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 third, consider that 5:4 is equivalent to 386 cents () and 9:7 is equivalent to 435 cents (). This difference is audible to the listener by comparing the tuning for each pitch of the western chromatic scale with the chromatic scale used in "The Well-Tuned Piano". "The Well-Tuned Piano" is based on a pitch lattice of perfect fifths and harmonic sevenths. "The Well-Tuned Piano", being improvisatory in nature, as well as ever-changing, has no specific form. The closest a listener can come to understanding the structure of Young's piece is by studying the liner notes from the 1981 Gramavision recording.