## Intervals level 4

### In this guide...

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### Introduction

We have already looked at different intervals above the tonic in major and minor keys. Now we will develop these ideas to look at other intervals in a key.

### Number and quality

In Intervals level 3 we looked at a formal way to describe an interval, in terms of:

*Number*: The gap between the degrees of the scale that form the interval*Quality*: Major, minor, or perfect

Here are a few intervals to remind you of this system. Look closely at how many semitones form each interval, and at the differences between the major and minor versions.

### Other degrees

So far we have only considered intervals above the **tonic**. It is possible, however, to use the same system to describe the interval between *any* two notes in the scale.

Let's consider, for example, the interval between the 2nd degree and the 6th degree in C major, i.e. the notes D and A:

#### Number

First of all, let's consider the **number**. This is quite easy to deduce - just as the interval between the 1st and 5th degree is a 5th, so the interval between the 2nd and 6th is also a 5th.

Indeed, any two notes that are 5 notes apart are also at an interval of a 5th. So, other fifths in the same scale are:

- E to B (3rd to 7th degree)
- F to C (4th to 1st degree)
- G to D (5th to 2nd degree)
- A to E (6th to 3rd degree)
- B to F (7th to 4th degree)

Note that for this purpose we simply start again after the 7th degree with the 1st degree, but one octave higher:

#### Quality

Secondly let's consider the **quality** of this **fifth** between D and A. You have previously seen that the interval between the 1st and 5th degree is a **perfect fifth**, and this interval between D an A is no different: it is also a **perfect fifth**.

You can see that this is an identical interval by either:

- Counting the semitones between C and G (there are 7), and between D and A (also 7), or
- Counting the semitones between bottom notes (C and D - 2 semitones) and the top notes (G and A - 2 semitones).

This interval, then, is also a **perfect fifth**. But what about the others listed above in the same scale? Let's count the semitones:

- E to B: 7 semitones = perfect 5th
- F to C: 7 semitones = perfect 5th
- G to D: 7 semitones = perfect 5th
- A to E: 7 semitones = perfect 5th
- B to F:
**6 semitones! = ???**

### Diminished fifth

This last interval, from B to F is also a fifth, as there are 5 degrees from B to F, but it is not a *perfect* fifth, because it has only 6 semitones.

This kind of fifth, a "shrunk" version of the perfect fifth, is called a *diminished 5th*.

### Augmented fourth

Let's look now at the interval of the **perfect fourth**, which we have seen between 1st and 4th degrees. This interval spans **5** semitones. Let's count the semitones between the other degrees that are a fourth apart, in C major:

- C to F: 5 semitones = perfect 4th
- D to G: 5 semitones = perfect 4th
- E to A: 5 semitones = perfect 4th
- F to B:
**6 semitones = ???** - G to C: 5 semitones = perfect 4th
- A to D: 5 semitones = perfect 4th
- B to E: 5 semitones = perfect 4th

Clearly we have a similar problem here with the interval from F to B. It is a kind of fourth, because there are 4 degrees from F to B, but it cannot be a *perfect* 4th, because that would require **5** semitones.

This interval, from F to B, is an "expanded" version of the perfect 4th and is called an *augmented 4th*.

#### Be careful...

You might be tempted to think that a perfect fifth reduced by one semitone would be a "minor 5th", and a perfect 4th expanded by one semitone would be a "major fourth", in the same way that a major third reduced by one semitone is a minor third.

This is not the case, however!

You should instead think of the **perfect** intervals being equivalent to **major and minor** intervals. We require "diminished" and "augmented" to describe the "shrunk" or "expanded" versions of the fourth and fifth.

As you will soon see, and in Intervals level 5, we also require these terms for shrunk and expanded major and minor intervals!

### Minor scales

Let's look again at the minor scale and see if we can spot any other unusual intervals. In this case, let's look at the **harmonic minor** scale in A minor, over two octaves:

### Thirds and sixths

Let's look at all the intervals of a **third** and a **sixth** in C major and A minor, just to check there is nothing unexpected there.

We already know that the interval from the 1st to 6th degree in C major is a **major 6th**, and between 1st and 3rd degree the interval is a **major 3rd**; but that in A minor the same intervals are a **minor 6th** and a **minor 3rd**.

The difference between these intervals is, again, apparent in the number of semitones. A **major 3rd** spans **4** semitones and a **minor 3rd** spans **3 semitones**, and a **major 6th** spans **9** semitones while a **minor 6th** spans only **8 semitones**.

Let's look at all of the 3rds in C major:

- C to E: 4 semitones = major 3rd
- D to F: 3 semitones = minor 3rd
- E to G: 3 semitones = minor 3rd
- F to A: 4 semitones = major 3rd
- G to B: 4 semitones = major 3rd
- A to C: 3 semitones = minor 3rd
- B to D: 3 semitones = minor 3rd

No surprises there, but do watch out for the minor 3rds mixed in among the major 3rds. It's clear that **major** scales contain **minor** intervals as well as **major** intervals.

What about the 6ths in C major?

- C to A: 9 semitones = major 6th
- D to B: 9 semitones = major 6th
- E to C: 8 semitones = minor 6th
- F to D: 9 semitones = major 6th
- G to E: 9 semitones = major 6th
- A to F: 8 semitones = minor 6th
- B to G: 8 semitones = minor 6th

#### Major / minor?

So, just why do we have minor intervals in a major scale? Why do we call them "minor" intervals?

The answer is clear if you consider the minor 3rd from D to F. In C major, these are the 2nd and 4th degrees, but in **D minor** these same notes are the 1st and 3rd degrees.

We first saw the minor 3rd as the interval between the 1st and 3rd degrees, (D and F in D minor for example), and now as we consider intervals starting on other degrees we find the exact same interval again.

It doesn't change name just because we're in a different key. D is D and F is F, so the interval between these notes is always called a **minor 3rd**.

Now let's do the same exercise in the minor key - and use the **harmonic minor** scale in A minor. Let's begin with thirds:

- A to C: 3 semitones = minor 3rd
- B to D: 3 semitones = minor 3rd
- C to E: 4 semitones = major 3rd
- D to F: 3 semitones = minor 3rd
- E to G sharp: 4 semitones = major 3rd
- F to A: 4 semitones = major 3rd
- G sharp to B: 3 semitones = minor 3rd

Again, no surprises, but we must be careful to spot the major and minor versions, as we must with the 6ths, too:

- A to F: 8 semitones = minor 6th
- B to G sharp: 9 semitones = major 6th
- C to A: 9 semitones = major 6th
- D to B: 9 semitones = major 6th
- E to C: 8 semitones = minor 6th
- F to D: 9 semitones = major 6th
- G sharp to E: 8 semitones = minor 6th

It can be helpful, when given a 3rd or 6th to identify, to think in terms of the lower note as the tonic of a key.

Take E to C, for example: clearly a 6th, but is it a major or minor 6th?

So - if E is the tonic of E major, then C is **not** the 6th degree in the scale of E major (that would be C **sharp**!)

By contrast, if E is the tonic of E **minor**, then C **is** a valid note - the 6th degree - and therefore the interval is a **minor** 6th.

### Augmented second

Look at the interval between the 1st and 2nd degree in the minor scale: it's a **major second**. What about the intervals between the other degrees that are only a **second** apart?

- A to B: 2 semitones = major 2nd
- B to C:
**1 semitone = ???** - C to D: 2 semitones = major 2nd
- D to E: 2 semitones = major 2nd
- E to F:
**1 semitone = ???** - F to G sharp:
**3 semitones = ???** - G sharp to A:
**1 semitone = ???**

Here we have two more types of **second**, one with 1 semitone (as in E to F) and one with 3 semitones (as in F to G sharp).

Just as a **third** can exist in major and minor versions, so can a **second**. In this case, a **second** that consists of 1 semitone is simply a *minor 2nd*, which you have briefly met in Intervals level 3.

But what about the **second** with **3** semitones? It is definitely a kind of **second**, but it is an "expanded" major second. As you might guess, we call this an *augmented 2nd*.

### Diminished fourth

Now let's look at the fourths in the minor scale, again using the **harmonic minor** in A minor. We already know that the interval between the 1st and 4th degrees is a **perfect 4th**, but what about the other fourths in the scale?

- A to D: 5 semitones = perfect 4th
- B to E: 5 semitones = perfect 4th
- C to F: 5 semitones = perfect 4th
- D to G sharp:
**6 semitones = augmented 4th** - E to A: 5 semitones = perfect 4th
- F to B:
**6 semitones = augmented 4th** - G sharp to C:
**4 semitones = ???**

You can see a couple of **augmented 4ths** in there, with 6 semitones instead of 5, but what about this kind of 4th with only **4** semitones?

This "shrunk" version of a perfect 4th is called a *diminished 4th*, and works on the same principle as a **diminished 5th**: a normal or "perfect" fourth shrunk or "diminished" by a semitone.

### Augmented fifth

Finally, let's look at the fifths in the minor scale, once again using **A harmonic minor**:

- A to E: 7 semitones = perfect 5th
- B to F:
**6 semitones = diminished 5th** - C to G sharp:
**8 semitones = ???** - D to A: 7 semitones = perfect 5th
- E to B: 7 semitones = perfect 5th
- F to C: 7 semitones = perfect 5th
- G sharp to D:
**6 semitones = diminished 5th**

Along with the diminished 5ths and perfect 5ths, we have another kind of 5th between C and G sharp, with **8** semitones.

Using the same principle as the **augmented 4th**, this interval is called an *augmented 5th*: a perfect 5th that has been expanded or "augmented" by a semitone.

### An important warning!

We have now come across every kind of interval that it's possible to encounter in diatonic (major / minor) scales.

You might quite reasonably ask, however, why a **diminished 4th**, with 4 semitones, has a different name to a **major 3rd**, which also has 4 semitones?

**This is the greatest trap in naming intervals!**

Never forget about the **number** part of an interval, and don't be sidetracked by looking only at the **quality**. G sharp to C is clearly a kind of **fourth** (a diminished 4th), and A flat to C is clearly a kind of **third** (a major 3rd).

Even if both of these two intervals are made up of 4 semitones, and even if they are enharmonically equivalent, the fact that the notes have different names is hugely important, as it makes one a 4th and the other a 3rd!

So, to remind you again - to correctly identify an interval you must follow **two** steps:

- Identify the
**number**: 2nd, 3rd, 4th, 5th, 6th, or 7th - And
*after*identifying the number, identify the**quality**: major, minor, perfect, augmented, diminished.

If you always follow this order, you will find it much easier to identify intervals - and you will especially need this when we come to look at intervals again in Intervals level 5!

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