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I have a typography scale for mobile devices with a baseline of 23px and a base font size of 16px.
I want to increase the scale and line height for tablets and then desktop but in increments that keep the scale intact. What's the formula for doing this? Are there any good/bad ways to do it?
There is no one specific formula for this. It depends on the content, audience, desired feel, purpose, and opinion.
I recommend to make your font (and whole site) look good on small screens (~300px) including the font size. Make sure it has the feel and fulfills the purpose that you want it to. Then make the screen bigger and see if it still accomplishes the goal that you want.
There will likely be a place where it stops feeling the way you want to. Change the font size to what it needs to be at this point. Then repeat this process until you've covered all screen sizes that you're looking to create for (perhaps including large TVs with a large pixel count).
