If you shift F away from that ratio, you're not doing equal temperament anymore. Which is fine. There are many different tuning systems [ https://en.wikipedia.o

If you shift F away from that ratio, you're not doing equal temperament anymore. Which is fine. There are many different tuning systems [ https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the_twelve-note_chromatic_scale https://en.wikipedia.org/wiki/Musical_tuning#Systems_for_the... ], and they all involve tradeoffs. Equal temperament's benefit is its flexibility, but that doesn't make it 'better'.