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
Guitar tunings tuned fifth string can provide a reference to tune the remaining strings by ear. Tuning forks which provide the pitch of the high E string (329.63 Hz) are also common. The guitar is conventionally an equal-tempered instrument. The frets are positioned logarithmically, creating equally-tempered pitches along each string. However, guitarists who tune by ear will typically tune “clean” so that dissonant beating between particular strings is minimized. In this way, open intervals can be more consonant. This is known as just intonation, which is at variance with equal temperament. When the guitar is tuned in this way, open tunings theoretically