Many styles of music—modern and traditional—use polyrhythms, such as 3 against 2, or 4 against 3. Polymeters, on the other hand, are where more than one time signature is used at the same time: Imagine two instruments sharing the same quarter-note pulse, but one instrument plays in 3/4 while the other plays in 5/4.
In his self-published book, Polymetric Puzzles, Jeff Fineberg provides a set of exercises, many in the form of puzzles that progress from simple to complex, for developing hand independence through the use of polyrhythms and polymeters. However, the examples and exercises are presented in an easy-to-understand way, with material that is both fun to play and musically satisfying. Mastering these concepts will help players improve their technical skills and musicality, whether they play Bach, modern classical, Latin styles, or rock.
Fineberg, himself, began organ lessons at the age of 12, and within two years got his first synthesizer—a Moog Satellite. He later became interested in progressive rock, learning the music of Rush, Yes, Genesis, Gentle Giant, and ELP among others. “I believe that as we absorb the various musical elements we find interesting,” Fineberg explains, “these elements tend to resurface during the creation process.”
How did the concept of this book come about?
I have always had a fascination in keyboard playing with one of its most challenging aspects—maintaining the independence of each hand. I also have a strong interest in music that utilizes odd meters. Having written some pieces that utilize polymeters between both hands, I thought it might be interesting to create a series of short music segments (initially called ‘widgets’), which exploit this difficulty in the most simplistic manner. I began creating a series of these small challenges, which I later renamed Polymetric Puzzles.
What music raised your awareness of polymeters?
In terms of polymeters, examples that I find particularly interesting include Led Zeppelin’s “Kashmir” and Rhys Chatham’s “Die Donnergötter.” Another influence for me was discovering the interesting use of odd meters. You can find examples in pop music such as Rush’s “Subdivisions” and Genesis’s “Back in N.Y.C.”
How do you apply odd meters in a band setting?
As a keyboardist playing in an ensemble, I found it interesting to experiment with patterns that were outside of the group’s meter. For example, I may decide to play in a meter of 5/8 while the drums were played in 4/4. This tends to create an interesting texture of interplay between instruments. I also experimented with these ideas in solo keyboard music, whether composing or improvising. It was this approach that helped me to formulate the book.
What do players find most difficult about working with polyrhythms and polymeters?
With polyrhythms it can be difficult trying to figure out exactly how the ratios translate to timing when performing. To address this concern, there are polyrhythm audio examples on the website. There are also grid diagrams in the book to illustrate how a given polyrhythm is constructed to further help the musician play it correctly.
With polymeters it can be a challenge to keep track of the number of repeats while trying to perform patterns containing multiple time signatures. For example, in the book there is a piece containing a polymeter of 4/4 and 11/4. In addition to concentrating on maintaining independence of both hands, it can be difficult trying to remember how far along you are in the cycle while playing. For example, in the above case, to complete an entire cycle of an 11:4 polymeter, you need to play 11 measures of 4/4 and 4 measures of 11/4.
To learn more, and to see videos of Fineberg playing examples from his book, visit polymetricpuzzles.com.