The distance that seperates two notes is called the interval. With this term you can also regulate the harmonic ratio that exists between the two notes. It's very important to know very well the relationship between the notes, because it is due to these intervals that we can build any type of scale or chord. I therefore suggest that you read well this part.
To know the interval between two notes, you must have the MDS (major diatonic scale) of the lowest note, after which, using the table below, we will analyze the place where the other is found. The table illustrates five catagories of intervals (there should be seven, but we will look at the most common). The MDS is divided in order to combine to every degree of the scale at a determined interval. The intervals are called perfect, major, minor, diminished
and augmented. Lets use an example with the MDS of C, which we can see in the table below.
| |
DIMINISHED |
MINOR |
PERFECT |
MAJOR |
AUGMENTED |
| I° |
|
|
C |
|
|
| II° |
|
|
|
D |
|
| III° |
|
|
|
E |
|
| IV° |
|
|
F |
|
|
| V° |
|
|
G |
|
|
| VI° |
|
|
|
A |
|
| VII° |
|
|
|
B |
|
| VIII° |
|
|
C |
|
|
As you can easily see, the eight notes have been "distributed" over two catagories. In fact, in the MDS, the I°. IV°, V° and the VIII° are considered perfect intervals, while the II°, III°, VI° and the VII° are major intervals. This distinction is given by the harmonic relationship of the various degress with the root (C). If we want to know the distance that seperates the C from the E note, we can say that we have an interval of third major, which is equal to the physical distance of two tones (C - D = 1 tone, D - E = 1 tone).
Or the distance between C and B, which is a seventh major interval or between C and F (fourth perfect).
This is in when the root is C major. Now, in another root the harmonic relationship remains the same, and therefore the root is always a I° and so on for all the other notes belonging to their interval catagory. Lets look at an example of the root of E major, and therefore the MDS of E. |
| |
DIMINISHED |
MINOR |
PERFECT |
MAJOR |
AUGMENTED |
| I° |
|
|
E |
|
|
| II° |
|
|
|
F# |
|
| III° |
|
|
|
G# |
|
| IV° |
|
|
A |
|
|
| V° |
|
|
B |
|
|
| VI° |
|
|
|
C# |
|
| VII° |
|
|
|
D# |
|
| VIII° |
|
|
E |
|
|
As you can see, the notes of the scale are inserted in their interval cell maintaining any eventual alterations to the root, which are sharp (as in the root of E), or flat,
as for example the root ofBb that we see in the table below. |
| |
DIMINISHED |
MINOR |
PERFECT |
MAJOR |
AUGMENTED |
| I° |
|
|
Bb |
|
|
| II° |
|
|
|
C |
|
| III° |
|
|
|
D |
|
| IV° |
|
|
Eb |
|
|
| V° |
|
|
F |
|
|
| VI° |
|
|
|
G |
|
| VII° |
|
|
|
A |
|
| VIII° |
|
|
Bb |
|
|
Lets return to the MDS of C and see how to obtain the other intervals. Lowering the major interval by a half-step we get a minor interval. |
| |
DIMINISHED |
MINOR |
PERFECT |
MAJOR |
AUGMENTED |
| I° |
|
|
C |
|
|
| II° |
|
Db |
|
D |
|
| III° |
|
Eb |
|
E |
|
| IV° |
|
|
F |
|
|
| V° |
|
|
G |
|
|
| VI° |
|
Ab |
|
A |
|
| VII° |
|
Bb |
|
B |
|
| VIII° |
|
|
C |
|
|
Lets use some examples. What is the interval between C and Eb? One third minor: at the E note (third degree major) we have removed a half-step, obtaining Eb. What interval is C - Bb? One seventh minor, because also in this case we have removed a half-step from the B (seventh degree major).
If we lower the perfect or minor interval a half-step, we get a diminished interval. |
| |
DIMINISHED |
MINOR |
PERFECT |
MAJOR |
AUGMENTED |
| I° |
unfit for play |
|
C |
|
|
| II° |
Dbb |
Db |
|
D |
|
| III° |
Ebb |
Eb |
|
E |
|
| IV° |
Fb |
|
F |
|
|
| V° |
Gb |
|
G |
|
|
| VI° |
Abb |
Ab |
|
A |
|
| VII° |
Bbb |
Bb |
|
B |
|
| VIII° |
Cb |
|
C |
|
|
The double flat is created when we remove a half-step from a note (which makes it flat) from a note that is already flat (Eb automatically becomes Ebb). Note that Dbb in reality is a C, as Ebb is a D, etc. Remember that the note that is combined to the degree must keep its name, to which the alterations are added or removed. Its not possible to obtain the I° diminished.
The augmented interval is obtained by raising the the perfect or major interval by a half-step. Therefore: what is the interval between D and G#? A fifth augmented interval, which is obtained by raising the fifth degree (G) a half-step (G#).
Or what is the interval between C and D#. A second augmented interval, obtained by raising the second major (D) by a half-step (D#). The augmented interval is also called the excess interval. The other two types of intervals that we haven't seen are: the over diminished interval, which is obtained by lowering the diminished interval a half-step, and the over augmented interval (or over excess), which is obtianed by raising the augmented interval a half-step. See the chart below. |
| |
DIMINISHED |
MINOR |
PERFECT |
MAJOR |
AUGMENTED |
| I° |
unfit for play |
|
C |
|
C# |
| II° |
Dbb |
Db |
|
D |
D# |
| III° |
Ebb |
Eb |
|
E |
E# |
| IV° |
Fb |
|
F |
|
F# |
| V° |
Gb |
|
G |
|
G# |
| VI° |
Abb |
Ab |
|
A |
A# |
| VII° |
Bbb |
Bb |
|
B |
B |
| VIII° |
Cb |
|
C |
|
C# |
|
