Call these A, B, and C. I think we can describe these three tetrachords as all the pairs of 5ths that contain at least one 1/2 steps? Of these three pitch collections the A remains fashionable, and has been fashionable for a long time. It is a collection that is particularly associated with Brahms.
B is now the cutting edge fashion in music that wants to be a bit more daring. This collection is the least ambiguous tetrachord. It can only exist in one diatonic scale, and yet it is a signature 20th C. sound. I think I got my biggest dose of it playing Jolivet. It's all over Ben Monder's music too. I use it as the hinge in the first part of my Unexpected Reunion. It's a key sound in Matthew Greenbaum's *Nameless*. I'd say it's now a fashionable collection. Utilizing the B collection involves dropping a note and alluding to the A collection. B and A work together.C is Carter's collection, a subset of the famous all-trichord tetrachord. It has become very familiar to us because of our familiarity with Carter's music; but it's hard to argue that this collection has achieved fashionability. As A and B play off of each other, so with C. The three are just very short steps away from each other and so they can hinge off of each other nicely. Note also that these two fifths alternate throughout Schoenberg's Op. 27 #4. I think I've heard the move from one of the two C fifths to the other in jazz.
We can think of the Schoenberg hexachord as the A tetrachord plus A transposed up a major third. We can certainly also think of it as Brahms collapsed--the focal collections in Brahms Op. 88 or Op. 18, plus their major third transpositions. And in Brahms, the major third becomes the secondary region of choice, as opposed to the dominant, which is the secondary region *of nature*. Schoenberg's hexachord was fashionable within a small circle for a short period, perhaps? I'm not sure.
We can't understand the fashionability of these collections without paying some attention to what is unfashionable. Minor-third based collections are unfashionable. The unfashionability of minor-third-cycle harmonies can be blamed on the sad reality that we've been bombarded with music by composers who don't care about pitches. When you don't care about pitches you usually fall right into the pit of minor third symmetries. For such composers pitch is merely a matter of playing around with octotonic scales and occasonally enlarging on subsets of the octotonic scale that are diatonic. This is a worthy strategy, but it's usually done in an annoying way that rankles me. It's unfashionable with me. Even Lou Harrison's 8 note stuff in his piece for guitar and percussion is OK with me because it juggles the 8 note scale with the diatonic scale in a way that keeps the yin and yang of the two in constant flux. That's successful for me. So, it's not a matter of myrejecting simplicity, it's that I demand balance. Terry Champlin's Harp of David has a nice balance. Beethoven & Schubert walk the fine line.
These three tetrachords above are for composers who are sick of octotonic harmony. These three tetrachords are still not overplayed. They're fashionably piquant. Of course that means they are in danger of becoming overplayed some day.
There are two composers whose work tells us clearly that they are aware of the problem of collection fashion. Carter's use of the all-trichord hexachord and Babbitt's use of all-trichord rows show us how to dodge the issue of collection fashion altogether.
In Swan Song No. 1 Babbitt's use of all the trichords is one sphere of activity. On another plane there is a very special, quite virgin collection--0127. It ends the piece, and it appears in the very beginning.
I've yet to explore the fat middle for the role of 0127 throughout. But we see Babbitt taking great pains to serve us very specific sounds. 0127 is equal parts semitone cycle and 5th cycle, isn't it? (!!). The flow of trichords throughout the piece also mediates between the diatonic and non-diatonic sound worlds. There's almost a sense that one can take the non-diatonic trichords as moments that float through to the next diatonic moment; OR NOT, take them instead as giving equal time for equal collections.
Carter's music is also interested in this problem of collection fashion. Carter cares deeply about staying aware of all the different collections of every number of pitches. His love for the all-trichord tetrachord makes us think of that hexachord when we think of Carter, but that's not exactly fair. In Luimen he avoids that harmony for the most part. There, what I remember in the opening is a different interval cycle prevailing for every attack rate. (!!) (Schoenberg's Chamber Symphony collapsed upon itself.) The lovely thing about the 12 trichords--some are *of* interval cycles, some are combinations of interval cycles. I need to understand how this works in Carter. I have not studied it enough. I think the emphasis is on the vertical arrangement of these things into pitch fields.
More on fashion later. I need to think about fashion as a tribal function regarding notions of what's possible. One tribe says something's impossible to hear. Another tribe bases its work entirely upon the goal of making that heard, and coming up with remarkable results whether it's heard or not.
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