JT 4.1 - Altering Perfect Intervals

When an interval is enlarged ('raised') or shortened ('lowered') by a semitone it changes in quality.

When a perfect interval is raised by a semitone it becomes augmented.
When a perfect interval is lowered by a semitone it becomes diminished.

The symbol for augmented is : + or aug

The symbol for diminished is : o or dim

In above example the intervals C-Gb and C-F# are the same, but are called differently according to how they are notated.
(Gb and F# refer to the same note. They are called enharmonic equivalents)

Likewise C-Fb and C-E are also the same, but written as C-E it is called a major 3rd, written as C-Fb is a diminished 4th.
(Again Fb and E refer to the same note, and are enharmonic equivalents.)

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JT 4.2 - Altering Major Intervals

When a major interval is raised by a semitone it becomes augmented.
When a major interval is lowered by a semitone it becomes minor.

For example :

The symbol for minor is : m or min

Again, the name of the interval depends on how it is notated.

C ---> D# (+2) is the same as C ---> Eb (m3)

C ---> Db (m2) is the same as C ---> C# (+unison)

C ---> Ab (m6) is the same as C ---> G# (+5)

D# and Eb
C# and Db
G# and Ab

are enharmonic equivalents

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JT 4.3 - Altering Minor Intervals

When a minor interval is raised by a semitone it becomes major.
When a minor interval is lowered by a semitone it becomes diminished.

For example :

C-Ebb ('E double flat') is the same as C-D (major 2nd)

C-Abb (dim6) is the same as C-G (perfect 5th)

(Don't worry too much about all these enharmonic equivalents, it is not a vital part of this course.)

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JT 4.4 - The Five Interval Qualities

We have now dealt with all five possible interval qualities.
They are :

P = perfect

M = major

m = minor

+ = augmented

o = diminished

The Interval Qualities Diagram (IQD) below shows how these five interval qualities are related to each other:

Here you see that the major and perfect intervals both become augmented when raised (#).

But when lowered (b) perfect intervals become diminished, while major intervals first become minor. Only when these are lowered once more (a semitone) they also become diminished.

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JT 4.5 - How to Identify any Interval

To identify an interval you need to know :

The major scale of the bottom note of the interval
The Interval Qualities Diagram (IQD)

The examples below show how it works.

Example A
Identify these intervals.

The major scale of the bottom note, F, is :

F
1

G
2

A
3

Bb
4

C
5

D
6

E
7

f
8

If the top note is in the F major scale the interval is either perfect or major.

Case 1 (F-Bb) : Bb is the 4th note of the F major scale. F-Bb is therefore a perfect 4th (P4).

Case 2 (F-B) : B is not in the F major scale. B is a semitone above the nearest note (and letter name)Bb.
F-Bb is a P4. Therefore F-B is a 'raised P4' which, according to the IQD, is an augmented 4th (+4).

Case 3 (F-Eb) : Eb is not in the F major scale. Eb is a semitone below the nearest note (and lettername) E.
F-E is a major 7th (M7). F-Eb is therefore a lowered major 7th, which (according to the IQD) is a minor 7th (m7).

Example B
Identify the upper note for each of these intervals.

The major scale of the lower note, D is :

D
1

E
2

F#
3

G
4

A
5

B
6

C#
7

d
8

Case 1 : count 3 notes up on the D major scale --> F# = M3

Case 2 : count 4 notes up the D major scale, G, raise this note G# = +4

Case 3 : count 6 notes up the D major scale, B, lower this note Bb = m6

Case 4 : count 3 notes up the D major scale, F# = M3, lower this F = m3, lower this again : Fb = o3

Major Scale in Every Key

C = C - D - E - F - G - A - B - C
D = D - E - F# - G - A - B - C# - D
E = E - F# - G# - A - B - C# - D# - E
F = F - G - A - Bb - C - D - E - F
G = G - A - B - C - D - E - F# - G
A = A - B - C# - D - E - F# - G# - A
B = B - C# - D# - E - F# - G# - A# - B
C# = C# - D# - E# (=F) - F# - G# - A# - B# (=C) - C#
Db = Db - Eb - F - Gb - Ab - Bb - C - Db
Eb = Eb - F - G - Ab - Bb - C - D -Eb
F# = F# - G# - A# - B - C# - D# - E# (=F) - F#
Gb = Gb - Ab - Bb - Cb (=B) - Db - Eb - F - Gb
Ab = Ab - Bb - C - Db - Eb - F - G - Ab
Bb = Bb - C - D - Eb - F - G - A - Bb

To simplify, you can memorize this formula to form a major scale = whole step - whole step - half step - whole step - whole step - whole step - half step or w - w - h - w - w - w - h.

Table of Major Scales

C major
G Major		F Major
D Major		Bb Major
A Major		Eb Major
E Major		Ab Major
B Major		Db Major
F# Major		Gb Major
C# Major		Cb Major

Key Signatures

a. A key signature is the grouping of chromatic signs that have been extracted from a scale and placed after the clef sign. The number of flats or sharps in a key signature determines the key of a composition.

b. The E Major scale has a key signature of three flats (Figure 2-6).

Figure 2-6: Extracting Accidentals for Key Signatures.

c. The E Major scale with the key signature in place, looks like this (Figure 2-7).

Figure 2-7: E Major Key Signature.

Placement of Sharps in a Key Signature.

a. Sharps are placed on the staff in the following order (Figure 2-8).

Figure 2-8: Order of Sharps.

b. To determine this order, begin on F (the first added to the staff). Count up five letter names to C. Then begin on C and count up five more letter names to G sharp. Continue this pattern until all seven sharps are identified (Figure 2-9).

Figure 2-9: Determining Order of Sharps.

c. Sharps are placed on a staff in a specific pattern. The first sharp, F , is placed on the fifth line of the treble staff and the fourth line of the bass staff. The second sharp, C, is placed below the first sharp. The third sharp is up, the fourth sharp down, the fifth sharp down, the sixth sharp up, and the seventh sharp down. Figure 2-10 indicates the correct placement of sharps in a key signature.

Figure 2-10: Placement of Sharps.

Placement of Flats in a Key Signature.

a. Flats are placed on the staff in the following order (Figure 2-11).

Figure 2-11: Order of Flats.

b. To determine the order of flats, begin on B flat (the first flat added to the staff). Count up four letter names to E. Then begin on E and count up four more letter names to A. Continue this pattern until all seven flats have been identified (Figure 2-12).

Figure 2-12: Determining Order of Flats.

c. The first flat, B, is placed on the third line of the treble staff and on the second line of the bass staff. The second flat, E, is placed above the first flat. The third flat is down, the fourth up, the fifth down, the sixth up, and the seventh down (Figure 2-13).

Figure 2-13: Placement of Flats.

NOTE: The order of flats in a key signature is opposite the order of sharps (Figure 2-14).

Figure 2-14: Order of Flats and Sharps.

Grade 11

Table of Major Scales