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There are 49 functions of all notes (F, C, G, D, A, E, B, etc). I've been told by guys with music degrees who spend most of their time learning about the history of Gregorian Chants (and the like) that it isn't relevant. And maybe you'll agree, but in my mind if you can solve the X as the Y degree of scale Z, you pretty much know what you're doing, Personally, it advanced my knowledge of modes, positional playing, and the circle of fifths/fourths.

It's probably best to tell you that the X is what note you are focusing on, the Y has 7 degrees, and that the note X is only in 7 Z scales. 7*7=49

The awesome part is that you have to memorize scale formulas (not just patterns) to solve the equation. I'm thinking if you have a reason to memorize the things you'll be more than willing to put forth the effort. To be honest, guitar players can make do without knowing such things. It really has a lot to do with your personality (the way you learn). I have no problem whatsoever with patterns.

There are 7 modes. Ionian (major), Dorian, Phrygian, Lydian, Mixolydian, Aeolian (minor), and Locrian. Respectively, they are assigned the numbers 1, 2, 3, 4, 5, 6, and 7.

Ionian - 1

Dorian - 2

Phrygian - 3

Lydian - 4

Mixolydian - 5

Aeolian - 6

Locrian - 7

Therefore, we can never go over the number 7. Even though the equation sometimes add up to over 7. If that's the case we subtract a 7.

1 + 4 = 5

2 + 3 = 5

3 + 2 = 5

4 + 1 = 5

5 + 0 = 5

6 + 6 = 12 - 7 = 5

7 + 5 = 12 - 7 = 5

Also, MENTALLY we have to think of the second number in the equation with and additional 1 added to it. As we are dealing with more than 6 modes.

1 + 4(5) = 5

2 + 3(4) = 5

3 + 2(3) = 5

4 + 1(2) = 5

5 + 0(1) = 5

6 + 6(7) = 5

7 + 5(6) = 5

When we write it out it would be...

1st of Z Mixolydian = C Mixolydian

2nd of Z Lydian = C Mixolydian

3rd of Z Phrygian = C Mixolydian

4th of Z Dorian = C Mixolydian

5th of Z Ionian = C Mixolydian

6th of Z Locrian = C Mixolydian

7th of A Aeolian = C Mixolydian

Solve for Z.

Choose a core note.

C

Choose an equation.

3+2

3rd of Z Phrygian = C Mixolydian

The formula for Mixolydian is 1 2 3 4 5 6 7

Apply to C major

C D E F G A Bb

What scale has only one flat?

F G (A) Bb C D E

Z=A

The 3rd of A Phrygian = C Mixolydian

Learn formulas for...

Ionian - 1 2 3 4 5 6 7

Dorian - 1 2b 3 4 5 6 7b

Phrygian - 1 2b 3b 4 5 6b 7b

Lydian - 1 2 3 4# 5 6 7

Mixolydian - 1 2 3 4 5 6 7b

Aeolian - 1 2 3b 4 5 6b 7b

Locrian - 1 2b 3b 4 5b 6b 7b

Learn that the...

key of C is C D E F G A B

key of Bb is Bb C D Eb F G A

key of Ab is Ab Bb C Db Eb F G

key of G is G A B C D E F#

key of F is F G A Bb C D E

key of Eb is Eb F G Ab Bb C D

key of Db is Db Eb F G Ab Bb Cb

The note C is on the circle of fourths/fifths within the following keys.

That should cover all 49 functions for the core note C.

It's probably best to tell you that the X is what note you are focusing on, the Y has 7 degrees, and that the note X is only in 7 Z scales. 7*7=49

The awesome part is that you have to memorize scale formulas (not just patterns) to solve the equation. I'm thinking if you have a reason to memorize the things you'll be more than willing to put forth the effort. To be honest, guitar players can make do without knowing such things. It really has a lot to do with your personality (the way you learn). I have no problem whatsoever with patterns.

There are 7 modes. Ionian (major), Dorian, Phrygian, Lydian, Mixolydian, Aeolian (minor), and Locrian. Respectively, they are assigned the numbers 1, 2, 3, 4, 5, 6, and 7.

Ionian - 1

Dorian - 2

Phrygian - 3

Lydian - 4

Mixolydian - 5

Aeolian - 6

Locrian - 7

Therefore, we can never go over the number 7. Even though the equation sometimes add up to over 7. If that's the case we subtract a 7.

1 + 4 = 5

2 + 3 = 5

3 + 2 = 5

4 + 1 = 5

5 + 0 = 5

6 + 6 = 12 - 7 = 5

7 + 5 = 12 - 7 = 5

Also, MENTALLY we have to think of the second number in the equation with and additional 1 added to it. As we are dealing with more than 6 modes.

1 + 4(5) = 5

2 + 3(4) = 5

3 + 2(3) = 5

4 + 1(2) = 5

5 + 0(1) = 5

6 + 6(7) = 5

7 + 5(6) = 5

When we write it out it would be...

1st of Z Mixolydian = C Mixolydian

2nd of Z Lydian = C Mixolydian

3rd of Z Phrygian = C Mixolydian

4th of Z Dorian = C Mixolydian

5th of Z Ionian = C Mixolydian

6th of Z Locrian = C Mixolydian

7th of A Aeolian = C Mixolydian

Solve for Z.

Choose a core note.

C

Choose an equation.

3+2

3rd of Z Phrygian = C Mixolydian

The formula for Mixolydian is 1 2 3 4 5 6 7

Apply to C major

C D E F G A Bb

What scale has only one flat?

F G (A) Bb C D E

Z=A

The 3rd of A Phrygian = C Mixolydian

Learn formulas for...

Ionian - 1 2 3 4 5 6 7

Dorian - 1 2b 3 4 5 6 7b

Phrygian - 1 2b 3b 4 5 6b 7b

Lydian - 1 2 3 4# 5 6 7

Mixolydian - 1 2 3 4 5 6 7b

Aeolian - 1 2 3b 4 5 6b 7b

Locrian - 1 2b 3b 4 5b 6b 7b

Learn that the...

key of C is C D E F G A B

key of Bb is Bb C D Eb F G A

key of Ab is Ab Bb C Db Eb F G

key of G is G A B C D E F#

key of F is F G A Bb C D E

key of Eb is Eb F G Ab Bb C D

key of Db is Db Eb F G Ab Bb Cb

The note C is on the circle of fourths/fifths within the following keys.

That should cover all 49 functions for the core note C.