For the traditional Mass, I would say that the document most commonly cited on these issues is Inter Sollicitudines, a motu proprio by Pius X on the liturgy.
For example, while Inter Sollucitudines instructed that only men be part of the schola cantorum. Musica Sacra states:
Wherever such a choir cannot be organized, a choir of the faithful, either mixed or consisting only of women or girls, can be permitted. But such a choir should take its place outside the sanctuary or Communion rail. The men should be separated from the women or girls so that anything unbecoming may be avoided. Local Ordinaries are to issue precise regulations about these matters, and pastors are to see to their enforcement (Decr. Auth. SCR 3964, 4210, 4231, and the encyclical Musicæ sacræ disciplina: AAS [1956] 23).
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