Karlheinz STOCKHAUSEN: Mantra

The piece was composed in 1970 and premiered in autumn of the same year in Donaueschingen. The work is scored for two ring-modulated pianos; each player is also equipped with a chromatic set of crotales (antique cymbals) and a wood block, and one player is equipped with a short-wave radio producing morse code or a magnetic tape recording of morse code.

The piece is the first determinate work (that is, the score is completely written down, though there are some passages involving a modest degree of improvisation) that Stockhausen composed after a long phase of indeterminate compositions.

This work involves the expansion and contraction of a counterpointed pair of melodies, which the composer calls a "formula". In this particular work (the first of a long succession of compositions to use formula technique), Stockhausen chose the term "mantra" in order "to avoid the words theme, row or subject, as in a fugue", and "Mantra" also became the title of the entire work. In Mantra, the two-strand formula is stated near the outset of the piece by piano I. The entire work is based on this formula and is divided into 13 cycles, each marked at the beginning by a crotale stroke on a pitch corresponding to a successive note of the mantra. Though this mantra recurs constantly, the structure of the composition is not a theme and variations as found in classical composers such as Beethoven and Bach, because the material is never varied, only expanded and contracted (both in duration and in pitch) to different degrees; not a single note is ever added, it is never "accompanied" or embellished. The comparatively strict predetermination of the form plan is occasionally broken and altered through the use of insertions, additions, and small deviations and exceptions. Near the end of the composition there is an extremely fast section that is a compression of the entire work into the smallest temporal space; in this section, all of the expansions and transpositions of the mantra formula are summarized as fast as possible and in four layers.

The "mantra" (melody formula) which is displayed above, is made of an upper and lower voice; it is divided temporally into 4 segments with silent rests between segments. The 13 notes of the mantra's upper voice form a 12-tone row where the 13th note returns to the first note A. The lower voice consists of an intervallic inversion of the upper voice with transposed segments, so that, for example, the first segment of the lower voice corresponds to the inversion of 2nd segment of the upper voice and vice versa.

Each of the 13 notes of the mantra has an attached characteristic, or "pitch form"; the 13 notes of the upper voice have in order the following characteristics:
1. periodic repetition at the beginning (on A in the original transposition)
2. accent at the end of a duration on B
3. G-sharp without any characteristic
4. a turn around the beginning of the note E
5. slow tremolo between F and D
6. an accented chord at the end of the Fโ€“D oscillation
7. a sharp accent (with a single repetition) at the beginning of a duration on G
8. a descending chromatic scale connecting the G to the following E-flat
9. staccato (very short duration) on D-flat
10. irregular repetition ("Morse code") of the note C
11. an inverted (upper-note) mordent (trill nucleus) on the beginning of B-flat
12. sharp attack with an echo: sfz (fp), on G-flat
13. arpeggio connecting the previously articulated pitch (E flat in the other voice, an augmented eleventh lower) upward to A

In addition to its articulative characteristic, each of the thirteen notes is assigned a particular dynamic, in approximate inverse proportion to its durationโ€”that is, the softer a note's dynamic is, the longer is its duration. The very first note is the sole exception to this rule:

a. with constant intensities:
pp: 5.5 x ๐…˜๐…ฅ = character V
p : 6 x ๐…˜๐…ฅ = character XIII
p : 4 x ๐…˜๐…ฅ = character IV
p : 1 x ๐…˜๐…ฅ = character I (exception)
mp : 4 x ๐…˜๐…ฅ = character XI
mp : 3 x ๐…˜๐…ฅ = character III
mf : 1 x ๐…˜๐…ฅ๐…ฎ = character VI
f : 1 x ๐…˜๐…ฅ = character IX

b. with crescendo or decrescendo:
(m)p > : 7 x ๐…˜๐…ฅ = character X
< mf : 2 x ๐…˜๐…ฅ = character VIII
sfz (fp) : 2 x ๐…˜๐…ฅ = character XII
(p)โ€“f : 2 x ๐…˜๐…ฅ = character II, where f = 1 x ๐…˜๐…ฅ๐…ฏ
ff > : 5 x ๐…˜๐…ฅ = character VII, where ff = 1 x ๐…˜๐…ฅ๐…ฏ

The thirteen cycles of the composition are based on the 13 notes of the mantra and the 13 characteristics detailed above. Each cycle is dominated by its corresponding note and characteristic.

The sounds of each piano are picked up by microphones and fed into an apparatus at the player's left side. This consists of a microphone amplifier, a compressor, a filter, a ring modulator, a scaled sine-wave generator, and a volume control. By means of this device, each piano's sounds are ring modulated with a sine tone tuned to the central pitch corresponding to the note of the mantra formula governing each of the thirteen large segments of the composition, and the modulated sound is played over loudspeakers placed behind and above the performers. The first pianist presents the upper thirteen tones, the second pianist the lower thirteen tones. Because the starting/ending pitch of the mantra is successively transposed onto these central pitches, they sound completely "consonant", like ordinary piano tones. The other mantra pitches sound "dissonant" to varying degrees, and differ also from a normal piano to varying degrees in their timbre. "Hence one perceives a continual 'respiration' from consonant to dissonant to consonant modulator sounds, resulting from the precisely tuned relationships between the modulating sine tones and the modulated piano notes".

source: wikipedia.org >>>

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