Oh, crews onboard 16th century vessels loved music, and used every chance to make some festivities, and play music and dance, which they happily recorded in their sea logs or letters, so we have a pretty good idea of what instruments they used. We have less of an idea of what kind of music was played, but I wonder if there is some music historian here who might shed some light.

The most common instruments used were trumpets, drums, bagpipes and fifes.

Trumpets are probably the most commonly mentioned instrument, used in variety of situations. Like we see in a quote describing a nice festivity that occurred between the crew and the local Africans from journal of voyage of Vasco Da Gama of 1497-1599

On Saturday [December 2] about two hundred negroes came, both young and old. They brought with them about a dozen oxen and cows and four or five sheep. As soon as we saw them we went ashore. They forthwith began to play on four or five flutes, some producing high notes and others low ones, thus making a pretty harmony for negroes who are not expected to be musicians; and they danced in the style of negroes. The captain-major then ordered the trumpets to be sounded, and we, in the boats, danced, and the captain-major did so likewise when he rejoined us.

Trumpets, besides their musical role, also accompanied captain-major (leader of the expedition) or his envoys on meetings with native chiefs on land, as shown also in a description of Da Gama's voyage:

The general then sent Aries Correa, the factor-general of the fleet, on shore to deliver the letter and presents, accompanied by most of the principal officers, and having all the trumpeters of the fleet sounding before him.

The journal of Cabral's journey (1500-1501) to India, the second Portuguese expedition, and the one that bumped into Brazi, mentions bagpipes frequently, with one particular episode standing out, when Diogo Dias (brother of Bartolomeu Dias ) seeing some friendly natives around South Africa:

He is an agreeable and pleasure-loving man, and he took with him one of our bagpipe players and his bagpipe, and began to dance among them, taking them by the hands, and they were delighted and laughed and accompanied him very well to the sound of the pipe.

If only such examples of friendly playing of the instruments with the locals continued, and not become replaced with industrial scale slaving.

Portuguese and Spanish ships and their crew also had a habit of celebrating many major events, like start of journey, or meeting a friendly lost ship or entering a new port with music of drums and also ringing of bells, and especially fring their cannons. Like from the start of Columbus first voyage:

The captain came on board, the Admiral in great pomp with drums, trumpets and pipes, offering to serve him in any way he desired.

In the voyage of Da Gama we see celebration of reunion of lost ships on the sea.

They, too, had lost sight of the captain-major. Having joined company we pursued our route, but the wind fell, and we were becalmed until Wednesday [July 26]. At ten o’clock on that day we sighted the captain-major, about five leagues ahead of us, and having got speech with him in the evening we gave expression to our joy by many times firing off our bombards and sounding the trumpets.

And, from a voyage of Pedro Fernandez de Quiros of 1606, celebrating entering a harbor:

All the artillery was fired off; and when the natives heard the noise and the echoes resounding over hills and valleys, they raised great shouts. We sounded drums, rang the bells, had music and dancing, and had other forms of rejoicing, in which the men showed great pleasure.

The above passage also shows that the firing of the artillery more often then not had a frighting effect on the locals, something that I suspect the Iberians knew, and did on purpose anyway, to demonstrate their power.

Lastly, the opportunities for music weren't only joyous ones, and instruments were used in funerals, especially of dignitaries. The funeral of adelantado (governor) Alvaro de Mendana of 1596 is described in following way:

In the afternoon, with as much pomp as the circumstances would admit, we prepared for his sepulture. The body was placed in a coffin covered with black cloth, and carried on the shoulders of eight persons of the highest rank. The soldiers stood with their arquebuses reversed, in accordance with usage at the funerals of Generals. The procession went with two banners displayed, and from two drums covered with mourning cloth came slow and muffled sounds, while the fife expressed the like sentiments. Arrived at the church, the Vicar performed the service, and we then returned to the Governess to condole with her on her misfortune.

After I provided textual evidence of the instruments used, I might as well give some images depicting them.

They aren't exactly images of ship-use of musical instruments, but they are contemporary images of Portuguese in India that among other things show some musical instruments. They are part of series of tapestries Deeds and Triumphs of Dom Joao de Castro dating to 1555-1561, and from those, this image in particular shows a drummer and a fifer in the front row and if you look in the background in the middle row you will see some trumpeters. Another image shows more trumpeters and drummers in the middle and back rows