Major scale

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In music theory, the major scale (or major mode) is one of the diatonic scales. It is often considered to be made up of seven notes (eight if one includes the octave which is actually the first note of the next octave of the scale). When the octaves are compounded (as they usually are in practice as opposed to the more theoretical concept of the seven-note system), they are considered to be divided into two groups of four, the tetrachords. The pattern of steps in each tetrachord is, in ascending order:

tone, tone, semitone, (tone)

The major scale has seven notes (plus the inclusion of the tonic of the next scale to complete an octave, in practice), which in solfege are the syllables "Do, Re, Mi, Fa, Sol, La, Ti (or Si) (and Do)." The simplest major scale is C major (see figure 1). It is unique in that it is the only major scale not to use sharps or flats on the musical staff and consequently uses only the white notes on the piano keyboard.

Listen to the C major scale.

When writing out major (and minor) scales, every line and space on the stave has to be filled, and no note can have more than one accidental. This has the effect of forcing the key signature to feature just sharps or just flats; ordinary major scales never include both.

The major scale is the same as the Ionian mode.

1 Constructing major scales
2 Note names
3 Harmonic properties
4 Difference between major and minor

[edit] Constructing major scales

To construct any major scale, start with your chosen note (which can be a white or black key on a piano) for the root or starting note; this will be your tonic. Then move up in pitch two notes (without regards to whether the keys are white or black) (referred to as a whole step), up again two notes, up one note, up two notes, up two notes, up two notes, and finally up one note. This is commonly shown as:

 1   2   3   4   5   6   7   8
   W - W - H - W - W - W - H

Above, W means "whole step", which is simply moving up two notes; and H means "half step", which is simply moving up one note. These "steps" in the order shown are how you construct every major scale in western music. The C major scale has no sharps or flats. If you look at a keyboard, you can see that the distance from C to D is two notes, if you count the black key in between them. The distance from D to E is two notes, also counting the black note between them. Then from E to F is only up one note. Therefore, if you wanted to construct the D major scale, you would start by moving up from D to E (two notes) and then from E to F♯ (again two notes) and then from F♯ to G (one note) just exactly the way you did in the C major scale; two whole steps, then a half step. This would be followed by three more whole steps and a half step to complete either the C or D major scale. You use these steps for every major scale: W - W - H - W - W - W - H

[edit] Analysing scales with sharps

Scales and key signatures are closely linked in music. It is necessary to construct a key signature - consisting of a number of sharps or flats - in order to know which notes a particular major scale will have. An easy, but time consuming, way to do this would be to use the pattern of tone/tone/semitone/etc... given above. If we choose to write the scale of D-major, we know immediately that the scale begins on a D. The next note will be a tone above - an E. The note after that will also be a tone above, however it is not simply an F as would seem obvious; because the difference between an E and an F is actually a semitone (look on a piano keyboard, there is no 'black note' in-between them), it is necessary to raise the F so that it becomes an F♯ to achieve a difference of a whole tone.

This could be followed to create a whole scale, with all the sharps (or with a different scale, flats) put correctly in. However a more clever way of constructing scales arises from analysing patterns in the whole series of major scales. Starting with the scale of C major, there exist no sharps or flats. If you start a new scale on the 5th of C major - G major - you will find one sharp, augmenting the F. Starting the scale on the 5th of G major (a D), it will be necessary to put 2 sharps in - an F♯ and a C♯. Writing this pattern out for all the scales looks like this:

C  maj - 0 sharps
G  maj - 1 sharp  - F♯
D  maj - 2 sharps - F♯, C♯
A  maj - 3 sharps - F♯, C♯, G♯
E  maj - 4 sharps - F♯, C♯, G♯, D♯
B  maj - 5 sharps - F♯, C♯, G♯, D♯, A♯
F♯ maj - 6 sharps - F♯, C♯, G♯, D♯, A♯, E♯
C♯ maj - 7 sharps - F♯, C♯, G♯, D♯, A♯, E♯, B♯

In this table it can be seen that for each new scale (starting on the fifth of the previous scale) it is necessary to add a new sharp. The order of sharps which need to be added follows: F♯, C♯, G♯, D♯, A♯, E♯, B♯. This pattern of the sharps can be easily remembered through the use of the following mnemonic:

F       C          G     D     A       E        B       
                                                        
Father  Charles    Goes  Down  And     Ends     Battle

Looking closer, the last accidental added matches the unaltered tonic (first note) of the scale two-fifths before it (in this table, two lines up). A useful rule for use in recognising major scales with sharps is that the tonic is also always one note above the last sharp (for instance, in a major key signature with 4 sharps, the last sharp is D♯, hence the key is a semitone higher: E major).

[edit] Analysing major scales with flats

A similar table can be constructed for major scales with flats in them. In this case each new scale starts on the 5th below the previous one:

C  maj - 0 flats
F  maj - 1 flat  - B♭
B♭ maj - 2 flats - B♭ E♭
E♭ maj - 3 flats - B♭ E♭ A♭
A♭ maj - 4 flats - B♭ E♭ A♭ D♭
D♭ maj - 5 flats - B♭ E♭ A♭ D♭ G♭
G♭ maj - 6 flats - B♭ E♭ A♭ D♭ G♭ C♭
C♭ maj - 7 flats - B♭ E♭ A♭ D♭ G♭ C♭ F♭

Here, a similar pattern can be recognised; each new scale keeps all the flats of the previous scale but adds a new one in the order: B♭, E♭, A♭, D♭, G♭, C♭, F♭. Interestingly this is the direct inverse of the pattern of sharps given above. Luckily (!) the mnemonic can now be reversed to form the sentence:

  F         C          G        D        A        E        B
  Fat     Cows         Go       Dancing  At       Every     Bar

Again there is a similar, but reversed, relationship between tonics and accidentals: the tonic matches the second to last flat added on (for instance, in a major key signature with 4 flats, the penultimate flat is A♭, hence the key is A♭ major). The "sharpest note" rule also works (as for sharps): the note that would be next in the sequence, but that has not been flattened (Amer: "flatted"), is the note immediately below the tonic (again, in a major key signature with 4 flats, the next flat would be the 5th flat, that is, G; as the G is natural, it is the sharpest note, hence the key is a semitone higher: A♭ major).

[edit] The circle of fifths

The information gathered from analysing scales can be used in constructing the circle of fifths:

This is a useful way of finding key signatures of major scales. Starting clockwise from the top C each new letter represents a new scale, a fifth above the one before it. This means that each new scale (clockwise) requires an extra sharp to be added to its key signature. The exact sharps to be added are found by reading off the letters starting from the F (to the left of the C). For example, if we needed to know how many, and which, sharps a scale of E major requires, we note that E is at position 4 - it requires 4 sharps. These sharps are (reading off from F): F♯, C♯, G♯, D♯. If you were faced with a major scale with a key signature of 5 sharps, you would count off 5 from the top to arrive at B - it is the scale of B major.

Fig 2. The B major scale

Similarly, key signatures with flats can be created. Each new letter starting from F represents a new scale, and the position of the letter indicates how many flats it has. The actual flats are read anticlockwise from the B♭ on position 2. B♭ is on position 2, so it has 2 flats: B♭ and E♭.

[edit] Note names

Each of the eight notes in a scale has a name:

1st note - Tonic
2nd note - Supertonic
3rd note - Mediant
4th note - Subdominant
5th note - Dominant
6th note - Submediant
7th note - Leading Tone (or Leading Note)
8th note - Tonic

[edit] Harmonic properties

The major scale may predominate because of its unique harmonic properties. It allows:

three-part major or minor chords, both stable and consonant, on every scale degree but the seventh
a diminished fifth within the seventh chord built on the fifth degree, the dominant
motion by a minor second from the leading tone to the tonic
root motion by perfect fifths, the strongest root motion, from nearly every degree in either direction, the two exceptions being up a perfect fifth from the seventh degree, and down a perfect fifth from the fourth degree
the first six notes of the harmonic series provide a consonant major chord, the fourth to sixth of which form a major triad, and seven of the nine notes between the 8th and 16th harmonics (the 7th and 15th overtones) are notes in the major scale in just intonation