'If any man speaks in a tongue, let it be by two, or at the most three, and that in turn; and let one interpret. But if there be no interpreter, let him keep silence in the church, and let him speak to himself, and to God.'
So if a man does come with a tongue, it should be by two, or at the most three, and should be 'in turn'. And even then it must be interpreted. And if no interpreter is present then the person should 'keep silence'. He should rather speak quietly and privately to himself and to God.
The restriction is quite specific. Three should be the upward limit of tongues, and this in a gathering which will last several hours. And the fact that it is to be 'in turn' might indicate that in practise in the past people have been speaking in tongues at the same time, conflicting with each other and causing disruption. Thus they are not to use tongues in unison.
We carefully note the grammar here. Paul begins by speaking to the individual who commences speaking in tongues. He then diverts to consider how many individuals shall be permitted to do this. He then returns to the individual and declares that his tongues must be interpreted. (Thus the interpretation directly follows the tongue). Indeed if no interpreter is present he must refrain from speaking in tongues, as must the possible other two. This demonstrates that the idea that the two or at the most three is simply referring to the number before an interpretation takes place is fallacious. It has nothing to do with when the interpretation takes place. It refers to God's limitation on the number of times this means of revelation can be used.
'Let one interpret.' In a verse where numbers are in use the emphasis on 'one' may signify that the interpretation should be left to only one interpreter. Perhaps when people spoke in tongues interpreters had been so eager that a number had done so at the same time. Or perhaps the emphasis is on the fact that the same interpreter should interpret in each case to maintain continuity of thought and idea. Interpretation was not necessarily to be seen as word for word translation.
There was clearly a great deal of content to their gathering that is not mentioned here. We may probably see it as being occupied by prayer, the reading of the Old Testament Scriptures and exposition on the same, as in the synagogue, hearing some of the traditions of the life of Jesus from someone knowledgeable, almost certainly given word for word from memory as delivered to him (see 1 Corinthians 11:2), or even from a written source (Luke 1:1), followed possibly by an expounding of the tradition, a reading of any letters received from important sources (1 Thessalonians 5:27), psalms and hymns, and then a common meal followed by, or including, the Lord's Supper (compare 1 Corinthians 11:17-34, but the Corinthians were misusing the idea). Not necessarily of course all in this order.
This passage might suggest that a specific amount of time was to be laid aside for exercising the charismata. It was to be a blessed time, but restrained. Thus three interpreted tongues would be quite sufficient and leave room for the exercise of other gifts. And as time was precious (this would for many be the only worship gathering of the week because of their duties), they should only be exercised if they were to be interpreted and thus bring blessing to all. Otherwise they should leave room for more edifying ministry.