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
String (music) longitudinal force increases with the square of the pulse amplitude, so the differences diminish with increasing amplitude. The elastic (Young's) modulus for steel is about 40 times greater than for nylon, and string tensions are about 50% greater, so the longitude and transverse force amplitudes are nearly equal. Tuning a stringed instrument such as a guitar to pitch puts the strings under a large amount of strain, which indicates the amount of stress inside the string. Stress is relative to the stretch or elongation of the strings. As the string is tuned to a higher pitch, it gets longer and