For many years I have taught rhythm not by counting but by two different but complementary methods: 1) as a function of bodily gesture as expressed in geometric figures drawn two-handed with colored pencils while singing several verses of a song in different tempi and with varying emotional intent; 2) as a function of ratios.

The ratio concept clarifies a lot about how rhythm actually feels: why, for example, two hands at the piano are so difficult to coordinate. It also explains why more than one person may be necessary to express the underlying energy of a piece of music.

In a Beethoven symphony it is not unusual to have a ratio of 1:128, the single unit being a tone sustained by the French horn in a tie over 4 bars in 4/4 time, the 128 parts corresponding to 32nd notes in, say, the flute. In between one might find
1:2, the 2 corresponding to a two-bar tie in the double basses; 1:4 the 4 being whole notes in the bassoon; 1:8 = half notes in the cello; 1:16 = quarter notes in the clarinets and oboes; 1:32 = eighth notes in the viola and second violin; 1:64 = sixteenths in the violins.

With all these layers of energy--all these different gears, so to speak, it is perfectly sensible that a symphony requires many people for adequate realization.

One difficulty posed by easy-access-flattened-out music reproduction is that it all sounds so simple, so easily reduced to 1 - 2 - 3 - 4.