STM-Online vol. 3 (2000)
Edward Jurkowski, University of Lethbridge, Alberta

Joonas Kokkonen’s “Free” Dodecaphonic Composition?

A Study of the Passacaglia from the String Quartet No. 2

Edward Jurkowski, University of Lethbridge, Alberta


Like many composers, the oeuvre of the Finnish composer Joonas Kokkonen may be divided into three stylistic periods. Kokkonen’s first period includes compositions written up to 1958 and contains strong neoclassical traits; examples of this style include such important works as the Piano Quintet (1951-53) and the 1957 Music for String Orchestra (the latter composition is one of the finest examples of post-World War II Finnish string ensemble writing). Kokkonen’s third period consists of works written after 1968 that are typically described as neo-romantic or neo-tonal in style; the most celebrated composition from this period is his 1975 opera The Last Temptations. While some literature has proven beneficial to understand features of the music from these two periods, it is the compositions from Kokkonen’s second stylistic period, i.e., the works written between 1958 and 1967, which have proven difficult to comprehend.1 Specifically, while it is acknowledged that these works are primarily constructed from dodecaphonic techniques, it is rare to find only one particular row form of a row ordering (or any of its forty-seven related row forms) employed in a composition. Further, not only it is common to find different row orderings for each movement of a multi-movement composition, but also simultaneous presentations of these different row orderings within an individual movement. In short, the numerous row orderings, the frequently incomplete row statements, and melodies or harmonies which at times seem to bear no relationship to a precompositionally assumed row ordering have caused writers on Kokkonen’s music to either generalize such licenses from the compositional practices of such classical dodecaphonic composers as Schoenberg and Webern as “free” twelve-tone composition,2 or to simply avoid altogether any commentary on a work’s specific twelve-tone procedures.


This paper challenges the notion of Kokkonen’s supposed dodecaphonic freedom. As we shall see, Kokkonen’s dodecaphonic works (and, in this respect, like the twelve-tone works of Alban Berg, a composer Kokkonen much admired) contain a highly sophisticated and imaginative use of the twelve-tone system, where dodecaphonic procedures are not compositional ends in themselves but, instead, serve larger structural intentions in a work. As a model of explanation of Kokkonen’s twelve-tone compositional style, our focus of inquiry will be the passacaglia-designed first movement from his String Quartet No. 2. The composition is a worthy candidate for study on several counts. First, the quartet is not only the last composition from Kokkonen’s second-period body of works but, additionally, contains some of the composer’s most advanced thinking in terms of dodecaphonic composition. Second, the passacaglia contains attributes that are viewed as trademarks of Kokkonen’s compositional style – for instance, the Golden Section proportions that govern the formal design of the movement. Third, the dimension of the movement, both in terms of length and number of instruments, makes it feasible to explore the entire movement within the scope of the present paper.


Kokkonen began work on the second quartet in late 1964. His original intention was for this quartet to be a single-movement passacaglia. However, an illness during February of 1965 halted progress on the work for several months and when Kokkonen returned to the piece during the summer months he realized that his conception of the composition had changed: while the original passacaglia idea was retained, it became positioned as the first of four movements. This opening passacaglia is followed by a second-movement intermezzo, a third movement allegro vivace (preceded by an andante introduction), and a fourth movement adagio. Overall, there is a somber quality to the quartet: only the light-hearted intermezzo stands in contrast to the severity of the other movements. In fact, the complex textures, consistently dissonant harmonic language, and long, angular melodies make Kokkonen’s second quartet the most enigmatic and austere from his quartet cycle – arguably, the most austere work from his entire oeuvre – features which have no doubt contributed to its lesser familiarity, especially when compared with the popularity of its two siblings.

Listen to the beginning of the movement. 472kB. (All excerpts are from BIS CD 458, and used with the kind permission from BIS.)


Like most other multi-movement dodecaphonic compositions by Kokkonen, each movement of the second string quartet is based upon a different row ordering. The third movement alone contains two orderings: one for the andante introduction and another ordering for the allegro vivace proper. While such compositional practice may not be unique – consider, for instance, the various changes to the first movement’s row ordering in subsequent movements of Berg’s Lyric Suite for string quartet – what is somewhat unusual is Kokkonen’s penchant to simultaneously utilize row orderings from these different movements. In the first string quartet, for instance, prominent row forms from earlier movements continually return in subsequent movements – in fact, the finale is a virtual compendium of the significant row forms used during the work. We shall return to this recurring feature of Kokkonen’s music at a later point in this article.


The passacaglia is based upon the following twelve-tone row: C, C#, B, E, D, Eb, A, Ab, Bb, F, G, F#. An interesting feature of the row’s ordering is the symmetrical presentation of the pitch classes from each hexachord by a tritone (shown in example 1): for example, C-C# and G-F#, both interval-class (hereafter, ic) 1s, are matched together, C#-B and F-G, both ic 2s, are matched, etc. Note also that the ordering of the pitch classes generates four contiguous [012] trichords and that these trichords are also tritone-related to their corresponding members in each hexachord.3 The row’s symmetry suggests an indebtedness to the celebrated row from the first movement of Berg’s Lyric Suite, i.e., F, E, C, A, G, D, Ab, Db, Eb, Gb, Bb, B. For instance, a reordering of each hexachord from Berg’s row generates an incomplete interval-5 cycle (i.e., E-A-D-G-C-F from hexachord 1 and Bb-Eb-Ab-Db-Gb-B from hexachord 2), a feature which Berg fully exploits in his work.4 By contrast, each hexachord from the row ordering of Kokkonen’s passacaglia movement contains an incomplete interval-1 cycle: B-C-C#-D-D#-E from hexachord 1 and F-F#-G-G#-A-Bb from hexachord 2.


The inherent symmetry of the row’s structure may be interpreted as an analogue for the symmetry of the movement’s overall formal design. As a point of departure to this idea, let us examine the passacaglia statements themselves. As is well known, the traditional means to construct a series of passacaglia variations is to use a recurring melody as the basis from which melodic and harmonic elaboration is presented. A common strategy is to present the recurring melody in the baseline and after a number of repetitions, it might migrate to the upper voices, thereby reducing the harmonic limitations inherent within the recurrent baseline. The length of the passacaglia “theme” is typically identical, thereby providing a sense of consistency to the events of the variations (although deviations are certainly common – less so, however, during the beginning stages of a composition).


Kokkonen’s plan diverges from the just-described conventions of a passacaglia. First, while the passacaglia theme consists of a twelve-tone row, the theme frequently changes, as it is based upon several row forms from two different row orderings. Second, instead of the passacaglia theme used as a baseline, it is more often found as a Klangfarbenmelodie between several instruments in an upper voice (for example, between violin 1 and violin 2 in mm. 122-129) or as part of a vertical sonority (for instance, the four-voiced chord in m. 90). Third, the length of these passacaglia variations constantly changes. The number of measures of each variation is based upon successive elements of a Fibonacci number series; the pattern to the number of measures is 3 – 5 – 8 – 13 – 8 – 5 – 3 (example 2 indicates the occasional deviations to this pattern). This pattern of an increase and decrease of measure numbers occurs three times and forms the basis of an arch-form design. Specifically, as the number of measures of each variation from the outer sections increases, there is an increase in rhythmic activity, overall dynamic, and exploration of instrumental tessitura; these musical attributes diminish with a decrease in the number of measures of each variation. The middle section, however, reverses this pattern: as the length (i.e., the number of measures) of each variation increases, there is a decrease in dynamic, rhythmic activity, and instrumental range, only to increase as the section comes to a close. Example 2 outlines each variation from the three sections. Each row on the chart provides the following information of each successive passacaglia thematic statement: the length (in measures), the measure numbers corresponding with each theme, the row forms and row orderings used, and the instrument(s) used to play the passacaglia theme.5


Example 2 shows that a ternary form can be forged from the specific row choices made for the various statements of the passacaglia theme. Significantly, however, this ternary form correlates with the just discussed tripartite arch form generated from such surface features as dynamics, tessitura, etc. For instance, the passacaglia themes are generated exclusively from the T0P form of movement one’s row ordering until the latter part of Section I. By contrast, the majority of the row forms used for the various passacaglia themes in Section II include T4P, T4I, and the T4P forms of movement two’s row ordering (the specifics regarding this latter row ordering will be discussed at a later point). Section III’s return to Section I’s primary row form T0P engenders a sense of familiarity to the pitch structure used during the outset of the movement (note that Section III also contains one instance of the related T0I, as well as one instance each of T4P, a row form also found in Section I, and its related T4I).

Example 2

Outline of Length, Row Forms, and Instruments used for the Various Passacaglia Themes in Kokkonen, String Quartet #2, Mov. 1

Section I

Measure #s Length

(in measures)

Row Form Instruments used for Passacaglia Theme
1-3 3 T0P all instruments used, with a variety of colours
4-8 5 T0P cello and violin 1 (violin 2 included at end of variation)
9-16 8 T0P exclusively by cello
17-30 *14* T0P exclusively by cello
31-37 *7* T0P viola and cello
38-42 5 T4P violin 1
*3* (not contained in Section I)

Section II

Measure #s Length

(in measures)

Row Form Instruments used for Passacaglia Theme
43-45 3 T4P all instruments used simultaneously
46-50 5 T4P cello and violin 1
51-58 8 T0I viola and cello
59-71 13 T0P viola and cello
72-79 8 T4P shared between all instruments
80-84 5 T4I (or T4P mov. 2?) T4I played by violin 1; T4 (mov. 2) played by viola and cello
85-89 *5* T0I shared between all instruments
90-92 3 T4P and T4P/T0P shared between all instruments as chords, followed by statements of T4 and T0

Section III

Measure #s Length

(in measures)

Row Form Instruments used for Passacaglia Theme
93-95 3 T0I violin 1 and cello
96-100 5 T4I violin 1
101-109 8 T0P cello
110-121 13 T0P shared by all instruments
122-129 8 T0P violin 1 and violin 2
130-134 5 T4P shared by all instruments
135-137 3 T0P shared by all instruments


There are three important row forms that compete with the many statements of T0P. The first is T0I – C, B, C#, G#, Bb, A, Eb, E, D, G, F, F#. As seen in example 3, there is a close relationship between T0P and T0I, one largely the result of the tritone relationship between hexachords discussed earlier (refer back to ex. 1): trichords I and IV from both row forms are pitch-class invariant, while trichords II and III from T0P are pitch-class invariant with trichords III and II, respectively, from T0I. The upshot is that the two rows contain four slightly reordered pitch-class invariant [012] trichords, thereby providing both harmonic similarity and difference between the two row forms.


T4P is a second row form offering contrast to T0P; the row is E, F, Eb, G#, F#, G, C#, C, D, A, B, Bb. Notable with this row form is the [012] trichord {F#,G,G#}. Although of minor importance in this movement, the trichord anticipates its presence within {F#,G,G#,B}, a significant tetrachord in the remaining movements of the composition. For instance, in the first and second movements the choice of row forms, in general, tends to maximize the [012] pitch-class elements of this tetrachord (i.e., F#, G, and G#), while in the third and fourth movements, the primary row orderings are such that the pitch-classes F#, G, G#, and B represent the first four contiguous row elements from each movement’s respective row. The upshot is that the gradual increasing prominence of this tetrachord, and in particular, one that is forged from row re-orderings of prior movements, suggests that the row orderings have harmonic significance beyond their relevance within individual movements. We shall explore this idea later in this paper.


A third row competing with T0P is the T4P form of movement two’s row ordering, i.e., E, A, F#, G, Bb, D, B, C#, C, Ab, Eb, F. Example 4 illustrates the relationship between this row and the T0 from movement one’s row ordering. Specifically, the two mutually exclusive trichords from the first hexachord of T4 row ordering <E,A,F#,G,Bb,D>, i.e., <E,A,F#> and <G,Bb,D> are [025] and [037] trichords, respectively; the trichords are forged by taking a pitch-class from each of trichords II, III, and IV from movement one’s T0P (for instance, in the pitch-class set {E,A,F#}, the E is obtained from T0P’s trichord II, the A from trichord III, and the F# from trichord IV). The trichords from the second hexachord are <B,Db,C> (an [012] trichord), a pitch-class set invariant with the trichord I from T0P and <Ab,Eb,F>, an [025] trichord, which like {E,A,F#} and {G,Bb,D}, may be created by taking one pitch class from each of the latter three trichords from movement one’s row.


As was witnessed in example 2, T4P, and, in particular, the hexachord <E,A,F#,G,Bb,D>, is prevalent in the middle section of the passacaglia. Further, this hexachord is consistently partitioned into the two trichords identified in the previous paragraph: {E,A,F#} is played by violin 1 and {G,Bb,D} by violin 2, a partitioning pervasive throughout the middle of the movement (mm. 51-69 constitutes this middle section; example 5 illustrates the partitioning in mm. 59-60). It seems nonplused that a segment from a different movement’s row ordering should be emphasized during the central point of this movement, especially when the one trichord, {G,Bb,D}, is a representative of [037], a set class not even present in movement one’s row ordering. However, a possible rationale for this unusual harmonic feature may be determined if we instead focus upon the other trichord, {E,A,F#}, a member of set-class [025]. As example 6 illustrates, there are four imbricated [025] trichords in movement one’s row ordering, a number as prevalent as set class [012]. In this sense, then, the {E,A,F#} [025] trichord generates a direct harmonic relationship with a prominent trichord from movement one’s row ordering: the partitioning of the hexachord into two prominent trichords from movement two, then, suggests an important structural relationship between these first two movements. Viewed from this perspective, it seems fitting, then, that this hexachordal segment from movement two’s row ordering should be highlighted for such a long duration at the midpoint of this movement: the hexachord’s presence may be interpreted as one strategy to harmonically link together two seemingly disparate movements.

(Listen to measures 59-71. 469kB.)

(Listen to Example 5. 94 kB.)

All musical exerpts are with the kind permission of Warner/Chappell Music Finland.


Let us now turn our attention to the relationships between both forms of T4P from the row orderings of movements one and two and, specifically, the pitch-class invariances between order positions 1, 2, and 3 from movement one’s T4P ordering (i.e., the pitch-class segment <F,Eb,G#>) and order positions 9, 10, and 11 from movement two’s T4P ordering (i.e., the pitch-class segment <Ab,Eb,F>); this relationship is seen in example 7.6 (While the invariant row segment could be extended to four pitch classes, i.e., order positions 0, 1, 2, and 3 from movement one’s T4P and order positions 9, 10, 11, and 0 from movement two’s T4P, the point to be presently made involves a relationship only with trichords.) Earlier, we discussed an association between T0P from movement one’s row ordering and T4P from movement two’s row ordering, namely, the invariant [012] trichord, {B,C,C#}, while the remaining trichords are forged by combining singleton pitch classes from each of three trichords from T0P (for example, the <E,A,F#> segment from movement two’s T4P row is generated by taking the E from trichord II, the A from trichord III, and the F# from trichord IV; this process was shown in example 4). Example 8 illustrates that by rotating the order positions of movement one’s T4P ordering by one (in other words, pitch-class E, formally order position 0, now becomes order position 11) the invariant trichordal segment <F,Eb,Ab> assumes the order positions 0, 1, and 2. Repeating the process of extracting one pitch class from each of the three remaining trichords from movement one’s row obtains the three trichords from movement two’s T4P ordering (for example, by extracting the F# from trichord II, the A from trichord III, and the E from trichord IV will create trichord I from the T4 form of movement two’s ordering, i.e., <E,A,F#>. In short, the harmonic relationships between T0P and the T4P form of movement two’s row ordering identified earlier are also present between the two forms of T4P (i.e., from the row orderings of movements one and two), supporting our earlier supposition that movements one and two are structurally linked because of the association the [025]/[037] trichordal partitions from movement two’s T4P hexachord may share with movement one.


A further harmonic relationship between the row orderings from movements one and two is witnessed between the opening tetrachords from both rows. Specifically, the first two mutually exclusive dyads in all the prime and inversion row forms from movement one’s row ordering are an ic 1 and an ic 5. However, these interval-class values are reversed in all prime and inversion row forms from movement two’s ordering – in other words, ic 1 follows ic 5. This harmonic association between row orderings is exploited as early as mm. 4-6 (i.e., from the second variation): while the music in variation one, mm. 1-3, articulates trichordal harmonies from the T0P row form, harmonic and melodic dyads are the focus of variation two. As example 9 illustrates, the passacaglia theme unfolds between the cello and violin, articulating a melodic ic 1 (cello C2 to violin 1 C#5)7 followed by an ic 5 (violin 1 B4 to E4). However, movement two’s row ordering is simultaneously presented as harmonic dyads of ic 1 followed by ic 5 by the violin 2 and viola. Notice, however, the harmonic contrast between this reciprocal relationship of interval-class values and the events in m. 6: harmonic dyads of ic 4 and ic 2, played by the violin 2 and viola, contrast with the cello’s ic 1 (from the D3 in m. 5 and the Eb3 in m. 6; two ic 1s are also present in m. 6 between the cello’s A3 and the both the Ab3 and the Bb3 from the violin 1 trill). The upshot is that the similarity of interval-class values between melody and harmony in m. 4 evokes a sense of harmonic unity between the initial portions of these two row orderings, an association which is abandoned during the remainder of the row presentation.

(Listen to Example 9. 94 kB.


This paper has explored some ideas to explicate the choices of row forms and different row orderings in the passacaglia-designed movement from Kokkonen’s second string quartet. We have seen, for instance, that the presentation of the various row forms from two different orderings correlates strongly with the surface ternary form of the movement, suggesting a symbiotic relationship between formal design and the harmony that results from these particular row forms. Further, the three row forms from movement one’s row ordering, i.e., T0P, T0I, and T4P, share important pitch-class relationships not only amongst themselves but also – and significantly – with the primary row form of movement two’s row ordering, i.e., T4P. The relationship with this latter row ordering is of great importance, for it is Kokkonen’s use of the T4P form of movement two’s row ordering – most overtly, at the central point in the passacaglia – that illustrates an important aspect of his compositional thinking, namely that dodecaphonic (and, as a corollary, harmonic) associations need not be restricted to an individual movement, but that specific row forms from carefully constructed row orderings can be used as a powerful strategy to achieve coherent inter-movement harmonic organization.


Space obviously precludes an exhaustive examination of this movement; however, the ideas presented in this paper should be sufficient to provide an understanding of some of the salient dodecaphonic strategies from this passacaglia. And while we have purposely restricted our attention to only one movement from his second string quartet, it should be noted that analogous compositional practices may be found in most of Kokkonen’s other second-period compositions. Further study of these works will be pertinent, then, to forge a generalized theory of the composer’s dodecaphonic compositional practices, thereby formulating a more complete understanding of one of Finland’s most important compositional voices from the latter half of the twentieth century.


1. The literature on Kokkonen is too vast to cite here. A substantial bibliography devoted to the composer, however, appears in Pekka Kuokkala, Ooppera Viimeiset kiusaukset Joonas Kokkosen säveltäjäkuvan heijastumana, Master’s thesis, University of Jyväskylä, 1992. [Back]

2. Some of the standard precepts of classical dodecaphonic composition are identified in George Perle, Serial Composition and Atonality: An introduction to the Music of Schoenberg, Berg, and Webern, 6th edition (Berkeley: University of California Press, 1991), 2-3. [Back]

3. The convention adopted in this paper is that pitch-class sets are categorized into families via the TTOs Tn and TnI. Therefore, {C,C#,D} and {A,Bb,B} are both members of Tn/TnI-class [012], {C,D,F} and {E,G,A} are both members of Tn/TnI-class [025], etc. [Back]

4. For discussion specifically about some of the twelve-tone practices in the Lyric Suite, see Dave Headlam, The Music of Alban Berg (New Haven, Conn.: Yale Univ. Press, 1996), 250-283 and George Perle, The Operas of Alban Berg, Volume II, Lulu (Berkeley: Univ. of Calif. Press, 1985), 10-15. [Back]

5. A fixed do system is used to label row forms: for instance, T0P is C, C#, B, E, D, Eb, A, Ab, Bb, F, G, F#; T3P is Eb, E, D, G, F, F#, C, B, C#, G#, Bb, A; T0I is C, B, C#, G#, Bb, A, Eb, E, D, G, F, F#; T0RP is F#, G, F, Bb, Ab, A, Eb, D, E, B, C#, C; and T0RI is F#, F, G, D, E, Eb, A, Bb, G#, C#, B, C. [Back]

6. This paper adopts the convention that order positions of a twelve-tone row are numbered from 0 to 11. Therefore, order position 1 is actually the second pitch class in a row ordering, order position 3 is the fourth pitch class in a row ordering, etc. [Back]

7. C4 represents middle C; C3 is the octave below middle C, C5 is the octave above middle C, etc. [Back]

©Edward Jurkowski, University of Lethbridge, Alberta, 2000

STM-Online vol. 3 (2000)


ISSN: 1403-5715