The time signature of a piece of music plays a central role in its character and is the basis of its structure. In traditional, straight forward time signatures (3/4, 4/4, 6/8 etc), the beat emphasis falls in a simple repeating pattern which gives the listener a framework which they can easily latch on to.
More complex time signatures change this pattern of emphasis, which can have the effect of disturbing the flow of the music. For example in 5/4, the beats are usually arranged in alternate groups of 2 and 3, so the emphasis also alternates between every second and every third beat. A good example from pop-music is ‘All you need is love’ by the Beatles; the verse of this song is in 7/4 and has the feeling of skipping a beat.
A yet more complex arrangement is ‘variable metre’ – a concept invented by Boris Blacher, a German composer and mathematician born in 1903. Composers have been altering the time signature in the middle of a piece of music for centuries, but Blacher was the first to apply a mathematical sequence or formula to determine the number of beats per bar. For example his piano concerto no. 2 (Op. 42) has an initial time signature of 12/8, but from bar 2 onwards uses a notation underneath the score to indicate how many beats are in each bar. You can follow along with the score on this YouTube video:
The first section of movement 1 has the following sequence of beats per bar:
12 8 12 8 7 12 8 7 6 12 8 7 6 5 12 8 7 6 5 4 12 8 7 6 5 4 3 12 8 7 6 5 4 3 2 12 8 7 6 5 4 3 2 1
I think it succeeds in creating a very effective unsettling mood. I’m not sure what the significance of the number 12 is, but one effect of inserting this long bar in between each sequence is that it is quite easily identifiable and acts as a good anchor so that the listener isn’t completely lost. The second allegro section has a more complex pattern which sounds quite random (at least on a first listen!) and reflects the faster and more chaotic style of the music.
Another of Blacher’s pieces which is on the OCA’s suggested listening list is his ‘Orchestral Variations on a Theme by Paganini’ (Op. 26). Listening to this work without the score it can be difficult at some points in the music to be able to tell the time signature. I found that the sections which appealed to me the most were the ones where there was at least a clearly recognisable pattern to the rhythm, even if it was difficult to determine exactly what it was. For example the variation which has the string section playing in pizzicato succeeded in hooking me in for this reason.
A more well known example of the use of variable metre is the Beatles song ‘Good morning good morning’ (from the Sgt Peppers Lonely Hearts Club Band album), which frequently changes between the time signatures 3/4, 4/4 and 5/4.