Violin where a stopped note sounds a unison or octave with another (open) string, causing it to resonate sympathetically. Students often use these ringing tones to check the intonation of the stopped note by seeing if it is harmonious with the open string. For example, when playing the stopped pitch "A" on the G string, the violinist could play the open D string at the same time, to check the intonation of the stopped "A". If the "A" is in tune, the "A" and the open D string should produce a harmonious perfect fourth. Violins are tuned in perfect fifths, like
Pitch space musical instruments: by moving one's hands a very short distance on a violin string, one can move arbitrarily far in these multiple-dimensional models. For this reason, it is hard to assess the psychological relevance of distance as measured by these lattices. The idea of pitch space goes back at least as far as the ancient Greek music theorists known as the Harmonists. To quote one of their number, Bacchius, "And what is a diagram? A representation of a musical system. And we use a diagram so that, for students of the subject, matters which are hard to grasp with the