Why, for what purpose and from what cause was the double beat theory "invented" at the time, around 1970/1980, and especially by Willem Talsma? There were 2 reasons for this. 1. He felt that today's musicians played too fast. 2. The MM numbers from the 19th century in particular were so fast that no one could play them fast enough. According to him, there had to be a solution. He came up with a way to get out of this problem. He did so in response to Dr. Schwandt who had discovered that L'Afillard, a Baroque theorist, had published French court dances with pendulum tempos. According to Schwandt, they most closely matched the danced versions if you halved these pendulum marks. Talsma figured that if you cut all pendulum marks and all MM marks in half, you would be out of trouble. He did make an exception for the slow pieces. They didn't have to be halved. But if you assume that MM numbers, and also pendulum marks, do not have to be strictly monitored, you will already solve part of the problem. Various writers, including Czerny, give very clear instructions in their writings where you can (even have to) make ritenutos while playing the piece. Those ritenutos give the whole piece of music a less strict tempo. Such a strict tempo, by the way, sounds very mechanical and machine-like. In addition, composers in fast pieces like to give MM marks a little too fast, by way of a surplus, an extra. Just as a runner's trainer says to his athletes, if you want to run the Marathon, you have to be able to run at least 50 km.