Here’s what I found on the subject:
There are several documents regarding this theme. The 1967 instruction on liturgical music, “Musicam Sacram,” addresses the question of the organ and other instruments in Nos. 62-67. To wit:
"62. Musical instruments either accompanying the singing or played alone can add a great deal to liturgical celebrations.
"The pipe organ is to be held in high esteem, for it is the traditional musical instrument that adds a wonderful splendor to the Church’s ceremonies and powerfully lifts up the spirit to God and to higher things.
"But other instruments also may be admitted for use in divine worship, with the knowledge and consent of the competent territorial authority. … This may be done, however, only on condition that the instruments are suitable, or can be made suitable, for sacred use, are in accord with the dignity of the place of worship, and truly contribute to the uplifting of the faithful.
"63. One criterion for accepting and using musical instruments is the genius and tradition of the particular peoples. At the same time, however, instruments that are generally associated and used only with worldly music are to be absolutely barred from liturgical services and religious devotions. All musical instruments accepted for divine worship must be played in such a way as to meet the requirements of a liturgical service and to contribute to the beauty of worship and the building up of the faithful.
"64. Musical instruments as the accompaniment for singing have the power to support the voice, to facilitate participation, and to intensify the unity of the worshipping assembly. But their playing is not to drown out the voice so that the texts cannot be easily heard. Instruments are to be silent during any part sung by the priest or ministers by reason of their function.
"65. …] Solo playing (of the organ or other approved instruments) is allowed at the beginning of Mass, prior to the priest’s reaching the altar, at the presentation of the gifts, at the communion, and at the end of Mass.
"66. Solo playing of musical instruments is forbidden during Advent, Lent, the Easter triduum, and at services and Masses for the dead.
“67. It is, of course, imperative that organists and other musicians be accomplished enough to play properly. But in addition they must have a deep and thorough knowledge of the significance of the liturgy. That is required in order that even their improvisations will truly enhance the celebration in accord with the genuine character of each of its parts and will assist the participation of the faithful.”
According to this document, therefore, solo playing of the organ is prohibited during Advent.
However, while the above criteria are substantially still valid, there appears to be a small opening to solo playing during Advent in the new General Instruction of the Roman Missal.
No. 313 says: "In Advent the organ and other musical instruments should be used with a moderation that is consistent with the season’s character and does not anticipate the full joy of the Nativity of the Lord.
“In Lent the playing of the organ and musical instruments is allowed only to support the singing. Exceptions are Laetare Sunday (Fourth Sunday of Lent), Solemnities, and Feasts.”
Thus the express prohibition to solo playing of the organ found in “Musicam Sacram” is now limited to the Lenten season while during Advent it now appears possible to do so albeit with moderation and selecting music appropriate for a penitential season. "
