Shell Function

In the previous session, the concept “In-chord Degree” was introduced. The position of the melody relative to the chord root has a significant impact on the impression of the melody. Now, what we will learn is the meaning of each fundamental degree: 1, 3, 5, and 7.

When we consider 1, 3, 5, and 7 from the perspective of “harmonic tendency,” they all have an effect of easing the original (horizontal) tendency to a great extent. Then, are all of the degrees musically equivalent in melody making? Of course not.

For example, when the chord is C, if the melody is C it means that the melody is reinforcing the root power, and if the melody is E, it means reinforcing the color of 3^rd. Since the melody is the most ear-catching part, determining which part the melody reinforces naturally has a strong influence on the musical impression. This is what we discuss this time.

1. Shell Function

As mentioned in Chapter.I, each note of the melody inherently comes with a “kernel.” However, when the chords are played, additional roles and qualities are superimposed on these kernels. For instance, even if a note originally has low harmonic tendency, when it becomes an even-degree within the chord, its tendency increases. It can theoretically be viewed like it’s receiving additional qualities based on its relationship with the chord.

The original qualities of the melody have been named “kernel,” but these “additional qualities” do not have a name yet. Without a name, it will be problematic for future explanations. Therefore, in LMT we will call these “additional qualities and roles given to the melody based on in-chord degree a shell function, or simply Shell.

…The terminology has gotten a bit congested in the past few sections, so let’s summarize it once more.

Term	Kernel	Shell
Meaning	Roles and qualities based on the relative distance from the tonal center	Roles and qualities based on the relative distance from the chord root
Determining Factor	Scale Degree	In-chord Degree
Perspective	Horizontal	Vertical

This is how it is. The qualities of the melody learned in Chapter.I are called “kernels,” and composing lines with this awareness is called “horizontal composition”. On the other hand, what we will learn from Chapter.II, the “qualities derived from the relationship between chords and melody”, are referred to as “shells”. By being aware of shell qualities, you can also become capable of “vertical composition.”

Each note of the melody has a kernel, and when a chord is added, the melody dons another layer, a shell, evolving into a more complex entity. Depending on the chords, the color and form of this layered shell differ. I want you to imagine the melody’s structure in that way.

When you can comprehend the melody with this “dual-layered structure” of kernels and shells, the amount of visible information in music analysis dramatically increases. Moreover, during songwriting and arrangement, this concept becomes a powerful guideline.

2. Kernel and Shell

The kernel of a certain tone remains unchanged as long as the key remains constant. On the other hand, the shell can change simply by changing the chord. From this perspective, the kernel can be seen as having a more fundamental nature, while the shell is somewhat more supplementary and superficial in nature. In extreme cases, it’s even possible to change shells while the melody repeats the same phrase.

This is the song “Licorice”, already introduced in Chapter I, where the chorus consists entirely of repeated mi (C♯ in A major key). However, the progression of chords ensures the development of the song—And what is happening at this time is not just a change of chords, but the feel of the melody with just repeated notes is also being changed each time.

In this way, starting from a slightly tense 7^th state, then turns simpler odd degrees, and sometimes even degrees, automatically making the waves of tension/release.

Shells created by chords are like “masks” for the melody. The note mi cannot escape its role as the kernel of mi, but by changing the chords, you can “dress it up” in different shells.

Until now, it was probably basic to think of chord progressions as chord progressions and melodies as melodies separately. However, it becomes important from here to get used to the mechanism where melodies and chords are mutually related, and changing the chords also changes the impression of the melody, like a puzzle!

3. The Differences in Shells

So, while Chapter.I provided an understanding of “kernels”, it’s now clear that we haven’t stepped into “shells” at all! The world of melody theory is vast. Let’s start by looking at the characteristics of the shells for the fundamental 1, 3, 5 degrees, and then the 7 degrees, seen as equally important one in jazz. We’ll save the characteristics of the 2, 4, and 6 degrees for later, as they are more theoretically advanced…

Considering the Law

The theory of shells is deeply connected to chord theory. When you learned about major and minor chords in Chord Chapter.I, you studied a bit about the quality of each tone, through the sound comparison. 3^rd is a vital degree that determines the chord quality. In contrast, 5^th has a transparent, colorless quality that supports the resonance. In this way, the sound of the chord is constructed.

Consequently, what quality of “shell” each tone will possess is naturally deduced¹.

Let’s compare them by listening through audio samples, evidence speaks louder than words.

Root Shell

VI_mIII_mIVIII_mVI_mVII_m^(-5)III

The first notes on chord change are important on sound impression, so in the example above I set Rt shell for all the first notes on chord change so that you can confirm the character of each shell.

Since there are no comparisons yet, it might not be evident, but it has a very straightforward sound that creates a simple impression.
In fact, Root Shell can be quite peculiar, and when it repeats like this, it becomes too synchronized with the bass, lacking diversity in sound. The decisive feeling at the beginning is quite nice, but when it resolves to I, it becomes a bit too simple and feels uninteresting.

However, there are situations where this straightforwardness shines, and I will introduce them in the coming articles. For now, let’s continue with the comparisons.

3rd Shell

Now all the shells on chord transitions here are set 3^rd. Melodies based on 3^rd shell enhance the color of major/minor, providing a rich emotional contents. In the world of melody writing, the 3^rd undeniably plays an ace role.

3^rd is easy to form lines, pleasant to listen to, a convenient note that rarely goes wrong. You can even stick to the 3^rd throughout, and there’s no problem at all.
The song above is in relatively minor key but the mood is more about “nostalgia” than “sadness,” and it doesn’t feel too gloomy. This might be due to the emphasis on brightness as well as darkness, by the power of 3^rd shell.

5th Shell

I believe there’s something powerful about the mood, different from 3^rd. It might be the strongest expression of the “sadness” inherent in the minor tonality. Compared to 3^rd shell based melodies, it’s much more straight and possesses a striking quality. This is largely influenced by the fact that 5^th is a note that has nothing to do with major/minor qualities.

In terms of straightness, it’s quite similar to Rt, but the key point here is that it maintains a certain richness of tone, as it doesn’t harmonize in unison with the bass.

7th Shell

7^th shell is similar to 3^rd in terms of emotional vibes, but due to its complex dissonance, the conveyed texture becomes more intricate. The overall sound is warm and mellow, not much giving the impression of being in minor key. It excels in a mature expression, while it lacks directness and powerfulness.

In this way, you might have felt that even with the same chord progression, the same rhythm and sound, changing the pivotal shell alters what the overall composition conveys. The straightest Rt Shell, followed by 5^th Shell, 3^rd Shell that governs major/minor colors, and 7^th Shell that controls sound complexity and richness.

The four pieces above, by emphasizing the uniformed shell, each acquired their distinct identity as a song. Therefore, being sensitive to these textural differences is quite essential in songwriting!

Guide Tones

The 3^rd and 7^th notes hold a special significance as they determine the quality of the chord. In jazz theory, these notes are referred to as Guide Tones. Perhaps these tones were named as such because they serve as “guides” for chord quality.

So all jazz players, even though they don’t use the word “shell”, understand how 3^rd and 7^th contribute to the harmony, and on songwriting they utilize such characteristics of tones.

Melodic Outlines

Normally there are multiple melodic notes per a single chord, making it difficult to care about every single note. In a simplified analysis/practice, it’s a good idea to focus only on the essential notes; which include the first note when the chord changes, sustained notes, and notes held in higher positions, etc. Some people refer to these crucial notes collectively as Melodic Outlines².

Kernel and Shell

Creating lines while consciously considering both shell of each note is undoubtedly a high-level skill. Moreover, you shoudn’t neglect the aspects of kernel as well. However, melody makers in the world have mastered these textural differences and their use, whether through theory or experience, to craft captivating melodies. As mentioned at the beginning of Chapter I, while understanding melody theory may be easy, mastering it takes time.

In Chapter II, we will delve into how to construct these “shells.” In the upcoming sections, we will explain the practical application of each shell with examples.

Summary

• The acoustic characteristics added to the melody based on in-chord degrees are referred to as “shell”.
• The combination of the fundamental characteristics “kernel” and the additional characteristics “shell” largely determines the expression of the melody.
• In the order of Rt – 5^th – 3^rd – 7^th, the character of a shell transitions from a powerful (straight) sound to an emotional (rich) sound.

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