When the harmonic or melodic outcome of an interval is harsh, tensed, unpleasant and disagreeable, such an interval is said to be dissonant. There are two classes of dissonant intervals:

**Diatonic Dissonant Intervals**: These are dissonant intervals formed from the combination of a bass note and other natural tones in the key of the bass note.

**Chromatic Dissonant Intervals**: These are dissonant intervals formed from the combination of a bass note and accidental tones in the key of the bass note.

## Chromatic Dissonant Intervals

Considering that we’ve covered diatonic dissonant intervals in earlier posts, our focus in this article will be on chromatic dissonant intervals. However, we’ll limit our study to the earliest known chromatic dissonant intervals, which are the *augmented fourth* and the *diminished fifth*.

In the key of C:

Here are the two *earliest *chromatic dissonant intervals discovered:

**F-B (Augmented 4th)**

The interval above is bigger than the perfect 4th. Therefore, it is called an **augmented 4th.**

**B-F (Diminished 5th)**

The interval above is smaller than the perfect 5th. Therefore it is called a **diminished 5th.**

The chromatic dissonant Intervals above have something in common. Both of them contain F and B tones.

If we organize the intervals above into quality and quantity, we’ll have:

**Quantity** – Fourth | Fifth

**Quality** – Augmented | Diminished

## Stability vs Instability

Intervals of the Augmented 4th and Diminished 5th sound *unstable* and *tense*. Perhaps a slight comparison between diminished fifths and perfect fifths will make it plain.

**Perfect Fifth vs Diminished Fifths.**

**Perfect Fifth:**

Perfect intervals are called perfect because they do not change their quality when inverted. It’s also important to note that the perfect fifth interval *in traditional practice *is said to be universally stable.

**Diminished Fifth**

The diminished fifth sounds unstable. It is smaller than the perfect fifth by a semitone progression. It involves a relationship between the bass note (B) and a chromatic note (♭5) on the B Major scale.

## What is The Relationship Between an Augmented 4th and a Diminished 5th?

Let’s cover the similarities between the augmented fourth and the diminished fifth. Let’s narrow it down by exploring the relationships these intervals have.

Just like diatonic dissonant intervals, chromatic dissonant intervals are related by the simple process of inversion. This relationship bridges the gap between these two dissonant intervals.

Let’s explore these changes in quality and quantity that come from inversion and its effect on chromatic dissonant intervals.

**Relationship #1 – Quantity**

Intervals can be described using numbers that are equivalent to the number of letter names they encompass. Let’s look at the two *quantities* of chromatic dissonant intervals:

Intervals described as **fourths** span four letter names. For example, **F-B** spans F, G, A and B.

Intervals that encompass five letter names are called **fifths**.For example, **B-F** spans B, C, D, E and F.

Inversion of these intervals will show us the relationship between these intervals.

**Inversion of Fourths**

Intervals can be inverted using the* Octave Transposition Technique*. Therefore, fourths like F-B can be inverted by transposing either the melody note an octave lower or transposing the bass note an octave higher.

**F** is the bass note and **B** is the melody note.

**Approach #1 – Octave transposition of bass note**

Octave Transposition of F to a higher octave will yield B-F.

**Approach #2 – Octave transposition of melody note**

Octave transposition of B to a lower octave will also yield B-F.

Great Job! We’ve succeeded in inverting F-B into B-F.

**“Okay, so what’s the size of B-F?”**

B-F encompasses B, C, D, E and F, which is five letter names. Therefore, inversion of a fourth (F-B) will yield a fifth (B-F).

Let’s move on to inversion of *fifths*.

**Inversion of Fifths**

Octave Transposition of the melody note by an octave lower than given or the bass note an octave higher will invert an interval.

In the case above (B-F), B is the bass note and F is melody note.

**Approach #1 – Octave transposition of bass note**

Octave transposition of B to a higher octave will yield F-B.

**Approach #2 – Octave transposition of melody note**

Octave transposition of F to a lower octave will also yield F-B.

Having covered the inversion of B-F into F-B, let’s look at the outcome of this inversion.

F-B encompasses F, G, A and B, which is four letter names. Therefore, inversion of a fifth (B-F) will yield a fourth (F-B).

**Relationship #2 – Quality**

Intervals can be described using adjectives that correspond to their harmonic property. Let’s look at the two qualities of these chromatic dissonant intervals:

**Augmented intervals are intervals that are larger than scale tone intervals by a semitone.**

For example, the quality of the interval F-B, is determined by the major scale of F (which is the bass note).

Therefore, considering that B is a semitone higher than B♭ (which is a scale tone in the major scale of F), the interval between B and F it is described as being “augmented.”

*Augment* is to make larger while *diminish* is to make smaller.

Therefore F-B is an augmented interval.

– *larger* than F-B♭ (perfect fourth).

**Diminished intervals are smaller than perfect and minor intervals by a semitone.**

The quality of the interval (B-F) can be determined with the major scale of B:

An interval of a perfect 5th is between the bass note and its 5th scale step (B-F♯).

The interval we are concerned with (B-F):

…is a semitone smaller than the perfect fifth (B-F♯).

Therefore, B-F is a *diminished* interval.

So far, we’ve covered two chromatic dissonant interval qualities – *Augmented* and *Diminished*. Let’s look at the outcome of the inversion of these intervals.

**Inversion of Augmented Intervals**

The augmented fourth (F-B) is a principal chromatic dissonant interval. It can be inverted by transposing either the melody note an octave lower or transposing the bass note an octave higher.

**F-B** – F is the bass note and B is the melody note.

**Approach #1 – Octave Transposition of the bass note.**

Octave transposition of F to a higher octave will yield B-F.

**Approach #2 -Octave Transposition of the melody note.**

Octave transposition of B to a lower octave will also yield B-F.

This gives us a new interval (B-F). **Let’s determine its quality.**

The quality of B-F will be determined with the major scale of B (its new bass note).

Our new interval (B-F):

…is closer to the perfect fifth (B-F♯) in the key of B. Same letters.

Considering that B-F is smaller than B-F♯ by a semitone progression, B-F is described as a *diminished* interval.

Therefore, inversion of an augmented interval will yield a diminished interval.

**Inversion of Diminished Intervals**

The diminished fifth (B-F) can be inverted by transposing either the melody note an octave lower or transposing the bass note an octave higher.

**B-F** – B is the bass note and F is the melody note

**Approach #1 – Octave Transposition of the bass note.**

Octave transposition of B to a higher octave will yield F-B.

**Approach #2 – Octave Transposition of the melody note.**

Octave transposition of F to a lower octave will also yield F-B.

Now, that we’ve inverted B-F into F-B, **what is the quality of F-B?**

The quality of F-B will be determined with the major scale of F (its new bass note).

Our new interval (F-B):

…is closer to the perfect fourth (F-B♭) in the key of F. Same letters.

Considering that F-B is bigger than F-B♭ by a semitone progression, F-B♭ is described as an *augmented* interval.

Therefore, inversion of a diminished interval will yield an augmented interval.

**1st Relationship**– All Fourths and Fifths are related by inversion of

**quantity**.

**2nd Relationship**– All Augmented and Diminished intervals are related by inversion of

**quality**.

Let’s end by looking at the outcome of the inversion of chromatic dissonant intervals.

## Inversion of the Augmented Fourth and the Diminished Fifth

Let’s put all that we’ve learned in this article together to see possible harmonic outcomes. In this segment, we’ll do a complete inversion (quality and quantity) of chromatic dissonant intervals. It will seem redundant by now but this is the final step.

**Inversion of an Augmented 4th**

** Inversion of Quality** – Augmented becomes Diminished.

**Inversion of Quantity** – 4th becomes 5th.

**Inversion of an Augmented 4th yields a Diminished 5th.

If we reverse the process:

**Inversion of a Diminished 5th**

** Inversion of Quality** – Diminished becomes Augmented.

**Inversion of Quantity** – 5th becomes 4th.

**Inversion of a Diminished 5th yields an Augmented 4th.

## Diabolus in Musica

The intervals covered in this article are the earliest chromatic dissonant intervals that were discovered. When these intervals were discovered, they were called *Diaboli in Musica*, which means *Devil in Music.*

These intervals sounded scary and were forbidden in church music because of their extreme dissonance. Over time, things have changed. The devil in music has evolved from being yesterday’s dissonance to today’s consonance.

Often times, the term *tritone* is associated with the earliest chromatic dissonant intervals that were discovered. You may need to read this article on relating with the devil in music to learn more.

I’ll be back in another post to show you, step-by-step, how to form chords using these chromatic dissonant intervals.

Until then.

#### Chuku Onyemachi

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great