Quartal Harmony: Tetrachords

In today’s post we will continue our series on quartal harmony with a quick look at quartal tetrachords. When we began with dyads, we saw there are three quartal dyad types: P, A, and D. With quartal trichords, there are nine types (3 * 3). With quartal tetrachords, we now have twenty-seven types (3 * 3 * 3). These are summarized in Figure 2. Of the twenty-seven, only eleven occur in our four scale harmonizations.

As before, the most common tetrachord type is based on stacked perfect fourths, PPP. This type occurs nine times in total across the harmonizations, making it once again the most harmonically ambiguous chord type. PPP occurs four times in the Major harmonization, twice in the Melodic Minor, and once in each of the other harmonizations.

After PPP, the next most common tetrachords are PPA and APP, both of which occur four times, once in each of the harmonizations. Both of these are very useful voicings. APP can easily serve as a Maj7#11 and PPA can serve as a dominant, as we shall see next.

When looking across the four harmonizations, we see an interesting detail on the both the supertonic and dominant degrees: they each share the same tetrachord across the harmonizations. In all cases, the supertonic is a PPP, and the dominant is a PPA. In other words, the II-V quartal tetrachords are the same for Major, Melodic Minor, Harmonic Minor, and Harmonic Major.

We mentioned the Viennese trichord in our last post. Any tetrachord that contains either PA or AP is a superset of the Viennese trichord. Our next most common tetrachord is PAP, which occurs three times in the harmonizations. Once can see PAP as an interlocked PA and AP, or an interlocked Viennese trichord. A Viennese tetrachord perhaps? This voicing also functions well as Maj7 11 chord.

Quartal tetrachords harmonized with the major, melodic minor, harmonic minor, harmonic major scales.
Figure 1. Major, Melodic Minor, Harmonic Minor, Harmonic Major scales harmonized with Quartal Tetrachords.
Quartal Trichords in scale harmonizations.
Firgure 2. How many times does each tetrachord appear in the four scale harmonizations?

Key Takeaways

From a practical standpoint, here are a few things to keep in mind using quartal tetrachords for comping or soloing:

  • The texture of a quartal tetrachord is getting fairly thick and might be a practical upper limit for comping, especially on guitar
  • The quartal tetrachord material for II and V is the same for each of the four scales, so work on those quartal II-Vs and you will get a lot out of them!

Quartal Harmony: Trichords

Today we continue the discussion on quartal harmony with trichords. Yesterday’s topic on quartal dyads was a bit of a warm-up. Things are getting more interesting now. There are three varieties of fourth: perfect, augmented, and diminished, or using our labels, P, A, and D. In order to construct a trichord, we need two intervals. That gives us a total of nine different types of quartal trichord. These are shown in the Fig. 2 chart below. When looking at the harmonizations of our four scale types, Major, Melodic Minor, Harmonic Minor, and Harmonic Major, we can make some observations about how often the trichords appear.

Two of the trichords, AA and DD, do not appear in any of the harmonizations. In AA, the outer voices form an augmented seventh, which is enharmonically equivalent to an octave. In DD, the trichord is enharmonically equivalent to an augmented triad.

We saw yesterday that P was the most common dyad, and see now that PP is the most common trichord. It occurs five times in the Major harmonization, three times in the Melodic Minor, and two times in each of the Harmonic Minor and Harmonic Major. So then, just like the P dyad, the PP trichord is the most harmonically ambiguous of the quartal trichords.

The next most common trichords are two of my favorites. They combine an outer major seventh, and inner perfect and augmented fourths, or PA and AP. I love both of these sonorities and used them often in my early composing. (Berg and Webern loved them too, so much so that they are sometimes referred to as the Viennese trichord.)

Two of the trichords occur in only one harmonization. PD occurs in only the Harmonic Major harmonization, and DP occurs in only the Harmonic Minor. As a result, these two trichords are the most harmonically specific.

I find it interesting to look at the similarities and differences among the four harmonizations. One thing that leaps out is that all four harmonizations share the same trichords on modes 1, 2, and 5, or on the tonic, supertonic, and dominant. So, for example, a riff on the tonic and supertonic trichords would be completely harmonically ambiguous; it would fit with any one of the four scales. Somewhat surprisingly, the dominant is the same for all four.

Not surprising is where the most variation occurs between the harmonizations: on the mediant and leading tone. Both of these degrees (or modes) contain both the third and the sixth, which is where all of the variation between these four scales takes place. Contrast this with the subdominant and submediant. The subdominant trichords contain the third, so the two with the lowered third are the same, and the two with the natural third are the same. For the submediant, the two with the lowered sixth are the same, and the two with the natural sixth are the same.

Quartal trichords harmonized with the major, melodic minor, harmonic minor, harmonic major scales.
Figure 1. Major, Melodic Minor, Harmonic Minor, Harmonic Major scales harmonized with Quartal Trichords.
Quartal Trichords in scale harmonizations.
Firgure 2. How many times does each trichord appear in the four scale harmonizations?

Key Takeaways

From a practical standpoint, here are a few things to keep in mind using quartal tichords for comping or soloing:

  • The texture of a trichord is very useful for comping, especially on the guitar
  • Any quartal trichord material built on I, II, and V will work for each of the four different scales
  • The quartal trichord material on II, VI, and VII is where all the harmonic differences are

That’s it for today’s installment. In later posts, I will look at quartal tetrachords, as well as usage of inversions for the trichords we looked at today.

Quartal Harmony: Dyads

More follow-ups to my recent visit to the Aebersold Summer Jazz Workshop. I attended master classes with four great jazz guitarists: Corey Christiansen, Dave Stryker, Mike Di Liddo, and Craig Wagner. All four of these musicians gave me things to work on. One of the discussions that we got into with Corey was about quartal harmony, something I had worked with him on previous visits. I decided that it would be good to do an in-depth study on this material, so I plan on doing a series of blog posts.

My ultimate goal will be to incorporate this material into my jazz comping and soloing. But I am going to start out with a high-level survey of the territory. To do this, I’ll look at quartal chords of various size, dyads, trichords, tetrachords, pentachords. For each size of chord, I’ll look at all of the different quartal chord types, that is, all of the different combinations of the interval of a fourth. I’ll also look at where these different types of chord appear in harmonizations of four different scale types: Major, Melodic Minor, Harmonic Minor, and Harmonic Major. (These four scales correspond to the twenty-eight different modes I made reference to in my previous post.)

Let’s start with dyads. There are three different qualities of fourth that I will look at: Perfect Fourth, Augmented Fourth, and Diminished Fourth. Since we are only dealing with fourths, I’ll use a simple label and just call them P, A, and D. The first figure below shows where each of these three different dyads occur in harmonizations of our four different scale types.

Quartal dyads harmonized with the major, melodic minor, harmonic minor, harmonic major scales.
Figure 1. Major, Melodic Minor, Harmonic Minor, Harmonic Major scales harmonized with Quartal Dyads.

The next figure contains some statistics about how often each dyad type occurs in the different harmonizations.

Quartal Dyads in scale harmonizations.
Firgure 2. How many times does each dyad appear in the four scale harmonizations?

There are a few things to note. First, it’s clear that the prefect fourth appears the most often: eighteen times out of twenty-eight in total. In a sense, this makes the perfect fourth the most ambiguous of the three dyads, since it occurs in so many contexts. Another interesting insight is concerning the augmented fourth. Since the augmented fourth only occurs once in the Major scale, it has traditionally been taken that it serves well to establish the scale type and key. In contrast, the augmented fourth appears twice in each of the Melodic Minor, Harmonic Minor, and Harmonic Major scales. This arguably makes each of these scales more harmonically ambiguous than the Major. It also strikes me that the Melodic Minor, Harmonic Minor, and Harmonic Major scales have the same number of occurrences of the different dyads P (four times), A (two times), and D (one time).

That’s it for today. Next time, I’ll do the same treatment for quartal trichords.

A Mode For Every Day Of The Year

I just got back from two weeks at the Jamey Aebersold Summer Jazz Workshop. It was amazing, as always, and especially important since this is the final session before Jamey retires after running the “camps” for over fifty years. I sat in on Pat Harbison‘s advanced music theory class, and I got some great ideas out of that.

One idea in particular got me thinking about digging deeper into the sound of specific modes. Pat mentioned something along the lines of “twenty-eight modes ought to be enough.” Since there are about twenty-eight days in a month, and twelve months, I saw how you could practice a different mode on a different root note every day of the year. Take the month as your root, and the day as your mode number. The base scales I chose were Major, Melodic Minor, Harmonic Minor, Harmonic Major. For the extra days in the month, up to three in a month with thirty-one days, I added Diminished (mode 1), Diminished (mode 2), and Whole Tone. Today is July 17, so that means my mode of the day is the second mode of Harmonic Minor, with a root note of F# or Gb. The whole scheme is summarized in the charts below.

How to practice a different mode every day of the year.
Figure 1. How to practice a different mode on every day of the year.

Key Takeaways

If you are stuck in a rut practicing modes, try this method. You don’t need to keep it up for a year, but if you try it for a while, you will learn that some of the modes you never practice are really beautiful.

The Second Great Quintet

It’s nice to be blown away. The cynical, jaded layer that forms like a crust over gets its fuel from the despair that it’s all been seen, no more epiphanies to be had. But sometimes, by stripping away expectations and allowing yourself to open up like a neophyte, something gets through to you and humbles and excites you at the same time. And sometimes it just sneaks in surprises you. Pardon the purple prose, but I’ve been listening to to the music of Miles Davis‘s so-called “Second Great Quintet”. And it’s kind of stunned me.

In the mid-to-late sixties, Miles was peaking, although health problems were already bothering him. Non-self-inflicted health problems, that is. From ’65 to ’68, he was recording with Wayne Shorter, Herbie Hancock, Ron Carter and Tony Williams. That’s just a crazy collection of talent. The greatest jazz quintet ever assembled? Maybe. And the sidemen were all kids. All virtuosos, great improvisers and composers.

This is transition period art. Bop went out on a rocket ship and reached orbit here, in the post-bop zone. Eventually, the orbit decayed, the ship started to break up, disintegrating into fusion. But that’s still a few years off; for now, the musicians are fully enjoying the new-found effects of weightlessness. There forms are loose and quirky. There’s still an occasional smidge of functional harmony, but it’s more for flavour than function. The lines, especially Hancock’s remind me of the Brownian motion stuff I used to do. And the sonorities are sweet. But mostly, man, these guys just play.

It’s exciting.

Theatre Review: Jazzabel

London, Ontario came to New York this week in the guise of Jazzabel, the one-woman (and three-guy) show produced by a trio known collectively as “Femme Fatale.” The show is the product of chanteuse Denise Pelley, author Jacquie Gauthier, music director & composer Jeff Christmas, and producer (and ex-high-school-colleague-of-mine) Louise Fagan. Londoners of note, all.

The show has been the buzz of the London theatre scene for a while, and the excitement leading up to the New York run was high. I missed the Gala opening and the opportunity to hang with the Canadian Consulate muckity mucks. Instead, I caught the show on a wickedly cold Saturday night, surrounded by an audience of imported Canadians, some of whom seemed to have just put down their martinis moments before entering the house.

The idea for the show is promising, if not Earth-shattering: in between sets of hot jazz from the ’30s and ’40s, two jazz singers, played by one woman, tell their story. The two singers couldn’t be more different. Grace is green, excited, a little afraid, and clean cut, if not a complete square. Jane, who becomes Jazzabel, is hard-living, substance abusing, rather tragic. Parallels in jazz history are many. Ella and Billie are the quickest to come to mind, but if they were men, they could just as easily have been Bird and Diz.

As much as I enjoyed the show, and it is enjoyable, it did not completely hit the mark. I’ll talk about the music first. Jazz is, we all know, an improvised art form. When all the parts are written out, solos and all, you get something out that isn’t quite jazz. It’s jazz-substitute, processed jazz food, an edible jazz product. But it’s not jazz. Christmas actually did an admirable job on the arrangements. But the band could have really cooked if they had run though his charts once or twice and then tossed them out. Denise Pelley’s voice is great. No problem there at all. The artifice of the show had her a bit too removed from the boys in the band. I think that the intent was to show that the sidemen weren’t really on the stage with, that they were in the pit or something. Again, jazz is all about communication, people listening and interacting with each other. In such an intimate setting, her lack of contact with the band was a little unsettling.

The script has some issues, too. While I buy the story line, Gauthier’s dialogue, or monologue, I guess, doesn’t sell it. Big, long sentences that don’t always ring true. Here’s another radical idea: letting Pelley internalize the script and then throw it out would help. More improvised music, more improvised story-telling, less constraint, and in short, more jazz.

Smokin’ on the UWS

Headed up and to the left last nite to listen to some B3 grooves, and help out in some belated birthday activities. The venue was Smoke, an old-fashioned uptown boite de jazz. This place is what a jazz club should be, it’s small, has good sight-lines everywhere, good sound system, not too expensive (unlike those downtown tourist traps), nice vibe and comfy couches. And, as someone at our table pointed out, Smoke, sans smoke, is nice. (I could digress into a brief request that we pillory all those fools who screamed that banning smoking would kill the city’s night life–the place was packed, and not an iron lung in sight.)

As for the band, the Mike LeDonne quartet played them some good grooves. I was most impressed with tenor man Eric Alexander. This cat’s good. And he has that cool, serious, young jazz genius thing down, think Steve Dallas in The Sweet Smell of Success. In fact, Eric pretty much stole the set. I thought that guitarist Peter Bernstein would finally get his moment during a scorching slow blues–that’s guitar turf, man! But Bernstein is so intent on doing this quiet, unassuming melodic style, that he still held back. By the end of his solo, the blues had worn down to a funeral march. It was a weird moment. I liked his playing and loved his tone, but I wanted to hear much more. Peter, cut loose once in a while, you’ll feel good!