Interval (2) Full Interval Names

Once again, Chapter III is the chapter where you learn various types of chords and become familiar with chord names. As you already know, the naming rules for chord names are solely determined by the intervalic structure of the chord tones.

Until Chapter II, to minimize the burden of memorization, we introduced the “full names” only of 3^rd and 7^th. Reflecting on it, we haven’t even introduced what the full name of 5^th of major chords or minor chords is.

However, in Chapter III, not only the 3^rd and 7^th but also the 5^th, 2^nd, 4^th and 6^th degrees come into play. It’s about time to become a little more familiar with the concept of intervals in this session. It’s perfectly fine to proceed with memorization after learning chords in Chapter III, but for now, it’s important to at least establish a basic understanding of these concepts.

1. Quantity and Quality

First, let’s get a bit more technical with the terms. Within the elements that constitute an interval, the numerical part is referred to as “Quantity” and the characteristics such as mahjor/minor as “Quality.”

“Quantity and Quality” are words often used in combination, and in the world of music theory, these two “Qs” become important too.

2. Types of Quality

First, let’s comprehensively cover qualities other than major/minor.

Perfect Intervals

The interval of the 5^th in major chords or minor chords, is called the “Perfect 5th“. It’s not about being major or minor; it’s simply “perfect”.

When you count the number of semitones, it totals to 7 semitones for the perfect 5th. As mentioned in Chapter I, it produces a transparent and clear sound, often used to reinforce the thickness of chords.

Among other quantities, 4^th and [8th] (=octave) has its quality named “perfect”.

The reason they’re called “perfect” is a bit complex, but roughly speaking, these 4th, 5th, and 8th intervals have a particularly clear sonority¹.

Augmented and Diminished Intervals

If you pick two notes from a major scale to create a 4^th or 5^th, most will turn out to be “Perfect 4th” or “Perfect 5th”. The only exception occurs when combining ti and fa.”

Diminished 5th

When you stack the notes ti–fa this forms a kind of “5th”, but its distance is not the same as the normal 5th.

Compared to a perfect 5th, this distance is reduced, hence it’s called Diminished 5th.

Augmented 4th

Similarly, when you stack fa – ti, it forms a kind of “4th”, but this time, the distance is longer than the normal 4th.

In this case, as the distance is increased, it’s called Augmented 4th.

Furthermore, in the case of do–so♯, the distance is here again increased compared to the perfect 5th, so it’s also “augmented 5th”.

Tritone and Enharmonic

ti–fa and fa–ti are both a distance of six semitones, which forms what is known as an evil interval called “tritone,” a keyword mentioned in the “Secondary Dominant” section.

So The term “tritone” is a convenient word that encompasses both “augmented 4th” and “diminished 5th” intervals².

Although “ti–fa” and “fa–ti” are the same in terms of the number of semitones, they differ in degrees – “Ti–do–re–mi–fa makes it a 5th,” and “Fa–so–la–ti makes it a 4th.” This kind of relationship is referred to as an Enharmonic Interval.

Enharmonic Interval

A term referring to the relationship between intervals with different names but the same number of semitones, such as “augmented 4th” and “diminished 5th.”

It’s akin to the concept of “enharmonic” in note names such as A♭ vs G♯.

Diminished 7th

Apart from 4th and 5th, “augmented” and “diminished” qualities appear also in other intervals. For instance, in the case of a “jminor 7th,” if the distance of the already short 7th gets even smaller, it becomes a “diminished” 7th.

So, imagine that the regular states are “major/minor/perfect”, and when it goes beyond that, the qualities “augmented/diminished” appear.

There are essentially only these 5 types of qualities ³.