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Let's go more in depth with key signatures (probably should've done that sooner).
Natural keys:
Cmajor/Aminor: no sharps or flats
Sharp keys:
Gmajor/Eminor: F#
Dmajor/Bminor: F#, C#
Amajor/F#minor: F#, C#, G#
Emajor/C#minor: F#, C#, G#, D#
Bmajor/G#minor: F#, C#, G#, D#, A#
F#major/D#minor: F#, C#, G#, D#, A#, E#
C#major/A#minor: F#, C#, G#, D#, A#, E#, B#
I know what you're thinking. "There's no such thing as E# or B#!" Well there are. E#=F, and B#=C. Why not just use F and C then? Because those keys already have a form of F and C. You can't have the same letter twice in the same diatonic scale.
Flat keys:
Fmajor/Dminor: Bb
Bbmajor/Gminor: Bb, Eb
Ebmajor/Cminor: Bb, Eb, Ab
Abmajor/Fminor: Bb, Eb, Ab, Db
Dbmajor/Bbminor: Bb, Eb, Ab, Db, Gb
Gbmajor/Ebminor: Bb, Eb, Ab, Db, Gb, Cb
Cbmajor/Abminor: Bb, Eb, Ab, Db, Gb, Cb, Fb
Fb=E and Cb=B, same rule I explained above.
Harmonizing scales
Remember that mode+tonic=scale. This means take an intervallic structure (like Ionian, WWhWWWh) and apply it to a tonic (the "1" note, like F) and we get a scale (the Fmajor scale). Today we'll be harmonizing heptatonic scales. "Heptatonic" means the scale has 7 notes. We've already studied plenty of heptatonic scales. We'll be harmonizing in thirds, because you've already learned "tertian harmony."
For our first example, we'll use the Fmajor scale. The Fmajor scale has a Bb, so the key signature looks like this:
So the B is always flat in this piece of music unless you add an accidental (a natural, sharp, or flat sign next to the note during the piece). Let's create the Fmajor scale now:
The only example I could find is accross two octaves and comes with tab. That should be fine, maybe even better.
Now let's add a 3rd to every note. We don't know if it'll be a minor third or a major third, that depends on the note and on what is diatonic.
The 3 of F is A-something. We know its natural because the A in the Fmajor scale is natural.
The 3 of G is B-something. We know its flat because the B in the Fmajor scale is flat.
The 3 of A is C.
The 3 of Bb is D.
The 3 of C is E.
The 3 of D is F.
The 3 of E is G.
Now let's add another third on each of those thirds, to turn each of those dyads into triads.
The 3 of A is C.
The 3 of Bb is D.
The 3 of C is E.
The 3 of D is F.
The 3 of E is G.
The 3 of F is A.
The 3 of G is Bb.
So this gives us the following triads:
(I)F-A-C, (ii)G-Bb-D, (iii)A-C-E, (IV)Bb-D-F, (V)C-E-G, (vi)D-F-A, (vii0)E-G-Bb
This is why those roman numerals work out the way they do. These are the chords of all the heptatonic modes we've discussed (diatonic or otherwise):
Diatonic Modes
Ionian: I-ii-iii-IV-V-vi-vii0
Dorian: i-ii-III-IV-v-vi0-VII
Phrygian: i-II-III-iv-v0-VI-vii
Lydian: I-II-iii-iv0-V-vi-vii
Mixolydian: I-ii-iii0-IV-v-vi-VII
Aeolian: i-ii0-III-iv-v-VI-VII
Locrian: i0-II-iii-iv-V-VI-vii
Harmonic Minor Modes
Aeolian natural7: i-ii0-III+-iv-V-VI-vii0
Locrian natural6: i0-II+-iii-IV-V-vi0-vii
Ionian#5: I+-ii-III-IV-v0-vi-vii
Dorian#4: i-II-III-iv0-v-vi-VII+
Phrygian natural3 or Mixolydian b2, b6: I-II-iii0-iv-v-VI+-vii
Lydian#2: I-ii0-ii-iv-V+-vi-VII
Locrianb4 bb7 or Altered Diminished or Hyper Locrian:
Melodic Minor Modes
Ionianb3: i-ii-III+-IV-V-vi0-vii0
Dorianb2 or Phrygian natural6: i-II+-III-IV-v0-vi0-vii
Lydian#5 or Lydian Augmented: I+-II-III-iv0-v0-vi-vii
Lydianb7 or Lydian Dominant or Mixolydian#4: I-II-iii0-iv0-v-vi-VII+
Mixolydianb6 or Aeolian natural3: I-ii0-iii0-iv-v-VI+-VII
Locrian natural2 or Aeolianb5: i0-ii0-iii-iv-V+-VI-VII
Locrianb4 or Altered Scale or Super Locrian: i0-ii-iii-IV+-V-VI-vii0
You have to work out the 7s and etensions on your own. You won't learn anything if I do all the work for you. And you probably can't find the answers anywhere on the internet.
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