Formal ritardando

A)Tone lake

The infinity series can be used to suggest a tempo shift by drawing in previously 'unheard' in-between notes, and this characteristic can also be exploited to create ritardando at a formal level. The tone lakes are especially suited to this. Since a tone lake is a kind of closed infinity series, is it also something like a repeatable passacaglia structure.

B) 5th Symphony

In the 5th Symphony we find such a formal ritardando composed by using tone lakes. There are three sections based on tone lakes with transitional passages in between. The first one (bars 370-399) appears to be a freely-composed interlacing pattern, which is intoned by a solo cello and then after a while, but only briefly, is in phase in a 12-tone lake.

After a freer passage, the music once more (bars 428-469) arrives at a sound that reminds one of bar 370. This time it is the solo bassoon that comes in, starting on the same note as the solo cello. At this point, the whole movement is based on a 12-tone lake, making use of irregular rhythms that are constantly expanding and contracting.

Another, freer, passage follows, ending in a violent outburst followed by silence. And then in bar 503 the music opens out again with the sound from bars 370 and 428, and once more a solo bassoon is used. On this occasion, the tempo has to be slower, because now the music is moving in a 36-tone lake, though we do catch a glimpse of a 108-tone lake, at which the music arrives after a massive ritardando (bar 540).

To the non-specialist it sounds as if the music continues at the same tempo after this, but this is not the case. In fact, the tempo is considerably slower, as the notes of the music surface now from out of a 108-tone lake.