Variable meter is a musical method invented by Boris Blacher, where the different meter changes systematically occur in each bar, following ‘a preconceived arithmetic plan.’ (Friskin and Freundlich, 1973: 194) In adapting Shoenberg’s idea of serialism to the rhythm, Blacher was also influenced by rhythmic structures of Stravinsky. This is why I decided to start with Stravinsky’s pieces that have alternating meter, and then, after listing all the Blacher’s pieces I listened to, I will also include other composers that have experimented with the concept of the variable meter.
Igor Stravinsky – Rite of Spring (1913)
Reading about Blacher’s variable meter, I found McCredie (2002: 71) talking about the historical conceptual sources of the system, starting with Stravinsky’s Danse Sacrale (Sacrificial Dance) in Sucre du printemps (Rite of Spring). I have known about the piece since completing the course on EdX ‘First Nights – Rite of Spring’ some time ago. It mentioned the Sacrificial dance, and I remember finding the rhythm and the changing time signatures – 3/16, 2/16, 2/8, 5/16 very intriguing. As such, this was a great opportunity to learn more about Stravinsky’s rhythmic pattern. I came upon Messaien’s analysis, in which he stated that Stravinsky, consciously or unconsciously, used the Hindu taal simhavikridita (Fig. 1), which is divided into two rhythmic cells, one that progressively augments and diminishes by a basic value, while the other stays the same. (Benitez, 2013: 7) Messaien did a whole scheme of the rhythmic pattern. (Fig. 2) Interestingly, I have already done some research about the Indian taal system for Project 1 Example 3 for finger cymbals, and thus, this was very exciting to read. Click here to see this post.
Fig. 1. Simhavikridita taal with the counting
Fig. 2. Sacrificial Dance, rhythmic scheme by Messaien
I should also mention that beside the Spring Rounds, this is my favorite section of the whole piece. I have yet to hear music that sounds as dramatic and eerie, perfectly painting the atmosphere of a girl that is about to be sacrificed, dancing to death while surrounded by old men. This was actually a scene in the dream Stravinsky had that inspired the piece:
“I had dreamed of a scene of pagan ritual in which a chosen sacrificial virgin danced herself to death.” (cited in Hill, 200: 3)
Although it is rarely performed as a ballet, here is a video with the original choreography by Nijinsky, which I was completely taken by:
Lastly, to go back to the variable metre, regarding Stravinsky’s influence on Blacher, Taher (2009: 3) goes even futher and argues that Blacher’s technique of variable meters not only reflects the influence of Stravinsky, but is “in effect, the systematization of the latter’s earlier practice of alternating meter signatures.”
Blacher – Ornamente (1950); Sonata (1951); Divertimento for four woodwinds (1951); Orchestra Ornament (1953); Two Inventions for Orchestra (1954); Orchestra-Fantasie (1956); Variations on a Diverging C Minor Chord for String Quartet (1967) Concerto for high trumpet and strings (1970); Trio for Piano, Violin and Cello (1973)
Based on the idea of variable meter, the Ornamente for piano consists of seven etudes of varied character, where each measure is in different meter. I am not a mathematician, and therefore, I couldn’t recognize all the patterns. As such, it’s really helpful when I found the explanation by McCredie of all the arithmetical relationships found in the studies:
It’s really curious how the arithmetics, and mathematics in general, can interact with music, and even create something peculiarly beautiful. Before listening to the studies, I have to admit, I thought they would sound completely mechanical and dry with no musical value. This is how I felt for the first part of the first Vivace etude – only my cognitive side was involved in trying to establish the rhythmic pattern. However, near the end, a more lyrical quality appeared, despite the mathematical framework, which continued to materialize in the other studies as well, such as the second Andante and sixth Moderato, that sounded so esoteric and mystic to me. This interestingly successful mix of qualities – a seemingly perfect balance of the cognitive and the artistic, the mechanical and the lyrical, the mathematical and the musical, develops and surfaces in such absolutely fantastic ways in the etudes; it completely shocked and surprised me! Along these lines, I really enjoyed all the Ornamente studies, as well as the later Orchestra Ornament, where the added colors of all the instruments in orchestra, and the larger form, produce even more exciting results. Astonished also by his other works that I have listed above, I can definitely see myself experiment with this unusual style and technique in my own music in the future.
Bartok – Fourth String Quartet ()
Among the other experimentations with the concept variable meter, it’s interesting how Bartok may be technically classified in this group. His asymmetric and Bulgarian rhythmic techniques also tend to go towards a metrical system with fixed mathematical relations, and for example, in his Fourth String Quartet, there are section in which the number of quarter notes in the measure grows and then declines. (Stuckenschmidt, 1963: 10)
Karl Amadeus Hartmann – Concerto for piano, wind instruments, and percussion.
Hartmann also used the idea of the variable meter.
Hans Werner Henze – String Quartet
Klebe -has evolved a very advanced style revealing the influence of Blacher’s variable meters and of Schoenberg’s and Webern’s serial techniques.
Stuckenschmidt, H. H. (1963) ‘Contemporary Techniques in Music’ In: The Musical Quarterly 49 (1), pp. 1-16