MANTRA

Stockhausen's original sketch of the form plan.
At bottom are the longest MANTRA themes,
which are overlaid by the shorter versions above them. 
(© www.karlheinzstockhausen.org)

No. 32: MANTRA
for 2 pianos with 12 antique cymbals, 1 woodblock and 2 ring modulators (and shortwave radio/tape)
1970 [65'-72']

Development
     During Stockhausen's stay in Japan performing open-form pieces like SPIRAL at the World's Fair Expo Pavilion, he worked on a duo piece for the pianists Aloys & Alfons Kontarsky.  The genesis of this work came from a melody which surfaced spontaneously while traveling by car many years before, as well as from his interest in refining ring modulation techniques . 
     It is reported that some of his intuitive music collaborators were feeling unhappy about the open nature of the "free" music they were playing and beginning to contest ownership of the composition rights.  On the other hand, Stockhausen has been described as being unhappy with the "dilettantish interpretations" he was getting from his players.  When a performer was in a physically or mentally distracted state (sick or depressed), the music suffered as well.  This "fragility" of intuitive music would not be as present in fully-notated music.  MANTRA is completely composed down to the last tenth of second, though in a sense it is "intuitively-composed" as the product of one person's intuitively-based musical deliberations (at a much slower pace..).

Introduction
     This epic piece is a big one and a little hard to stay with for its full duration for some (including myself!). In fact it's probably the longest single piano work I have in my music collection.  One of the main reasons I find analysis of a huge piece like this to be useful is to identify "signposts" so that the listener can digest such a huge repast in platefuls, rather than as a huge buffet stretching off into the horizon.  However after finishing collating all the data and superimposing the theoretical design structure onto MANTRA, I actually found the theory to be kind of...distracting.  In fact, the structural breaks that Stockhausen himself marked in the score (and used to create CD tracks) usually don't adhere to the structural design.
     What I think happened here is that Stockhausen's manipulation of the elements unregulated by the mathematics (as well as a fair share of "cheating") was done with so much panache that his stylistic and musical "personality" became a bit more important than the underlying mathematical break points.  So why study the math?  Admittedly there are a few tables in the analysis below, which at first don't seem to add much to the listening experience.  But Stockhausen gave lectures on these theories because he believed that learning of the techniques involved gave the listener an opportunity to expand one's consciousness on some level (musically and otherwise) and would enrich the listening experience.  For the most part I totally agree, but in this case the MANTRA formula is so melodically, rhythmically and structurally warped that it's apparently easier to follow it as a narrative/fantasia, rather than as a formula-variation form.  Also it's worth noting that in the same lecture, Stockhausen maintains that theoretical understanding of MANTRA is no more necessary towards its enjoyment than knowledge about astrophysics is necessary in order to be moved by the stars in the night sky. 
     So, in any case I first present an analysis of MANTRA as a formula with multiple poly-structural layers, and then afterwards as a "highlights" narrative at the end.

Form Structure
     MANTRA is basically a giant crystal created from a small snowflake.  In other words, this (ca.) 70-minute work is a melodic and thematic explosion, derived from a 1-minute tune.

The MANTRA formula.
(© www.karlheinzstockhausen.org)

     The original vinyl album cover shows the MANTRA "formula".  The top staff has circled numbers, 1 through 13, which label the parts of the formula and their special properties (the pink numbers are duration measurements).  Basically, Stockhausen takes this 8-bar theme (the left hand is actually a permutated inversion of the right hand part), stretches it vertically (harmonically) and horizontally (temporally) until he has (roughly) 156 versions, and then layers them into a poly-thematic 3-level ziggurat (pyramid) as sketched out at the top of the page.

     The full MANTRA work has 13 large sections (derived from the 13 parts/notes of the MANTRA formula above) with each section focusing on one of the special "musical behaviors" below (also derived from the MANTRA itself).

Musical Behavior	From Bar	Beginning (root) note
1. Regular Repetition	12	A
2. Accent at the End	61	B
3. "Normal"	89	G#
4. Grace note group around a Central Tone	125	E
5. "Tremolo"	205	F
6. Chord (accented)	282	D
7. Accent at Beginning	445	G#
8. "Chromatic" Connection	488	Eb
9. Staccatto	538	Db
10. Irregular Repetition (Morse Code)	587	C
11. Trills	611	Bb
12. Sforzando accent	641	Gb
13. Arpeggio-Connection	673	A

     The piece starts out with a 4 chord intro (made from the notes of the formula), then states the MANTRA formula in it's "plain" form (bar 3-10), and then begins the first of the 13 large sections.  These sections each have 12 MANTRA formula repetitions (13 x 12 = 156), each expanded/compressed in 1 of 12 ways (see below) and superimposed on each other.  In fact, the entry sequence of the first set of 12 Expansion forms goes like this: 1 - 3 - 12 - 8 - 9 - 6 - 11 - 7 - 5 - 4 - 2 - 10, which also happens to be the relative pitch sequence of the original MANTRA (though the sequence is different for each large section).  However as indicated before, these Expansions are not single-threaded, they are actually played on top of each other, creating up to 3 simultaneous voices:

(1)-----------------------------------------------------------------------------------------------------------------------------------
(3)-------------------------------------------------------    (9)--------------------------------------                        (11)-------
        (12)------------                            (8)---------------                                                        (6)----------------------

     Each of these 12 Expansions also attempts to incorporate a different one of the 13 musical behaviors (one is actually doubled).  After the 13th and last "Arpeggio-Connection"-themed large section, MANTRA does a hyper-fast compressed melodic "revue", followed by one last statement of the formula.

MANTRA Expansions
     In order to stretch the formula vertically (from lowest note to highest note) Stockhausen created 11 additional artificial scales.  Each artificial scale's 12 notes take up more and more room on the keyboard (become wider), until the largest scale requires the entire keyboard to play just one artificial "octave".  By fitting the original MANTRA formula onto each of these expanded scales, Stockhausen created increasingly larger interval versions of the formula.  Then, by expanding or reducing the durations of each note, he created versions of the formula which were as compressed as 3 seconds and as stretched out as 3 1/2 minutes.  One other technique to create a great variety of MANTRAs was that Stockhausen would sometimes enforce the rhythm of one phrase on another phrase, filling in any missing notes with repetition or grace notes.

Table of the 156 MANTRAs (beginning bar nos.).
Top row indicates the 13 sections, 1st column indicates the 12 subdivisions in each section.
Notice that Expansion I.1 starts at the same time as Expansion I.3, and I.12 starts in the very next measure.
This matches the diagram above in red.
(from Richard Toop's "Six Lectures from the Stockhausen Courses Kurten 2002")
(© www.karlheinzstockhausen.org)

     The idea of compressing/expanding the pitch ranges of melodies would later be further explored in SIRIUS (through electronic manipulation), and in Xi and YPSILON (through new microtonal wind instrument fingerings).

Percussion

This sequence (bar 611) includes, woodblocks (WOOD), shortwave radio (KW) and cymbals (CYMB).
(© www.karlheinzstockhausen.org)

     Antique cymbals (crotales) and woodblocks are used to sometimes punctuate sections and repetitions of the MANTRA in its many layers.  These percussion elements also are meant to evoke one of the 13 musical behavior types and root notes, and occur in the same frequency as the MANTRA pitch scale itself (1st iteration, 3rd, 15th (which is 3 + 12), 23rd (15 + 8), etc...).  Cymbals dominate the beginning half (12 occurrences, followed by 12 more inverted and an ending recap note (see below table), and the woodblocks occur more often in the later sections (as an inversion).  The woodblock hits also "have the function of marking and emphasizing certain attack and decay accents" (interview with Jonathan Cott).

Table 1: Cymbal Events (1st 12 on left, remaining 13 on right, inverted).
Roman numerals in column 3 indicate which pianist plays the cymbals.
(Click to enlarge)
 (from Ádám Siska: LIVE ELECTRONICS New Tools for Composition in the 20th Century (2013 thesis))

Table of Ring Modulation tones for each performer
(Click to enlarge)
 (from Ádám Siska: LIVE ELECTRONICS)

Ring Modulation
     Stockhausen also gives each piano a ring modulator effect box ("MODUL 69B", designed by Stockhausen himself).  This effect can cause timbral "roughness", distortion, or even transpose the pitch itself (or all 3).  This idea actually came to him while working on the piece KURZWELLEN MIT BEETHOVEN (Shortwaves with Beethoven) where he applied ring modulation effects to Beethoven works, including the piano sonatas.
     The ring modulator of the 1st pianist is tuned to the pitch "roots" for each of the 13 sections, and the more dissonant the note being played is to the section "tonic", the more noisy the ring modulation effect is (when playing a "root" note the effect is minimal).  The ring modulator for the 2nd pianist is tuned to the inverted MANTRA pitch sequence (mostly).  At times the ring modulation controls are also manipulated to create vibrato and glissando effects. 

I have no idea if this video below is appropriate in a 

serious analysis of MANTRA, but it's pretty entertaining 

nonetheless... 

Maestro Ring Modulator RM-1. 
Demonstration Record. 1972

Inserts

The ring modulations twist and bend the sustaining chords at bar 421.
(© www.karlheinzstockhausen.org)

     Additionally, whenever Stockhausen felt like it, he would deviate from the form structure and insert a kind of "exploratory cadenza" of some texture or idea he felt merited further extemporization on.  These inserts are not ruled by the MANTRA formula at all, but are more like little breakout "explosions", much like the ones found in IN FREUNDSCHAFT, CARRÉ and many other places (also called "Inserts" or sometimes "Windows").  Some of these excursions occur at bars 132 (ring modulated slow oscillations), 212 (wide interval "banging" contest), 325 ("record skipping"), 422 (swooping ring modulation), 572 (looping notes), 578 (Morse code on shortwave radio), and 639 (modulated vocal chants).

     Note: Most of the information for the above analysis of MANTRA (except for the Siska tables) was culled from Richard Toop's excellent book "Six Lectures from the Stockhausen Courses Kürten 2002", available from http://www.stockhausen-verlag.com.  HIGHLY RECOMMENDED.

A Narrative Analysis
     So here I ignore all the scale Expansions and tone rows and just approach MANTRA as 26 "moments" (following the "official" Kontarsky Brothers' recording), which seems ideologically at odds with the MANTRA formula concept, but...it works better for me.  Below each track "impression" I also note the 13 "musical behavior" sections, as well as if 1 of the 12 MANTRA scale Expansions occurs immediately at the beginning of the track (also Cymbal strike "types").

Track	Bar	Duration	Features
1	1-2	0:30	- Intro: 4 chords from the 4 phrases of the MANTRA  - CYMBAL: Regular Repetition
2	3-10	1:13	- The MANTRA
3	11-70	3:56	- MANTRA sequence using regular repetition (tremolo), alternating pianos  - CYMBAL: Final note accent  - SECTION I: Regular Repetition (from bar 12)  - SECTION II: Final note accent (from bar 61)
4	71-108	2:41	- Moderately Fast, slowing down  - Expansion II.8 begins  - CYMBAL: Flurries around center note (at bar 73)  - SECTION III: Normal (from 89)  - CYMBAL: Slow Tremolo (at 89)
5	109-120	1:51	- Slow descending/ascending scales/notes against Morse code, rolled chords
6	121-131	0:51	- "Swinging"  - CYMBAL: Chord  - SECTION IV: Flurries around center note (125)
7	132-150	2:05	- Held chords with ring modulated oscillations  - Expansion IV.10 begins
8	151-188	5:06	- High bell tones, repetition and dialogue with melodic flurries  - SECTION IV Center Note Flurries Continues  - Expansion IV.11 begins (152)
9	189-211	1:13	- Cartoon-like, ending in slowing tremolo modulated chords  - SECTION IV Center Note Flurries Continues  - Expansion IV.7 begins  - SECTION V: Slow Tremolo (205)
10	212-237	1:41	- Wide interval "banging" contest  - Expansion V.12 begins
11	238-261	1:21	- Unstable tempos  - SECTION V Slow Tremolo Continues  - CYMBAL: gliss up (241)
12	262-298	5:00	- Languid, Morse code cymbals  - SECTION V Slow Tremolo Continues  - Expansions V.5 & V.7 begin  - SECTION VI: Accented chord (282)
13	299-323	1:10	- Ringing cymbal with woodblock accents  - SECTION VI Chord Accent Continues  - Expansion VI.7 ( begins 300)  - CYMBAL: Trilling (308), Sforzando (312)
14	324-421	2:07	- Staccato chords, "record skipping" with woodblock, changing tempo  - SECTION VI Chord Accent Continues  - Expansion VI.10 (begins 325)
15	422-434	4:00	- Swooping ring modulation on slow chord accents
16	435-491	3:26	- Melancholic, jazzy  - SECTION VI Chord Accent Continues  - SECTION VII: Accent (with 1 repetition) (445)  - SECTION VIII: Descending chromatic scale (488)
17	492-529	5:58	- Distorted lullaby/ballad ("ala Blade Runner"), fast arpeggios  - SECTION VIII Descending chromatic Continues  - Expansion VIII.12 begins
18	530-577	2:58	- Playful, fast looping notes insert (from 572)  - SECTION VIII Descending chromatic Continues  - Expansion VIII.4 begins  - CYMBAL: Flurries around center note  - SECTION IX: Staccato (538)
19	578-637	3:28	- Morse code radio, syncopation with woodblocks, cymbals  - SECTION X: Irregular repetition (587)  - SECTION XI: Trills (611)
20	638-640	0:56	- Modulated vocal chants "JO (yo) - HO - TA!"
21	641-655	2:02	- Quiet Morse code with cymbals and high piano key  - SECTION XII: Sharp attack (with echo)  - Expansion XII.1 begins  - CYMBAL: Irregular Repetition
22	656-686	3:37	- Cymbal trills, cascading low notes, etc…  - SECTION XII Sharp attack Continues  - Expansion XII.8 begins  - SECTION XIII: Arpeggio connection (673)
23	687-854	4:33	- Fast Compression Toccata
24	855-880	1:58	- High Rolled chords  - SECTION XIII Arpeggio Continues  - Expansion XIII.6 begins
25	881-883	0:28	- A Rising scale and a cadence  - CYMBAL: Crescendo (Repetition)
26	884-887	1:13 (0:45)	- MANTRA restatement

(64:25 - Total time of Kontarsky brothers performance)

Live Performance 
Yxus Ensemble: Kadri-Ann Sumera, Age Juurikas:

The performance video below is split up into the 13 musical behavior sections:
(Performed by Bernhard Fograscher and Jennifer Hymer at Making New Waves Festival, Budapest 2008)

As a side note, the MANTRA formula makes a full appearance in Stockhausen's DIENSTAG aus LICHT opera 1st Act, JAHRESLAUF, during the 3rd saxophone solo segment.

Links
Stockhausen's Lecture on MANTRA (Pt 1)
MANTRA (Kontarsky Brothers) samples, track listings and CD ordering
Purchase the Score
MANTRA Wiki
MANTRA (Live, Alack Karis & Kian Freitas,YouTube)
Sonoloco Review (Kontarsky Brothers)
Reviews (Pestova-Meyer Piano Duo) 
Ádám Siska: LIVE ELECTRONICS New Tools for Composition in the 20th Century (2013 thesis) 
Paul Miller talk on MANTRA, Library of Congress

HELIKOPTER-STREICHQUARTETT

MITTWOCH AUS LICHT
Greeting MITTWOCHS- GRUSS	Scene 1 WELT-PARLAMENT	Scene 2 ORCHESTER-FINALISTEN	Scene 3 HELIKOPTER-STREICHQUARTETT	Scene 4 MICHAELION	Farewell MITTWOCHS- ABSCHIED

No. 69: HELIKOPTER-STREICHQUARTETT
(Helicopter String Quartet, 3rd Act of MITTWOCH AUS LICHT)
for String Quartet and 4 Helicopters
1992/1993 [ca. 31']

      HELIKOPTER-STREICHQUARTETT is the 3rd scene of Stockhausen's dramatic music work MITTWOCH AUS LICHT (WEDNESDAY FROM LIGHT), which was the 6th-composed entry of his 7-part, 29-hour opera cycle LICHT (Light). LICHT is a work for acoustic and electronic operatic forces, divided into the 7 days of the week (one opera for each day).  This opera cycle revolves around 3 archetype characters, MICHAEL, EVE and LUCIFER, and over the 29 hours each of these characters are introduced, come into conflict, face temptation and finally come into union.  The music is almost entirely based on a "super-formula", which is a 3-layered melodic-thematic representation of the 3 characters.  These formula-themes are together and separately threaded throughout the opera's vocal and instrumental fabric. Story-wise, actors and narrative can (and often do) change from act to act and the libretto text is sometimes made up of non-traditional grammar or even purely phonetic sounds.

Development
     In the early 90s Stockhausen was asked to write a string quartet but initially refused, since he preferred to avoid musical forms developed in previous centuries.  However, he soon had a dream of 4 string quartet players in 4 separate helicopters, whose performances were being transmitted to TV monitors.  This was later followed by a real (waking) sighting of 4 helicopters in the skies above the Rhine River, so he took these as signs that the piece was meant to be.  Eventually this became the 3rd Scene of MITTWOCH AUS LICHT.

     In MITTWOCH's 1st Scene, an a cappella vocal group performs in the top floor of a skyscraper.  In the 2nd Scene, musicians of an orchestra suspended by cranes play, while swinging through the auditorium.  In this 3rd Scene, the string players are actually in the sky, kilometers apart.  The 4th and final Scene takes place in a single room again, but the setting is a "galactic setting for delegates of the universe".  Obviously the theme of spatial expansion is an important one.

Waveform analysis of the string players and the helicopter rotor sounds (from Bar 1).
(© www.karlheinzstockhausen.org)

Form
     The piece starts with a bit of verbal moderation in the auditorium, and continues as the string quartet players walk out to their respective helicopters.
     Then, as the helicopter engines start and they lift off towards a predetermined altitude, the players play an "Ascent" phase, mainly of slow upwards tremolo glissandi.
     After about a minute or two the string quartet proper begins ("Flight"), and Stockhausen here uses the compositional themes from his superformula for LICHT in order to develop melodic trajectories.  The LICHT superformula has 3 "voices" (staff lines) for MICHAEL, EVE and LUCIFER.  The string quartet navigates through this superformula 3 times over 18 minutes (with a brief coda).  The 3 cycles are also punctuated 9 times by vocal "counting" in different "voices" (meant to suggest vocal styles from around the world) in a round-robin sequence.  Each count to 13 signals the beginning of a new cycle iteration (the counting is actually a part of the LUCIFER part of the LICHT super-formula and occurs in many places in LICHT).  The Flight phase is followed by a slow descending glissandi of about 2-3 minutes ("Descent" phase) while the pilots make a synchronized descent. 
     After the string players return to the stage the Moderator interviews the performers (including the helicopter pilots).

Section	Bar	Stockhausen Edition 53a Track Durations	Event	Arditti Qrtt Edition 35 Track Timings, Features
0		7:43	Introduction Moderation
1		1:27	Turbines start	0:10
2	0	3:10	Ascent  (Aufstieg)	1:58 (Slow upwards glissandi,  accel. tremolo)
3	1	4:38	Flight  (Flug): 1st Cycle	5:16 (harmonics, sul pont., bow bouncing)
4	6		Count to 7, then 1 (Vocal style A)	6:47 (Vln 2 microtonal)
5	16		Count to 5 (Vocal style B)	8:26
6	20		Count to 13 (Vocal style C)	9:32 (sul pont, harm.)
7	22	9:17	2nd Cycle	9:55 (bow bouncing)
8	27		Count to 7, then 1 (Violin 2 only w hissing)	12:58 (high freq sul. pont.,  free noises, harm.)
9	37		Count to 5	16:17
10	42		Count to 13	18:26
11	43	4:38	3rd Cycle	19:12 (Vln 1 bow bouncing)
12	48		Count to 7, then 1 (Viola only, hoarse climbing pitches)	20:45 (Vln 1 bow bouncing)
13	58		Count to 5 (Viola only, hoarse climbing pitches)	22:22
14	62		Count to 13 (long final consonants)	23:27
15	64		Coda: Formation: ("14!") (becoming unison)	23:52
16	80	4:36	Descent, Landing (Abstieg, Landung)	26:53 (Slow downwards glissandi)
17		15:34	Player/Pilot interviews

Score

The beginning "Ascent" section.  The speed of the tremolo bowing mimics
the speed of the helicopter rotor blades speeding up. 
(© www.karlheinzstockhausen.org)

Beginning of the LICHT superformula showing the 3 "voices" of MICHAEL, EVE and LUCIFER.
(© www.karlheinzstockhausen.org)

     The 1st measure below (top half) shows how the HELIKOPTER-STREICHQUARTETT uses the same thematic material as the 1st measure of the LICHT superformula, except that the LUCIFER staff is on top, followed by the MICHAEL and EVA staves.  This order changes for each of the 3 LICHT superformula iterations (though ultimately that doesn't mean much since Stockhausen spreads the notes out to 4 different lines anyways - see below).  Additionally the formulas are transposed in each cycle to match certain pitches in the MITTWOCH section of LICHT.
     After Stockhausen put down the formula on 4 staves, he drew lines in 4 colors connecting the notes across the 3 voices, essentially redistributing the notes from the 3 LICHT voices to 4 string quartet voices, and drawing pitch curves to connect the notes in each instrument part.  The 4 staff lines in the bottom half (below) show the 4 string parts "untangled" for the same music material above it.

Beginning of 1st cycle.

Below is an example of the instructions for the 9 vocal inserts.

Counting to 13 just before beginning the 3rd cycle.
(© www.karlheinzstockhausen.org)

Live Performance
The Elysian Quartet performing in 2012:


Making of doc from Venice Biennial in 2013:

Sound Impressions
     I've always liked this piece for its vitality.  The fast tremolos are pretty fascinating as they attempt to blend with the helicopter rotor noises, and the rotor noises themselves are interesting to listen to.  I wondered if it might have been nice to have the "real sound" tracks of the helicopters in isolation as a bonus, as Stockhausen has done for the electronic parts of many other works (SIRIUS, OKTOPHONIE, etc...) but I suppose since the score does not have actual flight instructions it would be confusing to call it a "Stockhausen composition."
     I'm not sure if this is a good or bad thing but because of the constant micro-tonal glissing I never really feel like I'm hearing the LICHT formula.  I suppose that's a testimony to the adaptability of the formula to different compositional permutations.  However I wish I had felt more of a sense of structural change during the flight phase.  Based on the timings it appears that the 2nd cycle is generally a slower tempo than the 1st and 3rd cycles but because of the fast tremolo playing it all seems pretty consistent, for better or worse.
     In any case, this is a deep listen for it's subtle differences, and while watching a video of the performance one gets the feeling of being at a NASA space launch as much as at a chamber music recital, which even alone is quite an achievement.  This is probably Stockhausen's most famous work of the last 30 years and is also probably the only one of his records to be sold at Walmart.

Links
Stockhausen's Introduction
HELIKOPTER-STREICHQUARTETT samples, track listings and CD ordering
Purchase the Score
Wiki Article
Photos
Robin Maconie essay 1 "Helikopter-Streichquartett"
Robin Maconie essay 2 "Stockhausen's Musical Helicopters" PDF
CD Youtube clip
Review of Frank Scheffer's documentary about the HELIKOPTER-STREICHQUARTETT

KLANG: Hours 5 - 12, HARMONIEN Solo & Chamber Works

Work notes indicating 5 sections of HARMONIEN and the original pitch row from KLANG
(© www.karlheinzstockhausen.org)

No. 85: KLANG - 5th Hour: HARMONIEN (Harmonies)
     for bass clarinet (No. 85.1)
     for flute (No. 85.2)
     for trumpet (No. 85.3)
     2006 [15-16']
No. 86 - KLANG - 6th Hour: SCHÖNHEIT (Beauty) for bass clarinet, flute and trumpet, 2006 [28']
No. 87 - KLANG - 7th Hour: BALANCE for bass clarinet, English horn, flute, 2007 [32']
No. 88 - KLANG - 8th Hour: GLÜCK (Bliss) for bassoon, English horn, oboe, 2007 [30']
No. 89 - KLANG - 9th Hour: HOFFNUNG (Hope) for cello, viola, violin, 2007 [32'30'']
No. 90 - KLANG - 10th Hour: GLANZ (Brilliance) for bassoon, viola, clarinet, oboe, trumpet, trombone, tuba, 2007 [38']
No. 91 - KLANG - 11th Hour: TREUE (Fidelity) for bass clarinet, basset-horn, clarinet, 2007 [30']
No. 92 - KLANG - 12th Hour: ERWACHEN (Awakening) for cello, trumpet, soprano saxophone, 2007 [30']
KATIKATI for flute (No. 85.2 extra), 2006 [4']

Introduction
     While rehearsing LIBRA (part of the science-fiction themed work SIRIUS for vocal soloists, trumpet, bass clarinet and electronic tape), Stockhausen was inspired to write HARMONIEN for bass clarinet (solo), specifically for Suzanne Stephens.  Shortly afterwards, he wrote other instrument-specific versions for flute and trumpet.  HARMONIEN ended up becoming the 5th hour of KLANG, Stockhausen's cycle of works for the 24 hours of the day (of which hours 1 through 21 were completed).

     These 3 individual versions of HARMONIEN were then taken apart and layered on top of each other to form KLANG's 6th hour: SCHÖNHEIT (Beauty), a trio version using the same basic material, split into 5 continuous sections.  This was followed by KLANG hours 7 through 12: BALANCE, GLÜCK (Bliss), HOFFNUNG (Hope), GLANZ (Brilliance), TREUE (Fidelity) and ERWACHEN (Awakening), all of which are re-sequenced, rearranged and expanded versions of SCHÖNHEIT for different instrumental ensembles.  This method of using different instrumental ensembles on different sequences of events of the same basic material is kind of reminiscent of Stockhausen's prior habit of making re-arranged versions of pieces like TIERKREIS and IN FREUNDSCHAFT, combined with the mobile-like mutability of pieces like MOMENTE or MIKROPHONIE I.

CD Covers (© www.karlheinzstockhausen.org)

KLANG 5: HARMONIEN (HARMONIES)
     HARMONIEN, the "ground zero" of these works, is created from 5 pitch groups having 3, 4, 5, 6 and 7 notes (derived from KLANG's 24-note pitch row, plus a 25th 1st note repeat).  A group is stated relatively slowly (each time in a different melodic and rhythmic way) and then alternated with 1 to 4 "echos", each made up of usually fast repeating patterns of the group pitches without rhythm, and separated by pauses.  The effect Stockhausen aims to create with the fast repeating patterns is to create "a harmonic effect, like a vibrating chord".  These echoes also change speed and dynamic (and sometimes register).  From a rhythmic standpoint, the initial melodic statements have rhythms derived from the 12 families explored in KLANG's 1st Hour, HIMMELFAHRT (the 12 degrees of rhythmic densities).

     Additionally the piece is split into 5 sections, at the beginning of each, the player turns in a circle.  Just before and during the 5th section there are 2 short cadenzas, first in a lower register, and then a higher register.  Besides this general framework, Stockhausen adds drama and personality using trills, microtonal glissandi, changing vibrato, etc...as well as some extra cadential material between the statement/echo structures (each of which also have a different tempo).

Score
An example of a group statement followed by its echoes is below.  In this case a low 6-note melody is stated, followed by 3 higher register echoes of 3, 2 and 3 ostinato repeats, all with changing dynamics.

Below is part of the treble clef "cadenza" near the end of HARMONIEN.  "Klappentriller" means to trill on the instrument keys but produce nearly the same pitch, producing a kind of warbling effect.

(score excerpts © www.karlheinzstockhausen.org)

---

KLANG 6: SCHÖNHEIT (BEAUTY)
KLANG 7: BALANCE
KLANG 8: GLÜCK (BLISS) 
KLANG 9: HOFFNUNG (HOPE)
KLANG 11: TREUE (FIDELITY) 
KLANG 12: ERWACHEN (AWAKENING)

     As mentioned earlier, the material from the 3 different solo versions of HARMONIEN was used to create new multi-layered polyphonic compositions for 6 trios (and a septet below, GLANZ).   By juxtaposing these strongly identifiable figures (themes vs. patterns), some very amazing textural counterpoint is achieved.  Because of the different tempos between the 3 layers, Stockhausen sets things up so that every few measures there is an ensemble pause and the instruments realign.  This, and the way that Stockhausen sometimes adds extended rests for individual instruments, keeps things very coherent.  In fact this series of works ends up being possibly Stockhausen's most traditionally lyrical in years, which is quite amazing considering the nature of its parts.  It's quite a feat that these layered "vibrating chords", expressed in so many varying permutations, never feel like unrelated threads, but always an organic whole.  These vertical layers can be explored very simply, but on closer examination each combination reveals its own inner beauty, much like a crystal formation.

     One possible way to visualize the structure of a trio passage in simplified form could be this:

     In this picture I used different sizes to indicate the 3-7 note phrase, followed by small repetitions of grouped characters to show the ostinato "consequents".  The vertical line is to show the realignments that occur between the 3 players (this is not an actual example from the score).   Also in this visualization the larger characters are not exactly large versions of the small characters, since usually the melodic themes are changed in register.  This is of course a very basic "imaginary" example and doesn't include events such as duo and solo moments, as well as times when 2 or 3 players fall into unison. 

KLANG 10: GLANZ (BRILLIANCE) 
      GLANZ is scored for septet, but is actually more like a clarinet-bassoon-viola trio with a featured guest instrument in some of its sections. The featured instrument is included in "insert" material added to the ends of the 1st, 2nd and 4th sections and does not have the usual statement/echoes construction.  The insert for the 1st Section with add'l Oboe recalls the ending of HOPE.  The insert for the 4th Section with tuba features the ending from BLISS.  The Coda is a pre-echo of AWAKENING.

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Structure
     This table shows the (re)sequencing of the sections in each work, as well as the role (high, middle, low register) of its individual instruments. 

Section	KLANG 6: Schonheit (Beauty)	KLANG 7:  Balance	KLANG 8:  Glück (Bliss)	KLANG 9:  Hoffnung (Hope)	KLANG 10:  Glanz (Brilliance)	KLANG 11:  Treue (Fidelity)	KLANG 12:  Erwachen (Awakening)
1st	I	V + E. Hn Solo	IV	III	Intro + I  + Oboe Qrtt	V	Intro + I
2nd	II	IV + E. Hn. Solo	II	I	II  + Quintet w. Tpt & Tbn	III	IV
3rd	III	III  + Trio Cadenza	V	V	III  + Clr, Bassoon, Vla (w text)	IV	III
4th	IV	II	I	II	IV  + Tuba Qrtt	I	I
5th	V	I  + Coda	III  + Coda	IV  + Coda	V + Coda	II  + Coda	V
Stage Color	turquoise blue	bluish green	yellow-green	yellowish-green	sulphur green	zinc yellow	bright yellow
Voice:
High	Flute	Flute	Oboe	Violin	Clarinet	Eb Clarinet	Sopr, Sax
Middle	Trumpet	Eng. Horn	Eng. Horn	Viola	Viola	Bassett Horn	Trumpet
Low	Bass Clr	Bass Clr	Bassoon	Cello	Bassoon	Bass Clr	Cello
Spoken Text	"Lob sei Gott" ("May God be praised")	"Gloria in excelsis Deo / et in terra pax hominibus bonae voluntatis" (Glory to God in the highest / and on earth peace, goodwill to all people)	"Noten zu Klängen zu Kreislauf zu Glück" ([Written] notes to sounds to circular movement to bliss),  "GOTT ist GLÜCK" (God is bliss).	"Dank sei Gott  Danke Gott für das Werk… Hoffnung" (Praise be to God… Thank God for the work… Hope")	"Gloria in excelsis Deo / et in terra pax hominibus bonae voluntatis" (Glory to God in the highest / and on earth peace, goodwill to all people)	"Treue zu Gott" (Fidelity to God)	"Erwachen in Gott" (Awakening in God)

As described in

Harmonies and the Path from Beauty to Awakening: Hours 5 to 12 of Stockhausen's Klang" 
(Jerome Kohl)

Perspectives of New Music 50, nos. 1 & 2 (Winter–Summer 2012)

Live Performance
     Each of the hours of KLANG from 6 through 12 have specific colors for their performance attire.  HARMONIEN features several points where the performer spins in a circle to mark the beginning of a new secton.  GLANZ also includes a light sculpture as part of its performance which changes in brightness during the performance.

HARMONIEN Live performed by Fie Schouten, bass clarinet version
HOFFNUNG clip (London Contemporary Orchestra)
BALANCE clip (London Contemporary Orchestra)
TREUE live clip
The group musikFabrik  rehearses GLANZ under Kathinka Pasveer's direction

Images from Score Fronts
(© www.karlheinzstockhausen.org)

Sound Impressions
     These works are really quite beautiful and hypnotic.  The simple idea of using a pitch row to generate 5 serially-distributed chords and "vibrate" them through repeated ostinato patterns might sound structurally clinical, but Stockhausen uses every trick in the book to add life and drama to these pieces.  Most importantly, he (as always) breaks his owns rules when the needs of the music transcend the conceptual framework of the composition.
     The chamber ensemble works really show off Stockhausen's ability write in a more traditionally lyrical style, and wind up being possibly some of his most accessibly poetic writing since his chamber arrangements for TIERKREIS.  At the same time the juxtapositions of these "looping" phrases with the expanding and contracting melodic shapes provide for some amazingly witty and complex contrapuntal shapes.
     Amazingly enough, Stockhausen's next work, COSMIC PULSES would be a complete change, so much so that even he admitted in one interview that it might not even fall under the category of "music composition"!

Links
Samples and CD ordering:

• HARMONIEN & SCHÖNHEIT
• BALANCE & GLÜCK
• HOFFNUNG & GLANZ
• TREUE & ERWACHEN

Purchase Scores
KLANG Wiki
ERWACHEN Youtube clip
The Saxophone Works of Karlheinz Stockhausen (Essay on ERWACHEN, Elizabeth Bunt, PDF thesis)