[tarentel]

> I was not learning to name the key signatures

It was mentioned the person was trying to memorize all these with anki or something. There's actually no need. You only need to memorize 2 key signatures and the rest follow a pattern.

C major has 0 sharps/flats F major has 1 flat

Every sharp key is a half step up from the last sharp shown. G major has 1 sharp F#. G is a half step up from F#. In A major the last sharp is G#, etc.

In flat keys, it's the second flat to the right. Bb has two flats in the signature. Bb and Eb. Ab has 4 where Ab is the 3rd.

All minor keys are a minor third down from their major key. Of course, you have to look at more of the music to determine if it is a in major or minor key.

If you can remember that you can tell what any key signature is pretty quickly.

[tgv]

It's simpler: in the major scale, every fifth down removes a # or adds a b, every quint up removes b or adds a #, and it's the 7th degree. Other church modes can be derived from a major scale. But that doesn't help you while playing. You have to know the key and scale you're in, and read the accidentals (and what op didn't mention: naturals and double #/b).

[tarentel]

There are definitely other ways to derive all this but with a quick glance you don't really need to do any computation involving intervals. The key is either the second to last flat, a half step up from the last sharp, C, or F. To me this is much simpler than seeing 3 sharps and going, C->G->D->A. It's definitely good to know the latter but definitely not necessary for ascertaining the key.

[chthonicdaemon]

This still relies on being able to name the notes. My point was that you can play the music without knowing the names, so you need some other system like yours to get from the notated signature to the name (or other way around).