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    how are major scales built?

    Posted by paco on 5/29/2003, 1:06 pm

    I'm not an expert in music theory, but I want to share with you what I've learned about scales and hopefully you find it useful as well. I used to think this deal about scales and chords was some kind of black magic, but it really isn't.

    To build the major scales, first, we have to start with the chromatic scale. The chromatic scale is made up of 12 notes separated by half-steps or semi-tones. Here is the chromatic scale:
    1. C 2. C# 3. D 4. D# 5. E 6. F 7. F# 8. G 9. G# 10. A 11. A# 12. B

    It can also continue on indefinitely with the same 12 notes repeating over and over:
    C-C#-D-D#-E-F-F#-G-G#-A-A#-B-c-c#-d-d#-e-f-f#-g-g#-a-a#-b-c-c#-d-d#-e...

    On a piano, keyboard or piano accordion, these notes are arranged one after the other, repeating as many times as the instrument has octaves.

    Now, a major scale is made up of 7 unique notes from the chromatic scale. But which 7 notes?

    The following formula tells you which 7 notes to use: '2-2-1-2-2-2-1'. Each number represents how many half-steps there are between notes on the major scale.

    ---------------------------------------------------------
    EXAMPLE #1:
    ---------------------------------------------------------

    Let's say that we want to construct the C-major scale. So our first note will be: C
    C-major scale: 1.C,

    Now, according to our formula, the second note will be 2 half-steps away from the 1st note, so our 2nd note on the C-major scale will be [C + 2 half-steps] (C, C#, D):
    C-major scale: 1.C, 2.D,

    The third note on the C-major scale is 2 half-steps away from the second note so [D + 2 half-steps] (D, D#, E):
    C-major scale: 1.C, 2.D, 3.E

    The fourth note on the C-major scale is 1 half-step away from the 3rd note so [E + 1 half-step] (E, F):
    C-major scale: 1.C, 2.D, 3.E, 4.F

    The fifth note on the C-major scale is 2 half-steps away from the 4th note so [F + 2 half-steps] (F, F#, G):
    C-major scale: 1.C, 2.D, 3.E, 4.F, 5.G

    The sixth note on the C-major scale is 2 half-steps away from the 5th note so [G + 2 half-steps] (G, G#, A):
    C-major scale: 1.C, 2.D, 3.E, 4.F, 5.G, 6.A

    The seventh note on the C-major scale is 2 half-steps away from the 6th note so [A + 2 half-steps] (A, A#, B):
    C-major scale: 1.C, 2.D, 3.E, 4.F, 5.G, 6.A, 7.B

    The eighth note on the c-major scale is 1 half-step away from the 7th note so [B + 1 half-step] (B, c):
    C-major scale: 1.C, 2.D, 3.E, 4.F, 5.G, 6.A, 7.B, 8.c

    The eighth note on any major scale will be the same as the 1st note, but one octave higher. The scale can continue on indefinitely with the same 7 notes repeated over and over.

    Here is our final result:
    formula:---------2---2---1---2---2---2---1
    C-major scale: C---D---E---F---G---A---B---c

    ---------------------------------------------------------

    Applying this same formula (2-2-1-2-2-2-1), let's build the G-major scale:
    formula:----------2---2---1---2---2---2----1
    G-major scale: G---A---B---C---D---E---F#---g

    and the E-major scale:
    formula:---------2-----2----1----2---2----2-----1
    E-major scale: E---F#---G#---A---B---C#---D#---e

    ---------------------------------------------------------

    In this same manner, you can build any major-scale using this pattern (2-2-1-2-2-2-1) and the chromatic scale.

    The natural minor scale is built similar to the major scale but follows a different formula: (2-1-2-2-1-2-2)

    Let's apply this formula (2-1-2-2-1-2-2), to build the A-minor scale:
    formula:---------2---1---2---2---1---2----2
    A-minor scale: A---B---C---D---E---F---G---a

    and the E-minor scale:
    formula:---------2----1----2---2---1----2----2
    E-minor scale: E---F#---G---A---B---C---D---e


    Now, you'll notice that the C-major scale and the A-minor scale use the same notes. Likewise, the G-major scale and the E-minor scale share the same notes. So really, if you know the major scale for 1 key, you also know the minor scale of another key. Which one?

    Here's the C-major scale again (this time the numbers indicate the note sequence or degree of the scale):
    sequence:-----1---2---3---4---5---6---7---8
    C-major scale: C---D---E---F---G---A---B---c

    'A' happens to be the 6th note or degree of the C-major scale.

    For the G-major scale:
    sequence:-----1---2---3---4---5---6----7----8
    G-major scale: G---A---B---C---D---E---F#---g

    'E' happens to be the 6th note/degree of the G-major scale.

    So, for any major scale, the sixth note will help you find the relative minor scale of that major scale.

    There are other minor scales (harmonic minor, melodic minor) which are built using different patterns. You can read more at these sites which I've found to be invaluable sources of information:
    http://www.teoria.com/referencia/
    http://www.teoria.com/reference/

    regards,
    francisco