## Introduction

(Please read Constructing Major Scales before continuing)

A musical interval is simply a measure of distance between any two notes. An interval is notated in two parts: a description (major, minor, perfect, augmented, diminished) and a number (2nd, 3rd, etc.). Furthermore, all intervals are categorized as either diatonic or chromatic.

## Identifying Interval Numbers

We'll begin by learning how to identify the interval number for a set of two notes. For this example we'll use the interval from C up to A. We begin counting by labeling the first note, C, as one. The next note up is D, which we label 2. Continuing this we get E as 3, F as 4, G as 5, and A as 6. This tells us that the interval from C to A is a sixth interval. Note also, that adding the number 7 to any interval number increases the size of the interval by one octave (and vice versa).

# Diatonic and Chromatic Now we will examine the difference between diatonic and chromatic intervals. Diatonic is used to describe and interval where the upper note is contained in the major scale built from the lower note. Chromatic indicates that the upper note is not contained in the major scale built from the lower note. For example, consider the C major scale (C-D-E-F-G-A-B-C), and let C be the bottom note of our intervals. Now for any interval where the top note is contained in the C major scale, that interval is classified as diatonic. For instance, the interval from C to G is diatonic, while the interval from C to Bb is chromatic, since Bb is not in the C major scale.

## Identifying Interval Names

### Diatonic

We begin this section with a chart of the diatonic intervals contained in two octaves of the C major scale.
```Bottom Note       Top Note        Interval Name
-----------------------------------------------------------
C               D            Major 2nd
C               E            Major 3rd
C               F            Perfect 4th
C               G            Perfect 5th
C               A            Major 6th
C               B            Major 7th
C               C            Perfect 8th (octave)
C               D            Major 9th
C               E            Major 10th
C               F            Perfect 11th
C               G            Perfect 12th
C               A            Major 13th
C               B            Major 14th
C               C            Perfect 15th (2 octaves)

```

Now, note that the diatonic intervals are all named either major or perfect. Fourths, fifths, and octives are called perfect and all other intervals are called major.

### Chromatic

Before examining chromatic intervals, we'll discuss the concept of double accidentals. Accidentals, sharp (#) and flat (b), are used to modify note names. For instance, Bb (B flat) is one half step lower than B, and Bbb (B double flat) is a half step lower than Bb. This concept can also be used to raise a note. Raising A a half step results in A# (A sharp). Adding another half step brings us to Ax (A double sharp). Double accidentals may seem like a needless notational addition to interval theory, however, they are necessary because identifying a chromatic interval may require us to flat a note that is already flatted.

Now, what you've all been waiting for, the rules for chromatic intervals:

1. A major interval reduced by a half-step becomes a minor interval.
2. A minor interval reduced by a half-step ecomes a diminished interval.
3. A major interval increased by a half-step becomes an augmented interval.
4. A perfect interval reduced by a half-step becomes a diminished interval.
5. A perfect interval increased by a half-step becomes an augmented interval.

## Creating and Identifying Intervals

With the rules learned above, we should now be able to create or identify the interval between any two notes.

First we'll do an example of creating an interval. We will find the note which is a major 3rd above B. The first step is to identify the letter name of the note. To do this, we simply count up 3 notes, starting with the bottom. So B is the first, C is the second, and D is the third. The next step is to build a major scale from the bottom note up. The B major scale is as follows: B-C#-D#-E-F#-G#-A#-B. Now remember that a major 3rd interval is diatonic, so it's the third note in the major scale (D#). The third and final step then, is to qualify the upper note of our interval, namely adding a sharp to it, creating D#.

Now we will try to identify the interval from F to Bb. We begin by building the major scale from the bottom note. The F major scale looks like this: F-G-A-Bb-C-D-E-F. Looking at the scale, we can easily see that F and Bb create a diatonic interval, namely a perfect 4th.

The previous two examples both use diatonic intervals, however using the chromatic interval rules from above, you should be able to easily create and identify chromatic intervals.

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