Illustrated Architecture Dictionary
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The arcade which is seen in many vaulted churches below the clerestory
A shallow passage above the arches of the nave and choir loft and below the clerestory
If there is a barrel vault, there will be no space between the half barrel and the roof, and, consequently, no triforium.
Triforium chamber: "This is the space between the vault of the aisles and a lean-to roof of sharp pitch which is constructed to protect the masonry of the vault from the weather" - Gothic Architecture in England, by Francis Bond [1906 book with many illustrations]
Clerestory ... Arcade windows
In the interiors of medieval churches each bay of the nave wall customarily had three divisions in its height:
The triforium was thus located beneath the clerestory windows and above the side-aisle vaults and corresponded on the exterior to the lean-to roof over the aisle.
In the north the triforium had arched openings with apertures in the wall behind it to ventilate the roof space over the aisle.
In most Romanesque churches it appeared as a second-story vaulted gallery over the aisle and was equal to it in depth and sometimes also in height.
In Gothic churches, the depth behind the triforium arcades was generally limited to the thickness of the nave wall, into which a narrow passageway was built to furnish a second-story circulation around the church.
Developed French Gothic flattened the pitch of the aisle roofs, thus leaving the outside wall of the triforia exposed and free for glazing. The inside face retained its rich open tracery arcades.
Late Gothic subordinated the triforium between the higher main arcades and clerestory and sometimes omitted it entirely.
is an interior gallery, opening onto the tall central space of
a building at an upper level. In a church, it opens onto the nave
from above the side aisles; it may occur at the level of the
clerestory windows, or it may be located as a separate level below the
clerestory. Masonry triforia are generally vaulted and separated
from the central space by arcades.
Early triforia were often wide and spacious, but later ones tend to be shallow, within the thickness of an inner wall, and may be blind arcades not wide enough to walk along. The outer wall of the triforium may itself have windows (glazed or unglazed openings), or it may be solid stone.
- Wikipedia (online Dec. 2019)
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