I’m not sure that we fully understand the concept of singing a hymn.
Matthew 26:30
(KJV+) And G2532 when they had sung an hymn, G5214 they went out G1831 into G1519 the G3588 mount G3735 of Olives. G1636
(KJV) And when they had sung an hymn, they went out into the mount of Olives.
G5214 (Thayer)
ὑμνέω
humneō
Thayer Definition:
1) to sing the praise of, sing hymns to
2) to sing a hymn, to sing
2a) singing of paschal hymns these were Psalms 113 – 118 and 136, which the Jews called the “great Hallel”
Part of Speech: verb
A Related Word by Thayer’s/Strong’s Number: from G5215
G5215 (Strong)
ὕμνος
humnos
hoom’-nos
Apparently from a simpler (obsolete) form of ὕδέω hudeō (tocelebrate; probably akin to G103; compare G5567); a “hymn” or religious ode (one of the Psalms): – hymn.): – hymn.
If you have ever participated in the Passover Seder you will know the significance of this. Jesus and the disciples were singing one (or more) of these psalms.
Matthew 26:30 Gill
And when they had sung an hymn,…. The “Hallell”, which the Jews were obliged to sing on the night of the passover; for the passover, they say (l), was טעון הלל, “bound to an hymn”. This “Hallell”, or song of praise, consisted of six Psalms, the 113th, 114th, 115th, 116th, 117th, and 118th (m): now this they did not sing all at once, but in parts. Just before the drinking of the second cup and eating of the lamb, they sung the first part of it, which contained the 113th and 114th Psalms; and on mixing the fourth and last cup, they completed the “Hallell”, by singing the rest of the Psalms, beginning with the 115th Psalm, and ending with the 118th; and said over it, what they call the “blessing of the song”, which was Psa 145:10, &c., and they might, if they would, mix a fifth cup, but that they were not obliged to, and say over it the “great Hallell”, or “hymn”, which was the 136th Psalm (n). Now the last part of the “Hallell”, Christ deferred to the close of his supper; there being many things in it pertinent to him, and proper on this occasion, particularly Psa 115:1, and the Jews themselves say (o), that חבלו של משיח, “the sorrows of the Messiah” are contained in this part: that this is the hymn which Christ and his disciples sung, may be rather thought, than that it was one of his own composing; since not only he, but all the disciples sung it, and therefore must be what they were acquainted with; and since Christ in most things conformed to the rites and usages of the Jewish nation; and he did not rise up from table and go away, until this concluding circumstance was over; though it was allowed to finish the “Hallell”, or hymn, in any place they pleased, even though it was not the place where the feast was kept (p) however, as soon as it was over,