Contents
Entering Chapter II-III, new chords other than the prime chords, namely “non-prime chords“, have been introduced. In this article, we will explain how to apply nexus theory to non-prime chords.
1. Review of Nexus Theory
First, let’s revisit the characteristics of each nexus:
| Nexus | Meaning | Characteristics |
|---|---|---|
| 2▲2▼ | 2nd up/down | Gentle and smooth, rich in color |
| 5▲ | 5th up | Clear propulsive force, distinctive |
| 5▼ | 5th down | Clear propulsive force, easy to listen to |
| 3▲ | 3rd up | Minimal sound change, unique sense of elevation |
| 3▼ | 3rd down | Minimal sound change, stable |
The main theme this time is to apply such classification and analysis to non-prime chords.
2. Nexus of Non-Prime Chords
Actually, analysis on non-prime chords is nothing different. It’s essential to consider how the “control factors”, namely the changes in quality and root, are changing and, as a result, how many common tones a nexus has. Let’s look at some examples.
Nexus from II to IV
For example, II to IV involves 3▲, and it still has the same kind of ethereal elevation as IIm to IV. Now the drama of “minor to major change” is eliminated, but on the other hand, the change in texture increases slightly due to the reduction in common tones by one note.
maj to maj, 1 common toneNexus from IVm to V
IVm to V is also 2▲ like IV to V, but as it moves from minor to major, it brings a change in the mood, resulting in a more dramatic development.
min to maj, no common tonesSo, when you feel that the energy level is lacking with just IVV, it seems effective to switch to IVm, for example.
Flat-Root Chords and Nexuses
Even with 
VI or VII that have new roots, the difference is not significant.
- VI→V is 2▼. Since there is no change between major and minor and it’s a half-step difference, it is a quite smooth progression.
- VII→V is 3▼. Upon listening, it indeed has a calm developmental quality similar to 3▼ in the prime chords. However, due to the flattening of ti, the common tone has decreased by one note, so the change may feel slightly stronger.
Notably, all flat-root chords have a pattern of smoothly descending by a half step. The half-step motion has an even smoother quality among the 2nd nexuses, but within the prime chords, it was only between IIIm⇄IV. Now you have much more choices.
The changes in quality, root, and the resulting number of common tones. Since these are all key-independent information, even with non-prime chords outside the key, their connections can be analyzed consistently.
Slash Chords and Nexuses
Determining how to interpret a “slash chord” where the content is divided between the “numerator” and “denominator” can be challenging. Ideally, it is recommended to use slashes also in the nexus analysis, observing the connections individually for both the numerator and denominator.
This allows for a more precise understanding of what is happening, such as, “In terms of the overall sound impression, there is a clear and stable propulsive force of 5▼. However, its propelling energy is restrained by shifting the bassline to 2▲,” providing a detailed insight into the chord progression.
3. Application of Nexus Theory
While there’s total freedom regarding chord connections, involving special chords like sharp-fifth or flat-fifth are inevitably limited in their “effective” usage. In such cases, the only option is to memorize the fixed patterns…
However, in some cases, considering from the perspective of a control factor can provide creative guidance. For example…
Connection of dim7 Chords
This inquiry seeks to create progressions involving the familiar eerie sound of diminished sevenths, a type of composition not found in the pop music textbooks.
How to connect various diminished seventh chords? Let’s use nexus theory as a guide to construct chord progressions.
(1) Made with 3▼
Remember that the symbol “o7” represents a diminished seventh chord. Here, we have a progression with the root C-A-F♯-E♭. The defining feature of Diminished Seventh is that “all chord tones are minor third intervals apart.” In this progression, as you can see, the members of the chord tones remain entirely unchanged1.
From the perspective of nexus theory, the characteristics of this progression can be described like “3▼ in succession, creating a calm atmosphere” and “no change in chord tones, resulting in a very static feeling with minimal musical development”.
(2) Made with 2▲2▼5▼
On the other hand, this progression follows 2▲–5▼–2▼. Connecting dim7 with a 2nd interval results in a complete change in all four members, leading to a significant sonic transformation. In this case, it seems to create a sense of tension accumulated even higher. Additionally, 5▼ provides a distinct propulsive energy.
Comparing the two, the previous example has a strong sense of stagnation in one place, giving the impression that the story is not unfolding. Therefore, even with the same “horror back track” the first pattern fits well with a scene like “lurking somewhere in silence”, while the second pattern, conversely, suits a scene like “slowly walking through a dark corridor”. This illustrates how you can consider the emotional atmosphere of the music from a theoretical perspective.
Non-prime Chords and 3rd Nexus
As explained in nexus theory chapter, in jazz and orthodox pops clear and strong progressions are often favored, but it varies by genre — In techno and dance music, for example, a less dynamic 3rd nexus is also preferred.
And in the world of film music, it has become a common practice to connect non-prime chords with 3rd nexuses.
In this example, It alternately connects between C major and the chords rooted on E. What’s interesting is that it’s not diatonic Em, but E or EmΔ7, adding a touch of grandeur to the music despite the simplicity of the progression.
When a progression is formed like C→E, the next one likely to come is Am, in the pop music format. But such emotional progression would be too conspicuous in background music like this. Instead, the calm movement created by 3▲3▼ imparts a cosmic expansiveness to the music.
This example uses more seventh chords to add complexity, starting with a C chord but introducing CmΔ7 as the third chord, considered a particularly distinctive parallel minor. The final Am is also quite unique in the context of the C major key, which you hardly see in ordinary pop songs. Such chords 3rd away from tonic (=III, VI, III♭ or VI♭) with accidentals are collectively referred to as Chromatic Mediants.
On considering progressions like this, the fundamental principle of nexus theory remains valid: “The more common tones, the less acoustical change, and the smoother the connection.” This applies even when dealing with chords containing accidentals or chords with seventh or ninth. For example, the progression from EΔ7 to CmΔ7 may seem unconventional at first glance, but in reality, the tones B and D♯ (=E♭) are sustained as common tones. In the example above, this feature is utilized to smoothly connect the two chords. In a sense, nexus theory becomes especially useful in arranging such progressions involving non-prime chords.
Theory and Music Styles
Some may not have considered implementing progressions like “four consecutive dim7 chords” or “freely using non-prime chords”. However, what is explained in Chapters I-II are more like “rails for easily creating listener-friendly pop music”. If you want to create something different, you are always free to deviate from such “rails”. As knowledge accumulates inside your mind, there’s a tendency to think within the confines of that knowledge. It’s crucial to always remember the existence of the “uncharted territories” beyond that knowledge.
