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Something I was thinking about while rewatching K-On here: In all of the EDs, as we've noticed before, Ritsu has a generally more somber demeanor than the rest of the girls. Yui, Mio, Mugi and Azusa are all depicted as rather cheery in the ED music videos, but Ritsu alone tends to be depicted as frowning and generally darker of mood.
Going off of the idea that the ED music videos are from an alternate timeline where Houkagou Tea Time makes it big and gets signed to a major record label, I have two ideas, then:
1. When the record label first started to market HTT, they decided that they needed at least one of the girls to be the "cold and moody" sort of character, just for marketing purposes. Potentially they thought it would be funny to make the most cheerful and energetic person in the band take up the mantle of "cold and moody", or maybe due to Ritsu's general appearance they thought she would make the best "cold and moody" character for the band's image.
2. When HTT first started to establish their image as a major band, Ritsu thought that it would be fun to try on a persona that is completely opposite of who she is for the band, just for shits and giggles. After the first video got released, though, or something similar, there was immense positive reaction to Ritsu's pseudo-persona, with lots of people talking about how cool they thought she was, being so "cold and moody". Ritsu, always a fan of praise and being called "cool", kept up the fake persona as part of her image for HTT.
I didn't articulate that as well as I wanted to, but I hope you understand what I was getting at. I really like the idea of the latter, where Ritsu, normally so happy and full of life, intentionally portrays herself as sort of "dark" and stuff so that she can have a "cool" band image. It just seems so much like her.
"Ah, there I am in the music video! Don't I look cool?! Don't I, don't I?! Don't make that face, you know that your Ritsu-senpai is the coolest!"