8-Channel Surround Sound Electronic Music
2006-2007 [32 min.]

      COSMIC PULSES is the 13th "hour" of Stockhausen's originally-planned 24-part cycle KLANG ("SOUND") which is based on the 24 hours of the day.  This electronic work is composed of 24 layers of synthesizer-generated melodic material, with each layer having a different speed and pitch register.  The layers enter one by one, starting from the lowest/slowest layer, and go up in sequence to the highest/fastest layer.  After a period of several minutes where all 24 layers are active, the layers begin to individually drop out, again starting from the lowest layers and moving upwards (gradually leaving just the higher/faster layers).  This "draw down" is about twice as fast as in the "build-up".  

Form Structure
     Stockhausen's form scheme below describes the structure of COSMIC PULSES.  The time values along the top of the graph show the timing of the layers.  During the first 15 minutes and 20 seconds, Layers 24 up through 2 enter (from lowest/slowest to highest/fastest) with 40 seconds between entry of each new layer.  Then Layer 1 (the highest/fastest layer) enters, and all 24 Layers continue for 8 minutes and 40 seconds.  Starting at 24 minutes in, the Layers begin to drop out every 20 seconds (twice as fast as the build up), again starting from Layer 24 and going up to 1.  Layer 24 however, does return intermittently (as shown in the bottom right dashed line), and the piece ends with a duo between this, the lowest layer, and Layer 1, the highest Layer..
  • 23 Layers accumulate from lowest to highest (15' 20")
  • 24th Layer arrives and all layers active (8' 40")
  • 24 Layers dissipate from lowest to highest (8')
     Each Layer ("Schleife", column 5 in the above graph) is a looped pitch row with 1 to 24 unique pitches (some pitches receive an extra octave grace note, as seen in the cover to the PARADIES CD).  As shown in graph columns 1 and 2, the 24 "basic" durations of the notes are from 0.03" to 6.4", resulting in 24 "basic" loops from 0.15" to 2'33.6" (I characterize these values as "basic" because the loops are actually drastically manipulated in the Motion Models, see below).  The number of notes in each single loop is written in RED above the top-positioned music staff with the Layer numbers.  Each Layer is assigned 1 of 24 unique tempi (seen in graph columns 3 and 4: tempo 1 is slow, 24 is fast), and then also assigned 1 of 24 unique pitch ranges (which altogether spreads over 7 octaves).  The pitch range for each Layer loop is also shown in the staff at top (except Layer 2 of course, which is just a 1 note loop).

     One thing which is not really shown is that the synth sounds for the Layers, "realized" by Antonio Pérez Abellán, are not all the same.  For example, Layer 6 has a loud high overtone element, Layer 5 has a parallel oscillation timbre, Layer 4 has a metallic reverb effect, and Layer 3 has a counter-melody created from accents.  In general, the 24 timbres selected are somewhat similar to the ones Abellán used in HIMMELFAHRT, though there are many unique "treatments" to these which are not heard in that work.  One initial idea to enrich the loop Layers was to add a sub-layer of accent notes to each loop, though in the end this was only done with just a few loops (for example in Layer 3 as mentioned previously).  Finally, the initial pitch of each loop is one of the notes in the KLANG pitch row (in fact, all of the staff notes are based on the KLANG pitch row in various sequences).

     Below is a sketch for PARADIES (from the CD cover of Stockhausen CD 99, PARADIES) showing the shapes of the 24 ritornelli (repeating melodic loops) in the 24 Layers of COSMIC PULSES (with some octave and register shifts).  For example, reading backwards from the last measure, Layer 1 has a repeating 5-note loop, Layer 2 is just a 1-note tremolo, Layer 3 is a 6-note loop ritornello with a lower octave grace note before the first note, etc...  The circled notes are the lowest note in that measure, which is used as a central tone in the flute part of the work PARADIES.
     The table below gives an idea of how the loops change in number of notes and tempo.  The table at left shows that the number of notes changes irregularly for each new loop entry, but the tempo gradually increases for each new arrival.  The sequencing of loop entries is based on pitch register (see Jerome Kohl's note below).  The table at right is useful for comparing the 24 loops (excerpts of each are included on the CD) as they increase in the number of notes.
     (The "+" or "++" symbols following the numbers mean that there are 1 or 2 additional octave grace notes in the loop - ie - the first loop, Loop 24 actually has 26 pitches).

In order of Appearance
Nr. of
24   24++ 1
23   10+ 2
22   8 3
21   9+ 4
20   19++ 5
19   23++ 6
18   17+ 7
17   13+ 8
16   18++ 9
15   3 10
14   2 11
13   4 12
12   11+ 13
11   7+ 14
10   12+ 15
9   21+ 16
8   20+ 17
7   22++ 18
6   16+ 19
5   14+ 20
4   15++ 21
3   6+ 22
2   1 23
1   5 24
In order of Nr. of Notes
Nr. of
  1 23 2
  2 11 14
  3 10 15
  4 12 13
  5 24 1
  6+ 22 3
  7+ 14 11
  8 3 22
  9+ 4 21
  10+ 2 23
  11+ 13 12
  12+ 15 10
  13+ 8 17
  14+ 20 5
  15++ 21 4
  16+ 19 6
  17+ 7 18
  18++ 9 16
  19++ 5 20
  20+ 17 8
  21+ 16 9
  22++ 18 7
  23++ 6 19
  24++ 1 24

     Some additional observations about the loop melodies from Jerome Kohl:
     Stockhausen extracted 24 different note-segments to treat as loops for continuous repetition at different speeds and in different registers. They are made by progressively selecting one note (E), two notes (C and F), three notes (D,C#, D#), and so on, wrapping back to the beginning of the row and continuing up to a segment consisting of all 24 notes, which happens to start with the 13th member of the original series, D#. There are therefore 300 notes in all. However, these segments are not presented in order of size, but rather according to the numbers of the registral position of the successive members of the original row. Therefore, the highest layer, 1, is assigned the five-note segment; layer 2 has the one-note segment, layer three the six-note segment, and so on. There is an exception with the 24-note segment, however, which according to this scheme would be layer 21. Stockhausen moved it to the 24th layer probably so that he could start the composition with the complete 24-tone row, at the slowest speed, in the lowest register...Almost every loop has one note displaced downward by one or two octaves.  Loop 23, already in a very low register, has its ninth note, D#, taken down three octaves. This is the lowest “note” in Cosmic Pulses - at 9.724 Hz. This cannot be heard as a pitch, but can quite clearly be heard as a rhythm.

Motion Models
     Each group of 3 consecutive layers (24-22, 21-19, 18-16, etc...) is assigned a unique sequence of 8 "Motion Models" (indicated in thick multicolored circles) which are used to create sometimes drastic variations in loop tempo and pitch (Stockhausen actually characterizes them as "quite narrow glissandi", but I suppose it's all relative).  There are actually 10 Motion Models, but Motion Models 9 and 10 are only used for Layers 1-3 (from 16:00 to 21:00).  In any case, the Motion Models have 2 parts: a RED line indicating tempo manipulation, and a BLUE line indicating pitch-shifting of the loop (naturally, the higher the line, the faster the tempo/pitch transposition, and the lower, etc..).  The tempo variation range goes from 12 times slower (1/12) to 12 times faster.  The pitch shifting interval range (starting from original pitch) was from a major 3rd in the lower Layers (24-19), up to a major 10th in the highest Layers (3-1) (the ranges are indicated by the "Gliss." notations with brackets).  The number and timing of these Motion Model variation shapes were aleatory (freely distributed) within the indicated Motion Model time periods (each lasting 3 minutes for the first 24 minutes, and then 1 minute afterwards).  The manipulations in this case were done by Kathinka Pasveer.
COSMIC PULSES' Motion Models (1 through 10).
The RED-outlined waves are the shape of the tempo adjustments to the Layer loop in that section.
The BLUE-outlined waves show the same for pitch-shift adjustments.
The Motion Models are applied independently to 3 consecutive Layers for each section.

Spatial Movement
     The 24 Layer tracks are also given spatial movement trajectories over an 8-speaker octagonal surround sound system.  Each of the 24 Layers goes through 8 to 12 unique trajectory "shapes" (labeled from 1 to 241, though some shapes repeat), with each shape associated with a Motion Model.  The trajectory shapes of all the active layers collectively change at the same time when a new Motion Model is reached.  The shapes for a layer tend to progress from 3 or 4  "corners" to the maximum of 8 corners (see below).  The shapes also have a range of 24 rotation speeds from as long as 1 shape circuit per 16 secs to as fast as 16 rotations per 1 second (!), with the tempo generally increasing as the Layers rise in pitch register.  Apparently, the length of the shapes does not correlate with the length of the loops in each Motion Model (that would have been insanely hard to do anyways, considering all of the tempo variations).  Finally, additional Layer volume mixing to accentuate certain loops and textures was done by Stockhausen during the final mixdown (this from a conversation with Kathinka Pasveer).
These are Layers 17 to 24 (circled numbers at left), and correlate with the bottom 8 Layers in the form scheme earlier.  Each of the "Motion Models" is given a box above showing the shape which is created by the spatial movement of the sound.  Each box has a beginning and ending time indicated, but basically for the first 24 minutes, every 3rd minute the trajectories for all active layers change en masse, and from then on to the end, the trajectories collectively change every 1 minute. The numbers in diamonds enumerate the 241 different trajectory shapes.
       OKTEG software was developed by collaborators at the Experimental Studio for Acoustic Art in Freiburg (Joachim Haas and Gregorio Karman) which was used to spatialize the 24 layers according to Stockhausen's 241 spatial trajectories.  The initial layers were created by Antonio Pérez Abellán on synthesizer.
Time Chart - Stockhausen's form scheme above (and included in the CD booklet) is fairly easy to follow the music with, but the table below may make a few things clearer...


0:00 24 1

0:40 23
1:20 22
2:00 21
2:40 20

3:00 2

3:20 19
4:00 18
4:40 17
5:20 16


6:00 15 3

6:40 14
7:20 13
8:00 12
8:40 11

9:00 4

9:20 10
10:00 9
10:40 8
11:20 7


12:00 6 5

12:40 5
13:20 4
14:00 3
14:40 2

15:00 6

15:20 1

18:00 7
21:00 8


24:00 every 20 secs
(3 per min) starting from Layer 24 and moving upwards
25:00 6
26:00 5
27:00 4
28:00 3
29:00 2
30:00 1
31:00 8

Sound Impressions
     This is one Stockhausen work which I think is both very easy to get into and very hard, and I assume it probably has a divided audience.  On one hand I find it very easy to just "enjoy the ride" and experience the waves of melodic loops building and subsiding like a "statistical" tidal wave.  On the other hand, I could attempt to listen to the 24 accumulating loops with an ear to picking out the looping pitch rows and following the polyphonic tempo and pitch modulations - but frankly that's pretty hard, and even Stockhausen stated that a prodigious amount of "lucidity" would be required to follow all of the orbits (and of course, an 8-channel surround sound system would be necessary once the loops became denser).  Either way it's a challenging work, which brings additional rewards on repeated listenings.  Admittedly, the synthesizer timbres may lack the warm, rough, analog texture of the early tape pieces (KONTAKTE, etc...), but the spacial element seems to be the aspect that Stockhausen was most excited about, and COSMIC PULSES is easily his most spatially complex work.  On CD there are only 2 channels so of course much of the 8-channel surround motion is lost, but some listeners have reported that the spatial motion is so dense and complex that even in an 8-channel surround projection, the motions can only be gleaned in a "sidelong" manner.

     A third way (and my preferred way) in which to experience this work (on headphones) is to first pick a texture to concentrate on.  Before long, it fades and some new texture surfaces which one can latch onto.  This listening style of "hopping from stone to stone" I feel is just as rewarding, and may even be encouraged due to the seemingly deliberate mixing of various sound-textures surfacing and submerging.  In my personal listening experience, the design of the 24 tandem layers is not as intimidating as it might sound (no pun intended), since I can only really perceive a few layers at a time, even during the densest part (usually the "higher" layers).  But it goes without saying that this work should be played at the loudest possible volume without causing actual discomfort :).

(from COSMIC PULSES CD booklet)
     Jerome Kohl wrote an interesting report on the Stockhausen Forum of his experience with the work, which jibes with my last paragraph in some respects:
     " any case, I find COSMIC PULSES a daring piece of music, the effect of which depends largely upon the subjective results of the sonic overload. Only a little of this can be perceived in the stereo mix, and even this depends in part on knowing what to listen for, as a result of having previously heard the "real thing". To start with, every performance has been quite literally an entirely different piece. This is because there is so much sonic information that the ears are forced to select what to listen to at every moment.  One aspect of this is that certain peculiar effects, such as the well-known "whispering voices illusion", may occur at different points and in different registers (men's voices, women's voices, mixed voices), for longer or shorter periods of time. Similarly, there is a sensation of the sound rising and falling in space (even though there is no vertical dimension to the physical sound movement), and this, too, occurs at different points in time and to different degrees of intensity—even in the same hall using the same playback setup (I heard it three times straight through, in the Sülztalhalle at the courses in 2008). Different halls of course produce different senses of space for any piece of music, and this is, if anything, even more true for COSMIC PULSES because it depends so heavily on spatial relationships for its audible effect. From time to time, you can just detect familiar melodic fragments from the KLANG row against the dense background, but they vanish like ghosts or elves as soon as you notice they are there.  More difficult to describe (and consequently also harder to remember from one performance to the next) are the constantly changing timbres within the swirling walls of sound, like glittering, intermixed flecks of colour within which similarly hued groups momentarily coalesce into patches that evaporate again—Gregorio García Karman aptly describes these as "where the perception of movement leads to audible modulation range effects, binding a connection between space and timbre." This is certainly the most unusual and unforgettable feature of COSMIC PULSES."

        The CD track for COSMIC PULSES is one long track and not divided into sections as is usually done on Stockhausen Complete Edition CDs.  Also there is no 9 second silence preceding the start.  This is probably so that it's easier to follow the timing on the form scheme.  The CD also includes the first 90 seconds of each of the 24 Layers, with a brief introduction by Stockhausen.  With these, one can more easily hear how the Motion Models are applied to each Layer.  The 8 remaining works in the KLANG cycle (Hours 14-21) use sets of 3 consecutive Layers as "background material" (such as was done with OKTOPHONIE, UNSICHTBARE CHÖRE, etc...) for solo compositions (4 for voice and the remaining for basset horn, flute, horn and soprano sax).  These CDs also each provide the 3-Layer sets without the soloist, so one could even listen to those tracks to "learn" to hear the intricacies of COSMIC PULSES before tackling the full experience.

     At the 2015 Stockhausen Courses and Concerts in Kuerten, I was able to finally experience COSMIC PULSES in a properly projected spatial environment.  The experience is pretty indescribable, so I won't really try, but I can share one bit of advice which I learned:  Since the speakers are typically mounted high above the audience, if one is able to listen while looking straight up at the ceiling (preferably from the center of the room), the spatial trajectories can be more easily perceived and visualized as following the spatial diagrams above....

COSMIC PULSES samples and CD ordering 
COSMIC PULSES May 7th 2007 in Rome Premiere concert program
Stockhausen live interview 2007 discussing COSMIC PULSES (Vimeo)
Studio Report: Spatialization of Karlheinz Stockhausen’s COSMIC PULSES (Gregorio García Karman)
Gregorio García Karman's site
Youtube Clip of COSMIC PULSES
Nicholas Collins' review of the German premiere at the 2007 Stockhausen Courses
Sonoloco Review