## Standard 4: Intervals

Our objectives:

• Determine the size and quality of a given interval, from perfect unison to perfect octave.
• Complete a given interval by adding either a note above or below a given note.

### 4.1 What's an "interval"?

An interval is the distance between two pitches, usually measured in two components: 1) the size, and 2) the quality.

The term interval regularly refers both to:

1. The distance between two pitches on a scale, as described by the size and quality (e.g. major 2nd), and;
2. Two pitches that are separated by that distance (e.g. G and A).

A melodic interval describes the distance between two pitches that are sounded one after another (as in a melody). A harmonic interval describes the distance between two pitches that are sounded together, at the same time (as in harmony).

### 4.2 Interval Size

We can describe the interval between two notes first by stating its size, which is the number of letters that we can count from the the bottom pitch to the top pitch, including both pitches in the count.

For example, here are two examples of a 2nd: both as a melodic interval and a harmonic interval

To find the size, begin with the letter names only. That is, treat C, C-sharp, and C-flat all as C for the time being. Next, count the number of steps (different letters) between the two pitches in question, including both pitches in your count. Start from the bottom pitch and count up the musical alphabet to the top pitch. Remember, you must include both pitches of the interval in your count!

Here's an example of a 4th. The letters are C-D-E-F. We are igoring the F# here when we count the size of this interval.

Review this interactive demonstration on counting interval size. Note: in this demonstration, "generic interval" means the same thing as interval size.

### 4.3 Interval Quality

Often more specificity is needed than what the interval size can provide. That specificity comes in the form of an interval's quality. Combining the size and quality gives us the full description of that interval.

There are five possible interval qualities:

• augmented (A)
• major (M)
• perfect (P)
• minor (m)
• diminished (d)

We will begin with the major and perfect intervals.

### 4.4 Diatonic Intervals

The term "diatonic interval" describes the interval between two notes, where the top pitch is part of the major scale built on the bottom pitch. For example, here are eight different harmonic intervals all built on the C major scale, with C as the bottom note:

The names of the intervals above are as follows, from left to right. These are called diatonic intervals:

• Perfect Unison (P1)
• Major 2nd (M2)
• Major 3rd (M3)
• Perfect 4th (P4)
• Perfect 5th (P5)
• Major 6th (M6)
• Major 7th (M7)
• Perfect Octave (P8)

When you count the number of half-steps between each pair of notes, use the piano keyboard to help you. Start with the bottom pitch, and move up by half-steps until you reach the top pitch. In counting the half-steps, make sure that you start with the first pitch as "zero" (i.e. with just one note, there are no half steps), and count up from there.

The number of half steps in each diatonic interval is as follows:

Interval Name Half-Steps
Perfect Unison (P1) 0
Major 2nd (M2) 2
Major 3rd (M3) 4
Perfect 4th (P4) 5
Perfect 5th (P5) 7
Major 6th (M6) 9
Major 7th (M7) 11
Perfect Octave (P8) 12

We will be referring to these diatonic intervals as we describe minor, diminished and augmented intervals. So it's a good idea to memorize the relationship between a given diatonic interval and the number of half-steps that it includes.

### 4.5 Minor, Diminished and Augmented intervals

To round out our tools for describing the quality of an interval, we will also use three additional qualities: minor, diminished, and augmented.

Major Intervals:

• When a major interval is decreased by a half-step, it becomes a minor interval.
• When a minor interval is decreased by a half-step, it comes a diminished interval.
• When a major interval is increased by a half-step, it becomes an augmented interval.

Perfect Intervals:

• When a perfect interval is decreased by a half-step, it becomes a diminished interval.
• When a perfect interval is increased by a half-step, it becomes an augmented interval.

Take a look at the example below:

All three are examples of a third:

• The first interval, with the notes C - E, yields four half-steps, and therefore is described as a Major 3rd.
• The second interval, with the notes C - Eb, yields only three half-steps, and therefore is described as a Minor 3rd. (Note that this is still a third, because the letter names are the same.)
• The third interval, with the notes C# - Eb, yeilds only two half-steps (a half-step smaller than a Minor 3rd). This is an example of a diminished 3rd.

Remember: the size and quality of an interval depends entirely on how the notes are written on the staff. For example, even though the diminished 3rd in the example above are enharmonically equivalent to C# and D#, since the notes are written as C# and Eb, the interval must be described as a third.

Here is a chart that shows the correspondence between the half-step count, the size, and the resulting quality.

Half-Steps Unis. 2nd 3rd 4th 5th 6th 7th Octave
0 P1 d2
1 A1 m2
2 M2 d3
3 A2 m3
4 M3 d4
5 A3 P4
6 A4 d5
7 P5 d6
8 A5 m6
9 M6 d7
10 A6 m7
11 M7 d8
12 A7 P8

Take a look at this interactive demonstration on combining interval size and interval quality.