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Steps and Leaps
The concept of steps and leaps is introduced so early in the study of music that, in a study of harmony, it
appears more-or-less as a given. The intervals of a minor and major second (a semitone and a tone) are
considered steps, and "step-wise" motion is deemed conjunct or smooth.
This run of notes is made up of steps. Larger motions are referred to as leaps,
or as disjunct motion. There is ample evidence that this definition of steps and leaps is
consistent with the perception of both composers and theorists in our Western musical tradition. Scales are
made up of conjunct motion and the resolution of a dissonance is invariably by step.
There is also some evidence that there is a physiological basis for treating some intervals as steps and
others as leaps. The construction of our human ears may be an important factor. Within the inner ear is a
coiled tube called the cochlea. This tube contains fine hairs that vibrate when sound waves enter the ear. If
a single frequency is played into the ear a particular set of these hairs will vibrate. The hairs are connected
to nerve endings, which transmit signals to the brain and thus, the cochlea is the point in our bodies where
physical vibrations of a particular frequency are converted into nerve impulses. Experiments have been
done to try to determine how well the cochlea can distinguish different pitches. One experiment is
performed as follows.
Two identical pure sine-wave pitches are played, with equal and constant intensity into a person's ears.
This requires headphones and electronic sound generation. The experiment will not work without this
careful setup and thus, unfortunately, this experiment cannot be tried on your piano at home or using midi
files on your computer. The experiment begins with two identical pitches. One of the pitches is changed
slowly and the listener is asked to describe what he hears. For a while he hears only one pulsating tone.
He then hears two distinct tones, but the effect is rough. Eventually the pitches are sufficiently separated so
that the subject can hear two distinct tones sounding smoothly together.
Throughout most of the pitch range used in classical music, the point at which two pitches begin to be
heard as cleanly separate tones occurs somewhere between the interval of a major second and a minor third.
Our choice of seconds as "steps" may be related to our ears' ability to distinguish frequencies. Our
definition of "smooth" motion probably stems - at least party - from the fact that conjunct steps cause
vibrations in overlapping areas in the cochlea.
© 2005 Andrew Hodgson
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