A clarification: COSMIC PULSES is not an "octophonic" piece in Stockhausen's terminology, where this refers to speakers set at the corners of a cube. (Other writers sometimes use the term to refer to any kind of eight-channel configuration.) The speakers in COSMIC PULSES are stationed around the audience in a circle (or octagon, if you prefer), on stands as high as possible above the heads of the audience, though with subwoofers on the floor.

Stockhausen used the octophonic setup compositionally in OCTOPHONIE (from DIENSTAG) and ORCHESTER-FINALISTEN (from MITTWOCH), though in public performances this same speaker array could be routed for other works with fewer channels of music at the source (e.g., GESANG DER JÜNGLINGE or KONTAKTE).

Your characterisation of 14–21 is about right, though the layers of electronic music correspond only approximately to the register of the soloists. This is especially true because of the "distortions" of the loops, which not only involve the glissando deviations above and below the nominal pitches, but also the occasional displacement by one or two octaves (in one case, in layer 23, three octaves) of a note in each loop. Listen to the sample tracks of the 24 loops on the COSMIC PULSES CD, and you will get the idea. That one note in layer 23 is the lowest of the entie composition, and is in fact well below the threshhold of pitch perception, though the fundamental can still be heard as a rhythm, at about 9.6 Hz! In general, though, the flute in PARADIES is accompanied by the highest-pitched layers 1–3, and the bass voice in HAVONA by the lowest layers 22–24, with the other six pieces in between, roughly according to instrumental/vocal range. The density of events in the solo parts, however, does not follow a similar scale. If memory serves, the sparsest solo part is in JERUSEM, while the baritone in ORVONTON is very busy indeed, though not as much as the flute in PARADIES. The sound projectionist in these pieces is in fact little more than a monitor, once the performance is under way. Unlike many other pieces, the projectionist here is instructed to leave things largely alone, barring accident.

Yea .. I know that CP isn't octophonic. I was thinking of stuff like OKTOPHONIE in relation to CP where it is more of a cube. Interesting how you say those older 4-channel works would work in a cube format .. but probably not as effective in terms of exploiting that?

An octophonic speaker array works perfectly well for quadraphonic music. It is just a matter of coupling together the upper and lower squares. In a certain sense, it enhances the experience, in that it lifts the sounds of the quadraphonic square up over the audience.

Sure it works, but what I meant is that its not working the same way as OKTOPHONIE is per se .. exploiting the config in that sense.

Jerry is right to remind us that the COSMIC PULSES speaker setup is 8ch horizontal, like SIRIUS. CP attempts to take the "dancing eigentones" of the earlier work to an entirely new level. There is a logic and a history to what is going on here: allusions to Helmholtz's work with sirens in the mid-19th century, and as far back as Ohm and Fourier in the early 1800s. Ohm and Fourier developed theories of harmonic integration in relation to speech and also to organ pipes. In both cases harmonious musical tones are created when white noise (a stream of air) meets structural resistance (the pipe, the mouth cavity). In CP structural resistance is provided by the speakers, and the activating noise element or 'wind' is the composed note content. As I have said elsewhere, this is an exercise in manufactured turbulence not dissimilar to blowing air through an organ pipe. (The principle is demonstrated by the children's toy consisting of a plastic ribbed tube like a vacuum cleaner tube, which emits musical tones when it is whirled in the air.) A key reference is Meyer-Eppler's paper in Die Reihe I "Statistic and Psychologic Problems of Sound" in which the author suggests using filtered low frequency noise as a natural tremulant - called "an aleatoric" - to make sounds move between speakers in a natural sounding and unpredictable way. Another key influence is Beyer and Eimert's vocoder study in rotating layers "Zu Ehren von Igor Stravinsky" (Wergo LP 60009, a demonstration of how recorded speech can be layered, modulated, rotated, and recombined from bandwidths of colored noise spinning at different speeds. Technology using filtered white noise as source material to synthesize percussion sounds (cymbals, triangle, woodblock etc) was already well known and incorporated in Milton Babbitt's RCA Synthesizer at Columbia-Princeton, and the theory behind it is a part inspiration of ZYKLUS (1959). In composing CP Stockhausen consciously reverted to the primitive synthesis technique of Studie II (square wave arpeggios, added reverberation) and is relying on the sirenlike speed of rotation of material in up to 8 channels to "harmonize" the result after the style of a Helmholtz siren. But he also expressed doubts that it would succeed ("it may not even be music") and by studying the history of acoustics one can identify the problems. First, the profession as a whole, Fourier and Ohm through to Harry Olson in the 1950s, assumed all along that musical sounds were essentially static phenomena, and this is a mistake: sounds are naturally dynamic. Second, Ohm excluded friction from his theory of turbulence and the harmony of organ pipes because the alternative was too hard to compute, and for the following 150 years acousticians have continued vainly to characterize the onset noises of the organ, wind instruments, and the violin as "unwanted noise" when in fact they embody the characteristic onset resistance that makes sounds recognizably musical. This remains an egregious theoretical flaw of computer sound synthesis even today, and a major reason why synthesized computer music sounds metallic. What KS might have done, taking Meyer-Eppler's advice to heart, would have been to use white noise as his entire basic material and focus on the rotational mechanisms within the score plan to filter and convert white noise into complex but natural sounding harmonies.

I'd imagine 13-21 being particularly effective as a simultaneous event in a special building where the public could traverse from room to room freely. Ditto the group of 5-12 as another separate simultaneous event. I've read all "The pieces are based on a 24-note series (each note of a two-octave chromatic scale) that has essentially the same all-interval sequence as the series for Gruppen" [...] [Toop 2008a], however hours 1-4 are certainly more distinct and separate, and I see these as sticking out and not really fitting into a simultaneous event. And in my opinion, it is these opening hours that are the strongest in the entire cycle.

If you will categorize, you could say: KLANG hours 1-5 and 13 are the main works, and the other - in German you would say: Nebenwerke; they are in a second row.

I've always viewed 5-12 as being a distinct family, and 13-21 another distinct family .. where 5 & 13 are the distinct mother works but with many children, so each family work together and have much in common - which is obvious. But 1-4 are all separate individuals so to speak. To me, a sign that perhaps he rushed things midway, or perhaps saw more potential with the material of 5 & 13 which inspired this different direction (?)

It is more charitable to assume that Stockhausen "saw more potential with the material of 5 & 13", and so developed the separate subcycles of 5–12 and 13–21, but probably more realistic to acknowledge that he "rushed things midway". I have pointed out in my article on the 5–12 subcycle (which I call the "Sufi" subcycle, since the names can be traced to one of Stockhausen's favourite books, Hazrat Inayat Khan's Sufi Message, though admittedly not with the same degree of certainty as the "Urantia" titles of hours 14–21) that Stockhausen would have been 86 years old before the cycle was completed, had he continued at his original pace of about six months per piece. It seems very likely that he did not believe he was going to live so long (until this year at least), and had to decide whether to leave more than half of the cycle unfinished, or change his methods in order to complete as much of it as possible.

Another feature that sets off the "Sufi" subcycle from the rest is that it uses the inversion of the 24-tone row, expanded to 25 tones by bringing back the initial note at the at the end. The structure of HARMONIEN (and consequently of the trios as well) is based on sets of fives, so this extension of the row makes sense numerically. Another distinction is made by distributing the pitches in a different registral disposition from the one used in hours 1–3 (HIMMELS-TÜR of course does not use the pitch row, because of the nature of the instrument) and in TÜRIN. It is this constructive feature of hours 5–12 that is most responsible for creating the evident subdivision of the cycle into subcycles.

It is pure conjecture on my part that Stockhausen might have returned to something more like what he did in hours 1–4, had he lived long enough to complete hours 22–24—that is, composing each work according to independent criteria, without a "mother work". If he did this, it would result in three subcycles: the "Sufi" and "Urantia" subcycles of 8 and 9 pieces, and an "overnight" cycle stretching from hour 22 to hour 4, totaling 7 pieces, therefore producing a distributional-serial division of 7:8:9 for the entire KLANG cycle. We know that such a plan was not originally foreseen. Stockhausen said at the courses in 2006 that he had "no plan," and was simply composing each piece as he came to it. This does not necessarily rule out the possibility that such a simple scheme as this 7:8:9 division could emerge as work progressed. When he began composing COSMIC PULSES in August 2006, it was to be hour 6, following an hour 5 consisting of three solos and a trio combining them, together titled AKKORDE (this became the separate hours 5 and 6, HARMONIEN and SCHÖNHEIT). Did he move COSMIC PULSES to hour 13 precisely because it would permit him this 7:8:9 division of the cycle? Or was this just an accidental byproduct of the fact that hour 13 is assigned the same central tone as hour 6 (E-flat, though in different octaves) in a scheme projected from the 24-tone KLANG row, so that he could move COSMIC PULSES to that position without having to reconfigure all of its pitches? Even assuming this was the logic behind the move, did he then see that this three-part division of the cycle would be made possible if he created eight solos to follow COSMIC PULSES rather than, say, six (using four layers each of electronic music, instead of three)? We will probably never know the answer, but it is a tantalizing speculation.

And on the night before he passed, he finished the 2nd set of orchestral TIERKREIS. Another series of works that shows how KS could get a lot of mileage out of his raw material, he saw almost infinite possibilities .. as in LICHT.

Back to KLANG ..

Another observation is the duration of the works .. for 13-21, we have CP which is 32 min., and then for 14-21 .. the works go from ca. 25 min (HAVONA), to 24, 23, 22, etc. down to about ca. 18 min (PARADIES). Do these times correspond with how these layers enter the polyphony of CP.