I am not sure what you mean by church liturgies exactly – but the “liturgy of the hours” has its origins in temple/synagoge worship.
The psalms, even at the time of Jesus, were sung at temple/synagoge with the congregation divided into two parts – those singing the strophe, and those singing the antistrope, etc. So that the psalm was prayed/sung line by line from opposite sides of the temple at set times.
Vespers is quite an enjoyable way to spend the evening if it is offered in your area.
Hope this helps.