Transformation 

You have an initial key signature, then you perform one or more altered diatonic chord operations to transform into another key signature.

An altered diatonic chord is an operation you perform on a default diatonic chord. The default diatonic chords used are I, II, III, IV, V, VI, VII.

Commit to your memory the default diatonic chords.
I and IV are XM7 chords.

II, III and VI are Xm7 chords.

V is a X7 chord.

VII is a half diminished chord.

Definition: [Pre Operation][Default Diatonic Chord][New Chord Character] 

Name: Altered diatonic chord.

Explanation: An altered diatonic chord is an operation you perform on a default diatonic chord. 

Use case: They are used in song improvisation and composition to indicate where a song comes out of key.

Definition: ->

Name: Transformation symbol.

Description: Used when moving from one key to another key signature after a altered diatonic chord operation. The transformation are the operations you need to perform.

Use case: When composing music, coming out of key will make the music more interesting. Understanding how the music comes out of key gives you more options to decide on the new direction taken.

Definition: [Initial Key Signature][(Operation1,Operation2,...)]->[Key Signature]

Name: Transformation operations.

Description: You have an initial key signature, then you perform a altered diatonic chord operation to transform into another key signature.

Examples:
Eb(IIM)->Bb 

Eb(IIM, VIM)->F

Eb(IIM, VIM, IIIM) ->C

Eb(IIM)->F 

C(IIM)->G 

C(IIM, VIM)->D

C(IIM, VIM, IIIM) ->A

C(Vm)->F

C(Vm, Im)->Bb

C(Vm, Im, IVm)->Eb

Example 1

Any minor chord has three associated modes which exist. in three key signatures 

bIm has three pure transformation solutions for all twelve keys.

• Ionian -> Dorian

• Ionian -> Phrygian

• Ionian -> Aeolian

bIm has three keyed transformation solutions starting in the key of C

• C Ionian key C -> Bm Phrygian Key G

• C Ionian key C -> Bm Aeolian Key D

• C Ionian key C -> Bm Dorian Key A

Example 2

Vm has three pure transformation solutions for all twelve keys.

• Mixolydian -> Dorian

• Mixolydian -> Aeolian

• Mixolydian -> Phrygian

Vm has three keyed transformation solutions starting in the key of C

• G Mixolydian key C -> Gm Dorian key F

• G Mixolydian key C -> Gm Aeolian key Bb

• G Mixolydian key C -> Gm Phrygian key Eb