This is an interesting way to view key signatures. Normally, we’re taught about how many flats or sharps there are in a given key and how they relate to the circle of 4ths/5ths, but no emphasis is given to the natural notes.
Give this a try. Try thinking of every key as a series of natural notes plus either sharps or flats. For example, D Major has 2 sharps and 5 naturals. Or, Ab Major has 3 flats and 4 naturals. You’ll notice that the sum of all notes will always add up to 7 because there are 7 notes in every major scale.
Here’s where this concept was particularly useful for me. I had always confused Gb Major and Db Major, and which one had 5 or 6 flats. It wasn’t until I noticed an interesting relationship between keys with the same letter name that i was able to fix this issue.
The relationship is that keys of the same letter name will always have the inverse number of naturals and accidentals to each other.
G Major = 6 naturals and 1 sharp
Gb Major = 6 flats and 1 natural
D Major = 5 naturals and 2 sharps
Db Major = 5 flats and 2 naturals.
Bb Major = 5 naturals and 2 flats
B Major = 5 sharps and 2 naturals
For me, this really helped me solidify how keys are organized and to be able to quickly identify the accidentals (and naturals) of any key by referencing another key with the same letter name.