Thirteen ways of looking at the Augmented Coscale

For years I've been playing major seventh chords in a cycle of major thirds as a kind of "atonal major tonality". I talked about that here and in other places on this blog. But lately I've been trying major sixths as well, and they produce something similar but different. In fact it's the negative image of something very familiar.

1: A Cycle of Major Sixths

The idea I started with is to play, say, CMaj6, EMaj6 and G#Maj6 and move freely between them in a modal jazz kind of way. The major sixths don't overlap as much as the major seventh do. Instead of the Augmented Hexatonic 1-#2-3-5-b6-7 we get a nine-note scale, 1-b2-#2-3-4-5-#5-6-7. Visually this is three groups of three notes; in each group the notes are a semitone apart and they're separated by whole tones.

Another way to look at it is that it's the chromatic scale with an augmented arpeggio removed, specifically the one built on the 2 of the root note. So I'll call it the Augmented Coscale. Here's how that looks to me on the fingerboard, with the ghostly white notes representing the augmented triad you don't play:

So a way I like to play this is to freely combine those major sixth chords, which are rooted on the middle note of each three-note grouping and which together cover all the available notes. This gives a more spicy effect than the major sevenths version because you also get flatted ninths, which are a very interesting effect in the context of a prevailing major seventh harmony.

2: Both Modes of Augmented Hexatonic

If you wanted to, you could also visualize this as playing both modes of Augmented Hexatonic at once. That's illustrated by the colours in this diagram -- if the root is one of the middle notes, green notes belong to the "major seventh" mode and red notes to the other, weirder one:

Since Augmented Hexatonic is just the Coltrane Cycle in scale form, this tells us there are two Coltrane Cycles buried in the Augmented Coscale; we'll revisit that in a moment.

The green mode in the diagram above is 1-b3-3-5-b6-7, a major 7 sound with the "bluesy" b3 and the rather mysterious b6 that comes from Harmonic Major. The red mode is 1-b2-3-4-#5-6, a very peculiar selection of notes that still just about has that Major 6 quality, but with a #5 and b9 that would imply an "altered sixth" chord if such a thing existed. Maybe it does now?

3: Linear Patterns

When you have this many notes in a symmetrical layout, it's interesting to look for patterns within them that allow us to play them in different ways rather than just giving in to the temptation to run up and down. In particular, I like simple patterns that spread the notes out across multiple octaves -- we do this all the time with chords, but for some reason it feels weird to do it with scales. But it feels weird in a good way and I'd like to explore it more in the future.

Here are a few examples to try; it's not hard to invent your own:

4: The Coltrane Cycle and the "Double Harmonic Move"

Essentially, Augmented Coscale is what you get when you combine the Coltrane Cycle with the idea of shifting between Maj 7 chords a semitone apart -- what we might call the "double harmonic move". There are actually two moves here, which in the interests of not being too fancy I'll call "slipping up" and "slipping down".

Suppose we have in mind C Maj 7, which is C-E-G-B. If we "slip up" we simply move the whole thing up a fret, obtaining Db-F-Ab-C. If we combine the two arpeggios together we get C-Db-E-F-G-Ab-B, which is C Double Harmonic. This is the scale in which Miserlou is written, a traditional tune made famous by the great Dick Dale:

As an aside, if you're considering spamming Double Harmonic in your next movie score to evoke the mysterious orient, here's 90 glorious minutes explaining why that might not be quite as cool as you think it is:

Well, you know by now that if there's an idea that involves moving something in one direciton, around here we like moving it in the other direction as well. If you "slip down" from C Maj 7 you get B Maj 7, which is B-D#-F#-A#. Again, combining the notes we get C-D#-E-F#-G-A#-B, which is Rasikapriya, which is of course a mode of Double Harmonic. While "slipping up" retains the overall Maj 7 quality, "slipping down" really makes it more of a dominant thing, although it's a bit of a weird dominant sound if you're trying to use it in a jazz context -- maybe more Lydian than Altered, but odd either way.

Here's the important thing if you want to stay within the Augmented Coscale: you have two Colttrane cycles a semitone apart, so you have to slip from one to the other but always in the "right" direction. For example, C Augmented Coscale is C-Db-D#-E-F-G-G#-A-B. The twto Colttrane Cycles are:

  • Lower cycle: C Maj 7 (C-E-G-B), E Maj 7 (E-G#-B-D#), G# Maj 7 (G#-C-D#-G)
  • Upper cycle: Db Maj 7 (Db-F-G#-C), F Maj 7 (F-A-C-E), A Maj 7 (A-Db-E-G#)

If you want to keep that Augmented Coscale sound, you can "slip up" from the lower cycle or "slip down" from the upper cycle but not vice versa. Each time you do, you imply either Double Harmonic when you slip up or Rasikapriya when you slip down. This gives the two Coltrane Cycles potentially quite different identities.

5: Other Common Chord Qualities

The major sevenths can be varied by playing them as minor-major-7s instead but, perhaps more interestingly, there are actual minor 7 chords hiding in the scale, too. These are rooted on the top note of each three-note group. For example, suppose you're playing "in" F major. Your major sixth chords are F, A and C#. The minor 7 chords fall on the roots a semitone above, i.e. on Gb, Bb and D. This links them with an idea I called "expanded Lydian", although sadly you can't upgrade those m7 arpeggios to minor pentatonics without stepping out of the scale.

You can actually play these as m7, minor-major 7, m7b5 or even major 7 or dom 7 chords and you're still in the scale. The dom 7s in particular give a nice tension-resolution option when you want that, since they're nothing but old tritone substitution beloved of the bebop folks -- but watch out for the b9, which isn't in the scale (b5, #5 and #9 are, though).

I've lately been particularly taken with the option of combining a minor-major-7 chord with the half-diminished chord a semitone above it. This pair can be rotated through the major third cycle and the effect is much stronger and more characterful harmony than I'd have expected from a nine-note scale. The combination of, say, CmM7 with Dbm7b5 yields CmM7b9, a pentatonic scale that also pops up in relation to Minor 6 Suvarnangi.

6: The Whole Tone Scale

You also have the whole-tone scale rooted on either side of the roots of the Maj 6 chords, which makes a connection with the Neapolitan scale -- there's more on this connection here. The Augmented Coscale is a sort of "Super-Neapolitan" in that it's three Neapolitan scales laid on top of each other -- I reckon that's the most Neapolitan you can have before it turns into nonsense.

Thinking in this way, you get access to all the basic whole-tone chords and some of the added-note whole tone chords as well. Great for modern dominant sounds or floaty atonal stuff alike.

7: Quartal Chords

The Augmented Coscale contains some nice quartal chords that, as you'd expect, fall into clear visual patterns on guitar.

I don't have much to say about these except that they offer a way to build harmony from it without building triadic harmony, which often sounds as if it wants to resolve even though, in this setup, that's not very likely.

8: Heptatonic Subsets

The Augmented Coscale is a nine-note scale, which would usually mean there are lots of ways to delete two notes from it to get to a seven-note one (72 on paper, although not all will make sense). However, its symmetry means the number of different results we can get is actually much smaller and there are only 8 different scale groups in there. Some of them have traditional Carnatic or Western names: the Forte numbers are 7-13A, 7-26B, 7-21A (Neetimati), 7-30A (Sulini / Dhenuka / Chitrambari), 7-33 (Neapolitan), 7-z17 (Yagapriya), 7-22 (Rasikapriya / Double Harmonic) and 7-z37.

I don't have much to say about these either, at least in isolation. We've already seen how 7-22 can arise quite naturally and we'll encounter a couple more in the next section.

9: Minor 6 Pentatonic

C Aug Coscale is precisely C Minor 6 Pentatonic plus Dbm7, a very playable way to approach it without just running the pattern up and down:

This suggests we might want to look at the hexatonic consisting of just the C minor and Db minor triads, Forte number 6-z29, which is 1-b2-b3-b4-5-b6. Adding one note to this makes a heptatonic, and there are 3 options without going outside the parent scale: the 4, 6 or 7. These make (modes of) something very exotic (7-Z37), Double Harmonic (again!) and Neetimati respectively.

10: Vertical Slices

This one is similar to the Linear Patterns idea as it's mostly about finding unexpected melodic movements in this very chromatic, symmetrical collection of notes. Since there are a lot of notes in the scale, the idea is to limit ourselves to only those we can reach in a limited span of two or three frets. This forces you to make intervallic leaps you might not otherwise -- I especially like the two-fret versions for that reason.

Here are some ways to do it. As usual, just play the notes of one colour, but in this case yellow notes are "in the background" and don't count as a pattern. The two-fret versions contain almost, but not quite, all the notes in the Augmented Coscale while the three-fret ones contain all of them:

11: All-Interval Tetrachords

Augmented Coscale contains some AITs -- you can read more about those here. They come in two flavours, which on guitar I like to think of as "sort of major" and "sort of minor".

The sort of major one is 1-b2-3-b5 (4-z15), a major triad with a b5 and a b9 but no seventh to round it out into a "normal" altered dominant sound. The sort of minor one is 1-b2-b3-5 (4-z29), which is just a minor trad with the b9 added (again, no seventh).

These are interesting, rather open-sounding chords with a bit of crunch. There's an alternate universe very similar to ours where people find these to be pretty and innoffensive but can't digest a major seventh chord. They're definitely nice sounds to experiment with if you're trying to build harmony without going outside the Augmented Coscale.

They're not super-convenient to play on guitar and you sometimes have to skip some strings, but they sit nicely inside the Augmented Coscale. The major version is on top, the minor version below:

12: MiP, MaP, AlP and AmP

Some years ago I did a series of posts here on a group of (eventually) four made-up pentatonics that I flippantly called "Hungarian". If you absolutely had to you could read through all those posts as follows:

Augmented Coscale contains all four of my "Hungarian" pentatonics, so it would be remiss of me not to include them here even though there's nothing miraculous about that -- all nine-note scales contain almost all possible pentatonics (some, but not this one, literally contain every one).

All four pentatonics can be played at the b2, 4 or 6 of the Augmented Coscale. Here I've shown them built at the 6. The complements of AlP and AmP in Augmented Coscale (i.e. the notes in the latter that aren't in the former) are common chords so I've pointed that out; maybe the other two are interesting as well, I don't know:

13: It Is Not Diminished

Most big structures contain a chunk of half-whole diminished language. Now, any nine-note pitch collection contains every three-note one, so we can find diminished triads here easily (they're rooted on the middle note of the three-note, two-semitone groups). The diminished triad (red notes) can even be extended to a Diminished Maj 7 (add the green note) or half diminished (add the note below the green note instead):

Still, some of the most characteristic four-note diminished chords are missing, including the diminished 7 chord itself. We can use this information to help us choose contrasting material to put alongside the Augmented Coscale. Often I like to do this by looking at the complement of a scale, but in this case the complement is of course the augmented triad, and the Augmented Coscale is full of those. So not only is a three-note structure a bit sparse to do much with, it doesn't even create much contrast.

Instead we can get contrast by switching to one of the two Half-Whole scales that contain the notes that aren't in the Augmented Coscale. All the chords they contain -- especially the characteristically diminished ones -- have the capacity to be good "tension chords" if your "home sound" is the Augmented Coscale.