What constitutes a choir for various pre-novus ordo monastic rites?
All the religious in the choir stalls are part of the choir, whether choir monks or Schola members. Lay brothers although not technically choir monks are part of the choir when assisting at the Divine Office or mass.
Basically a simple definition of what a pre-Vatican II choir would be a place within monasteries where the Divine Office is chanted in the stalls accommodating the monks or nuns and separated from the sanctuary and the faithful. This holds for both Rites within the Latin Rite.
This simple definition would be more narrowly defined that at mass there would be no or almost never concelebration at mass.
During the main high mass of the day the intonations of the chant would be intoned by one of the Schola Chanters from the side in which the priest (hebdomadarian) celebrating the mass was from. After the intonation the entire choir would continue with the piece intoned.
The hebdomadarian is “the priest or religious officiating for a week in a monastery or church. A hebdomadarian sings the conventual Mass each day, intones the various canonical hours in the Divine Office, sings the orations, and gives all the necessary blessings.”
During the regular Divine Office, the hebdomadarian intones the opening of the particular office. The psalms are chanted not in unison but alternated from side to side. At vespers the antiphon are intoned by a monk or nun of the same side of the hebdomadarian. The second antiphon would be intoned by a monk or nun of the other side. The alternate side changing as long as there are new antiphons and psalms being chanted. At the smaller hours the psalms are chanted straight through.
During major feast days, the Schola (4-6 monks or nuns, 4 being the norm) intones various pieces of the Divine Office and the psalms are alternated between the Schola and the rest of the entire choir. These Schola members of the community are the best of the monastic singers. On these days the Schola singers are dressed with copes of the liturgical colour of the day. The preceptor holds the precentor’s staff. Modern precentor staffs look like a bishop's crosier, topped with a statue of St. Benedict in lieu of a shepherd’s hook. When the abbot is to intone a certain piece the precentor will pass his staff to a second Schola monk who will advance to the abbot with the precentor’s staff in hand and intones the melody to the abbot in a low voice as an aid for the abbot to correctly intone the piece to be chanted. Sometimes the precentor will do this himself. The beauty of the liturgy is truly magnificent and awesome when executed well!
Some chapters have sub-chanters, those of Arras being among the honorary resident canons" (Migne, "Dict.de Jurisprudence", s.v. Grand Chantre, where also the quoted statutes of the Bishop of Dijon may serve to illustrate the modern idea of the office of precentor: "The Précenteur or Grand Chantre is the head of the choir and . . . brings the antiphon to the bishop when officiating pontifically. - Precentor
About the year 1100, after the introduction of the musical staff, they began to decline in importance. So thoroughly was music practised in the medieval song-schools connected with churches or monasteries, founded for the purpose of setting forth the liturgy with the utmost splendour and beauty, that until the Protestant Reformation the history of music is practically the history of church music. - Choir
Although the precentor is generally the best chanter and very knowledgeable about Gregorian Chant, he is not the choir director. That privilege rests with the choir master, who trains the entire monastic community, the choir monks and Schola.