b6, b7, 7, |
1dom + 7^{m6}
| 7 + bVIm7b5: 1, 2, 3, b5, 5, b6, b7, 7, |
Those Belonging to the Emperor
| mMaj7 + IImMaj7: 1, b2, 2, b3, 4, 5, 6, 7, |
| mMaj7 + bVIImMaj7: 1, b2, b3, 4, 5, 6, b7, 7, |
| mMaj7 + IIMaj7: 1, b2, 2, b3, b5, 5, 6, 7, |
| Maj7 + bVIImMaj7: 1, b2, 3, 4, 5, 6, b7, 7, |
One Last One...
As a parting gift, here's an extraordinary hexatonic example -- the only symmetrical one that's not composed of augmented triads in a crushingly obvious way. We already know that this scale is remarkable, but here's just a little bit more insight into it:
Augmented I
| mMaj7 + IIIMaj7: 1, b3, 3, 5, b6, 7, |
| mMaj7 + IIIMaj: 1, b3, 3, 5, b6, 7, |
| mMaj7 + IIIAug: 1, b3, 3, 5, b6, 7, |
| mMaj7 + bVIAug: 1, b3, 3, 5, b6, 7, |
| Maj7 + bVImMaj7: 1, b3, 3, 5, b6, 7, |
| Maj7 + IIIMaj7: 1, b3, 3, 5, b6, 7, |
| Maj7 + bVIMaj7: 1, b3, 3, 5, b6, 7, |
| Maj7 + bVIMaj: 1, b3, 3, 5, b6, 7, |
| Maj7 + bVIMin: 1, b3, 3, 5, b6, 7, |
| Maj + bVImMaj7: 1, b3, 3, 5, b6, 7, |
| Maj + IIIMaj7: 1, b3, 3, 5, b6, 7, |
| Maj + bVIMin: 1, b3, 3, 5, b6, 7, |
| Aug + IIImMaj7: 1, b3, 3, 5, b6, 7, |
| Aug + bVImMaj7: 1, b3, 3, 5, b6, 7, |
| Aug + bIIIAug: 1, b3, 3, 5, b6, 7, |
| Aug + VAug: 1, b3, 3, 5, b6, 7, |
| Aug + VIIAug: 1, b3, 3, 5, b6, 7, |
| Min + IIIMaj7: 1, b3, 3, 5, b6, 7, |
| Min + IIIMaj: 1, b3, 3, 5, b6, 7, |
