Triple Neapolitan: The Wholetone Trichord Coscale

Continuing my little exploration of nine-note scales made from diminished triads, we arrive at 9-6, the scale you get when you take the total chromatic and delete three notes that are a whole ton apart (in our example, they'll be E, F# and G#). Let's see what we can get out of it.

Here's a mode of 9-6 that shows off its inversional symmetry, with lines showing a portion of the circle of fourths. While 9-6 isn't very fourths-ful as nine-note scales go, this continuous cycle of fourths allows us to make some big quartal chords from it if we want to:

The white notes are the "wholetone trichord" that we're excluding to make 9-6. Throughout this post, as usual I'll assume the root is C to make it easier to refer to things in a way that doesn't need too many steps of thinking before you can play them.

An easy way to find this mode of 9-6 is as C Dorian with a chromatic enclosure around the root; here C Dorian is shown in blue and the enclosure (B-Db) is in gold:

Of course, we can do this with any major scale mode but the note that gets the enclosure will be different; obviously the root is very easy to find and remember which is a point in favour of starting with this one.

Another interesting approach is to start with C Neapolitan, which is Db Whole Tone plus the root note C. This is a seven-note scale; to make it up to 9-6, simply "fill in" the two more adjacent whole tone gaps as shown by the gold notes below (in this case, D and Bb)

If we think of "filling in a gap in the Whole Tone scale" as the "Neapolitan move", effectively this is three consecutive Neapolitan moves, which leads me to think of this scale as Triple Neapolitan. If you're used to playing the "side-slipped" Whole Tone scale, which I think is a great minor sound you can use in moderately adventurous tonal settings, this is again a very easy thing to find and play.

Let's do one more scale-based way to play 9-6, then we'll finish with some more chordal ideas. Here we start with C Minor 6 Pentatonic (C-Eb-F-G-A), a popular blues scale (shown in blue) and do a "double enclosure" around the root note (shown in gold):

This is a variation on both the Dorian and Whole Tone ideas. Of course Minor 6 Pentatonic is just Dorian with two notes removed; here we simply added them back in. On the other hand, you could see it as Whole Tone with two notes "coalesced" -- Db Whole Tone is Db-Eb-F-G-A-B, with a whole tone between Db and B, which can be merged together into the note between them, C. This is a fancy and perhaps silly way to think about it but it clarifies the connection with the Triple Neapolitan point of view. It also explains why Minor 6 Pentatonic has that Whole Tone vibe to it, and perhaps why the side-slipped Whole Tone idea isn't as wild as it looks on paper.

Let's look at a couple of chord structures in 9-6. We started our journey here because it's one of the ways to combine three diminished triads with no overlap -- in this case it's G dim (red), A dim (blue) and B dim (gold):

The fact that their roots go in whole steps isn't a big shock; in fact, 9-6 contains more whole tones than any other 9-note scale, and again that's not very surprising when you think we deleted half of a Whole Tone scale to make it, and the Whole Tone scale is its own complement, meaning 9-6 is made of 1.5 Whole Tone scales. I think it's rather pleasing that there's a way to look at such a Whole-Tone-centric object as nothing but an interlocking trio of diminished triads.

Let's end with what I think of as more "diminished language" -- 9-6 can be covered by three Susb2 chords or, equivalently, their inversions the Sus#4 chords. The Susb2 chords are on the left (Bb, C and D roots) and the Sus#4 chords are on the left (Eb, F, G):

These are variations on the co-called "Viennese trichord" beloved of serialists and are native to the octatonic Half-Whole diminished scales so they also tend to crop up in twentieth century classical pieces that lean heavily on those (think Scriabin or Stravinsky). You can mix these with the diminished triads if you're careful -- for example, CSusb2 + EbSus#4 + Bdim covers 9-6 exactly with no overlaps. That might be a good approach if you want lots of variety and a quasi-diminished sound without the cliches you get from the symmetrical octatonic scale but it does require a bit more brain power to do. You can also combine these in slash chords with more familiar triadic material.

Here's Berg's Piano Sonata. It's Viennese, still tonal but sounds to me as if it's full of the sort of harmony I've just been describing -- it's always worth hearing something that uses these ideas and isn't so far-out that it's impossible to scaffold onto things you might already know how to hear:

I think that's it for nine-note scales for now. The studio build is proceeding well and is probably in the "tinkering about with cabling" stage for the moment; I'll be happy to spend the winter doing that and get some more furniture and storage built when the weather improves in the spring.