Sequence, not circle, of fifths
I said above I find the wheel faulty, so given the favor it enjoys among pedagogues, I should explain. While it's true that the fifths (and fourths) form a cyclic pattern when enharmonic equivalence is factored in, it's rare that you actually use this feature. Instead, the main uses of the wheel focus on non-cyclic subregions of it, and to get the proper note or chord names as you move farther and farther from the C center, you need to treat the sequence as strictly linear. For instance, in the key of E, your note names and chords are (in fifths order) A E B F# C# G# D#, yet you almost never see the last two notes on a wheel; instead, it will tell you Ab and Eb, which are absolutely the wrong spellings, even if the pitches are the same.
The wheel is also strongly skewed to major keys. It can be used for minor keys (using the inner wheel of relative minors—if your wheel has one), but you have to disregard any labels dealing with relative chords and scale degrees. And for other modes like Dorian and Mixolydian, you're on your own.
The wheel presentation has the advantage of being compact and snazzy, but it's difficult to augment simply, and you have to keep changing your mental/spatial orientation to follow it around. It's also a bitch to jot down. (I've misplaced more wheels of fifths than I've ever used; I like aids I can quickly jot down and customize as needed.) So if you want to relabel the relative chord numbers to accord with minor keys, for instance, you're SOL.
Instead, when I've needed a tool to work with the fifths sequence, I preferred to use simple strips of paper—graph paper labelled or cut lengthwise works excellently for this. Much easier than drawing circles and dividing them into 12ths, and you never have to mentally reorient. You can even quickly jot what you need down on lined or blank paper.
If you've learned the FCGDAEB sequence (the order of sharps), it's easy to draw up a diagram anywhere that does everything the wheel does AND uses the right note names. Just start with that sequence, adding a flat after every letter, then repeat the sequence without flats, then repeat again with sharps. For the relative minors, put A(m) under C and fill in as above.
Code:
Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B#
Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B#
(You never use major key names beyond Cb and C# nor their relative minors Abm and A#m, nor does any key naturally contain a double-sharp or double-flat, so it's unnecessary to fill in the gaps at the end of these sequences.)
Since fifth progressions typically go
down rather than up by a fifth (i.e. they go
counterclockwise on a wheel), it would make more sense to reverse the order, using the BEADGCF sequence and starting with sharps instead of flats. But the sharpward, up-by-fifths order is so endemic that it would probably be more confusing to reverse this frame of reference. Consequently, I won't pursue this suggestion until I describe the fretboard up-by-fourths lateral jog pattern.
Now for the relative chord/scale degrees, labelled with Roman numerals. This labeling is mode-specific. Write these sequences, spaced as on your chart above, on separate strips:
For major = Ionian: IV I V ii vi iii vii° (central [no sharps/flats] key is C)
For minor = Aeolian: VI III VII iv i v/V ii° (central key is A)
For Lydian: I V II vi iii vii iv° (central key is F)
For Mixolydian: VII IV I v ii vi iii° (central key is G)
For Dorian: II VII IV i v ii vi° (central key is D)
Uppercase means the chord is naturally major, lowercase means the chord is naturally minor, and the little circle means the chord is naturally diminished. For clarity, many folks (like me) prefer to use lowercase m, as in regular chord names: IIm or iim. Mark the I or i prominently in your strip, Align it over your key name and you're good to go.
For a general transposition tool, rather than use fifths order (which has nothing to do with transposition), it's much more natural to use chromatic strips in normal semitone order: you know where to find each note. One strip needs to repeat the full set of notes, the other only needs a single set. Align the key names and you're ready to transpose. But if you're concerned about chord spelling, you may prefer to write up a custom chart: write out the scale of your "from" key, then below it write out the scale of your "to" key. Omit the notes in between (clutter), though if you want a reminder, you can leave an empty cell between whole steps in the scale. For example:
Code:
I ii iii IV V vi vii°
Eb F G Ab Bb C D (Eb)
A B C# D E F# G# (A)
Then, to find the spelling of a natural chord in the key, like F#m in A, just leapfrog notes: F# A C#. If you don't like cycling round, write out the "to" scale twice. The time it takes to draw up such a chart should be dwarfed by your use of it, and you don't have to deal with anything non-essential, like inapplicable enharmonic equivalents.