Lesson 2

Intervals

Introduction
An interval is what we call the "distance" between two notes. This distance has two properties. One, the quantity, we learned about in Lesson 1. The quantity is determined by counting the letters involved in the interval. Count the first letter as one, and then count each letter until the final letter is reached. The number of letters counted is the quantity (or interval number) for that interval. Thus, three letters equals a third, five letters a fifth, and so on.

The Quality of the interval is much more difficult. The quality is determined by figuring out the actual distance in steps. This allows us to differentiate between intervals of the same quantity. For example, c to e and c to eb are both thirds. We need some way to distinguish between these thirds. By labeling the interval number with a name, the quality, we can tell the difference between them. In this case, c to e is called a major third and c to eb a minor third.


Perfect Intervals
The first intervals that we will look at will be perfect intervals. The reason for calling these intervals perfect is too long to explain here. Just learn which ones are perfect and you will be fine. Once you do some exercises, it will become simple.

In defining perfect intervals, we begin by using a major scale. We define the intervals by using the first scale step, 1 , and the scale steps 1 , 4 , 5 , and 8 , as perfect intervals. For example: 1 to 1 is a Perfect Unison; 1 to 4 is a Perfect Fourth; 1 to 5 Perfect Fifth; and 1 to 8 is a Perfect Octave. (See Table 2-1)


Method 1: Using the major scale.
It is critical to understand that we must use the major scale of the lower note in the interval to determine the quality. Intervals are defined by using ascending intervals only, so using the scale from the upper tone would often give us incorrect results. For example, if we want to find the perfect fourth above f, we must first know the make-up of an F Major scale. By looking at an F Major scale and counting up to the fourth note, you will find that the fourth is a bb. This is one of two ways to determine the notes in an interval.

Method 2: Counting Steps
It is also possible to figure out the intervals by counting half-steps and whole-steps (see Exercise 2-1). By counting up four letters from f, we find that a fourth above f is some type of a b note. Then, knowing that a perfect fourth covers 2-1/2 steps, the b must be changed to a bb because f to b is initially three whole-steps. Try using both methods in the following exercises.


Exercise 2-1 Use the correct interval label and figure out the corresponding number of steps in the interval.


Exerise 2-2 Fill in the correct note names fot the intervals below.


Major Intervals
We use the term major to label the rest of the intervals that occur within the major scale. Since 1, 4, 5, and 8 were all used as perfect intervals, that leaves us 2, 3, 6, and 7 to use as major intervals. As with the perfect intervals, major intervals are defined by going from the root note in the major scale up to the corresponding note of the interval. As a result, a Major 2nd (M2) goes from 1 to 2, a Major 3rd (M3) from 1 to 3 , a Major 6th (M6) from 1 to 6, and a Major 7th (M7) from 1 to 7. (See Table 2-2)


Exercise 2-3 Answer the following with the correct interval name and interval distance.


Exercise 2-4 Fill in the correct note name for the intervals below.


Exercise 2-5 In the following chord diagrams, fill in the diagram with the correct "dot" for the given interval. All intervals shall be ascending, so the note you choose should be higher in pitch than the note given. It is possible for the notes to be on the same string if necessary.


Minor Intervals
Now that we know how perfect and major intervals work, minor intervals are easy. A Minor Interval is simply a lowered (or flatted) major interval. For example, a minor 3rd (m3)* is a M3 that has been lowered one half-step. When lowering the major interval, DO NOT change the note names (letters). The note names must stay the same. Only the quality of the notes (#'s and b's) can be changed.

At first, the easiest way to determine the minor interval is to figure out the major interval and then flat it. For example, a M3 above d is f#. Therefore, a m3 above d is f. Now try the exercises below.


Exercise 2-6 Fill in the correct number of steps for each interval given below.


Exercise 2-7 Name the intervals given below. For example, c up to e is a M3, or d up to g is a P4.


Augmented and Diminished Intervals
Now that we have covered all other interval types, we shall cover augmented and diminished intervals. An augmented interval is either a major or a perfect interval that has been raised a half-step. A diminished interval is either a minor or a perfect interval that has been lowered a half-step.

Pay careful attention to the difference in the affected intervals. Both augmented and diminished intervals affect perfect intervals in a similar way. They work differently when dealing with major and minor intervals. The augmented interval raises a major interval, while the diminished interval lowers a minor interval.

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