Double Lipsean: The Quartal Triad Coscale

A couple of recent posts (here and here) have explored what I called "quartal-ish" language -- stuff that has lots of fourths in it and sounds kind of quartal but actually isn't. In the process we've seen the "quartal triad" (e.g. C-F-Bb) a few times and I thought it would be interesting to see what I could find in its complement, which has Forte number 9-9.

The way this arose in my earlier posts was as what might be termed "double Lipsean". There are two modes of the scale I call Lipsean that contain Minor Pentatonic at the root; this connects with another recent strand of posts on this blog that investigated minor pentatonic with two added notes. Well 9-9 is what you get when you play both at once -- Minor Pentatonic add 2 and 3 (one mode of Lipsean) and b6 and 6 (the other mode). Here it is with Minor Pentatonic in gold and the additional notes in blue:

("Lipsean" is one of my quirky invented names, by the way, and not to be taken seriously.) That's actually a pretty convenient way to find and play 9-9 but it doesn't give us much to work with so let's look at it in some other ways.

The first that I thought was quite arresting is that it's actually three interleaved diminished triads -- here they are shown in different colours (Adim in gold, D dim in green, E dim in blue):

It's a bit convenient that E-A-D (the roots of the diminished triads) forms another quartal triad, which might make this pattern easy to find on the instrument. In each case if you extend the diminished triad with a b7, making it a m7b5, you stay inside 9-9. However, extending them to fully diminished sevenths instead covers off all 12 notes. Although unrelieved diminished language can get wearing rather quickly, this is a strong flavour that I don't think has been explored much.

Another perspective comes from noticing that 9-9 is just Messiaen's Mode 5 (which has six notes) combined with another quartal triad, this time built a fifth away from the root. Here's a song by Messiaen that he calls out in Techniques as an example of his use of Mode 5:

Here's 9-9 visualized as Mode 5 (blue) and its accompanying quartal triad (gold):

If you drop the 4 and 5 so you're just playing a hypermode of Mode 5 + the root note (e.g. C-D-Eb-E-Ab-A-Bb) you get a mode of the melakatas Chalanata and Shubhapantuvarali. But I think I'd rather hang onto the quartal-ish theme and notice instead that Mode 5 itself is made of a pair of quartal triads, which might make for some interesting harmony:

This also shows how four quartal triads cover the 12 notes perfectly, which is completely unsurprising: all we've done is rediscovered the circle of fourths. This is the kind of diagram that people get very excited about but it doesn't necessarily tell us anything much. Still, treating 9-9 in this way seems decidedly promising to me.

Finally, here's 9-9 viewed as a pair of "quartal tetrachords" (e.g. C-F-Bb-Eb) over a root note:

A quartal tetrachord is of course just two quartal triads superimposed, which makes this view just a variation on the previous one:

Again, though, just because this isn't a deep theoretical insight doesn't mean it's useless as an idea about how to play this thing. Quartal tetrachords a semitone apart are a staple of modal jazz piano playing in the McCoy Tyner tradition and you wouldn't necessarily think of them in this context without spotting the patterns there.

I thought at first that 9-9 was a sort of offshoot of my "quartal-ish" explorations but I now wonder whether it's closer to the main trunk. A quick browse of this useful page shows that 9-9 has got the maximum number of fourths that it's possible for a nonatonic scale to have -- eight of them, meaning nearly every note in it has a note a fourth above in it too. I guess this is obvious when you see how many quartal triads it contains but still, this is perhaps a "parent scale" for my ridiculous quartal-ish harmony adventure.