Nr. 5: ZEITMASZE (Time-Measures)
for wind quintet (flute, oboe, English horn (cor anglais), clarinet, bassoon)
(1955-56)  [approx. 15 min.]

     The title ZEITMASZE (ZEITMAßE) can be translated from German as "Time Measures", or even just simply as "Tempos".  The conception of its opening section came to Stockhausen whilst in the middle of composing GRUPPEN and GESANG DER JÜNGLINGE in Switzerland.  Like GRUPPEN, this work also explores simultaneous layers of contrasting tempos, and like GESANG DER JUNGLINGE, there are also 5 "tracks".  After its first performance for a radio broadcast, Stockhausen added 5 additional passages ("inserts"), and this new version was premiered at the end of 1956 at Pierre Boulez's "Domaine Musical" concert series (conducted by Boulez).

Tempo Concepts
      ZEITMASZE uses contrasting ("polyphonic") tempo layers as a way to create new and interesting rhythmic textures, much like how serial 12-tone technique was used to create unpredictable melodic and harmonic textures.  Serial technique is still used in the beginning and ending sections, but the main body highlights alternating waves of rhythmic unison and disintegration.  In order to create variety in these contrasting layers, Stockhausen used the idea of "indeterminacy", in which some factors are left to the performer.  In this case, the performer's actual playing skill becomes a deciding factor in the compositional end result (this idea was also explored just previously in the second set of KLAVIERSTÜCKE (V–X)).  So, when "tempo polyphony" is desired, Stockhausen notates the score using 5 basic "time measures":
  • "so schnell wie möglich": tempo as FAST as possible, based on the performer's skill level.  Since the rhythm within the tempo are still observed, if the phrase has lots of sustained notes, it could still seem slow, but with some very fast moments.
  • "so langsam wie möglich": as SLOW as possible, based in how slowly a number of bars can be played on a single breath.  Just as in the above instruction, if the group has lots of notes, the tempo could still seem fairly busy
  • "schnell-verlangsamen": Fast and then SLOWING down to 1/4 of the initial speed (ritardando)
  • "langsam-beschleunigen": Slow and then SPEEDING up to the fastest possible speed (accelerando, initial speed is pre-calculated to be 1/4 of the final "fastest" speed)
  • Metronome tempo: just as pitches are organized as a 12-note scale structure ("row") in dodecaphonic serial music, here Stockhausen created a "chromatic scale" of 12 tempo values from 60 to 120 (representing a tempo "octave").  The starting tempo is 84.
     Tempo polyphony occurs when different tempo instructions are used on different instruments playing at the same time, but often the above instructions can also used on an ensemble level (and combinations in between).  For example, the group tempo could be set by a lead instrument, who is playing "as slow as possible". Obviously, this presents some interesting challenges for the interpreters.

...present-day man, with his cars, planes and machines of all kinds, perceives time quite differently, 
since he often experiences - especially simultaneously - 
several speeds, time layers multi-dimensionally.
 - Stockhausen concert introduction, 1992

Tempo Structures
(Copyright Universal Edition)
     On the page above (starting at m.29), the players all start at tempo 112, but soon go off into their own tempo structures, starting with the 3rd staff English horn ("as fast as possible").  The 1st staff oboe follows with "as slow as possible", and then the clarinet (4th staff) begins to slow down to a quarter speed.  Later on the flute (2nd staff) will also start playing "as fast as possible", while the bassoon stays at 112 (bottom staff).  Each of these layers is demonstrated individually in Stockhausen's concert introduction of a 1992 performance (available on DVD, see link at bottom).  In this introduction Stockhausen goes on to highlight a few other interesting devices used in this work:
  • the ensemble begins in a slow tempo and rises to "as fast as possible", based on the ability of a lead player (ex. flute, m.74-76).
  • "window": layers of tempo polyphony suddenly thin out (pause) so that a solo layer can be featured.
  • "time body": accents from the other players occur on top of an English horn playing "as slowly as possible" (creating changing levels of density) (m.87-90?).
  • Ex. 11: each of the 5 layers modulates between "points" (isolated accents) and "groups" (legato phrases).  It ends in a rhythmic ensemble structure.
  • Ex. 12: demonstrates "time junctures", where different layers go from unison to independent time measures.
  • Ex. 13: shows where note clusters can occur as ensemble attacks with individual fade outs, or the reverse (individual voices enter and sustain, building to a vertical harmony, and then stop in unison).  Variations of both of these 2 extremes occur as well.

     Another effect (not highlighted in the concert introduction, but worth mentioning anyways) is that sometimes a tempo may be started by one instrument, and then continued in another.  This creates another level of indeterminate tempo (and timbre) polyphony.
(Copyright Universal Edition)
     On the above page, several tempo layers are occurring, but are also being exchanged between partner instruments (independently).  The top line oboe plays "as fast as possible", passing on its tempo to the clarinet at m. 164.  Prior to this, the clarinet speeds up to its fastest speed and hands off its tempo to the bassoon at m.162, which begins to slow down.  On the second staff, after the flute slows down to a quarter speed, the English horn picks up its tempo (m.163) and begins to accelerate to 4 times faster (original tempo).  A sudden stop interrupts all 3 active voices at stable tempo 112.

     Performance-wise, the conductor often beats out a notated underlying tempo (derived from the chromatic tempo scale), and then instruments marked with indeterminate tempo instructions "split off" from the ensemble and play independently.  Later they return, etc...  Much of the drama of the work comes from this element of "renegade players" leaving and then returning to the ensemble, just as harmony and disharmony creates drama in traditional classical music. 
     One of the most important ideas not mentioned so far is that the "homophonic" tempo sections (all instruments in shared tempo) should be listened to as single melodic "tracks", but with varying "widths" (harmonies).  In other words, when the ensemble is "tempo-together", there is often a constantly changing density of voices, from single pitches to 5-part chords, but these should not be thought of as a polyphonic "dialogue".  In actuality the melody is "monophonic", but has a constantly changing homophonic harmonization. By listening this way, the transitions to the "free tempo" sections become much more meaningful.

(Treated score excerpt from LP cover.)

Form Structure
     ZEITMASZE is basically in 3 sections.  The 1st and 3rd sections are short and somewhat similar (both composed using "total serialism" on several musical parameters), with the 3rd section being more rhythmically complex.  The long middle section (m. 30-271), on the other hand, is based on 7 "character types" organized into 4 cycles of different sequences.  The character types are:
    • groups, phrases
    • polyphonic layers
    • sustained notes & points
    • points
    • rapid chords or sounds, polyphonically, with long general pauses
    • chords
    • chords and a few independent notes, legato
           This main body is also where the contrasting "time measures" (polyphonic tempo layers) occur.  The 1st and 3rd sections also have changing tempi, but they are applied to the entire ensemble.

           Each of the 3 sections are also characterized by a "core instrumentation".  For example, the 1st section is written for a quartet made of flute, English horn, clarinet, and bassoon, the 2nd section is for a flute, oboe, and clarinet trio, and the last section uses the full quintet.  The players outside of the "core group" usually chime in on chord accents or add more subtle background layers.

           After the initial performance of ZEITMASZE, the piece was revised almost immediately to include 5 "inserts", or cadenza-like additions (actually "cadenza" may not be exactly appropriate, since the whole work from beginning to end is fairly virtuosic in character!).  The 2nd section has four of these insert additions, and the 3rd section has one. 
      Stockhausen and Pierre Boulez. 
      Boulez premiered ZEITMASZE with the additional "inserts" at his Domaine Musical concert series.

           In the spirit of "polyphonic time measures", the below table charts the formal structure of ZEITMASZE in 3 different ways.  The main text ("General Highlights") is my impressions based on the divisions indicated by the CD tracks chosen by Stockhausen.  The column "Tempo Layer Harmony" is derived from Chris Kelsall's division of the piece into "Vertically Constant" and "Vertically Irregular" sections (in his excellent thesis "Compositional techniques in the music of Stockhausen (1951-1970)").  In the chart below, "U" ("Unison") indicates homophony with shared tempo, and "I" ("Individual") means polyphonic textures, often with independent/indeterminate tempos.  Finally, in the last column, is "Structure", based on the 3 main sections and on the 5 "inserts" added in the revised version.  These measure numbers are from Richard Toop's superb "Six Lectures from the Stockhausen Courses Kürten 2002"The track numbers and timings are from the recording of ZEITMASZE on Stockhausen Edition CD 4, featuring a recording by the London Sinfonietta (Janet Craxton: oboe, Sebastian Bell: flute, Robin Miller: English horn, Antony Pay: clarinet, and William Waterhouse: bassoon).
      General Highlights Measure Time Tempo

      Unison tempo layers, but homophonic/polyphonic melodic layers.  Oboe is basically silent (aside from a few harmony accents) until 1:48.
      A clear harmony phrase occurs at 0:50, followed by a brief flute solo at 1:09.  
      Ends at 2:01 on a clear harmony cadence.
      1 0:07 U

      Section 1
      (4-part texture:
      fl, E. hn, clr, bss)
      21 1:34 I

      Tempo Disintegration: each layer enters using one of the 5 time measure tempo types, resulting in contrasting (polyphonic) tempo and melodic layers
      The 5 layers reintegrate at the end (0:34, tempo 112)
      29 0:00

      INSERT 1
      41 0:34 Section 2
      (3-part texture:
      fl, ob, clr)

      Unison tempo layers, a harmony phrase occurs at 0:17, followed by contrasting held notes and isolated accents (ensemble tempo is set by the flute playing "as slow as possible") 44 0:00 U
      67 0:39


      Ensemble tempo increases, led by the flute (towards playing "as fast as possible").  
      At 0:23 a staggered climax occurs, followed by a harmony cadence.  After this, various "windows" open up in the loosely homophonic texture, featuring solo voices/layers.
      73 0:00
      74 0:01 INSERT 2
      83 0:33 U


      Mostly features oboe, flute and clarinet, modulating between homophony and polyphony.  The bassoon sometimes surfaces briefly.  

      At 1:04 a lively group cadenza occurs.
      103 0:00
      104 0:04 (Section 2 cont'd)
      106 0:08 I
      107 0:10

      133 0:58 U
      152 1:33


      Tempo Disintegration: Each player enters one by one, starting from tempo 112, but each tempo quickly becomes independent (again, 5 time measure tempo types).  
      A tutti rest occurs at 0:33, followed by a harmony phrase.  After another rest, the tempo layers diverge once again.
      After yet another tutti rest at 0:53, the ensemble "regroups" at tempo 80.  Shortly afterwards (0:59) a held harmony disintegrates, layer by layer.
      From 1:17, blocks of harmony are threaded through by short solos from the flute, clarinet and bassoon (starting from 1:26)
      153 0:00

      I INSERT 3
      174 1:17 U

      188 2:09 I
      190 2:13

      After an oboe solo, ensemble is led by clarinet playing "as slow as possible".  The ensemble plays blocks of harmony around a clarinet/bassoon duet.
      After a rest at 0:35, another layered climax occurs
      191 0:00

      207 0:51 (Section 2 cont'd)

      Mostly features oboe, flute and clarinet, loosely in rhythmic harmony (homophonic).  208 0:00 U


      Ensemble is led by bassoon playing "as slow as possible".  Held textures are contrasted with isolated accents and fast ornamental phrases. 230 0:00 I INSERT 4

      Serial construction, the ensemble basically shares a common tempo scheme, but there are many tempo variations and changes in layer density.  

      This section probably has the most "organic" modulation between homophony and polyphony.
      265 0:00
      266 0:03 Section 3
      (5-part texture)
      271 0:14 U
      272 0:16
      275 0:20 INSERT 5
      290 0:55 (Section 3 cont'd,
      but varied
      295 1:04

      337 2:21 U
      352 2:52

      Live Performance
           The instruments are arranged left to right: 
      Oboe -  Flute - English Horn - Clarinet - Bassoon.
      On Stockhausen Edition CD 4 they are heard in this spatial arrangement in stereo.

      Sound Impressions
           The use of independently-changing tempo layers is a brilliant technique for creating "non-harmonic" rhythms (ie - they are not multiples or subdivisions of each other).  This creates a kind of "noise" effect in terms of polyrhythms, just as upper harmonic tones and chord clusters are used to create dissonant harmonies.  As mentioned previously, the somewhat indeterminate "as fast as possible" concept was first introduced in Stockhausen's second set of Piano Pieces, but here in ZEITMASZE they are explored in many new and different ways and put into more complex structures.  It's interesting to note that the idea of using "performer ability" as an aleatoric factor would be revisited in the "New Complexity" movement (for example in Brian Ferneyhough's earliest works).

           Aside from the "theoretical" elements, this piece has alot of wit.  It may take a few listens to be able to easily discern the "homophonic tempo" sections from the "polyphonic tempo" sections (the table above should help), but once one gets used to it, it's alot of fun to follow the "social trends" exhibited by the 5 voices. 

           It's also worth reiterating that the first section is very useful in that it helps the listener get used to the idea of a "basic" melodic texture with a constantly changing density.  Even though in other musical contexts this section might be considered polyphonic, in this work, due to its "tempo agreement", this section acts as a more single-minded starting point.  As can be seen in the narrative, the players generally go back and forth between unity and seeming anarchy, but somehow they always (hopefully) land on their feet. 

      Stockhausen's Essay "...How Time Passes...", discussing concepts in ZEITMASZE (PDF)
      Sound samples, tracks listings and CD ordering
      Buy the Score 
      Wiki entry
      DVD Dress rehearsal, introduction and concert of ZEITMASZE conducted by Stockhausen (1992 with Ensemble Modern)
      English transcript of DVD Concert Introduction and analysis by Stockhausen (PDF) 
      10 DVD set of 1992 Rehearsals 
      Six Lectures from the Stockhausen Courses Kürten 2002 (Richard Toop)
      Compositional techniques in the music of Stockhausen (1951-1970) (Kelsall, 1975)
      The Music of Stockhausen (Jonathan Harvey)
      Works of Karlheinz Stockhausen (Robin Maconie)