Lesson 31 - Determining key signatures and modes given a collection of notes.

Modal harmonic formulas

The first important bit of information you'll be given is the harmonic interval formulas for all the natural modes in the western major scale. These formulas are easily derived by investigating the intervals within the key of C and writing them down for each mode.

Ionian 1 2 3 4 5 6 7

Dorian 1 2 -3 4 5 6 -7

Phrygian 1 -2 -3 4 5 +5 -7

Lydian 1 2 3 -5 5 6 7

Mixolydian 1 2 3 4 5 6 -7

Aeolian 1 2 -3 4 5 +5 -7

Locrian 1 -2 -3 4 -5 +5 -7

The Process

The process involves writing down all the unique notes within a bar of music. Choose a bass note, this may be any note although the correct note will make life a little easier. Using the bass note as the reference, determine all the harmonic intervals and write down the formula. The final step is to compare all the intervals with the natural modes for best fit and then write down the alteration operations. Let's break this into four easy steps.

Step 1: You need to decide on the root note of the melody. If you are unsure which note to choose, just choose the lowest note and go through the process, in this case it will be the note G.

Step 2: Write down all the unique notes, they are, G, 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 key signatures. The objective is to find the best possible fit for the key signature and mode. Knowing the mode will suggest the chord to use.

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 3? Looking down at the keyboard will help because you can easily read the intervals when your head is referenced in the key of C.

To transform from Ionian having harmonic formula 1 2 3 4 5 6 7 -> 1 -2 3 4 5 ; Ionian b2 R6 R7

To get from Dorian having harmonic formula 1 2 -3 4 5 6 -7 -> 1 -2 3 4 5 ; Dorian b2 #-3 R6 R-7

To transform from Phrygian having harmonic formula 1 -2 -3 4 5 +5 -7 -> 1 -2 3 4 5 ; Phrygian #-3 R+5 R-7

To transform from Lydian having harmonic formula 1 2 3 -5 5 6 7 -> 1 -2 3 4 5 ; Lydian b2 b-5 R6 R7

To transform from Mixolydian having harmonic formula 1 2 3 4 5 6 -7 -> 1 -2 3 4 5 ; Mixolydian b2 R6 R-7

To transform from Aeolian having harmonic formula 1 2 -3 4 5 +5 -7 -> 1 -2 3 4 5 ; Aeolian b2 #-3 R+5 R-7

To transform from Lydian having harmonic formula 1 -2 -3 4 -5 +5 -7 -> 1 -2 3 4 5 ; Locrian #-3 #-5 R+5 R-7

All the pure 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 b2 R6 R-7 

Aeolian b2 #-3 R+5 R-7 

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

All  the above pure modal scales have the exact same harmonic formula of 1 -2 3 4 5.  

Step 5: 

Determine all possible key signatures, when G is the root note. To find the key, you need to know the following.

Ionian is 1.

The key for Dorian is a tone down the keyboard to the root note 1.

The key for Phrygian is a two tones down  the keyboard to the root note 1.

The key for Lydian is a perfect fourth down the keyboard to the root note 1.

The key for Mixolydian is a perfect fifth down the keyboard to the root note 1.

The key for Aeolian is a minor third up the keyboard to the root note 1.

The key for Locrian is a minor second up the keyboard to the root note 1.

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 when they are at the end, 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

Choosing another note as the root note

Let's repeat the above but choose another note as the root note.

Step 1: Let's choose the note C

Step 2: The unique note are, C , D, G, Ab and B.

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

Harmonic formula: 1 2 5 +5 7

 ( Notice how the formula will be different depending on the chosen root note, it's a related mode of the first harmonic formula, not a natural mode, just a mode of the original choice of notes. Remember, to produce a mode of any pattern, you simply keep on inverting the base notes.)

Step 4: 

To transform from Ionian having harmonic formula 1 2 3 4 5 6 7 -> 1 2 5 +5 7 ; Ionian R3 R4 b6

To get from Dorian having harmonic formula 1 2 -3 4 5 6 -7 -> 1 2 5 +5 7 ; Dorian R-3 R4 b6 #-7

To transform from Phrygian having harmonic formula 1 -2 -3 4 5 +5 -7 -> 1 2 5 +5 7 ; Phrygian #-2 R-3 R4 #-7

To transform from Lydian having harmonic formula 1 2 3 -5 5 6 7 -> 1 2 5 +5 7 ; Lydian R3 R4 b5 b6

To transform from Mixolydian having harmonic formula 1 2 3 4 5 6 -7 -> 1 2 5 +5 7 ; Mixolydian R3 R4 b6 #-7

To transform from Aeolian having harmonic formula 1 2 -3 4 5 +5 -7 -> 1 2 5 +5 7 ; Aeolian R-3 R4 b6 #-7

To transform from Lydian having harmonic formula 1 -2 -3 4 -5 +5 -7 -> 1 2 5 +5 7 ; Locrian #-2 R-3 R4 b5 b6 #-7

All the pure modal scales:

Ionian R3 R4 b6

Dorian R-3 R4 b6 #-7

Phrygian #-2 R-3 R4 #-7

Lydian R3 R4 b5 b6

Mixolydian R3 R4 b6 #-7

Aeolian R-3 R4 b6 #-7

Locrian #-2 R-3 R4 b5 b6 #-7

Step 5:

By knowing the following you can determine the key signature.

Ionian is 1.

The key for Dorian is a tone down the keyboard to the root note 1.

The key for Phrygian is a two tones down  the keyboard to the root note 1.

The key for Lydian is a perfect fourth down the keyboard to the root note 1.

The key for Mixolydian is a perfect fifth down the keyboard to the root note 1.

The key for Aeolian is a minor third up the keyboard to the root note 1.

The key for Locrian is a minor second up the keyboard to the root note 1.

All keyed modal scales: 

C Ionian R3 R4 b6 Key C

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

C Phrygian b2 R-3 R4 #-7 Key Ab

C Lydian R3 R4 b5 b6 Key G

C Mixolydian R3 R4 b6 #-7 Key F

C Aeolian R-3 R4 b6 #-7 Key Eb

C Locrian #-2 R-3 R4 b5 b6 #-7 Key Db