Test cricket has the play structure carefully designed to balance the game's demands with player welfare. This was done to ensure competitive integrity and adequate rest periods in each day's three sessions, with each lasting about two hours, separated by two main intervals: a 40-minute break for lunch and a 20-minute break for tea. This gives players good opportunities for rest and refueling with strategy for the sessions ahead. 

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Between innings, an inning interval is about 10 minutes long. This short break is given to teams so they can easily switch between batting and fielding positions. But of course, the inning interval is sometimes conditioned by its relationship with the scheduled meal breaks. In cases where the end of an innings occurs within 10 minutes of a scheduled lunch break, the inning interval merges with the lunch break to complete one 40 minute interval. Similarly, if an innings ends within 30 minutes of the scheduled tea break, the innings interval merges with the 20-minute tea break. These adjustments ensure a seamless flow of the game while accommodating players’ rest needs.

If an innings finishes with less than 10 minutes remaining in the allocated play of the day, then no more play is held for that day. The following innings will resume when the following day's allocated play begins. This way, there is proper time for preparation before the second innings, and it does not go to waste playing a little portion of play on the day end. 

These scheduled intervals along with their adaptive use are inherent to the cricket rhythm of Tests, ensuring both the continuity and breaks of play. The alternation between rigid and adaptive periods ensures that this game retains the traditional form yet accommodates all the practical aspects of modern playing.

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In summary, the intervals in Test cricket are structured to give the players the essential rest and time for strategic planning so that the game is well preserved and the athletes are treated with care. The flexibility of timing, particularly regarding innings breaks and their closeness to meal intervals, indicates the sport's adaptability in various match situations, maintaining the balance between tradition and practicality.