A quarter note is not consistently perceived as a quarter note the way a metronome might indicate, as time is not a stable mathematically precise constant for humans. Time is perceived by us depending on the time of day, how we feel, and the situation. I have noticed this when I compose, I hear the music a lot faster in my head as a pure non-physical abstraction and it makes total sense. Only when I hear it live might I say that the tempo is wrong. Sometimes when I am performing really fast Bebop jazz, time slows down and then when I hear it back later, I wonder how we were playing all those notes so fast.
If you play a concert at night in front of 10,000 pumped-up fans, your endorphins are pumped, and your senses heightened, and everything is moving at a faster pace. It is similar to walking in an airport on those people movers. Your walking is constant, but the entire escalator platform is moving thus you are moving the same, but the entire event perceived from an outsider is faster. If you record a concert like that and then listen to it the next morning in a calm house, the entire program will sound way too fast, as now your mind and perception of time is more relaxed. And vice-versa holds true: if you record a piece early on a quiet Sunday morning and then play that recording back later that night in a venue packed with 10,000 people, it would seem way too slow. We all have experienced time shifting, when you are bored sitting in a school math class times sits still, and when you are engaged in some action movie time bounces along. So, metronome markings are not an absolute but only an indicator of the tempos as these should change according to the emotional context, the venue and situation.......
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