Compositional Techniques in Karel Husa’s Early Serial
Works Poème and Mosaïques
Craig Cummings
Karel Husa was born in 1921 in
My
main reasons for not returning when ordered to were artistic, not only
political. I would study for two to four years in
Some observers describe Husa’s early compositions, such as the orchestra
pieces Overture (1944), Sinfonietta (1944), and Three fresques
(1947) and two early string quartets (1943 and 1948) as neo-Classic or
neo-Romantic in style.[2] Eventually,
however, Husa turned to serial techniques for creating musical compositions, though
always with his own approach and musical end results. In an interview
conducted in August 1995 and then published in ex tempore in 1996,
Robert Rollin and Husa discuss much about the composer’s life and
career. Several questions about serialism, along with Husa’s responses,
are quoted below.
RR: When did serialism begin to influence
you? When did you begin to experiment with serial techniques, and which
composers at that time influenced you?
KH: It was already starting in
RR: Schoenberg was at this
time in the
KH: Yes, he was in the
RR: So, who took his place as
the most dynamic figure? Was Boulez already involved?
KH: Boulez was
known, and already I had heard his First Piano Sonata. It was
mostly the works that I studied; it was not people. Stockhausen I knew
also in
Based on these comments, one might expect that Husa
would have turned fairly rapidly to using serial compositional
techniques. His life circumstances in the early 1950s may have temporarily
prevented such experimentation. Husa married and had children, and he
permanently left behind his Czech homeland, moving in 1954 to the
The important first serial pieces
came a few years later. Rollin’s conversation with Husa provides
interesting background:
RR: Returning to the question of serialism and the
new, more chromatic style that you were working on, which would you say, the Poème
for Viola and Chamber Orchestra (1959) or the Mosaïques for Orchestra
(1961), was the more pivotal piece for you in terms of serialism and the future
of your music for later years?
KH: I would say the Mosaïques
was more striking in colors, because I experimented with orchestral colors
especially. I liked the Poème too, because it’s more austere in a
way; it’s a piece for which I have affection, but it has less colors, because
it’s only strings, viola, oboe, piano, and horn.
RR: It’s within a more narrow
coloristic band, but still a very lovely piece.
KH: It’s a twelve-tone piece, but it’s in a style,
if you wish, of Schoenberg’s twelve-tone approach. Mosaïques is
already more what also Boulez and Stockhausen speak about. It’s not only
the twelve notes, but the rhythm and the dynamics are serialized too . . .
RR: I heard you
conduct a performance of it at Cornell with the Buffalo Philharmonic when I was
a student, and I remember thinking that it had an affinity to Webern, more than
to Schoenberg, which makes sense because of the coloristic aspect - perhaps
because of klangfarben, the very delicate movement of melodic material
from one instrument to the other. So, perhaps in a formal sense, the Poème
was the place where you first introduced serialism, then further developed it
in Mosaïques. Were there chamber pieces around that time also, or
were these the pieces in particular? KH: That [sic]
would be the pieces; then later came the Third String Quartet (1968) which
also uses some twelve-tone techniques, but it is much more free already.[4]
Husa’s Poème,
completed in 1959, thus marks a departure from his earlier style into a more austere
approach characterized by greater dissonance and serial procedures; it is a
turning point in his compositional output. It is interesting that its
original title, as found on the cover sheet of its sketch file, was Abstract
Poem. Within two years, Husa had completed his second largely serial
work, Mosaïques (1961) for large orchestra. As the composer himself
states, these pieces together represent an important change in Husa’s style and
technique. Accordingly, these seminal compositions are the works examined
in this study.[5]
Poème
By 1959, Husa had fully
settled into his new life, becoming a
Poème is cast in
three brief movements without breaks. The first movement, slow and
rhapsodic, is labeled improvvisando. The misterioso second
movement moves at a faster tempo and is the longest movement. The final
movement, labeled dolce, returns to a slower tempo and more
improvisational style. The first and third movements begin with lengthy
solo viola melodies and the piece concludes with the solo viola fading away
into silence.
Husa’s sketches provide an
interesting opportunity to examine the serial logic of Poème. Thirty-five
separate sheets are included in the sketch file for Poème, located in
the Husa Archive at
While each movement has
its own row, there are strong connections among the three rows - so strong, in
fact, that Husa thinks of the piece as being based on a single row.[8] An
especially interesting sketch page shows Husa’s creation of a row consisting of
three tetrachords that he labeled A, B, and C (see Facsimile 1). He then
rearranged the tetrachords to create rows for the other two movements. The
end result is shown in Example 1. Tetrachord A is a [0,1,2,7] pitch class
set, while tetrachords B and C are both [0,1,2,3] chromatic fragments, the
latter being a T5 transposition of the former. As is evident
from the example, the tetrachords labeled A, B, and C above the row for
Movement I are reordered into C, B, and A for Movement II and B, A, and C
for Movement III. Thus, each movement may be said to have its own
twelve-tone row, yet the underlying unity among the rows is obvious.
Example 1: Tone rows used in
Poème
Movement
I
Movement I is heard in two main sections: mm. 1 - 9
and 10 - 19. Section I begins with a dramatic solo
viola line, the orchestra’s first entry in m. 7 creating a strong subdivision
within the section. Section II also falls into two subsections: mm. 10 -
13 and 14 - 19. The first subsection is characterized by the viola
playing repeated, distinctive points of imitation in single
then double stops (see the first appearance in Example 2). The
orchestra accompanies with sustained pitches and suddenly reaches an apex
in terms of pitch density, registral expanse, and rhythmic complexity at the
beginning of the final subsection (m. 14). Interestingly, it is precisely
at this moment that the technical virtuosity in the solo viola abates. The second subsection moves directly into the second
movement. Figure 1 summarizes the first movement’s sectional
design. It is important to note that tempo changes and phrase breaks
create additional possibilities for sectionalization. Further, the manner
in which pitch classes are gradually unfolded in the orchestra and a larger
curve of gradually increasing musical intensity bind sections I and II into a
single larger unit.
Figure 1: Sections in Poème, Mvt. I
Example 2: Poème, Mvt.
I, m. 10, solo viola
Karel Husa POÈME © 1959
Schott Music GmbH & Co. KG © Renewed All Rights Reserved Used by permission
of European American Music Distributors LLC, sole
Constantly changing meters
- largely but not exclusively triple, quadruple, and quintuple - are prominent
throughout Movement I. Within the context of this slow, rhapsodic movement
these meters (and the changes in meter) seem relatively unimportant in
comparison with the overall effect. It is interesting to examine a sketch
for this movement from this perspective (see Facsimile 2). As is evident
in the sketches for Poème and a number of other works from the late
1950s and early 1960s, Husa would write a lead line (the main melodic line) in
black or blue ink. His lead lines at this time show a primary interest in
pitch logic; corrections of rhythm (and even additions of meter signatures) and
additions of dynamics and sometimes instrumentation were done later and in lead
or colored pencil. Here, we see the solo viola line in black ink. The
rhythmic values of
many of the individual
pitches are evident,
but the actual meter signatures
are absent. As with many of the sketches, the initial ideas written in
black ink are covered with many changes and additions in red, green, blue, and
lead pencil, and very occasionally in blue ink. These additions
demonstrate that Husa adjusted pitches, dynamic levels, and orchestration;
however, the absence of meter signatures might best be attributed to the
rhapsodic character of the movement as a whole.
Facsimile 1: Sketch of Tetrachords used in Poème
Facsimile 2: Sketch, Mvt. I of Poème
In his article exploring Husa’s life
and stylistic characteristics of his music, Lawrence W. Hartzell wrote:
in
this work [Poème], pitches, dynamics, row organization, and different
string sonorities are submitted to serialization. From this it can be seen
that it is not the traditional Schoenbergian technique that interests Husa, but
the various serial procedures that have come into being since World War II and
the methodology that they imply.[9]
Even without embarking
upon a comprehensive analysis, one may perceive Husa’s serial
techniques. Example 3 shows the initial twelve pitches heard in the piece;
below the staff, the interval classes between successive pairs of pitches are
shown.[10] The
emphasis on interval classes 1, 2, and 6, the limited use of 3 and 5, and the
exclusion of 4 are indications of Husa’s effort to depart from a neo-Romantic
style into a more dissonant, atonal idiom. Further, the dramatic tritone
at the opening is followed by several registrally distinct chromatic
groupings. The leap in m. 2 from A4 to the D4/E flat4 dyad presents
another tritone.
Example 3: Poème,
Mvt. I, Initial Twelve Pitches.
If one labels the initial tone row P0,
then the solo viola continues with P5 and then P1; the beginnings and
endings of rows are designed not to correspond with the junctures between
phrases. Husa immediately begins to reorder pitch classes within these
rows. The statement of P5 also features two registrally distinct [0,1,2,3]
pitch class sets in m. 4. Note that changes of the contour in P5 (relative
to the contour of the initial P0) unambiguously create the [0,1,2,3]
groupings. The iteration of P1 (mm. 5 – 6, second system
in Facsimile 2) becomes quite angular; almost all
interval class ones are heard as major sevenths or minor ninths. Husa
omits pitch class 11 (the note B) entirely, possibly because of its prominence
in earlier measures, or perhaps because a misnotated B in a sketch of the row
carries into the published version of the work. One might say that pitch
class 0 (the note C) returns “when it should not” as part of the beautifully
symmetrical gesture in m. 6. Row form I1 is then presented (circled
in green in second and third systems of Facsimile 2);
its final tetrachord is given special emphasis by virtue of fortissimo,
repeated pitch classes in m. 8. Row form R1 concludes section I (m. 9, fourth
system of Facsimile 2); here, Husa treats ordering
within the second and third tetrachords with some flexibility. As is evident
in the fourth system of Facsimile 2, the fortissimo A flat3 - G3
insertion was a later idea added to the sketch in green pencil; Husa
experimented with an earlier location (see the scratched-out dyad in green
pencil) before settling on the final location.
Such freedom of ordering continues during section II of the
movement. For example, the imitative passage in m. 10 (Example 2) is
derived most closely from I7. One might think that pitch class 6 (the F
sharp4, later respelled as G flat4) is moved to become the fourth pitch class
in the first tetrachord, though a sketch of this excerpt (not shown in
Facsimile 2) is written directly above a notated row form I7; the initial F
sharp in the row is put into parentheses, as if it were to be omitted. While
the imitation in double stops remains a constant, several other sketches reveal
that Husa expended a great deal of thought as he crafted the viola line of mm.
10 - 13. The reorderings and the selection of row forms and their
transpositions throughout all of the Poème seem to be more closely
related to Husa’s musical preferences than to any particularly systematic or
arithmetic derivational processes. More generally, Husa’s compositions as
a whole show a greater concern with the final, musical result than with
strict allegiance to any mathematical systems. As Hans Hauptmann wrote in
a review of the premiere of Poème:
Karel Husa, the Czech composer now working in
Of course, this is not to say that
Husa’s works are anti-intellectual or were conceived with little
thought. Intricate compositional details emerge during the second
section. For example, the bass line from m. 10 through the end of the
movement traces a chromatic descent from C down to A; the horn solo in the
final measure replicates these four pitch classes, which of course form a
[0,1,2,3] set - an important tetrachordal subset of the row. Just as the
movement and the row began, tritones emerge at the end: the viola has a
prominent E- B flat in mm. 18 -19, and the horn solo begun in m. 19 effectively
concludes with the D4-G sharp4 dyad at the attacca beginning of Movement
II.
Movement II
The second movement, in some ways the 170 - measure centerpiece of Poème,
differs in many respects from the first. Rhythm, meter, tempo,
orchestration, form, pitch organization, and the serial techniques employed
provide significant contrasts. As in the first movement, the sections here
are most clearly heard as a result of changes in orchestration and other non-pitch
parameters. Figure 2 outlines the principal sections along with brief
textural descriptions of each. While the movement is lengthy and complex,
this essay will focus on rhythm and meter, serial pitch organization, and other
interesting compositional procedures found primarily in sections ‘b’ and ‘g.’
Perhaps the greatest contrast between
Movements I and II is in the area of musical time. The temporal
flexibility of Movement I is replaced in Movement II by a faster tempo and by a
constant 2/4 meter throughout the movement. Whereas the first movement
featured many different rhythmic patterns and groupings, the second is limited
almost exclusively to quarter, eighth, and sixteenth notes and rests. At
the same time, a fundamental similarity exists in both movements’ ambiguity of
meter; the simple duple meter of the second movement is not clearly heard
at first, and the sense of 2/4 gradually emerges as the movement proceeds.
A
syncopated rhythmic pattern evolves throughout the movement, as shown in
Example 4. Example 4a shows the rhythmic interjection heard in the piano
during mm. 33 - 35; it contrasts the even more stark and pointillistic material
in the strings surrounding it, and it foreshadows the later rhythmic
developments. Example 4b is similar; it depicts the rhythm in the tutti
strings beginning at m. 61. In more than one sketch, Husa labels measures
such as those shown in Example 4a with the letters A, B, and C respectively; it
is apparent too that he contemplated reordering these measures (by reordering
the letters representing them in the sketches) and then abandoned the
idea. The first three measures of section ‘f’ are shown in Example 4c;
throughout this section, the viola maintains the rhythm shown or some close
variant, while the responses in the orchestral strings vary more
widely. Note that the dynamics are fairly similar in the passages
represented in Examples 4a - 4c. Section ‘g’ of the movement features an
isorhythmic ostinato accompaniment in the piano, about which more is said
later; its talea is shown as Example 4d (note that this talea is now only 1.5 measures in
length).
Turning
now to pitch, Husa’s serial procedures show some influence from Schoenberg’s later
works in that he treats the three discrete tetrachords as individual
collections within which order may be varied. The pointillistic texture
and colorful use of timbres at the beginning of the movement, however, bear
some resemblance to Webern’s writing. The sketch page dealing with row
forms here is straightforward and efficient (see Facsimile 3). Husa writes
out P0 (refer to Example 1 to review its order), then on separate lines he
writes I0, P9, P0 again (but crossed out), I8, P8, P9 again, I1,
mm.: 1-4 5-32 33-35
36-60 61-84 85-99 99-128 129-153 154-160 161-170
idea: a b
c d e f g h i j
a:
horn introduction (completes the
transition from mvt. I to mvt. II)
b:
pointillistic passage; emphasis on
varied timbres and on tetrachords
c:
rhythmic interjection in the piano
d:
continuation of
passage ‘b'; buildup of instrumentation and intensity to all strings and fortissimo
by m. 60
e:
beginning of persistent sixteenth-note rhythmic interplay
f:
more texturally transparent rhythmic interplay between solo
viola and orchestra
g:
ostinato in piano; melodies added in viola then horn;
orchestral strings gradually join solo viola
h:
climactic passage; orchestra gradually thins out and
dynamics grow softer
i:
beginning of transition to mvt. III; harmonics in viola
j:
remaining transition to mvt. III; primarily oboe
solo
Figure 2: Sections in Poème,
Mvt. II
Example 4: Syncopated rhythmic patterns in Poème,
Mvt. II
and P0. These row forms (and their retrogrades)
are among the most frequently used in the movement. In addition, on the
right-hand side of the page, one sees these collections of letters: “O - RI - I
- R,” “R - I - RI - O,” “RI - I - R - O,” and “I - R - O - RI.” Here, Husa
is working out possible orderings of row forms; note that he uses “O” (for
“original”) for the prime form (symbolized in our discussion by “P”). For
example, the movement begins with P0 (mm. 5 - 21), RI0 (mm. 21 - 30), and I0
(mm. 30 - 32). The piano
interjection in mm. 33 - 35
is based upon
row form P9 - although with
several reorderings of pitch classes - and the piano carries eight of the
twelve pitch classes; the orchestral strings
and solo viola complete the aggregate in incisive rhythmic counterpoint
against the piano. Husa then continues the opening process by making use
of R0 beginning with the anacrusis to m.
36.
Facsimile 3:
Sketch of Row Forms for Mvt. II of Poème
Facsimile 4: Sketch of a Passage from Mvt. II of Poème
In addition to carefully disposing
the row forms, Husa also does creative things with re-ordered pitch
classes. The discrete tetrachords comprise first two [0,1,2,3] and then
one [0,1,2,7] pitch class sets. In the beginning of the movement, each
[0,1,2,3] is first heard pointillistically distributed among the orchestral
strings, then it is heard again in a reordered burst of sixteenth notes in the
viola. The same holds for the [0,1,2,7] set, except the reordered
restatement is heard in the piano. The process of restating reordered
tetrachords continues well into the ‘b’ section of the movement.
Husa’s careful compositional control
in the opening of the movement extends beyond
pitch serialization into
deliberate ordering of
string timbres, dynamics,
and rhythm. One sketch page in particular makes Husa’s technique
clear: It features a rotational scheme in terms of timbre and also contains
several different orderings of dynamic levels (see Facsimile 4). Figure 3
recasts some of the information, showing measure numbers, timbre types, dynamic
levels, and rhythmic values. Each four-measure segment represents what is
heard in the orchestral strings; the measures in between contain interjections
by the solo viola (mm. 9, 15, and 21) silence (m. 10) or an interjection in the
piano (m. 20). The timbre rotation scheme is a model of clarity: mm.
5 - 8 establish four different string timbres, and each subsequent segment
rotates the first timbre to the end. Each timbre has its own particular
rhythmic value (or at least attack location within the measure); interestingly,
pizzicato would appear to be the exception to this pattern, though in a
compositional draft the rhythm associated with pizzicato articulation is
always as it appears in mm. 8 and 17. Thus, there may be errors in the
rhythms in mm. 13 and 22 in the published score. The dynamic patterning is
less consistent, though, in general, four different levels are always used, and
the louder dynamics are reserved for the pizzicato and harmonic
timbres. It is also worth noting that pitch here involves statements of
tetrachords from P0 or (in the case of mm. 22 - 25) RI0. [12]
The careful organization of both pitch and non-pitch parameters continues after
the piano interjection of mm. 33 - 35, then it gradually is overtaken by longer
notes and a large crescendo leading into section ‘e.’
Figure 3:
Control of Non-Pitch Parameters, Mvt. II of Poème
Section ‘g’ is fascinating and builds to one of the registral and
dynamic high points of the movement. As mentioned earlier, the piano
presents an isorhythmic ostinato throughout the entire section. The
repeated rhythmic pattern is two and a half measures in length, which means
that it is heard exactly twelve complete times during section
‘g.’ Further, this talea, which contains eight attacks, occurs in
association with a color that is thirty-two pitches in length; thus, the
color is heard three complete times during the passage. Each piano
hand carries a single line, and the two hands have identical rhythms (the talea)
throughout the passage. Husa’s color is quite economical; each hand
carries a [0,1,6] pitch-class set, and only four different pitch classes are
heard in both hands together throughout the entire passage, comprising a
[0,1,6,7] pitch-class set. Example 5 shows the first two times through the
talea (thus, one-half through the first iteration of the color). The
hands continue in contrary motion through the remainder of the passage; note
that every vertical dyad is interval class 1. Further, a pattern may also
be discerned in the dynamics - if one considers the talea to have four
rhythmic “groups” (the pair of sixteenths, each isolated eighth note, then the
group of four sixteenths at the end), then one sees that every fifth group is
louder than the surrounding ones. This results in different parts of the talea
emerging throughout the passage.
Example 5: Poème, Mvt. II, Mm. 99–103, Piano
Karel Husa POÉME © 1959
Schott Music GmbH & Co. KG © Renewed All Rights Reserved Used by permission
of European American Music Distributors LLC, sole
In the sketches, at least,
Husa’s interest in compositional techniques more typically associated with the
works of Olivier Messiaen goes beyond the isorhythm just described. The
viola and horn solos during this same passage contain some evidence that Husa
was experimenting with non-retrogradable rhythms.[13] Such
rhythms do not substantially appear in the published score, though they are
evident in the initial entries in both the viola and the horn (see mm. 105 -
110, and mm. 110 - 112, respectively). A separate and unnumbered sketch
sheet reveals the pitch logic of this section: using black ink, Husa
writes out various combinations of P and I row forms, aligned vertically in
such a way that the exact contour mirroring is readily apparent. He
finally arrives at the combination of P9 and I4, on which this section is
based. The fourth and the final pitch classes of each row are circled in
green pencil, and the two circles are connected. These four pitch classes
are the ones used in the piano ostinato. The initial viola and horn melodies
are based on I4 and as the horn finishes its I4 melody, the viola begins a new
melody based on P9 (mm. 117 – 128 in the score). All the while, the upper
strings of the orchestra gradually join the viola, culminating in a fortissimo,
tutti restatement of the P9 melody in diminution (mm. 129 -
133). After this climactic passage, the orchestra thins out and the
dynamics grow softer, leading eventually into the transition to Movement
III. In a manner rather similar to the transition from Movement I to II, the
solo oboe here carries an angular and rhythmically varied iteration of [0,1,2],
concluding with a sustained G5 at the end of Movement II. It is noteworthy
that the first pitch heard in Movement III is C sharp3: once again, Husa uses a
tritone to connect the movements.
Movement III
Movement III reverts to a
more traditional serial approach and recalls several prominent gestures as well
as the slow tempo, and the free, rhapsodic melodic style of the opening
movement. The plaintive character of the final movement is clear at its
outset in the long passage for solo viola. Despite its wide leaps and
range, this subdued melody has a lyrical quality perhaps because of its simple
muted, bowed timbre and its freely flowing rhythms.
Form
in the final movement is articulated by orchestration (see Figure
4). Sections I and III feature the solo viola. Section II is
characterized at first by interaction between solo viola and piano, followed by
a slightly longer subsection with full orchestra and little or eventually no
material in the solo viola. The concertante passages here differ
from those of the first movement in that they are more simple and lyrical, and
the viola sonorities are restricted to arco and con sordino.
Figure 4:
Sections in Poème, Mvt. III
Movement III is similar to Movement I in
its constantly changing meters, but a somewhat wider variety of meters is
encountered during the solo viola passages, while those including the piano
and/or orchestra are largely in triple or quadruple meters. The sketch of
this movement is similar to that of Movement I - Husa apparently wrote the solo
viola line first, using black ink. Here, however, much of the solo viola
line appears to have been notated in simple quadruple meter at first, then some
rhythmic values were altered to create the changing meters. Some meter
signatures were added later in pencil, which appears to have been the preferred
writing implement used toward the end of the creative process. The
sketches of the piano and orchestral material, all of which are in colored
pencil (red, blue, or green), show densely drawn musical gestures that bear
little relation to the meters found in the score itself.
The serial technique in this movement is
more conservative than in the others, although Husa does repeat pitch classes
and frequently makes use of overlapped rows in which the final pitch class of
one row form simultaneously acts as the first pitch class in the next - a
technique reminiscent of Webern’s approach. One interesting facet of the
row use in this movement is that Husa goes to some effort to conceal its
relationship with that of the first movement (the original row for this
movement, shown as the third line in Example 1, is not actually heard in the
movement). Example 6 shows the initial fifteen pitches heard in the
movement and reveals several interesting features. First, this disjunct
succession of pitches turns out to be row form I6, relative to the P0 shown in
Example 1. A sketch page for this movement makes these relationships
clear: Husa notated here the original row for this movement (labeled “O”
as shown in Example 1). Two staves lower, he notated what we have referred
to as I6 and it is labeled “I.” To the left of this staff, he wrote the
word “Begin.” Returning to Example 6, it is worth noting that Husa repeats
pitch classes D, F sharp and F before moving on to complete the row. The G
sharp at the end simultaneously functions as the first pitch class in the next
row form encountered, I1.
Example 6:
Poème, Mvt. III, Initial Fifteen Pitches
Without reviewing all of the many row
forms encountered in the third movement, it is worth noting that the viola and
its accompaniment each retain their own row forms (unlike the second movement)
and there is little “sharing” or dividing rows among the performing
forces. Similar to Movement I, the tone-row beginnings and endings here
are designed not to correspond with the junctures between phrases. Once
more as in the first two movements, the selection of row forms and
transpositions seems to be more closely related to Husa’s musical preferences
than to any systematic or arithmetic derivational processes.
Thus, Husa designed his Poème as an
arch, with Movements I and III evincing many similarities and Movement II
contrasting in many ways. The pitch logic for all three movements is
created via tightly-related twelve-tone rows built from three tetrachords and
by experimentation with ordering, overlap, and omission or repetition of pitch
classes. The second movement features additional compositional techniques,
including serial ordering of timbres, rhythm, and dynamic levels, isorhythm,
and occasional use of nonretrogradable rhythms. Such organizational
techniques are used freely as simple compositional tools that do not detract
from Husa’s own characteristic style. Poème features intensely
lyrical solo lines and colorful orchestration, yet its serial constructs mark
an important change in Husa’s compositional technique. The work also is
Husa’s first major “concerto” and therefore is an important composition in a
genre that later became one of the composer’s favorites.
Mosaïques
Another important genre in Husa’s ouevre
is works for larger instrumental ensembles, be they winds and percussion or
full symphony orchestra. Mosaïques is Husa’s first serial
composition for large ensemble. Commissioned by the Hamburg Radio, the
composer conducted the premiere of this five-movement work on
While the five movements in the
published version have no individual titles, the sketches show that Husa did
consider titling individual movements (see Table 1). As is evident in the
projected titles, and of course in the conversation with Robert Rollin, as
quoted earlier, Husa’s score evinces a great concern with orchestral
colors. Radice writes: “More than any of his works to this point, Mosaïques
employs each of the orchestral choirs fully and effectively,”[17]
and, in a personal letter to Husa, dated
Table 1: Movement
Titles for Mosaïques, As Found in the
Sketch File.
When
compared with those for Poème, the sketches for Mosaïques include
a larger number of sheets with tone row manipulations and/or with sketches
working out a specific compositional problem, and fewer recognizable complete
drafts of individual movements. On the other hand, the sketch file for Mosaïques does include three neatly written pages that
reveal some important details from each movement. What we will be calling
the “crucial overview” may well have been Husa’s own notes for a lecture on the
work.
Movement
I
Husa’s interest in color is perhaps most
evident in Movement I, whose provisional title, “Les cloches,” aptly describes
the instrumentation as well as the colors heard. The movement originally
was scored for xylomarimba, vibraphone, chimes, suspended cymbal and gongs,
celesta, harp, and piano; however, a note appearing along with the sketches and
manuscript score reads as follows: “Marimba should be used in Mosaïques
(not Xylomarimba).” The note, written in Husa’s hand and signed by him, is
dated
Figure 5: Sections in Mosaïques,
Mvt. I.
Measures 1 - 10 sound introductory and are
Webernesque in their delicate timbres, pointillistic texture, and angular
gestures, as mentioned by Rollin in the excerpt from “A conversation with Karel
Husa…” cited earlier. Example 7 shows a transcription of Husa’s notation
of the original tone row for Mosaïques (P0) along with its inversion;
the numbering of the pitch classes and mirror inversion are written carefully
by the composer. Interestingly, the introduction does not contain these
row forms; rather, it features row form R11 then a portion of P11. The
sketches contain Husa’s notation of P11 and I11; they are written exactly as
were P0 and I0, except down one half step. D4, the axis of symmetry, is
clearly heard in the chimes in mm. 1 and 6, perhaps bringing this important
pitch to the fore. While one can find suggestions of R11 in mm. 3 - 6,
Husa does make some use of reorderings here. Since it concludes R11 and
then begins P11, the tritone D - A flat is heard in mm. 6 - 7. In mm. 7 -
8, one hears the first portion of P0, though it is reversed with a Webern-like
palindrome in the piano. P0 does not come into full fruition so much as
Husa simply alludes to it, returning to the D - A flat tritone in m.
9. This tritone is heard prominently - indeed, exclusively, with the
exception of a grace note - in mm. 9 -10. These measures, rather static
(yet unstable) in pitch-class content, represent a transition ending the
introduction and announcing the beginning of section II at m. 11. The D -
A flat tritone forms the first two pitch classes in both P11 and I11, thus
creating a suitable transition.
Example 7.
Mosaïques, Transcription of
Sketch Showing Row Forms P0 and I0
What I will call section II, mm. 11-20,
begins with a melodic iteration of row form I11 in the
marimba, borrowing the A4 from the vibraphone to form a complete aggregate in a
single measure. The transitional D-A flat tritone carries over and
accompanies in the vibraphone and celesta. Over the course of just three
measures - mm. 12-14 - Husa introduces row forms R0, I10 (twice) and
P6. The chimes continue to present an important pitch - E flat4 -
during the second beat of m. 14, followed by an E flat-A tritone in the
vibraphone and marimba which is attacked on beat three and sustained for almost
four beats. The shift to E flat4 and to the E flat-A tritone is
significant, as these introduce row forms P0 and I0, which are then presented
simultaneously in the two hands of the piano and are completed by the D-E dyad
in the celesta on the downbeat of m. 15.
The
passage from the introduction of P0 and I0 in m. 14 through their retrograde,
concluding in m. 26 becomes remarkably complex, replete with many textural
layers articulating repeated patterns quite rapidly. The effect -
especially around the midpoint of the movement, where the retrograde begins -
is a quasi sound-mass in its layering and overall fabric of sound; the
instrumentation, repeated patterns and brief ostinati lend an almost Eastern
quality to the passage.
Rather than journey measure by
measure (and row by row) through this passage, I am electing to let an
interesting sketch by Husa stand for itself - see Facsimile 5. This sketch
page is published in the collection Notations by John Cage.[19] Some
explanation is in order. A note attached to Husa’s sketches, in his hand,
reads, “Esquises de Mosaïques ? - no. 5 given to John Cage (
Facsimile 5:
Sketch Page of Mosaïques, from
Notations score Collection by John
Cage
A
number of interesting features are present here. First, the sketch
features a lead line in what appears to be black ink; the sheet from which this
is cut out has notations of P0 and I0 in
black ink immediately above what is seen here (similar to what is transcribed as Example 7). This sketch is
extraordinary and efficient since it presents a compressed digest of the most important gestures of
the passage. The first system and all but the final flourish of the second
present the original musical ideas; from the final flourish to the end, the
ideas occur in retrograde, with some minor modifications. Mirror symmetry
is evident - for example, E flat4 is the axis for the first chime attack, then
again on the final sixteenth of the first full measure, leading to a reiterated
E flat4 on the next downbeat. In the remainder of this measure, P0 and I0
are presented such that A3 is the axis, though of course E flat may be heard as
a secondary one.
Measure two is a good example of a
passage that looks somewhat symmetrical due to contrary motion, but in fact is
not mirror symmetrical. Here, Husa distributes P0 with considerable
reorderings across the hands. In this movement as well as others, Husa
uses the chimes or sometimes celesta to complete the aggregate, or to launch a
new one. An interest in aggregate completion, which became somewhat less
important to Husa in later works, is evident in the first two complete measures
(and the final E flat4) of Facsimile 5. In summary, the gestures seen in
the facsimile are the most important ones encountered in the middle portion of
the first movement. They are heard many times in changing temporal and
textural contexts and combinations. Measures 26 - 29 complete what will be
called section III, and are of course a retrograde of mm. 11 - 14 which began
section II. Measures 30 - 39 conclude the movement quietly and gently
with a retrograde of mm. 1-10.
Movement
II
Movement
II provides a striking contrast in orchestral colors, as it features the string
section - both solo players and the full sections - and the xylophone, celesta,
and harp play a small but structurally important role. As shown in Figure
6, the movement falls into five sections suggesting an arch design in the
similarities between sections I and V and also II and IV. The introduction
consists of string gestures using a combination of row forms P4 and
I4. Example 8 is a transcription of a related sketch; essentially, nine
pitch classes from I4 - those connected by slurs - form the three melodic
trichord gestures heard in the solo violin, ‘cello, and viola. The
accompaniment is drawn from P4 and in particular from those pitch classes that
are circled. The final attack heard in the introduction, G sharp5 in the
viola, completes the aggregate.
In a manner similar to section I,
section V consists of the combination of two row forms
- here, R4 and RI4. Just as I4 did earlier, RI4
provides the nine pitch classes projected
melodically in a pitch-class retrograde of the nine from the
beginning. The accompaniment in section V is a bit different from that of
the introduction, but it still projects P4, only in retrograde. The
movement concludes with a sustained G3 in the solo ‘cello, completing the
aggregate launched at the outset of the section.
I: Introduction; gestures using a
combination of row forms P4 and I4; ends with aggregate completion (G# in
viola)
II: Expressively thematic, row forms P4 and
R4 in a myriad of configurations and rotations
III:
Wide-ranging, near mirror-symmetrical verticalities with aggregate completion and
initiation in celesta; row forms P0 and I11 and their retrogrades are
projected; row forms R0, I10, and three pitch classes from I2 projected in mm.
23-25
IV: Thematic
viola and ‘cello duet; row forms I2 (from section III) and then R12 are used
V: Mirrors
section I, but loosely in retrograde (combines row forms R4 and RI4); ends with
aggregate completion (G3 in ‘cello)
Figure 6: Sections in Mosaïques, Mvt. II
Example 8:
Mosaïques, Mvt. II, Sections I
and V, Transcription of Sketch (row forms P4 and I4)
Sections II and IV are similar in
their rhythmically diverse yet dramatically sustained lines. As mentioned
beneath Figure 6, the second section of the movement consists of row form P4
and its retrograde, arranged into a variety of configurations. Example 9,
a transcription of another sketch, provides some insight into Husa’s thought
process. Row form P4 is shown again, now partitioned into
trichords. As sometimes is his practice in such sketches, Husa then
numbers the twelve pitch classes. Each trichord is then assigned a
rhythmic profile - that is, the time span over which the three pitch classes
are to be projected. Note that the quarter note duration of the third
trichord may be thought of as a set of eighth-note triplets, or even as a set
of sixteenth notes. Each trichord is also assigned a dynamic level, with
trichord number two being either piano or pianissimo. Next,
Husa fleshes out pitch class reorderings - see the string of numbers. Row
forms P4 and R4 are projected in order. The 3 2 1 concluding R4
simultaneously launches a reconfigured P4 - each trichord contains its third
member, then second, then first. The
same process then occurs, but in retrograde. At the bottom of Example 9,
Husa’s sketch of the initial P4 and R4 is shown. The trichord
design is easily perceived, and the temporal design conforms with his initial
conception shown nearer to the top of the sketch, with occasional small
alterations of the rhythms, especially those of the first two
trichords. The sketch is played out quite clearly in section II of the
movement, along with interesting changes in instrumentation bringing out the
different trichords. A number of additional pages in the unindexed sketch
file confirm that Husa’s thought continues in this direction throughout section
II.
Example 9:
Mosaïques, Mvt. II, Section
II, Transcription of Sketch (row form P4)
Section IV, comprising mm. 26 - 30 and
carrying over into m. 31, is performed by only two instruments: solo viola and
‘cello. Its pitch logic is quite straightforward, continuing row form I2
which had been initiated in m. 25 in the harp, then turning it around into RI2
in mm. 28 - 30. The rhythm, while seeming to be freely syncopated, was the
product of precompositional planning as well. Example 10 is a
transcription of a small sketch in which Husa writes out row form I2 and
associates specific note values with each pitch class. The viola and
‘cello parts in mm. 26 - 27 adhere almost exactly with Husa’s plan, if one
allows a bit of freedom at the glissando in the ‘cello. Row form
RI2 also holds fairly close to Husa’s sketch, again allowing some margin of error,
especially near the glissando.
Example 10: Mosaïques,
Transcription of Sketch of Row Form I2 Pitch Classes with Associated Temporal
Values (Note that the row form in question for Mvt. IV is P4, not I2, but the
temporal succession still applies and appears in a different sketch.)
Section III,
the peak of the arch design, is radically different music than that of the
other sections. In just the first two measures (mm. 19 - 20), Husa
presents row forms P0 and I11 in a seemingly bewildering array of registers,
instruments, dynamic shadings, and rhythms. Example 11 is a graph of mm.
19 - 21, showing pitch vertically and elapsed time horizontally; the gradual
deployment of dyads is clearer there. Initially, P0 is the higher pitch in
each dyad, though at order positions 5 and 6 (using Husa’s 1 - 12 numbering),
both row forms contain the pitches C and F and they perform an exchange as P0
becomes the lower member of the next couple of dyads. The passage conveys
near mirror symmetry about an axis of G sharp3/A3, though some pitch classes
are in different octaves. Each dyad has its own dynamic level (with
duplications) and there does not appear to be a strict temporal logic at
play, though the last few dyad attacks do occur at closer and closer time intervals. The
first nine pitch classes of P0 and I11 are presented in this manner, and then
the celesta wonderfully completes both rows with a burst of major and minor
second clusters. These clusters then take on a new role, pivoting to
become the first three pitch classes in the retrogrades, R0 and
RI11. Afterwards, the remaining nine pitch classes of R0 and RI11 are
projected in a manner similar to that heard in mm. 19 - 20 (see Example
12). Here, the temporal logic is more transparent: the attacks of the
dyads grow further and further apart, moving from a distance of a single
sixteenth note to two, three, four, and so on. As these row forms are
completed in m. 23, the celesta reenters with an echo of the earlier clusters,
followed in mm. 24 - 25 with row forms R0 and I10. As shown in Example 12,
the large chords are sustained until the very end of m. 25.
Thus, the second movement of Mosaïques
evinces a wide-ranging variety of compositional techniques. Sections I and
V are created via vertical and horizontal presentations of row forms related by
inversion. Combinatoriality does not play a role, but each section
concludes after the aggregate is completed. Section II features an
interesting pitch-class rotational strategy - also projecting row form P4 and
then its retrograde - and dynamics and temporal values are also serially
organized. Section IV is
similar, though less
complex and bearing
a different precompositional temporal
organization. Section III is about gradual dyadic additions and registral
symmetry, with some minor asymmetries resulting from octave placement.
Example 11 and 12: Graph of Mosaïques,
Mvt. II, mm. 19-24. Pitch space (the vertical axis) is calibrated in
half steps at one square each. The
numbers in the left margin are standard octave numbers, where middle C is
labeled as C4. Time is shown along the
horizontal axis; the figure ‘19/1’ refers to m. 19, beat 1 and
so forth.
Each square thus represents a thirty-second note.
Movement
III
The third movement
begins with piano, percussion, and woodwinds, immediately establishing the
colors to be featured throughout the movement. Eventually, the entire
orchestra comes into play, though the strings do not enter until almost halfway
through the movement, and even then they play a minor role. Movement III
may be heard in five sections, creating a rather rondo-like form, as shown in
Figure 7. Section I begins with a three-measure introduction, after which
frenetic melodies are heard in the woodwinds.
In the “crucial overview” of the entire work, Husa writes “bird calls”
as representing these melodies, also writing down the names Janáček and
Messiaen. The additive and repetitive nature of the melody heard in the
piccolo in mm. 4 - 8 typifies a technique found in some of Husa’s later serial
works. An early sketch shows an even more comprehensive additive process
(see Example 13). The transcription clearly shows Husa gradually adding
pitch classes - and eventually eliminating the early ones - until all of row
form P3 has been presented. In the published score, Husa modifies the
comprehensive additive treatment in favor of chords articulating five or six
members of the prevailing row while the woodwind melody presents the rest in an
additive manner. Section I dissolves into a passage with rapidly repeated
notes (and chords); the woodwind melodies resurface at m. 34, accompanied by a
metronomic wood block.
Figure 7:
Sections in Mosaïques, Mvt. III
Example 13: Mosaïques, Mvt. III, Transcription of Sketch Showing Additive
Pitch-Class Process
Section
II is characterized by a melody in the strings and brass, accompanied by
woodwinds continuing frenetic rhythms, now as an obbligato accompaniment, along
with the metronomic percussion. Serially straightforward but metrically
complex, section II holds to alternating five-eight then seven-eight meters
throughout, heard in groupings 2 + 3 and 4 + 3. Interestingly, in an early
sketch for the movement, a black ink lead line contains no meter signatures,
but Husa does write 2 + 3 + 4 + 3 + 2 above the score, and the melody reflects
these groupings. A later iteration of the passage, notated on different
paper in blue ink, shows a four bar pattern: two-eight, three-eight, four-eight
(later simplified to two-four), then three-eight. Husa later used a red
pencil just above the passage, marking 5 then 7 and adding brackets at the
beginnings of two-eight with three-eight then two-four with three-eight
respectively. Thus, the metrical design of the passage gradually took
shape over time.
Section
III is a brief five-measure “break” where the woodwinds articulate their
frenetic, angular melodies, accompanied by the metronomic wood block and other
instruments. Section IV follows with the same basic idea as was discussed
above in relation to section II, though here the brass section is silent and
the melody is presented by piano and strings using glissandi, and the
alternating meter pattern is the reverse of before – 7/8 then 5/8. Section
V is coda-like, bringing back the repeated notes (and chords) along with a
brief iteration of the frenetic woodwind melody, though now in the
strings. The end result is a formal design that may be interpreted as
rondo-like: A B A’ B’ A’’.
Movement
IV
Movement
IV may be heard as a lengthy and complicated but still quite discernable
ternary form. The main idea in the outer sections is a series of brutal,
aggressive chords presented in varied, rhythmically incisive ways. The
chords are made up of four prime row forms occurring simultaneously: P1,
P5, P7, and P8. Facsimile 6 shows the logic found in the “crucial
overview” of the piece. As can be seen, each chord contains one pitch
class from each of the four row forms. The chords are then numbered: the
odd-numbered ones occur principally in the brass while the even-numbered ones
are heard mostly in the woodwinds and strings. After the piece opens with
these chords and little else, Husa retains them as accompaniment to an angular
melody in the lower brass, beginning two measures before rehearsal
‘D’. This melody adds row form P4 to the mix, and its rhythm was generated
by pre-compositional organization (refer back to Example 10). The melody
continues in such a manner for some time.
The
middle section is quite different from its outer counterparts in that it
features a more lyrical melody, but still with strong punctuations in the
accompaniment. Here, a repeating metric pattern of 3/8, 4/8, 5/8, 4/8, 3/8
occurs, cropping up as simply 3 + 4 + 5 + 4 + 3 in the sketches. The
similarity to the metric scheme in the contrasting sections of the previous
movement is obvious. Aside from metric complexity, Husa makes use of just
two row forms - R9 and RI10 - in a very free way (see Facsimile 7). Note that
“middle part, 7 after G:” points directly to row forms P9 and I10, notated to
the right. Those pitch classes circled in red are used in the melodies
written on the top two staves below the row notations, while those pitch
classes marked in green are used in the accompaniment. To be even more
specific, let us assume that the higher of the two melodies is accompanied
by the lower of the two accompanimental strata. The melody begins with C sharp, the first
pitch class in row form R9; it is accompanied by a B and then an F, which
represent the second pitch class in R9 and then the third pitch class in RI10 -
note the crossed arrows in the row diagram. The next pitch class in RI10,
shown as G flat3 in the row diagram, is circled in red and also in
green. It forms the next note in the melody (m. 2) as well as the first
pitch class in its three-note accompaniment, which is F sharp3 - D sharp3 - E2
in the score and is seen as the green-circled G flat3 skipping to E flat3 and
then E3 in the row diagram. The process continues in like manner and then
partially retrogrades itself. The flashes of mirror symmetry and
almost-mirror symmetry are not coincidental, as mirror symmetry plays an
important role in many passages in many of Husa’s works. One thinks here
of the important influence of Béla Bartók.
Movement V
The
calmer, almost elegiac fifth movement represents an interesting amalgamation of techniques from
earlier movements - especially Movements I and II. Following Movements III
and IV, in which the full orchestra is unleashed, the final mosaic also uses
the entire orchestra, though in a quietly retrospective manner (as evidenced by
the descriptive title “retrospective” found in the “crucial
overview”). Figure 8 presents the sectional design of Movement
V. During section I, the muted violins carry a sustained melody and the
harp, xylophone, marimba, and piano contribute brief interjections. The
violin melody consists of presentations of row form I2 and its retrograde; its
temporal logic is seen in the final line of Example 10: the succession of note
values is simply a doubled version of the succession from Movement II with the
exception of an eighth rest rather than what should be an eighth note as the
penultimate value. The melody in Movement V follows this succession (and its
retrograde) quite closely. Given that this melody projects the same row
forms and durational proportions as that from Movement II, mm. 26 - 30, it
represents a striking return of the earlier melody, especially when following
on the heels of a loud, aggressive ending to Movement IV. The marimba
interjection in m. 6 bears a striking timbral and pitch class similarity to a
passage in the marimba from Movement I, mm. 19 - 20.
Facsimile 6: Sketch of Chords from Mvt. IV of Mosaïques
Facsimile 7: Sketch of a Passage from Mvt. IV of Mosaïques
Figure 8: Sections in Mosaïques, Mvt.V
As is the case in the opening of many of Husa’s movements, the line
between sections I and II is deftly blurred. Here, section II contains
three subsections, represented by the letters a, b, and c. Subsection ‘a’
is only two measures in length, but it is important. In an obvious return,
Husa brings back the large verticality from the third section of Movement
II. Similarities to the earlier passage include range extremes,
approximate mirror symmetry, and gradually added dyads. The passage here
in Movement V differs in that it is a half step lower and the orchestration is
changed – almost all pitch classes are presented in the winds, along with
punctuations in the harp and piano. The aggregates are completed in a
manner similar to Movement II, although here the marimba, vibraphone, and
celesta all participate. Finally, the passage in Movement V projects a
clear cut accelerating durational pattern as the dyad attacks, initially
The large sonority assembled during
subsection ‘a’ recurs in subsections ‘b’ and ‘c’, with the very lowest note
changed from C sharp1 to C1. Thus, all three subsections are tied together
into a large section II. Subsection ‘b’ features an interesting
orchestrational development as the
strings sustain the sonority while the winds attack it
homorhythmically in groupings of one, two, four, then two attacks with varied
dynamic levels. The attack patterning, an important characteristic in most
all of Husa’s ouevre, is similar in its morse-code-like groupings to
passages from Movements III and IV. While the strings and winds are
concerned here with the large sonority, the percussion, celesta, harp, and
piano present motives from Movement I in a quite literal though more
fragmentary return.
Subsection
‘c’ begins at the anacrusis to m. 22, where the strings and winds overlap their
respective release and attack of the large sonority; the winds then take over
sustaining it while the strings rest. The wind releases occur in an
almost-additive pattern of two then 3, 4, and so forth sixteenth notes apart,
while the piano and harp present melodic fragments that begin with a single
sixteenth then grow in length through 2, 3, 4, 5, and more
sixteenths. Measures 25 - 26 have one foot in subsection ‘c’ and the other
in the larger section III. With the lone exception of the violas, one
hears just the notes C, C sharp, D, and D sharp, pointillistically articulated
during these two measures. This characteristic continues, although with
more sporadic attacks, during the final three measures of the piece. A
point of articulation can be heard at m. 27 simply because the flute enters
with a plaintive three-measure solo, projecting row form P6 (but not in its
entirety) to conclude Mosaïques as it began - gently and quietly.
Summary and
Conclusion
Both Poème and Mosaïques
contain compositional techniques that continue deeply through Husa’s entire ouevre. The
composer’s interest in sound color is most evident in his creative use of
percussion, various string effects, and the serialization of timbres and
dynamics. Textures are enormously varied, ranging from single instruments
to entire ensembles; in places, his textures might even be characterized as
pointillistic. Husa’s avid interest in musical time is evident in many
ways: meter signatures often function more as temporal/organizational
conveniences than as clearly articulated entities; surface rhythms vary from
rapid repetitions to lyrical sostenuto writing; and some passages convey
stasis, while others feature frenetic motion. Husa also uses some serial
durational procedures, usually somehow related to the pitch row. The
Messiaen-like isorhythm and non-retrogradable rhythms found in Poème
seem to be passing experiments that do not turn up regularly in later
works. Neither Poème nor Mosaïques contain Husa’s well-known
aleatoric outbursts, though their more rapid rhythms may foreshadow this
technique.
Much
may be learned from Husa’s approach to pitch. He experiments with
generating twelve-tone rows from tetrachords and trichords; the evidence in his
later sketches shows that he continues to generate twelve-tone rows by using
trichords. Even in the sketches seen here, his rows show an interest in
registral specificity by virtue of their melodic design, unexpected leaps, and
changes of direction. Husa also shows an interest in aggregate completion,
though not by using a systematic, combinatoriality-related procedure. His
choices of row form are made for aurally apparent reasons - one can hear the
ways in which he juxtaposes or superimposes P and R or I row forms. Husa’s
lifelong interest in pitch symmetry and mirroring is already evident in the
works under study here, both in the more abstract sense of combination of P and
I forms in the sketches as well as in concrete, clear vertical symmetries heard
especially in Mosaïques. We also note the great freedom with which
he uses reorderings and occasional omissions of pitch classes, processes in
which he begins with just one or two pitch classes and then gradually adds
more, and rotational schemes that take on more important roles in Husa’s later
works. In the end, however, we see that Husa’s interest in the final
musical result seems to outweigh any systematic or mathematical derivational
procedures.
Husa’s
nontraditional approach to musical form is evident in Poème and Mosaïques,
as are his use of blurred lines and dovetailing of sections. In a personal
conversation with the author, Husa noted that he treats each piece as a new
challenge - not only to steer clear of tradition, but also to avoid overt
repetition of his own ideas.
In
summary, Poème and Mosaïques are impressive examples of Karel
Husa’s eclectic approach to composition, presenting the contradictions between
adherence to compositional systems and freedom. Systems encountered in
both works - perhaps a manifestation of Husa’s early training as an engineer -
could appear to create a degree of rigidness. However, formal freedom, use
of serial techniques but without strict order limitations, rhythmic élan, and
especially Husa’s sure sense of timing and affective high points ensure that
any such perception of rigidness is tempered by the compositional freedom in
the hands of a master.