THE MAJOR SCALE.

A major scale is a progression from any tone to its octave in which chromatic steps are omitted between 1 and 2,—2 and 3,—4 and 5,—5 and 6,—6 and 7; from 3 to 4 and from 7 to 8 half steps are made.

Following is a diagram of a two octave keyboard:—

The keyboard shows white and black keys. The black keys are in groups of two and three. As can be seen in the diagram, the white key next to the left of the group of two black keys is c. The white keys in order to the right of c are respectively d, e, f, g, a and b. Following b is a repetition of c at the distance of an octave. Notice that between e and f there is no black key as is also the case between b and c. In these two cases, where no black key separates the white keys, the white keys are one semi-tone apart. Two white keys separated by a black key are one whole step apart. A black key is at the distance of a semi-tone from an adjoining white key. The black keys derive their letter names from the white keys. A black key is named from either of the white keys between which it is situated. The black key between c and d is named c sharp (#) or d flat (b).

Starting at c and sounding the white keys in order to the right as far as the octave produces the ascending major scale of C; sounding in order to the left produces the descending major scale of C. Notice that no black keys are necessary in the case of the C major scale, the whole and half steps being in their proper places; namely, whole steps between 1 and 2, 2 and 3, 4 and 5, 5 and 6, 6 and 7, and half steps between 3 and 4 and between 7 and 8. The student must constantly keep in mind the order of whole and half steps in all scales explained. In each scale explained the letters will be numbered and a curved line will connect those figures representing tones one half step apart.

All major keys except C major require one or more black keys. The number of sharps or flats required for a key is placed at the beginning of the staff and this is called the signature.

A sharp (#) placed before a note raises the tone one half step and a flat (b) lowers a tone one half step.

The sharp keys will be considered first and a sharp major scale will be built from each of the twelve tones.

Rule 1. The Fifth of a Scale is the Tonic (or 1) of the Scale having the next Number of Sharps.

C has no sharps, the fifth of C is g and therefore by following the rule, we find that G has one sharp. The scale of G is as follows:—

G a b c d e f# G
1 2 3∼4 5 6 7∼8

Notice that the seventh of the scale is a black key.

The fifth of G is d and has two sharps:—

D e f# g a b c# D
1 2 3∼4 5 6 7∼8

Notice that f remains sharped and the added sharp is the seventh of the scale. This is always the case, the added sharp is the seventh of the new scale.

The fifth of D is a and has three sharps:—

A b c# d e f# g# A
1 2 3∼ 4 5 6 7∼8

The fifth of A is e and has four sharps:—

E f# g# a b c# d# E
1 2 3∼4 5 6 7∼8

The fifth of E is b and has five sharps:—

B c# d# e f# g# a# B
1 2 3∼4 5 6 7∼ 8

The fifth of B is f# and has six sharps:—

F# g# a# b c# d# e# F#
1 2 3∼4 5 6 7∼ 8

Notice that e# is not a black key but the white key which has been previously considered as f. It must be called e# to retain the alphabetical order.

The fifth of F# is c# and has seven sharps:—

C# d# e# f# g# a# b# C#
1 2 3∼4 5 6 7∼ 8

In this scale all the notes are sharped. The b# as well as the e# is a white key.

The fifth of C# is g# and has eight sharps. This key necessitates one double sharp and f is double sharped. The double sharps are added in the same order that the single sharps are. The double sharp (designated thus: x) raises a tone one whole step.

G# a# b# c# d# e# fx G#
1 2 3∼ 4 5 6 7∼8

The fifth of G# is d# and has nine sharps (two double sharps, f and c):—

D# e# fx g# a# b# cx D#
1 2 3∼4 5 6 7∼8

The fifth of D# is a# and has ten sharps (three double sharps, f, c and g):—

A# b# cx d# e# fx gx A#
1 2 3∼4 5 6 7∼ 8

The fifth of A# is e# and has eleven sharps (four double sharps, f, c, g and d):—

E# fx gx a# b# cx dx E#
1 2 3∼4 5 6 7∼ 8

The fifth of E# is b# and has twelve sharps (five double sharps, f, c, g, d and a):—

B# cx dx e# fx gx ax B#
1 2 3∼4 5 6 7∼ 8

B# has taken us back to our starting key called by a different name.

All twelve keys have now been named with their sharp signatures. To continue counting five would take us over the same keys called by different names. The student is advised to do a little of this for mental discipline. If this is done beyond fourteen sharps, it will be necessary to add triple sharps. Of course, triple sharps are never used in musical notation and such a research would be entirely arithmetical.

The order of the letters in the sharp signature which follows should be committed to memory:—

F C G D A E B.

All keys having one double sharp or more would be difficult to read, and so instead of using the sharp signatures on such keys, the flat signatures are used. All twelve keys with their flat signatures will now be given.

Rule 2. The Fourth of a Scale is the Tonic of the Scale having the Next Number of Flats.

C has no flats; the fourth of C is f; therefore, by following the rule, we find that F has one flat:—

F g a bb c d e F
1 2 3∼4 5 6 7∼ 8

Notice the fourth of the scale is a black key.

The fourth of F is bb and has two flats:—

Bb c d eb f g a Bb
1 2 3∼4 5 6 7∼8

Notice that the b remains flat and that the added flat is the fourth of the scale. This is always the case—the added flat is the fourth of the new scale.

The fourth of Bb is eb and has three flats:—

Eb f g ab bb c d Eb
1 2 3∼4 5 6 7∼ 8

The fourth of Eb is ab and has four flats:—

Ab bb c db eb f g Ab
1 2 3∼4 5 6 7∼8

The fourth of Ab is db and has five flats:—

Db eb f gb ab bb c Db
1 2 3∼4 5 6 7∼ 8

The fourth of Db is gb and has six flats:—

Gb ab bb cb db eb f Gb
1 2 3∼4 5 6 7∼8

The fourth of Gb is cb and has seven flats:—

Cb db eb fb gb ab bb Cb
1 2 3∼4 5 6 7∼ 8

The fourth of Cb is fb and has eight flats. This key necessitates one double flat and b has the double flat. The double flats are added in the same order that the single flats are. The double flat (designated: bb) lowers a tone one whole step.

Fb gb ab bbb cb db eb Fb
1 2 3∼4 5 6 7∼ 8

The fourth of Fb is bbb and has nine flats (two double flats, bbb and ebb):—

Bbb cb db ebb fb gb ab Bbb
1 2 3∼ 4 5 6 7∼ 8

The fourth of Bbb is ebb and has ten flats (three double flats, bbb, ebb and abb):—

Ebb fb gb abb bbb cb db Ebb
1 2 3∼4 5 6 7 ∼ 8

The fourth of Ebb is abb and has eleven flats (four double flats, bbb, ebb, abb and dbb):—

Abb bbb cb dbb ebb fb gb Abb
1 2 3∼ 4 5 6 7∼ 8

The fourth of Abb is dbb and has twelve flats (five double flats, bbb, ebb, abb, dbb, and gbb):—

Dbb ebb fb gbb abb bbb, cb Dbb
1 2 3∼4 5 6 7 ∼ 8

Dbb has taken us back to our starting key called by a different name as was the case when we had twelve sharps. To continue counting four would take us over the same keys called by different names. As was advised in the sharp keys, this research should be continued by the student. If more than fourteen flats are considered, it will be necessary to add triple flats.

The order of the letters in the flat signature which follows should be committed to memory:—

B E A D G C F.

By comparing the order of the letters in the flat signature with that of the sharp signature, it will be seen that the order of the letters in the flat signature is that of the sharp signature reversed.

Notice that each key has more than one name; for example, the white key next to the left of the group of two black keys has been called C, Dbb and B#.

Rule 3. An Enharmonic Change is the Change of a Name of a Tone without Altering its Pitch.

Two or more scales played from the same pitched tone but called by different names are called enharmonic scales. In practice,[B] fifteen major scales are used, three of which are enharmonic scales. Following is a list of the major scales used in practice together with their signatures:—

C no sharps or flats
G 1 sharp (f)
D 2 sharps (f and c)
A 3 sharps (f, c and g)
E 4 sharps (f, c, g and d)
B 5 sharps (f, c, g, d and a)
F# 6 sharps (f, c, g, d, a and e)
C# 7 sharps (f, c, g, d, a, e and b)

F 1 flat (b)
Bb 2 flats (b and e)
Eb 3 flats (b, e and a)
Ab 4 flats (b, e, a and d)
Db 5 flats (b, e, a, d and g) enharmonical to C#
Gb 6 flats (b, e, a, d, g and c) enharmonical to F#
Cb 7 flats (b, e, a, d, g, c and f) enharmonical to B

The enharmonic keys used in practice are:—

B (five sharps) enharmonical to Cb (seven flats)
F# (six sharps) enharmonical to Gb (six flats)
C# (seven sharps) enharmonical to Db (five flats)

Rule 4. The Sum of the Enharmonic Flat and Sharp Signatures is Twelve. Notice that this is true in the above three keys.

By this rule the theoretical keys (that is, those having more than seven sharps or flats) are easily found. For example:—to find the key having eleven flats; the key having eleven flats is enharmonical to the key having one sharp (11 + 1 = 12). G has one sharp and changing its name to the enharmonic flat key, we obtain Abb which, therefore, has eleven flats. This process should be applied to all keys having eight to eleven sharps and eight to eleven flats inclusive.

As stated in the first chapter, the pitch of a tone is determined by the note's position on the staff. The staff of five lines with its spaces allows of the designation of but one octave and one step, whereas, in modern music, there is need of the notation of at least six octaves. This necessitates the use of symbols called clefs, and lines added to the staff called ledger lines. Ledger lines are short lines parallel to the staff lines added above or below the staff lines.

There are three clefs:—

1. the treble or G clef,
2. the tenor, movable or C clef,
3. the bass or F clef.

Middle C is the tone which all voices can sing. It is in the lower register of the high female voice and in the upper register of the low male voice.

The G clef (treble clef) is for high voices or instruments. Its symbol shows the position of the G next above middle C thus:

. Middle C is found on the first ledger line below the G clef, thus:

The tenor or C clef is for the use of medium voices or instruments. Its symbol shows the position of middle C. This clef is movable and may place middle C on any line or space of the staff. Its most common position is on the third line of the staff, thus: