Sunday, May 17, 2015

Formulae for Key Signatures: Major & Minor

Memorizing key signatures in major and minor keys is often made more difficult a task than it really should be.  My advice, don't try to memorize the individual scales at all. Just memorize the simple 4-step formula for constructing scales and finding the next scale on the circle of fifths.
As with all of my exercises, it is important to SING the pitches as you write them out - YES you must both WRITE and SING for this exercise to be effective - THEN play them on your instrument.
[*N.B. remember that the Major and minors scales are septatonic: in that they have 7 distinct pitches [A,B,C,D,E,F,G]. Each pitch carries a specific and unique musical meaning within the context of that particular key signature. (i.e. the pitch "A" the key of G Major carries a unique meaning distinct from the pitch "A" in the key of C Major (or any other key for that matter).  An interval is the measured distance between any two pitches.]

Key Signature Forumulae
1)   All major scales abide by the same stepwise intervallic formula of Whole and Half steps.

W-W-H-W-W-W-H

2)   In every major scale, The half steps (H) ALWAYS fall between the 3-4 and 7-1 scale degrees. (I don't use "8" to differentiate octave, I just start over with "1")

Formula for Sharp keys (raise the leading tone)
Key signatures using SHARPS move clockwise around the Circle of 5ths (i.e. up a 5th or down a 4th on a scale)

1) With the first scale (in this case “C major” in which C is the tonic) go up to the 5th degree. [In other words each new scale will begin on the 5th degree of the preceding scale. These keys are C, G, D, A, E, B, F#, C#]

2) The dominant (5th degree) of the preceeding scale becomes the tonic (1st degree) of the NEW scale (e.g. in C major, C is the 1st and G is the 5th degree.  -

3)  By doing this, the half step between the leading tone and tonic (7-1) of the preceeding scale becomes the mediant-subdominant (3-4) half step of the new scale on the circle of 5th. (e.g. B-C which is 7-1 in the key of C; becomes 3-4 in the key of G.)

4) Finally raise (sharp) the 7th degree to create the leading tone – tonic half step.


SCALE DEGREE
1
2
3
4
5
6
7
1
no sharps
C
D
E
F
G
A
B
C
F#
G
A
B
C
D
E
F#
G
F#, C#
D
E
F#
G
A
B
C#
D
F#, C#, G#
A
B
C#
D
E
F#
G#
A
F#, C#, G#, D#
E
F#
G#
A
B
C#
D#
E
F#, C#, G#, D#, A#
B
C#
D#
E
F#
G#
A#
B
F#, C#, G#, D#, A#, E#
F#
G#
A#
B
C#
D#
E#
F#
F#, C#, G#, D#, A#, E#, B#
C#
D#
E#
F#
G#
A#
B#
C#



Forumla for Flat keys (lower the 4th degree)
Key signatures using FLATS go counter-clockwise around the Circle of 5ths (i.e. down a 5th or up a 4th)

1) The 4th degree of the preceeding scale becomes the 1st degree of the NEW scale (e.g. in C major, C is the 1st and F is the 4th degree.) - These keys are C, F, Bb, Eb, Ab, Db, Gb, Cb

2) By doing this, the 3-4 half step of the 1st scale becomes the 7-1 half step of the next scale on the circle of 5ths. (i.e. E-F is the 3-4 in the key of C; it becomes 7-1 in the key of F.)

3) Lower the 4th degree of the new scale (i.e. in the key of F, lower B to Bb to create 3-4 half step)

SCALE DEGREE
1
2
3
4
5
6
7
1
no flats
C
D
E
F
G
A
B
C
flat: b
F
G
A
Bb
C
D
E
F
flats b, e
Bb
C
D
Eb
F
G
A
Bb
flats: b, e, a
Eb
F
G
Ab
Bb
C
D
Eb
flats: b, e, a, d
Ab
Bb
C
Db
Eb
F
G
Ab
flats: b, e, a, d, g
Db
Eb
F
Gb
Ab
Bb
C
Db
flats: b, e, a, d, g, c
Gb
Ab
Bb
Cb
Db
Eb
F
Gb
flats: b, e, a, d, g, c, f
Cb
Db
Eb
Fb
Gb
Ab
Bb
Cb



Finding the relative minor

The relative minor key to any major key begins on the sub-mediant (6th degree) of a given major scale. (e.g. in C major, the 6th degree is  “A”. 

The 6th degree becomes the new 1 of the minor scale.
The 1st degree becomes the new 3.

*please note, the following tables
SCALE DEGREE
1
2
3
4
5
6
7
1
C major/ a minor
no accidentals
C
D
E
F
G
A
B
C
G major / e minor
F#
G
A
B
C
D
E
F#
G
D major / b minor
F#, C#
D
E
F#
G
A
B
C#
D
 A major / f# minor
F#, C#, G#
A
B
C#
D
E
F#
G#
A
 E major / c# minor
F#, C#, G#, D#
E
F#
G#
A
B
C#
D#
E
 B major / g# minor
F#, C#, G#, D#, A#
B
C#
D#
E
F#
G#
A#
B
 F# major / d# minor
F#, C#, G#, D#, A#, E#
F#
G#
A#
B
C#
D#
E#
F#
 C# major / a# minor
F#, C#, G#, D#, A#, E#, B#
C#
D#
E#
F#
G#
A#
B#
C#

SCALE DEGREE
1
2
3
4
5
6
7
1
C major / a minor
no accidentals
C
D
E
F
G
A
B
C
F major / d minor
flats: b
F
G
A
Bb
C
D
E
F
Bb major / g minor
flats: b, e
Bb
C
D
Eb
F
G
A
Bb
Eb major / c minor
flats: b, e, a
Eb
F
G
Ab
Bb
C
D
Eb
Ab major / f minor
flats: b, e, a, d
Ab
Bb
C
Db
Eb
F
G
Ab
Db major / bb minor
flats: b, e, a, d, g
Db
Eb
F
Gb
Ab
Bb
C
Db
Gb major / eb minor
flats: b, e, a, d, g, c
Gb
Ab
Bb
Cb
Db
Eb
F
Gb
 Cb major / ab minor
flats: b, e, a, d, g, c, f
Cb
Db
Eb
Fb
Gb
Ab
Bb
Cb


1 comment:

  1. Break down the intervallic formula of W-W-H-W-W-W-H into two groups of W-W-H separated by a whole step. Then count on the fingers of each hand scale degrees, 1-2-3-4 (index, middle, ring, pinky - with the half steps between the ring and pinky) on one hand, and 5-6-7-1(8) on the other.

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