POOL TOOL Applied on Decelerating Shape (Part 2)

This second part is all about decelerating shapes without the grid of a steady pulse. (To part one: Decelarating shapes inside a steady pulse)

As it happens, the pieces I worked on here contain accelerating shapes more or less in the same amount than their decelerating counterparts. In part one of this double post, Rebonds A by Xenakis already also included many accelerating shapes, mixed in between the decelerations.

Applying the Pool Tool:


Decelerating shape which consists of several impulses without a steady beat. The deceleration is linear.


(I recommend listening to each whole piece before going into the details described)

Béla Bartók, Music for Strings, Percussion & Celesta, 3rd movement, Adagio, RIAS Symphony Orchestra, Ferenc Fricsay:

Shape appears 0:00-0:15

The Adagio movement starts with an isolated xylophone figure, which in this recording appears as an accumulation of perfectly accelerating and decelerating impulses. In other recordings, where the shape is executed more exact in rhythm, a pulse is recognisable behind it. Here, there is no pulse. It is just getting faster and getting slower again, that’s it.


Alvin Lucier, In Memoriam Jon Higgins, Liam Hockley:

Whereas here, the deceleration comes first, afterwards the acceleration. (Concept of the piece is explained in the description of the video)

Everytime the clarinet enters with a new, higher pitch, it is in friction to the still slightly lower sine tone. The sine tone approaches the clarinet pitch and as it does, the distance between the beatings gets bigger (deceleration). The moment the sine tone passes the unison, the distance between the reappearing beatings gets smaller again, until the connection between the two pitches gets lost (or the player loses his breath)

The shape appears throughout the piece, but its purest appearances are:
2:19-2:50 deceleration 2:50-3:09 acceleration
5:19-5:52 deceleration 5:52-6:11 acceleration
12:50-13:22 deceleration 13:22-13:42 acceleration

Is is also nice to think that a musical shape of such simplicity can have a duration of a whole minute.


Conlon Nancarrow, Study for Player Piano, No. 8, Jürgen Hocker:

Shape appears 1:26-3:15, each voice constantly decelerating and accelerating

This excerpt contains a body of three voices. The voices are built from permutating three-pitch impulses, with their sole rhythmical properties being stages of acceleration and deceleration. The independence of their movement creates a very lively counterpoint, above which a little high melody enfolds (2:08).

Rhythmically, the melody also simply consists of impulses first getting faster (2:08-2:12), then getting slower (2:12-2:16). Same thing then in the responding bariton melody (2:15-2:23). Afterwards, the melodic structure gets a little bit more complex. The accompaniment though, the body, remains exactly the same, all through the excerpt to the end of the part at 3:15.

It amazes me that no steady pulse is needed in order to create a build up to and appearance of a melody which is both easy and singable. And, same thing as in the Lucier piece: astonishing, how few ingredients are needed in order to create such rich shapes.

One comment

  1. Pingback: POOL TOOL applied on Decelerating Shape (Part 1) | F A A


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