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
Basic physics of the violin pitch, which may be described in terms of frequency. The playing tension of a violin string ranges from about to . The length of the string also influences its pitch, and is the basis for how a violin is played. Violinists "stop" a string with a left-hand fingertip, shortening its playing length. Most often the string is stopped against the violin's fingerboard, but in some cases fingertip contact alone is enough to stop the string at the desired sounding length. Stopping the string at a shorter length has the effect of raising its pitch. String material affects the quality of