Major and Natural Minor Scales
...and "diatonic" modes in general...
The circle of 4ths/5ths - since there are a million very nice versions you can find via google, I won't recreate one here. Instead, here is the theory behind it:
The order of flats is BEADGCF
The order of sharps is FCGDAEB (notice it is the order of flats, but reversed)
For major scales, if you start on C, you're at 0 sharps/0 flats. If you move up in 5ths:
C-->G-->D-->A-->E-->B-->F#-->C#
...add one sharp each step. For example, in B Major: If C is 0, G is 1, etc., B is 5, and your 5 sharps are F#,C#,G#,D#, and A# (from the order of sharps).
Or, if you move up in 4ths:
C-->F-->Bb-->Eb-->Ab-->Db-->Gb-->Cb
...add one flat each step. For example, in Db Major: If C is 0, F is 1, etc., Db is 5, and your 5 flats are Bb, Eb, Ab, Db, and Gb (from the order of flats).
Now, the next very important rule: in diatonic scales (i.e., major and its modes), you use each note in the musical alphabet (ABCDEFG) once, exactly once - no more than once.
If you want to find your key signature, look at the two sequences above, find your number of accidentals, figure out your sharps or flats, then go down the alphabet. For example, E major:
E major is 4 sharps (C=0, G=1, D=2, A=3, E=4). The 4 sharps are F#,C#,G#, and D#.
Writing it out with the musical alphabet, we get:
E F# G# A B C# D# E
Another example, Db Major:
Db Major is 5 flats (C=0, F=1, Bb=2, Eb=3, Ab=4, Db=5)
Writing it out with the musical alphabet, we get:
Db Eb F Gb Ab Bb C Db
It is important to note that the Db major scale used Gb, NOT F# - you cannot have an F# and an F natural in the same diatonic scale!
The order of flats is BEADGCF
The order of sharps is FCGDAEB (notice it is the order of flats, but reversed)
For major scales, if you start on C, you're at 0 sharps/0 flats. If you move up in 5ths:
C-->G-->D-->A-->E-->B-->F#-->C#
...add one sharp each step. For example, in B Major: If C is 0, G is 1, etc., B is 5, and your 5 sharps are F#,C#,G#,D#, and A# (from the order of sharps).
Or, if you move up in 4ths:
C-->F-->Bb-->Eb-->Ab-->Db-->Gb-->Cb
...add one flat each step. For example, in Db Major: If C is 0, F is 1, etc., Db is 5, and your 5 flats are Bb, Eb, Ab, Db, and Gb (from the order of flats).
Now, the next very important rule: in diatonic scales (i.e., major and its modes), you use each note in the musical alphabet (ABCDEFG) once, exactly once - no more than once.
If you want to find your key signature, look at the two sequences above, find your number of accidentals, figure out your sharps or flats, then go down the alphabet. For example, E major:
E major is 4 sharps (C=0, G=1, D=2, A=3, E=4). The 4 sharps are F#,C#,G#, and D#.
Writing it out with the musical alphabet, we get:
E F# G# A B C# D# E
Another example, Db Major:
Db Major is 5 flats (C=0, F=1, Bb=2, Eb=3, Ab=4, Db=5)
Writing it out with the musical alphabet, we get:
Db Eb F Gb Ab Bb C Db
It is important to note that the Db major scale used Gb, NOT F# - you cannot have an F# and an F natural in the same diatonic scale!
But what about natural minor scales?
They're the same, except they start on a different note. This is because the are modes of the major scale.
Each major scale has a relative minor, and vice versa. The relative minor of a major scale is the scale starting on the 6th note of a major scale, using the same key signature. The relative major of a minor scale is the scale starting on the 3rd note of a minor scale. For example:
The relative minor of C major is A minor (CDEFGA --> A is the sixth note), and it has no flats or sharps.
The relative major of D minor is F major (DEF --> F is the sixth note), and it has one flat.
The only difference between the circles for majors and natural minors is which note goes on top - for majors it is "C", for minors it is "a" (note: It is a common convention to use capital letters to represent major and lower case letters to represent minor).
Each major scale has a relative minor, and vice versa. The relative minor of a major scale is the scale starting on the 6th note of a major scale, using the same key signature. The relative major of a minor scale is the scale starting on the 3rd note of a minor scale. For example:
The relative minor of C major is A minor (CDEFGA --> A is the sixth note), and it has no flats or sharps.
The relative major of D minor is F major (DEF --> F is the sixth note), and it has one flat.
The only difference between the circles for majors and natural minors is which note goes on top - for majors it is "C", for minors it is "a" (note: It is a common convention to use capital letters to represent major and lower case letters to represent minor).