We're going to take a systematic approach to discover alternative key signatures and modes for each bar. The sheet music is in the key of Eb, however the melody may be represented as a harmonic interval series, a scale in which may blend with other key signatures.

An important observation in this examination is the actual physical notes as seen on the sheet music will note change, we're not going to transpose the music although we can easily do so, we're going to discover all modes and key signatures the above absolute notes will feel comfortable to determine possible solutions for the musical direction of the music.

Step 1: You need to decide on the root note of the melody. For this method, you'll use the lowest note in the melody, the note G as the root note 1.

Step 2: All the unique notes are, Ab, B, C and D.

Step 3: Using G as the reference find all the interval to produce the following harmonic formula.

Harmonic formula: 1 -2 3 4 5

A harmonic  formula is key independent, it's possible to transpose this pattern into any of the twelve notes on the piano, however here we'll only transpose the pattern into the key of C, C being the root note 1 while we discover the pure modal scale. Once we have a pure modal scale, we can transpose it back having the root note G. 

Step 4: Using the harmonic formula, put your head into the key of C, all the white notes. This is going to help you find all seven pure modal scales. Start with Ionian 1 2 3 4 5 6 7 and ask yourself, what operations do you need to perform resulting in the harmonic formula of step 2? Looking down at the keyboard will help because you can easily read the intervals when your head is reference in the key of C.

To get from Ionian having harmonic formula 1 2 3 4 5 6 7 -> 1 -2 3 4 5

-> = b2 R6 R7

To get from Dorian having harmonic formula 1 2 -3 4 5 6 -7 -> 1 -2 3 4 5

-> = b2 #-3 R6 R-7

To get from Phrygian having harmonic formula 1 -2 -3 4 5 +5 -7 -> 1 -2 3 4 5

-> = #-3 R+5 R-7

To get from Lydian having harmonic formula 1 2 3 -5 5 6 7 -> 1 -2 3 4 5

-> = b2 b-5 R6 R7

To get from Mixolydian having harmonic formula 1 2 3 4 5 6 -7 -> 1 -2 3 4 5

-> = b-2 R6 R-7

To get from Aeolian having harmonic formula 1 2 -3 4 5 +5 -7 -> 1 -2 3 4 5

-> = b-2 #-3 R+5 R-7

To get from Lydian having harmonic formula 1 -2 -3 4 -5 +5 -7 -> 1 -2 3 4 5

-> = #-3 #-5 R+5 R-7

All modal scales: 

Ionian b2 R6 R7

Dorian b2 #-3 R6 R-7

Phrygian #-3 R+5 R-7 

Lydian b2 b-5 R6 R7 

Mixolydian b-2 R6 R-7 

Aeolian b-2 #-3 R+5 R-7 

Locrian #-3 #-5 R+5 R-7

The  the above pure modal scales have the exact same harmonic formula of 1 -2 3 4 5. All the possible keyed modal scales when G is the root note are;

All keyed modal scales: 

G Ionian b2 R6 R7 Key G

G Dorian b2 #-3 R6 R-7 Key F

G Phrygian #-3 R+5 R-7 Key Eb

G Lydian b2 b-5 R6 R7 Key D

G Mixolydian b-2 R6 R-7 Key C

G Aeolian b-2 #-3 R+5 R-7 Key Bb

G Locrian #-3 #-5 R+5 R-7 Key Ab

There are seven modal descriptions for bar 1, choose the ones with the lease amount of operations. Remove operations are easy to deal with, you simply don't play the notes. You can see from the notation the maximum spread for the interval distance is a fifth, so the remove operation make perfect sense. 

G Ionian b2 R6 R7 Key G

G Phrygian #-3 R+5 R-7 Key Eb

G Mixolydian b-2 R6 R-7 Key C

By removing the remove operations,  you have removed clutter and pure modal scale is very simple, only one operation from a known mode. If this was your composition and you only had one bar, you now have options for the next bar of music in terms of the key signature and mode. 

G Ionian b2 Key G

G Phrygian #-3 Key Eb

G Mixolydian b-2 Key C

Chosen Keyed Modal Scale:  G Ionian b2 R6 R7

Key Signature: G

Possible Chords Choices: G, C

Possible Modal Direction: G Phrygian #-3 R+5 R-7 Key Eb

, G Mixolydian b-2 R6 R-7 Key C

Possible Key Changes: Eb, C

Possible Chord Movement:

Beat Pattern: |b_bb;b_b_;b_bb;b_b_|

Finger Placement Exercise:

G < RR4 M3 >R4 <T1 >I-2 R4 <M3 >R4 P5

Suggest chords and intervals

G           G

  4 3 4 1   2 4 3 4 5

Beat Pattern: |__bb;b_b_;b_bb;b_b_|

G Ionian b2 Key G

Timed box chords:

|G                              |

|_ _ 4 3|4 _ 1 _|2 _ 4 3|4 _ 5 _|

Root Note: C

Notes:            C D G  Ab B

Harmonic formula: 1 2 5 +5  7

Because we chose the note C as the root, the harmonic interval series is different. 

To get from Ionian having harmonic formula 1 2 3 4 5 6 7 -> 1 2 5 +5 7

-> = R3 R4 b6

To get from Dorian having harmonic formula 1 2 -3 4 5 6 -7 -> 1 2 5 +5 7

-> = R-3 R4 b6 #-7

To get from Phrygian having harmonic formula 1 -2 -3 4 5 +5 -7 -> 1 2 5 +5 7

-> = #-2 R-3 R4 #-7

To get from Lydian having harmonic formula 1 2 3 -5 5 6 7 -> 1 2 5 +5 7

-> = R3 R-5 b6

To get from Mixolydian having harmonic formula 1 2 3 4 5 6 -7 -> 1 2 5 +5 7

-> = R3 R4 b6 #-7

To get from Aeolian having harmonic formula 1 2 -3 4 5 +5 -7 -> 1 2 5 +5 7

-> = R-3 R4 #-7

To get from Lydian having harmonic formula 1 -2 -3 4 -5 +5 -7 -> 1 2 5 +5 7

-> = #-2 R-3 R4 #-5 #-7

All modal scales: All these pure modal scales have the exact same harmonic formula 1 2 5 +5 7

Ionian R3 R4 b6

Dorian R-3 R4 b6 #-7

Phrygian #-2 R-3 R4 #-7

Lydian R3 R-5 b6

Mixolydian R3 R4 b6 #-7

Aeolian R-3 R4 #-7

Locrian #-2 R-3 R4 #-5 #-7

Keyed Modal scales having root C:

C Ionian R3 R4 b6 Key C

C Dorian R-3 R4 b6 #-7 Key Bb

C Phrygian #-2 R-3 R4 #-7 Key Ab

C Lydian b2 R3 R-5 b6 Key G

C Mixolydian R3 R4 b6 #-7 Key F

C Aeolian R-3 R4 #-7 Key Eb

C Locrian #-2 R-3 R4 #-5 #-7 Key Db

Chosen Keyed Modal Scale:  Cm Aeolian R-3 R4 #-7

Key Signature: Eb

Chords: C5,C5M7,C5b6,C5add2,C5M7b6,C5M7b6Add2

Possible Modal Direction: C Ionian b2 R6 R7, C Lydian b2 b-5 R6 R7

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: |b_bb;b_b_;b_bb;b_b_|

Finger Placement Exercise:

C < RR1 M7 >R1 <T5 >I+5 R1 <M7 >R1 P2

Observations: Regardless  of what interval we choose as the root, you'll always end up with the same physical notes played. When modes are transposed, you always have the same notes, but different harmonic formulas. The possible direction for the song  will be to move into the key of C or the key of G. Removing the minor third interval is removing primary character leaving plenty of ambiguity. From the finger placement exercise you can see the second interval is used to lead into the next bar. There is a strong major seventh character across the bar. Finger placement exercises don't contain beat or melodic direction making it easier to visualise and analyse the interval choices. The melodic direction and beat can analysed separately if desired, here we're only extracting modal information. 

Important Observation: By removing the remove operations R for the other modal alternatives, choices are offered for the music direction. Let's investigate and see where this piece of music is going using the above analysis techniques. 

Suggest chords and intervals

C             C

  1 7 1 5    +5 1 7 1 2 

Beat Pattern: |__bb;b_b_;b_bb;b_b_|

Chosen Keyed Modal Scale: C Aeolian R-3 R4 #-7

Timed box chords:

|C                               |

|_ _ 1 7|1 _ 5 _|+5 _ 1 7|1 _ 2 _|

Root Note: C

Harmonic formula: 1 2 4 5 +5 7

All modal scales: 

Ionian R3 b6 

Dorian R-3 b6 #-7 

Phrygian #-2 R-3 #-7 

Lydian R3 b-5 b6 

Mixolydian R3 b6 #-7 

Aeolian R-3 #-7 

Locrian #-2 R-3 #-5 #-7

Keyed Modal scales having root C:

C Ionian R3 b6 Key C

C Dorian R-3 b6 #-7 Key Bb

C Phrygian #-2 R-3 #-7 Key A

C Lydian R3 b-5 b6 Key G

C Mixolydian R3 b6 #-7 Key F

C Aeolian R-3 #-7 Key Eb

C Locrian #-2 R-3 #-5 #-7 Key Db

Chosen Keyed Modal Scale:  C Aeolian R-3 #-7

Key Signature: Eb

Chords: Csus4,Csus4,Csus4M7,Csus4b6,Csus4add2,Csus4M7b6,Csus4M7b6Add2

Possible Modal Direction: C Ionian b6

Possible Key Changes: C

Possible Chord Movement: C, Cm, Eb, Fm, G

Beat Pattern: |b_bb;b_b_;bb_b;b_bb|

Finger Placement Exercise:

C > RI5 R1 <M7 >R1 P2 <T4 I5 M+5 I5 T4

Observations: The possible direction for the song  will be to move into the key of C  ruling out the key of G as the note F was introduced. 

Root Note: C

Notes:            C D Eb F  F# G  A  B

Harmonic formula: 1 2 -3 4 -5  5  6  7

Let's see what the Ian Ring chord finder calls this scale?

It's called a Bebop Melodic Minor.

All modal scales:

Ionian b3 A-5

Dorian A-5 #-7

Phrygian #-2 A-5 #+5 #-7

Lydian b3 A4 

Mixolydian b3 A-5 #-7

Aeolian A-5 #+5 #-7

Locrian #-2 b+5 b-7 A7

Keyed Modal scales having root C:

C Ionian b3 A-5 Key C

C Dorian A-5 #-7 Key Bb

C Phrygian #-2 A-5 #+5 #-7 Key Ab

C Lydian b3 A4 Key G

C Mixolydian b3 A-5 #-7 Key F

C Aeolian A-5 #+5 #-7 Key Eb

C Locrian #-2 b+5 b-7 A7 Key Db

Any note may be the root, however by making the root C, the physical location of the notes on the piano will be exactly the same as the notation.

By examining all the keyed modal scales we can determine the easiest way to describe the scales. The keyed modal scales with the least operations are;

C Ionian b3 A-5 Key C

C Dorian A-5 #-7 Key Bb

C Lydian b3 A4 Key G

It is interesting to observe the notation is in the key of Eb yet the Aeolian scale has three operations and isn't the best way to describe this bar of music. This is understandable since Bach decided to naturalise the notes Bb and Ab and include a F# for this bar.

Key Signature: C

Chords: Cm, Cdim, CmAdd6, CmM7, G, GM7

Chosen Pure Modal Scale: Ionian b3 A-5

Chosen Keyed Modal Scale:  C Ionian b3 A-5 Key C

Possible Modal Direction: C Lydian b3 A4 Key G, C Dorian A-5 #-7 Key Bb

Possible Key Changes: G, Bb

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

C <         RR5 M-5 >R5    <T1     >I-3 M5 <I-5 >M5 R6

C > LP-3 T1 <I7  I6   T5  I4 M-3 R2  P1  T-3      I2 M1

Observations: For the third bar, the better choice and easiest to remember when playing in real time is the the C Ionian b3 A-5. When playing this patten, you just play the C major scale and just flatten the second. Additions are easy, adding the note F#.  At first glace you would have never guessed bar three could be described as C Ionian b3 A-5.

Root Note:F#

Notes: F# G A Bb C D Eb 

Harmonic formula: 1 -2 -3 3 -5 +5 6

All modal scales:

Ionian b3 A-3 #4 #5 R7

Dorian b2 b4 b5 A+5 R-7

Phrygian A-3 b4 b5 R-7 

Lydian b2 A-3 #5 R7

Mixolydian b2 A-3 #4 #5 R-7

Aeolian b2 A3 #4 #5 R-7

Locrian b4 #6

All keyed Modal scales: 

 F# Ionian b3 A-3 #4 #5 R7 Key F#

 F# Dorian b2 b4 b5 A+5 R-7 Key E

 F# Phrygian A-3 b4 b5 R-7 Key D

 F# Lydian b2 A-3 #5 R7 Key Db

 F# Mixolydian b2 A-3 #4 #5 R-7 Key B

 F# Aeolian b2 A3 #4 #5 R-7 Key A

 F# Locrian b4 #6 Key G

Key Signature: 

Chords: 

Chosen Pure Modal Scale: 

Chosen Keyed Modal Scale:  

Possible Modal Direction: 

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

Observations: 

Root Note: C

Notes: C D Eb F G Ab A Bb

Harmonic formula: 1 2 -3 4 +5 6 -7

All modal scales:

Ionian b3 #5 b7

Dorian #5 

Phrygian #-2 R5 R6

Lydian b3 #5 

Mixolydian 

Aeolian 

Locrian 

All keyed Modal scales:

 Ionian 

 Dorian 

 Phrygian 

 Lydian 

 Mixolydian 

 Aeolian 

 Locrian 

Key Signature: 

Chords: 

Chosen Pure Modal Scale: 

Chosen Keyed Modal Scale:  

Possible Modal Direction: 

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

Observations: 

Root Note: 

Harmonic formula: 

All modal scales:

Ionian 

Dorian 

Phrygian 

Lydian 

Mixolydian 

Aeolian 

Locrian 

All keyed Modal scales: 

 Ionian 

 Dorian 

 Phrygian 

 Lydian 

 Mixolydian 

 Aeolian 

 Locrian 

Key Signature: 

Chords: 

Chosen Pure Modal Scale: 

Chosen Keyed Modal Scale:  

Possible Modal Direction: 

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

Observations: 

Root Note: 

Harmonic formula: 

All modal scales:

Ionian 

Dorian 

Phrygian 

Lydian 

Mixolydian 

Aeolian 

Locrian 

All keyed Modal scales:

 Ionian 

 Dorian 

 Phrygian 

 Lydian 

 Mixolydian 

 Aeolian 

 Locrian 

Key Signature: 

Chords: 

Chosen Pure Modal Scale: 

Chosen Keyed Modal Scale:  

Possible Modal Direction: 

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

Observations: 

Root Note: 

Harmonic formula: 

All modal scales:

Ionian 

Dorian 

Phrygian 

Lydian 

Mixolydian 

Aeolian 

Locrian 

All keyed Modal scales:

 Ionian 

 Dorian 

 Phrygian 

 Lydian 

 Mixolydian 

 Aeolian 

 Locrian 

Key Signature: 

Chords: 

Chosen Pure Modal Scale: 

Chosen Keyed Modal Scale:  

Possible Modal Direction: 

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

Observations: 

Root Note: 

Harmonic formula: 

All modal scales:

Ionian 

Dorian 

Phrygian 

Lydian 

Mixolydian 

Aeolian 

Locrian 

All keyed Modal scales:

 Ionian 

 Dorian 

 Phrygian 

 Lydian 

 Mixolydian 

 Aeolian 

 Locrian 

Key Signature: 

Chords: 

Chosen Pure Modal Scale: 

Chosen Keyed Modal Scale:  

Possible Modal Direction: 

Possible Key Changes:

Possible Chord Movement:

Beat Pattern: 

Finger Placement Exercise:

Observations: