I read in the baseball matches (formed of nine innings) that there exists a pause for spectators at seventh inning.
Why on this number of innings and not after fourth and before fifth? Potentially in the middle of match?
According to Wikipedia, the 7th Inning Stretch is something that is widely disputed, and no real record exists of exactly when it started. There are several accounts of what could have started it, but no real proof that any of them are the real reason it was started. Can't really comment on why it's in the 7th inning and not earlier in the game.
The origin of the seventh-inning stretch is much disputed, and it is difficult to certify any definite history.
One claimant is Brother Jasper (Brennan) of Mary, F.S.C., the man credited with bringing baseball to Manhattan College in New York City. Being the Prefect of Discipline as well as the coach of the team, it fell to Brother Jasper to supervise the student fans at every home game. On one particularly hot and muggy day in June 1882, during the seventh inning against a semi-pro team called the Metropolitans, the Prefect noticed his charges becoming restless. To break the tension, he called a timeout in the game and instructed everyone in the bleachers to stand up and unwind. It worked so well he began calling for a seventh-inning rest period at every game. The Manhattan College custom spread to the major leagues after the New York Giants were charmed by it at an exhibition game.
In June 1869 the New York Herald published a report on a game between the Cincinnati Red Stockings and the Brooklyn Eagles (home team): "At the close of the long second inning, the laughable stand up and stretch was indulged in all round the field."
Whether a stretch was observed nationwide is not known, but later in 1869 the Cincinnati Commercial reported on a game that was played on the West Coast between the Red Stockings and the Eagle Club of San Francisco: "One thing noticeable in this game was a ten minutes' intermission at the end of the sixth inning – a dodge to advertise and have the crowd patronize the bar."
However, a letter written in 1869 by Harry Wright (1835–1895), manager of the Cincinnati Red Stockings documented something very similar to a seventh-inning stretch, making the following observation about the Cincinnati fans' ballpark behavior: "The spectators all arise between halves of the seventh inning, extend their legs and arms and sometimes walk about. In so doing they enjoy the relief afforded by relaxation from a long posture upon hard benches." Another tale holds that the stretch was invented by a manager stalling for time to warm up a relief pitcher.
On October 18, 1889 Game 1 of the 1889 World Series saw a seventh-inning stretch after somebody yelled "stretch for luck".
A popular story for the origin of the seventh-inning stretch is that on April 14, 1910, on opening day, 6 ft 2 in (188 cm), 350-pound (160 kg), President William Howard Taft was sore from prolonged sitting at a game between the Washington Senators and the Philadelphia Athletics and stood up to stretch, causing the crowd to feel obligated to join their president in his gestures. This story is set at a far later date than the others, however, so he may only have given the presidential seal of approval to a longstanding tradition; the story that his physical problems forced him to stand up contradict this, but he might have just been waiting for the proper accepted time to relieve his pain; either way, he gave national publicity to the practice.
As to the name, there appears to be no written record of the name "seventh-inning stretch" before 1920, which since at least the late 1870s was called the Lucky Seventh, indicating that the 7th inning was settled on for superstitious reasons.
As you can see, there are many references to what may have started the ritual, but no real proof. It's just something that people observe, but no real reason is known as to why exactly it started. The tradition, at least now, is people sing "Take Me out To The Ballgame" during this 7th inning stretch.
There is no certain date when the tradition began, but the practice gained exceptional notoriety from broadcaster Harry Caray. Caray would sing the song to himself in the broadcast booth during the stretch while a play-by-play announcer for the Chicago White Sox.
After hearing him sing one day, White Sox owner Bill Veeck Jr., the famed baseball promoter, had Caray's microphone turned on so that the ballpark could hear him sing. When Caray moved into the Chicago Cubs broadcast booth, he continued the practice, sparking what has become a Cubs tradition by regularly leading the crowd in singing the song in every seventh-inning stretch.