Over the past 8 yea
rs I've been mulling over a few things in Swan Song.
Whither the 0127 at the end?
E and B hold while the cello plays E#-F# if E=0 then the other
members of the chromatic scale create the collection 0(E)1(E#)2(F#)7(B)
Then I found that the first non-diatonic collections that strike us in the opening are also 0127s. The opening, moreover, is a counterpoint of diatonic hexachords in the plucks; (023457) in the pizz. strings (B hexachord); followed by chromatic hexachords in the woodwinds.
I've discussed the fat middle of the piece in the Bridge Record notes. I'll touch on that later. First, a major epiphany about the 0127s. It should have occurred to me years ago, but I'm slow, and uninitiated. I hope to show that even an idiot can understand Babbitt with sufficient time, patience, and interest.
First--the decoded message:
"Till my last dying breath I shall care about making the chromatic and the diatonic universe work together."
(Remember Widow's Lament, with its interplay of chromaic hexachord and the diatonic hexachords.)
0127 is a beautiful hermaphrodite. A yin/yang symbol for the chromatic cycle and the 5th cycle. That hit me first. Then it hit me that this collection *must* M5 to itself. Please check my math. I'm just a guitar jock, remember!! Also B Hexachords (023457) played by the strings is another perfect hermaphrodite, it also M5s to itself. It is equal parts diatonic and chromatic, thereby mediating between the plucks (which begin with diatonic hexachords) and the winds, (which enter with chromatic hexachords).
The disposition of the final gesture enacts the yin and yang of 0127. A triumphant, comfortably familiar fanfare--
B is with an E below.
And then the chromatic element in the cello---
telling us we *can* have it both ways, and it's a jab in the ribs, at that. In the Bridge notes I call it a laugh, I think, or a chuckle. Gb, F or E#,F# appear in key places throughout the piece, always an enlargement of the first 0127 in the opening statement in the guitar.
Now the middle of the piece delivers (most of) the 12 trichords. There are crunchy trichords, including non-diatonic trichords that do not appear in the opening pair of complementary diatonic hexachords. However, the juncture between E and Bb hexachords in the opening is carefully disposed to have F#F,G,C 0127 dangling in registeral proximity to each other. (How much else might we find in the way this opening phrase is disposed?)
I mention in the notes that the non-diatonic trichords are often too dynamic to be "landed". They crunch on their way to the next comforting diatonic moment. In this way the diatonic trichords and non-diatonic trichords work very well together. They cooperate in creating fabulously large arcs.
I now think of this somewhat differently. The crunchy ones crunch for some. For others those moments are lovely in themselves. Get used to those crunchy moments in Swan Song, and then try to listen to Soli e Duettini. Soli e Duettini has plenty of diatonic material, but not as much as Swan Song, no? Is that fair to say? Swan song is required listening on one's way back to Babbitt's earlier work.
I'll try to get some jpgs of specific pages from the score, to shore this up.
Here we go--->
The opening disposition speaks VOLUMES--
Two complementary diatonic hexachords, layed out so that trichords are clearly delivered to the ear.
Over the seam between those first 2 complementary diatonic hexachords---0127 is registrally disposed, but not temporally.
Over the same seam 023457 temporally disposed, but the last member of the collection that appears (D--7), also includes 8 (Eb). At this point another 0127 is given D, Eb, E, A. The palatte cleanser of choice to bring the next diatonic collection.
More 0127s appear in this palate cleansing role, bridging between diatonic collections; and then the pizz. strings enter with 023457 hexachords.
0127 tetrachords at all junctures between diatonic collections in the opening. I'm looking for more appearances of 023457 over these seams.....
0127 and 023457 both M5 to themselves.
3 semitones and 3 5ths expands to 4 semitones and 4 5ths.
I'll need help with the question of how many collections have these properties; and how many *combinatorial collections* share this property. For the combinatorial questions the answer is likely that this pairing is unique.
Woodwinds enter with 012345.
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