Oud later), tuned in successive fourths. Curt Sachs said they were called (from lowest to highest pitch) "bamm", "maṭlaṭ", "maṭnā" and "zīr". "As early as the ninth century" a fifth string "ḥād" ("sharp") was sometimes added "to make the range of two octaves complete". It was highest in pitch, placed lowest in its positioning in relation to other strings. Modern tuning preserves the ancient succession of fourths, with adjunctions (lowest or highest courses) which may be tuned differently following regional or personal preferences. Sachs gives one tuning for this arrangement of five pairs of strings, d, e, a, d', g'. Historical
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",