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, |