``Fake'' Polyphony

Before getting into ``microscopic'' polyphony, the main subject of this essay, another series of experiments made by Ligeti at the Cologne studio worth mentioning.

We previously stated that by varying the dynamic levels of the layers sinus signals mixes different ``melodies'' could be heard. This is because our perception was creating connections between signals of different levels^1.9.

Ligeti also noted that the difference between the perceived intensity of a signal and its scientifically measured volume is releated to the signal's harmonic^1.10complexity. Complex (i.e. ``musical'') signals, when they are at the same volume than sinus waves are heard as if they were stronger.

That difference in hearing makes it possible to create a kind of ``layered'' polyphony which Ligeti describes as:[1]

By using different intensity levels for each note and each sound, and by integrating sounds which are harmonic, subharmonic and non-harmonic in between a succession of sinus waves, it is possible to create a ``fake'' polyphony inside a monophony. This is possible because of the mental connexions at higher levels that we can create between different kinds of sounds.

If the higher level signals are not too dense we perceive, inside the true single voice, a complex of several voices. By creating a more detailed sequence we reach a saturation point where the shape of the super-signals^1.11start to blur, too many layers neutralise each other and the phenomenon of ``fake'' polyphony is gradually lost.

Figure: Schematic representation of the perception of musical events as Koenig and Ligeti experimented on them at the Cologne studio

9#9

Ligeti made various experiments at the Cologne studio exploring the ``blurring'' of musical textures. He tried many collages of sounds by getting above and below the perception level.

In 1957, after having experimented with a piece called Glissandi to which he relates as an ``exercice to learn the studio techniques'', he elaborated another piece named afterward Pièce électronique N.3.

It is interesting to note that this piece was formerly called Atmosphères but in 1961, when Ligeti started a piece for large orchestra, he used that title for the orchestra piece and re-named the electronic piece Pièce électronique N.3[1]

The work on the orchestral Atmosphères was previously interrupted for the profit of another electronic piece called Artikulation which thereafter became Pièce électronique N.2.

The ``score'' for this Pièce électronique N.3 is drawn, as it was customary at that time for electronic pieces, by using a squared millimetric paper. The vertical axis represents the frequencies, the horizontal lines represent the length of magnetic tape fragments in centimeters. Vertical lines are the connecting points for the assembly.

Figure: Pièce électronique N.3. Fragment of the ``score''.

10#10

The ``score'' is actually a matrix view^1.12 of the music.

While the majority of the sounds used are sinus waves, some electronically filtered noises also appear. Those noises were filtered using a very narrow band filter and they are actually very close to sinus waves but, as described by the composer, they are made ``slightly blurred by an halo of external frequencies''.

The textures created are almost never static but always moving, evolving and transforming.

The frequencies are hardly legible in the reproduced score^1.13 which is shrank here to fit the page but it is interesting to note that frequencies were selected in order to produce various spectrums of harmonic and non-harmonic structures.

For harmonic structures, frequencies with plain integer ratios between them are used, higher harmonics are privileged in this piece. Those harmonic and non-harmonic spectræ create a resulting ``sound'' which is not ``created'' as the others but can only be heard at the actual audition of the piece. This is a ``resultant'' harmonic sound.

In autumn 1957, the ``score'' for frequencies were established and in November Ligeti started the realization of the piece in the Cologne studio.

He was first creating the sine waves at the preset frequencies without dealing with the intensities. But, soon the technology of the time made it impossible to continue.

The synchronizing of more than forty layers of sound was a practical impossibility with the technology of the fifties. The out-of-sync shifting created audible differences in the resulting textures which were deemed unacceptable by the composer.

After having completed the work on another electronic piece: Artikulation in 1958, Ligeti resumed working on Pièce N.3 .

This time he confronted with another difficulty: the scoring of the intensities were unrealizable because that necessitated working in three-dimensions... On the surface of the quadrilled paper, pitches were assigned to the vertical axis and time (durations) to the horizontal one.

So he started to notate the intensities on another sheet in close connexion with the frequency-time graph. But he stopped working altogether on that music and also abandoned completely the electro-acoustic realm. The practical impossibilities of composing music exactly as he wanted to do combined with the technical limitations of the equipment made him leave the electro-acoustic music studios forever.

He relates his leaving the studio in the article mentioned before[1]

As other tentatives for the realization of the piece revealed to be unsatisfactory as well, I promptly abandoned working on it and from summer 1958 I totally concentrated on the composition of pieces for orchestra.