Intervals
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## Intervals

In music theory we use the word interval when we talk about the pitch difference between two notes. We call them harmonic intervals if two tones sound simultaneously and melodic intervals if they sound successively.

Interval names consist of two parts. Some examples are "major third" and "perfect fifth". In Walter Piston's "Harmony" the two parts are called the specific name and the general name part. Wikipedia talks about interval quality and interval number. I have seen people talking about an interval's numerical size.

You find the general name by counting the steps on the staff, ignoring any accidentals. So if the interval you want to name goes from E to G#, then we count to 3 (E F G) and see that the general name is third.

The specific name tells the exact size of the interval. Unisons, fourths, fifths and octaves can be diminished, pure or augmented. Seconds, thirds, sixths and sevenths can be minor, major, diminished or augmented. A minor interval is one semitone smaller than a major interval. A diminished interval is one semitone smaller than a pure or a minor interval, and an augmented interval is one semitone larger than a pure or major interval.

Accidentals change the size of intervals. The interval becomes one semitone larger if you add a sharp to the highest tone or a flat to the lowest tone. And it becomes one semitone smaller if you add a flat to the highest tone or a sharp to the lowest tone. In the following sections naming of the intervals will be shown in greater detail.

### Seconds

Seconds are easy to recognise: the two notes are neighbours on the staff. One note is on a staff line, and the other one is in the space above or below. A minor second is one semitone step, also called a half step. A major second is two semitone steps, also called a whole step.

To learn to identify seconds, you first have to learn which seconds there are between the natural tones. As you can see in Figure 3.1, only the intervals E-F and B-C are minor seconds. The rest are major intervals. You can check that Figure 3.1 is correct by looking at a piano. You will see that there are no black keys between E and F and between B and C.

Figure 3.1.

If the second has accidentals, then we have to examine them to find out how they change the size of the interval. Let us identify a few intervals!

Figure 3.2.

We remove the accidental from the interval in Figure 3.2 and see that the interval F-G is a major second. When we add the flat to the highest tone, the interval becomes one semitone smaller, turning into a minor second.

Figure 3.3.

We remove the accidentals, and see that the interval A-B is a major second. You still remember Figure 3.1, don't you? Then we add the flat to the A, and the interval becomes an augmented second. And when we add the flat to the B, the interval becomes a major second.

Figure 3.4.

We remove the accidentals, and see that the interval E-F is a minor second. When we add a flat to the lowest tone, the interval becomes one semitone larger, turning into a major second. And when we add a sharp to the highest tone, the interval becomes one semitone larger, turning into an augmented second.

### Thirds

A minor third is one minor and one major second, or three semitones. A major third are two major seconds, or four semitone steps. Figure 3.5 shows the thirds between all the natural tones. You should memorise the major intervals, C-E, F-A and G-B. Then you know that the other four intervals are minor.

Figure 3.5.

Then you examine the accidentals to see if they change the specific name. This is done exactly the same way as for seconds.

### Fourth

A pure fourth is 2½ steps, or two major seconds and a minor second. Figure 3.6 shows all fourths between natural tones. You should memorise that the fourth F-B is augmented, and that the other six are pure.

Figure 3.6.

### Fifth

A pure fifth is 3½ steps, or three major seconds and a minor second. Figure 3.7 shows all fifths between natural tones. You should remember that all those intervals are pure, except B-F that is diminished.

Figure 3.7.

If an interval has accidentals, then we must examine them to see how they change the size of the interval. A diminished fifth is one semitone smaller than a pure interval, and an augmented fifth is one semitone larger. Below you will find a few examples:

Figure 3.8.

We remember from Figure 3.7 that the interval B-F is a diminished fifth. The lowest tone in Figure 3.8 is preceded by a flat that makes the interval one semitone larger and changes the interval from a diminished to a pure fifth.

Figure 3.9.

We know from Figure 3.7 that interval E-B is a perfect fifth. In Figure 3.9 the E has a flat in front of it, making the interval augmented. But then the B is preceded by a double flat that makes the interval two semitone steps smaller and changes the interval to a diminished fifth.

### Sixths

Sixths are easiest identified by inverting the interval and identifying the third. Then the following rule applies:

- If the third is diminished, then the sixth is augmented

- If the third is minor, then the sixth is major

- If the third is major, then the sixth is minor

- If the third is augmented, then the sixth is diminished

If you find inverting intervals difficult, then you can memorise that the intervals E-C, A-F and B-G are minor. The other four are major. Then you examine the accidentals to see if they change the specific name. This is done exactly the same way as for seconds.

Figure 3.10.

### Sevenths

Sevenths are identified the same way as sixths. When you invert a seventh, you get a second.

If you find inverting intervals difficult, then you can memorise that the intervals C-B and F-E are major. The other five are minor. Then you examine the accidentals to see if they change the specific name. This is done exactly the same way as for seconds.

Figure 3.11.

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