Running Head: fingerboard intonation chart a fingerboard intonation chart for the violin and viola

The following summarizes the construction of nearly equal tempered intervals using just intervals on an instrument with equal tempered open strings. In this case it is important to tune the instrument to equal tempered open fifths. All “quarter notes” are played to just consonance. In each case the resulting “whole note” interval is with 4% of equal temperament. This is only a theoretical precision, as so many other intervals must be also be correct to achieve it.

The last bar of passage (11) represents a unique approach to equal temperament, but only works for the minor sixth. If the open strings are tuned to equal temperament, and if both minor sixths are made equally dissonant, then these minor sixths will be equal tempered, exactly. It is difficult to assess the efficacy of this exercise, as one must use an electronic tuner to verify that both sixths are tempered. And this renders it impossible to determine whether it was passage (11) or the electric tuner that was responsible for learning this interval.

It is not uncommon for a student to spend many hours practicing something that is wrong. The point of these activities is that they can be self‑correcting by a student who practices alone. But, since these exercises do not place fingers exactly where they belong in ordinary playing and shifting, will they teach bad habits? A definitive answer would require careful experimental studies, so we must be content with expressing the question in the language of cognitive psychology. Behavioral psychologist Arthur Staats (1996) introduced the concept of Basic Behavioral Repertoires (BBRs), which has been applied to sensory‑motor skills by a number of researchers (Riedel, Heiby, & Kopetskie, 2001). The idea is that one must first master basic skills before progressing to more complex ones; much like learning how to print before progressing to cursive writing.

Studies of how people acquire a second or even third language might also be relevant. Perhaps basic skills such as shifting might be best learned as early as possible, just as language skills are best acquired at an early age. Anyone who has attempted to learn a third language will tell you that it was easier to become semi‑fluent in the third language, than it was to achieve the same level in the second language. (Bialystok & Hakuta, 1999; Perani, et al., 1998). This is especially true when one acquires the first language early on in development (Levelt, 1989).

Two other issues are a bit more problematical: (1) If the tempered scale is analogous to learning a second language, then perhaps it needs to be learned first. (2) These interval tests do not work well in keys such as A or E major. These intonation tests based on just intervals should not be viewed as a substitute for extensive exposure to music played at equal temperament, at the earliest possible stage in a child’s life. And, at some point the student needs to move beyond tests with just intervals.

We are grateful to Everet Kalcek for many helpful conversations about music instruction, as well as to David Smiley, a teacher and member of the San Francisco Symphony who introduced interval testing to young viola player back in the 1960s.