Personally, I think of this in terms of major and minor being modes (because they are), and then modify major or minor into the various major family or minor family modes:
Major (ionian)
- raise the
^4 degree to get lydian
- lower the
^7 degree to get mixolydian
Minor (aeolian)
- raise the
^6 degree to get dorian
- lower the
^2 degree to get phrygian
- lower the
^2 and ^5 to get locrian
The practical application of that is some thing like this:
- start with the given tonic (this is the likely scenario, someone says, for example, play in
F# dorian)
- determine the major/minor key signature, dorian is in the minor "family", so get the
F# minor key signature, which is three sharps, F# C# G#
- determine the
^6 degree relative to tonic F#, that will be some kind of D, specifically by the key signature it is a D natural, raise D natural to D#
F# dorian's key signature is four sharps F# C# G# D#
Your examples of...
Dorian who have 5 flats
...and...
which Locrian's signature is 7#
...seem more like music theory quiz questions, not practical situations. Who says "play in the dorian mode with five flats?"
Nevertheless, the way to answer those questions is still easiest, IMO, by reference to major key signatures first, then the various rotations of the major scale to the diatonic modes.
For example...
- five flats is
Db major, the dorian mode tonic is the ^2 degree of Db major, which is tone Eb, so Eb dorian has five sharps.
- seven sharps is
C# major, the locian mode tonic is the ^7 degree of C# major, which is tone B#, so B# locrian has seven sharps.
One comment on your method. I may be misuderstanding it but, this part...
C = 0
D = 2#
E = 4#
...will tell you how to get the major key signature on those given tonics. C major is zero sharps/flats, D major is two sharps, E major is four sharps, etc.
But, your mistake seems to be here...
Ionian NO-CHANGE
Dorain +2#
Phrygian +4#
...moving to relative terms raising two degrees (adding two sharps as you describe it) does not give us the dorian mode, it gives us the major scale on the second scale degree of the starting scale. So, if we were starting on Eb major, for example, F natural is the second scale degree, raising two tones, the Ab and Eb to A natural and E natural, leaving only the B, gives us F major.
If we look at it as Eb major, called Eb ionian, and we want to the dorian scale/key signature on the second scale degree of Eb ionian, there is no change to the scale/key signature. Eb ionian and F dorian are the same collection of tones, just starting on different points. The key signature is three flats, Bb Eb Ab, and the scales are Eb F G Ab Bb C D Eb and merely its rotation F G Ab Bb C D Eb F.
Your second chart would really be...
Ionian NO-CHANGE
Ionian transposed up M2 +2#
Ionian transposed up M3 +4#
...you can use 12-NUMBER of SHARPS...
I don't know why you want a system to handle 12 sharps/flats for key signatures. After seven sharps/flats, key signatures become theoretical key signatures. Those are not normally used, and they wouldn't use up to 12 sharps/flats anyway, they would use double-sharps/double-flats, with only 7 total signs in the key signatures.
Nevertheless, 7 sharps is C# major, 5 sharps is B major, basically adding 7 sharps to a key signature will just add a sharp to the tonic, in other words 5 sharps in B major, add 7 more sharps, it becomes B# major, or add 7 sharps to C# major makes it Cx major.
You sort of 'reset' adding sharps at the F, but make them double-sharps and add 5 of them, so Fx Cx Gx Dx Ax then the rest will be plain sharps until you have 7 total changes to the gamut of letters by fifths FCGDAEB, so E# B#, altogether the key signature of "12 sharps" for B# major is Fx Cx Gx Dx Ax E# B#.
Figuring out a theoretical key signature is the onerous part. But, after determining the theoretical key signature, finding the various theoretical modal key signatures is comparatively easy.
What is the locrian key signature using 12 sharps? 12 sharps minus 7 shaprs is 5 sharps, which is B major, so 12 sharps is B# major. The locrian mode starts on the seventh scale degree of B# major, which is Cx, and so Cx locrian has a key signature of 12 sharps.
There is no practical reason to do that.
The main things to understand for all these aspects of key signatures and modes are:
- sharps and flats get added to key signatures by ascending or descending perfect fifths
- the modes of any given major key "rotating" up the scale from the tonic are: ionian, dorian, phrygian, lydian, mixolydian, aeolian, locrian
If you become comfortable with those two sequences, it's relatively easy to "find" key signatures.
