On Stravinsky's birthday in 1946 George Balanchine brought Stravinsky a bottle of Grand Marnier with a musical greeting, a 32 note melody in whole notes. Stravinsky suggested that Balanchine harmonize it, but Balanchine deferred that he was not a composer, so Stravinsky, sitting in a chaise lounge by his pool, did so himself, on the spot. What's intriguing about this little piece, apart from its circumstances, is that it reveals a great deal about Stravinsky's conception of diatonic harmony. Of the 32 verticals, 17 of them are, purely from a pitch class set viewpoint, disregarding registration,different. That's a much higher percentage than a typical Bach chorale and Aus meines Herzens Grunde in particular. In the first example,Balanchine/ Stravinsky Chorale, each different PCS is assigned a number, with transpositions indicated with a T following a number. What's more, the tonic triad is heard only once, and there are only three triads in the entire piece. The most used PCS is 0,1,3,6 which occurs four times and remarkably is the only vertical repeated in exactly the same registration. In this regard, 31 of the verticals are unique.10 of the verticals are 3 note PCSs, 21 are 4 note PCSs and 1 is a dyad. The ratio of triads to four note verticals bears no relation to Bach. But this kind of tabulation doesn't account for the individuality of the piece. I began to ask myself if there was some experiment that could be applied to it that might yield another kind of insight in Stravinsky's choices. The result is the what I called the Balanchine/Stravinsky Chorale Reversed. This is what I did;
1) made a sequential table of each harmonization of the same note. For example, the note E above Middle C, occurs 5 times. The E an octave higher occurs only once.
2) reversed the position of the harmonization of every reoccurence of a melodic tone. Thus , for example,the first vertical in Stravinsky's piece now exchanges its position with the last appearance of E above Middle C, the first vertical of the third sytem. Since the high E occurs only once, it retains its position in both chorales. This happens with the highest note in the melody as well, the fourth vertical of the fourth system. Serendipitously it also occurs with the most common vertical (9), which retains its position in system two. The experiment also produces two 4 note canons.
From my point of view, the "reversed" harmonization does not sabotage the harmony, as it certainly does in the Reversed Aus meinem Herzes Grunde in which the same process is applied to Bach's chorale. I draw these conclusions from this;
1) Stravinsky's harmony, being so much less reliant on both step motion in the voice leading, as well as on the supremacy of the triad, is much more flexible in sequence than Bach's harmony.
2) The divorce of vertical emphasis from linear context results in the isolation of the vertical's uniqueness, rather than the emphasis of its membership in a community of likeness.
3) The flexibility of sequence in Stravinsky's harmonization is another manifestation of the key idea of all his music and the technical link between the three "periods" of his work.