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Tuning

The first six courses (a course is a string or pair of strings played as one) are tuned in fourths with a major third between the middle two courses.  This gives (just like the guitar) two octaves between the first and sixth course, and it's to the note shared by these two courses that we refer to when describing the pitch of a lute.

This is the tuning of a six course renaissance lute in G. Note the octave tuning on the lower three courses.  This is typical of early lute tuning, later tunings may have them in unison, or an octave only on the sixth course.
In the following discussion of further courses, the examples I give are assuming G tuning.

Seven courses

There are two common options for the seventh course, either a tone lower (F) than the sixth, or a fourth lower (D).

Eight courses

Typically one a tone lower than the sixth, and a fourth lower (F,D). To play music for a seven course with the low tuning, some people reverse the order of these two courses.

Nine courses

As for eight courses, but with the ninth a fifth lower than the sixth (C)

Ten courses

The four extra courses descend scale-wise from the sixth (F,E,D,C)

Other pitches

Treble lutes in D or C
Alto in A
Tenor in G or F
Bass in E, D or C

Ensemble music often specifies lutes at an interval (rather than the actual pitches) so you will see for example "two lutes in unison" (at the same pitch), "ad quartam" (a fourth apart), "ad quintam" (a fifth apart).
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