Tabula Rasa part one: Ludus

Richard Taruskin somewhat flippantly once referred to the history of music in the 20th century as "two zigs and two zags" by which he was referring to roughly four phases, two of which were devoted to increasing complexity and two to radical simplification. I talked about that in this post, The Second Zag: the New Consonance. The first zag was the simplification of the neo-classical phase of the 1930s and 40s. This was followed by the post-War zig of the complexities of the total serialists. That was in turn followed by the second zag, the simple pulse of the "minimalists" and the simple consonances of a number of composers from Eastern Europe including Arvo Pärt.

The first question the comes to mind in doing an analysis of this piece is what exactly do you analyze? For the first eight minutes of the ten minute plus piece, the harmony is A minor or A Aeolian. Basically one chord with passing notes. At the eight minute mark there is a cadenza for all instruments, again, mostly an A minor chord, but with an E in the bass which tips it slightly toward the dominant, a typical harmony for a cadenza. Then comes the third section which takes us to the end of the piece. This features a slower tempo and more harmonic complexity. The bass moves to F# then E flat and the harmonies above use those notes plus the A and C. This gives us a diminished seventh on F#. Ultimately the bass reverts to A while the F# and E flat continue above which just changes the inversion. Then the upper voices return to a simple A minor harmony and the piece ends with a fortissimo A and C in several octaves.

That paragraph describes the harmony. So, are we done? Not at all because obviously the harmony is not where the real action is. The first eight minutes, which I described the other day as a ritornello with ornamental sections needs to be described in much more detail, especially as regards durations. After the opening gesture, the two As at opposite ends of the tessitura, there is a Grand Pause over a measure of 8/2. Then the ritornello starts which simply consists of overlapping falling minor sixths dropping down to a bass A and then rising up again with rising minor sixths (C down to E and then E up to C) all accompanied by repeated As. Over this there is some brief ornamentation in the two solo violins using eighths, triplet eighths and sixteenths. This first statement of the ritornello takes seven measures. The last measure of the ritornello, which has all been 4/4, takes us to a two-measure passage of 5/4 followed by 6/4 with long very high As in one solo violin doubled with notes in the prepared piano (which, because of the preparation has a cluster of pitches resembling a bell). This is followed by another G.P. (Grand Pause) but this time on a measure of 7/4. I am going to label these three different ideas, the ritornello (R), the sustained high notes with prepared piano (S) and the G.P. (P).

Then the ritornello returns, but this time it is extended to ten measures in which the solo violins extend their ornamental passage from three measures to six measures. The second statement of S is now three measures instead of two and they are longer measures: 6/4. The P is shortened to 6/2.

Third statement of R is now twelve measures with the ornamental passages extended to ten measures. The S section is now five measures, again of 6/4. The P is shortened again to 5/2.

Fourth statement of R is now sixteen measures with thirteen measures of ornamentation for the solo violins. The S is extended to six measures in 6/4 and the P is shortened to 4/2.

The fifth statement sees the texture of the ritornello for the orchestra thickened and with passing notes so that the rising and falling minor sixths are now a scale passage falling from E down to D and rising again. The falling sixths are retained in the low bass. The solo violins are given much more to do as well with grace notes and passing notes. The R is now eighteen measures long. The S is shortened to two measures, 5/4 and 6/4, and the P is a measure of 3/2.

The sixth statement of R is extended again to twenty-two measures and the orchestra uses more of the scale passages. The solo violins develop their material and have an extended passage in triplets. S is also extended to nine measures and the P is now 2/2.

In the seventh statement the solo violins dominate the texture so thoroughly that we hardly hear the characteristic falling sixths of the ritornello. R is now twenty-four measures. S is extended to eleven measures and the P is 1/2.

This process continues in the eighth and final statement of R which is now thirty measures. At the end instead of continuing to S and P, there is a brief rallentando and the cadenza begins. You could argue that the cadenza replaces the S theme. The cadenza is twenty-two measures long. The final section, Meno mosso, is in 6/4 and takes seventeen measures. It essentially acts as a coda with the greatest harmonic variety of the piece.

One element I have not discussed is the function of the very low register chord in the prepared piano that acts as a punctuation point, a bit like the gong ageng in gamelan music. It occurs eight times, once in each statement of R. Here, counting from the beginning of R, is when the chord occurs:

• measure 4
• measure 5
• measure 6
• measure 7
• measure 8
• measure 9
• measure 10
• measure 11

So, at the same time the P is being shortened by one beat in each iteration, the piano chord is being moved one measure later in each iteration.

Pärt begins with a very simple ritornello with some elaboration in the solo violins. This is extended with each iteration. At the same time the S theme is also extended. The P idea is shortened with each iteration. Finally, the piano chord punctuation is moved one measure later in each iteration. This gives us four simultaneous processes being worked out in the A section. (I see three large sections in the Ludus movement: A is the RSP section, B is the cadenza and C is the coda.

The subtleties are in the areas of phrase and meter, not so much in harmony or melody. What is particularly attractive in this piece, which has been very successful with audiences since its premiere, is the choice of thematic material for the ritornello as well as the uniqueness of the structure.

So that's my analysis of the Ludus movement. Next, I will have a look at Silentium.

Please, leave me a comment. If you disagree with my analysis, that would be particularly interesting!

Update: Just adding a clip of the piece. Sorry, I couldn't find a clip with the score!

Also, here is the beginning of the 4th iteration of R. You can see the low piano chord in measure 50.