By Martín Rincón Botero
Two years after I presented my analysis of Eliasson’s Symphony No. 4, the first recording of this symphony was released. As the saying goes, “good things come to those who wait”. Well, this recording is certainly something to be happier about than my small contribution: it’s hard to be half as amused and inspired while reading an essay about the Symphony than when actually listening to it. But all great art, in addition to amusement, also makes us think. Like a Greek aoidos in Homeric times, Eliasson provides through its symphony both pleasure and wisdom.
The delay in writing this essay had to do, coincidentally, with the pandemic. It was, for me, a time period in which I further explored my harmonic world (an exploration that has been recently expanded by my discovery of David Lewin’s Riemann Systems), the harmonic language of Eliasson having always been an inspiration for me. The harmonic perspective I gained during this time allowed me to improve my original presentation in many points, which I now outline here. Even though back then I briefly talked about some aspects of the second and third parts of the Symphony (+ coda), I would like to concentrate here only on the first part (m. 1-413), which in itself already contains many of the principles and techniques elaborated in both subsequent parts.
One of the most inspiring facets of Eliasson’s music is the fact that harmony plays an articulating function in form. This is something obvious in much, if not all, of the music of the so-called “common practice period”. However, to find that kind of harmonic architecture in contemporary music is certainly unusual: the forces of harmonic progression necessary for the proper discernment of formal segments have been in much avant-garde music largely replaced by other factors such as texture and timbre. In the first measures of the Symphony we already find a harmonic progression that starts at a first tonic center (E) and descends towards Ab (Figure 1). This chord gravitates to A (as if the Ab was interpreted as a lead-tone to A, the enharmonic of G#, confirmed by the fact that the Ab chord uses Fb, which can again be enharmonically re-interpreted as E), and after some measures of harmonic instability (typical of a transitional zone), it establishes again on A.
Above is a schematic view of harmony of the first 23 measures. Measure numbers are marked with boxed numbers; consecutive measure numbers are not marked (f. ex., the measure before bar 15 is measure number 10). Below the measure numbers are the Forte pitch-class sets of each chord. As we can see, the whole passage is mainly made up of the pc set (0, 2, 3). Even if there are other pc sets marked, they all can be seen as supersets (i.e. the same chord with an added note) of the basic primary set. For example, in measure 4 we see the same first chord with an added D#. In the bass clef are “root tones” according to the harmonic theory of Hindemith. These are not here to claim any direct connection between Eliasson and Hindemith (or even to state that Hindemith’s theory has universal validity!), but instead to better visualize certain harmonic directions that are interesting in their own right (even if Eliasson didn’t think about it!), and, more importantly, to pose the question whether Eliasson actually had a root-tone plan for the harmony. This root-chord visualization reveals some interesting properties: the root sequence E, D#, C from measure 1 to 6 has the same intervals as the sequence that starts in the same measure C, B, Ab (minor second + augmented second). Both groups in themselves form the set (0, 1, 4), itself a subset of (0, 1, 3, 4) (cf. m. 4). We can also see how measures 6 to 9 are, harmonically, the first four measures transposed down a major third. The big surprise comes in m. 10, where my analysis shows “Ab (6b)” instead of a proper pc-set (Figure 2). This heptachord should be read as “the scale of Ab major with a flat sixth degree”. Interestingly, this chord is basically a combination of sets (0, 1, 3, 4) and (0, 1, 3), (0, 1, 3) being the inversion (and prime form) of the set (0, 2, 3), the core sonorities of this passage!
The same set-theoretical Forte nomenclature will be used throughout this essay.
Later this will bring us to some interesting reflections on the subject of “modulation” in the context of harmony and form.
The harmony of the Symphony is not only designed to play a coherent role intrasystemically, but also coordinates with other music parameters: it’s the case of form and orchestration, two allied forces of the harmony in this work. The first entrance of the timpani in the whole piece is in measure 73, where the arrival back to the “tonic” (E, F#, G) in m. 77 is announced (Figure 3). The chord that the timpani’s Ab forms with the rest of the orchestra is E, G, Ab, namely, a (0, 3, 4) set, a subset of (0, 1, 3, 4).
M. 117 is another place where the harmony is used as an “announcing force”. There we find a chromatic chord (all semitones from F# to A). This chord announces a section that starts in m. 124, which becomes progressively more unstable by means of rhythmical motives that become more and more unpredictable. This process is already quite audible in the cellos and double basses starting from m. 134 (Figure 4).
A new stable arrival is announced again by the timpani in m. 145 (also with an Ab), with the resulting chord G, Ab, Bb, Cb or set (0, 1, 3, 4), the “tonic” appearing in m. 147.
By now we should already see how orchestration and harmony are deeply connected in this work. So far, the timpani has been crucial in marking each new arrival to the “tonic”. In m. 168 the timpani plays again its usual quarter-note triplets, but in a totally different harmonic realm. Here we find the new set (0, 2, 5), a subset of the set (0, 2, 3, 5) (see m. 18 above), as well as the set (0, 1, 3, 6), another superset of the core (0, 1, 3) set, with an added tritone, historically used to add tension before a cadence. In the next figure (Figure 5) we see all intervening sets marked. The harmonic rhythm is half-notes, and we see how the first three measures have a certain “dominant-tonic”-like movement, at least from a dissonance perspective: the (0, 1, 3) set is more dissonant than the (0, 2, 5), so the first three measures have a tension-relaxation type of dynamic. The fourth and fifth measure have only tetrachords from the dissonant side of the spectrum. The last measure is the resolution to that tension ((0, 3, 5) is the inversion of (0, 2, 5) with notes B, D, E).
Although not in the example, the tuba plays a different note than the timpani in the last chord in m. 173. While the timpani has a D, the tuba plays a lower B. What does this B mean? If we take the B as the root-tone of the chord, then, since the first harmonic region at the beginning has E as the tonal center, it seems the piece somehow “modulated” to B (albeit with a different chord type), traditionally known as the dominant of E. But the root-tone of the chord might just as well be E (Hindemith would certainly support this view); the first chord of the piece has actually a different note in the bass than what we assumed to be the fundamental of the chord, and here we would logically also have a chord in inversion. One can only speculate if Eliasson actually thought of a fundamental or root-tone for every chord, but these “coincidences” here and there have certainly made me wonder if that’s the case.
Following the journey marked by the timpani, we arrive at measure 202, where, after a few tremolo notes, the timpani brings us back to E in m. 205. The arrival chord in this measure has the notes C, C#, D#, E, or set (0, 1, 3, 4) and the new harmonic region is prolonged for six measures with an E as pedal point.
Having come back to the “tonic” E for six measures, m. 211 destabilizes the musical flow with a very rhythmical section. The percussion here keeps playing a structural role. In this case it’s not the timpani with its harmonic articulating functions, but the rest of the percussion that gets introduced abruptly (xylophone, bongos, tom-toms, bass drum). Aurally, the rhythmical instability of this section is marked even more by the presence of these new timbres.
Our next harmonic arrival is this time not announced by the timpani but by the trombones and the tuba instead, with the usual announcing quarter-notes triplets. The tritone that was structurally important in m. 168 gains even more importance here. In m. 224 we find the notes F#, Bb, C, or set (0, 4, 6), a set distantly related to the set (0, 2, 3) only via multiplication. This new set interleaves with set (0, 1, 3, 4). In the next few measures, the quarter-note triplets (not in Figure 6) continue.
The logical instability of the quarter-note triplets, though, doesn’t give enough rest to this new arrival (and the new chord, set (0, 4, 6), is also not a sufficiently stable point in the context of the harmonic development). The force of the triplets keeps pushing this section forward. In m. 228 all strings (except for the double bass) add to this buildup with a unison passage to arrive to m. 233, with another tritone type chord with notes E, F, G, Bb, or set (0, 1, 3, 6), a set that we already had in m. 171.
We land at a section quite similar to the one in m. 211-220, which in retrospect means that the previous section wasn’t actually done (and it was indeed only a phrase that is part of a larger section). The quarter-note triplets phrase we just described needs to be formally understood as a part of the same section, namely, a phrase group that spans m. 211-248.
M. 249 has a consonant type chord with notes G, Bb, C, or set (0, 3, 5). If we stick to the idea that m. 173 had B as root-tone, G must be consequently here the root-tone of the chord, related by a minor third to the first center E, with yet another tonal reference to the first center.
In m. 251 the brass start with a short choral type of phrase that displays much of the harmonic language developed so far. The following harmonic scheme (Figure 7) stops where the harmony comes back to the first chord and the strings take over from the brass in m. 256. Interestingly, the melody that the first violins play, developing what the first trumpet left inconclusive, uses a scale that highly resembles the heptachord analyzed in m. 10. Here both constituting groups are simply exchanged (Figure 8).
Logical, of course, in the context of this work.
C.f. m. 173.
M. 259 takes us further away from the first tonal center E. Here we have the notes Eb, F, Gb, Ab, or set (0, 2, 3, 5) (c.f. m. 18), a known sonority with a chromatic transposition with regard to E (a transposition a half-step lower). This chromatic transposition reinforces the new instrumentation: solo cor anglais and solo clarinet begin a short duo in a question-answer, alternating, hocket-like fashion. These few measures (m. 259-263) have essentially only the cellos accompanying. This small duo is again taken over by the strings at m. 264. We start to see here what this section is about: a dialog between winds and strings, but also, initially between pairs of winds. A small kind of duo between bassoons and french horns proceeds from m. 267 to m. 275, followed by a counterpoint between bassoons and clarinets (m. 276-292) that begins with the same question-answer model but that by m. 285 has been progressively made polyphonic. This new polyphonic texture gets ever more intense (bassoons and clarinets get divided, each one playing its own melody) and by m. 293 brass (including damped horns and trumpets with bucket mute) and more and more strings (with some effects like pizzicato, harmonics and open-end glissandi) add to the texture. This complex texture is the background upon which the cor anglais has its most prominent moment, starting from m. 293 all the way to m. 310. At this point the percussion (without timpani) enters, adding more instability to the section. Violins play with forward-moving quarter-note triplets, and a variety of effects and small melodic figures create a complex atmosphere. This type of texture without melody continues, in bursts of sound that get every time rhythmically more dense, for several measures (m. 310-398).
In m. 398, we are greeted with the chord G, A, Bb, set (0, 2, 3), the core set of the work transposed a minor third. The next few measures progressively relax the atmosphere and prepare the journey for the second part (Adagio), where our aoidos embodies his wisdom to us with an improvisational flugelhorn solo.