Ad libitum
At will, in tempo and in scoring.
What it means
Ad libitum, abbreviated ad lib., means “at will” and leaves a decision to the performer. Various things may be meant, depending on what the marking refers to.
Standing at a part or an instrument, it means that its participation is optional: the work is complete even without this part. Its counterpart is obbligato, which denotes an indispensable part.
Standing over a section, it concerns the tempo: the section may be shaped freely, without strict time. In this sense it is close to phrases such as a piacere and the German frei.
Finally it may leave repetitions or ornaments free, for instance in a cadenza that the performer shapes themselves.
In the notation
The phrase stands in italics above the staff or in the part designation. In scores and on title pages it appears in scoring indications, for example when an instrument is marked as dispensable. In the case of tempo freedom it holds until a marking such as a tempo or tempo giusto.
Musical use
In the music of the seventeenth and eighteenth centuries the scoring was often flexible; parts marked ad libitum made it possible to perform a work with whichever musicians were available. In utility music and in arrangements this is usual to this day. As tempo freedom the marking stands in introductions, cadenzas and recitative-like sections.
In Baroque music ad libitum often designated a part that could be left out, for instance an additional flute. In jazz and pop ad lib. stands for free improvisation or repetition at will up to the fade-out.
Performance practice
First clarify what the freedom refers to — the scoring, the tempo or the execution. If it concerns the tempo, shape deliberately and settle the stretchings beforehand, instead of searching in the moment. If it concerns a part, check whether the work sounds complete without it. And coordinate within the ensemble: freedom for one means responsibility for all.