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
The Well-Tuned Piano octaves, with nine notes extending the bass of the piano. Young describes the pitches of his tuning as being, "derived from various partials of the overtone series of an inferred low fundamental E-flat reference ten octaves below the lowest E-flat on the Bösendorfer Imperial". Although it might seem that Young is giving a nod to Bach's "The Well-Tempered Clavier" with his title "The Well-Tuned Piano", musical tuning and musical temperament are two very different things. Temperament actually involves the deliberate mistuning of pitches to make the overall octave more or less usable in various different tones. In "The Well-Tuned Piano",