1 Starting from the Black and White Keys: The Smallest Structural Unit of the Music System

In previous articles (see:Awakening of the Voice · Basics (Part 1): Pitch Structure and Auditory Stability), I mentioned an important fact:The fifth relationship describes the auditory closeness and distance between pitchesFor example, C and G, G and D, are naturally close in perception; however, the piano keyboard is not arranged in this auditory order of pitches.

Instead, the keyboard projects these pitch names (C, D, E, F, G, A, B)in a way that suits two-handed performance and memory, onto a linear key structure—the seven most commonly used and easily integrated pitch names are retained to form the basic skeleton of the white keys; the remaining pitches are inserted in the form of black keys, thereby balancing playability and scale completeness within a limited physical space:

However, once we actually look at the keyboard, a question inevitably arises: why do the white keys repeat in the order of C–D–E–F–G–A–B–C′ ? And why, between E–F 与 B–C′(stepping into the next group of C), is there always a missing corresponding black key? If we look at it solely from the perspective of “convenience of playing,” all white keys are visually identical in width and evenly spaced. Under such a premise,having “gaps” only in these two places indeed seems somewhat counterintuitive. But when we return to actual hearing, we discover another thing: the distance between the two groups of notes, E–F and B–C′, is noticeably closer than that of other adjacent white keys. Because of this, they only need a half step between them to complete the transition from one note to the next—which implies a key fact:The white keys themselves are not equidistant.

Although the piano keyboard is a linear physical structure, the pitch relationships it carries present a non-uniform interval distribution within the white keys from the very beginning. If we take C to the next C′ as a complete observation interval, we will find a stable and recurring pattern:

• C–D: whole step
• D–E: whole step
• E–F: half step
• F–G: whole step
• G–A: whole step
• A–B: whole step
• B–C′: half step

That is to say, in this structure composed of seven scale degrees and resolved by returning to the octave,half steps are always fixedly located after the third and seventh degrees. This is not a clever design of the keyboard, nor is it a compromise made to “look neat,” but a direct result of a deeper structure:What the piano white keys present is not a patchwork of any seven arbitrary notes, but a complete, closed, and self-consistent scale structure.

From this perspective, the white keys are not the “notes selected first,” nor are the black keys “notes added later.” The actual order is quite the opposite—what existed first was a specific way of organizing intervals; the white keys are merely the simplest visual representation of this organization on the keyboard; the appearance of the black keys, on the other hand, serves to fill in the remaining possible pitch positions without destroying this framework.

And precisely because of this,C–D–E–F–G–A–B–C′ this group of notes can naturally form a structurally complete and auditorily stable scale model without relying on any accidentals. This is precisely the core viewpoint I have repeatedly emphasized in *The Awakening of Sound: Foundation (I)* and *Foundation (II)*—A stable auditory perception does not come from a single individual note, but from the smallest, closable musical structural unit formed by the fixed whole-step and half-step relationships between notes.

2 From Structure to Example: The Unfolding of C Natural Major and Minor

1 Natural Major: The “Cleanest” Structural Example

In the previous chapter, we have already seen that what the white keys of the piano present is not a random selection of seven notes, but a structural model with highly stable internal interval relationships that recurs repeatedly. It is precisely this structure that allows us to naturally perceive the tendencies of “stability,” “returning to the starting point,” and “ending” in our hearing.

In *The Awakening of Sound: Foundation (I)* and *The Awakening of Sound: Foundation (II)*, I have mentioned the two most fundamental scale forms, ”major” and ”minor,” many times. I will not repeat their conceptual definitions here, but instead look at them from a more intuitive perspective:If we were to choose an example on the keyboard that relies least on accidentals, is the most intuitive, and most completely presents this interval structure, then C natural major is almost an unavoidable starting point.

When we map the interval pattern summarized in the previous chapter—“whole-whole-half-whole-whole-whole-half” directly onto the white keys of the piano, we get exactly this group of notes: C – D – E – F – G – A – B – C′, where there is no involvement of any sharps or flats, and all pitches fall precisely on the white keys:

This is not because the note C is “special,” but because this interval structure herehappens to be fully unfolded in the form of minimal modification。

And precisely because of this, C natural major is often treated as a “reference model”: not because it is superior, but because itpresents the structure itself with the least reliance on external corrections。

From an auditory perspective, the stability of this scale does not come from any specific note, but from the following fact: the distribution of distances between the tonic and the other notes is non-uniform; the positions of the half steps are fixedly arranged after the third and seventh degrees; this non-uniformity, conversely, constitutes the strongest sense of direction and resolution.

In other words, the reason we “want to stop” on C is not because C itself has any magic, but because the entire set of interval relationships constantly pushes the auditory center of gravity back here.

2 Another Kind of Stability in Parallel: C Natural Minor

If we still start with C but reorganize the interval relationships, we will get another structure that is equally complete but has a noticeably different auditory feel: C – D – E♭ – F – G – A♭ – B♭ – C′, which is C natural minor:

In C natural minor, the scale still starts from C, but the distribution of half steps and whole steps changes—“whole-half-whole-whole-half-whole-whole”, and the result is:The tonic remains unchanged, the set of pitches changes, and the form of the sense of stability changes accordingly. This is precisely where the core difference between “parallel major” and “parallel minor” lies.

What needs to be emphasized in particular is that this difference is not about emotional labels like “bright” or “melancholy,” but a more fundamental fact: the distance between certain notes and the tonic is shortened; certain points of stability are weakened; auditory tension is redistributed within the scale. From the perspective of the keyboard, the piano has not changed at all; from an auditory perspective,the entire “route home” has become completely different。

This also happens to confirm the conclusion of the previous chapter once again:The keyboard is merely the shell that carries the structure; what truly determines the auditory experience is always the interval relationship itself.

3 Another Belonging of the Same Group of White Keys: A Natural Minor

If we do not change any pitches for the moment, but simply change the “auditory center of gravity,” things become even more interesting. Still using the seven white-key notes: C – D – E – F – G – A – B, but no longer treating C as the auditory starting and ending point, and instead letting the sense of stability naturally fall on A, then a new scale form emerges: A – B – C – D – E – F – G. This is precisely therelative minor of C natural major—A natural minor (For ease of understanding here, we will temporarily not distinguish specific octaves, but only focus on “which notes are used”):

Here, the set of pitches is identical, but the auditory experience changes significantly. The reason is not complicated: the point of stability has shifted; the direction of tension within the scale is reinterpreted; “where to return to count as the end” is no longer determined by note names, but by the way of auditory organization.

From a structural perspective, this is a very crucial expansion: it shows that—a scale is not just about “which notes are used,” but more importantly, “how these notes are understood around a center.” It is precisely in this sense that tonality, harmony, and the sense of voice belonging begin to have a basis for discussion.

Note: Since there is a “relative minor,” there naturally exists a corresponding “relative major.” By definition, they simply start from the same set of pitch materials but choose different auditory centers of gravity. However, in the context of this article, introducing “relative major” does not bring new conceptual value, but might instead draw attention to the naming system itself. Compared to the symmetry of terminology, this article is more concerned with:the changes in the sense of stability, tension, and direction of the music when the auditory center of gravity shifts. Therefore, this concept will not be expanded upon for now, and will be left to be discussed again later in a more appropriate context.

4 Summary: Scales Are Not Pitch Names, But an Auditory Order

Looking back at this chapter, we have always focused on a more fundamental question:When a group of notes is organized into a scale, how exactly does our hearing acquire a sense of stability?

Around this question, we have observed three situations that seem similar but yield completely different auditory results:

C natural major: In the most intuitive physical layout of the white keys, the interval relationship of whole-whole-half-whole-whole-whole-half unfolds naturally, with C becoming the stable starting and ending point, and the scale presenting a complete and clear sense of center.

C natural minor (parallel minor): Under the premise that the tonic remains unchanged, the interval structure is adjusted, and the distribution of stability and tension changes accordingly. With the same tonic C, the auditory character is already noticeably different.

A natural minor (relative minor): The set of pitches remains unchanged, still those seven white keys, but when the auditory center of gravity shifts from C to A, the original order is reinterpreted, and a new point of stability naturally emerges.

Through these three examples, a key fact can be seen:a scale is not a “collection of note names,” but an ordered structure established around an auditory center of gravity—the arrangement of the white keys is merely the projection of this structure on the keyboard; what truly determines “where we stand” and “where we return to” is not the physical position, but the relationships between notes.

And precisely because of this, when we talk about scales, we are never just discussing “which notes are used,” but how these notes are organized in our hearing, how they form a center, and how they establish expectations.

Only after understanding this layer do we have the conditions to move forward: we will introduce, on top of these scale structures,Vertical combinations of pitches, to see how the auditory order changes when multiple notes sound simultaneously.

As a side note on historical background: before the formation of the modern keyboard system, the cyclical order of note names was originally A–B–C–D–E–F–G, which was more in line with linguistic habits and facilitated early notation and singing.

The reason why the modern piano keyboard chooses to start from C to arrange the white keysis not because the note name system itself changed, but because in the course of later development, in order to simultaneously satisfyplaying convenience, visual patterns, and the intuitive presentation of scale structures, people reorganized the physical arrangement of the keyboard. In this adjustment process, the C natural major scale, which requires no sharps or flats to fully present the core interval structure of ”whole-whole-half-whole-whole-whole-half,” happened to become the most intuitive and stable reference model, playing a key role in driving the establishment of the final form of the piano's white keys.

But it must be emphasized thatthe white keys themselves do not ”serve the C major scale”They are more like a basic framework of pitch classes built around the cycle of note names, independent of the choice of the tonic. Therefore, when we map the A natural minor scaleonto this same set of white keys, although the auditory center of gravity falls on A and the modal color changes accordingly, there is no conflict between the cyclical order of the note names and the arrangement of the keyboard—they simply respond to different trade-offs made between historical evolution and practical usage needs on the “structural level” and the “auditory functional level” respectively.

Similarly, other church modes such as Dorian and Phrygian can also be established on the same set of note names and keyboard structure, with their differences reflected more in the choice of the tonic and the shift of the interval center of gravity.Since the principles are largely the same, we will not elaborate further here.

3 Chords: The Formation of Vertical Structure

1 Where Do Chords Come From?

In the first two chapters, we have repeatedly discussed the issue of scales. Whether it is the arrangement of the white keys or the structural differences between major and minor scales, they are essentially answering the same question:Among a continuous series of pitches, which notes are selected and form a stable auditory order around the tonic. But up to this point, the discussion has always remained under one premise—notes appear sequentially。

Melody, whether simple or complex, is the unfolding of notes on the timeline: one note after another, where the sequential relationship determines the direction, tension, and sense of resolution. However, if we change this premise even slightly, a new phenomenon immediately emerges. When two, three, or even more notesno longer appear sequentially, but are sounded simultaneously at the same moment, the auditory experience changes significantly.

Some combinations of notes sound exceptionally natural, stable, and blended; even without analysis, one subconsciously accepts their existence. Other combinations, even if all the notes come from the same scale, appear tense and restless, as if suspended in mid-air, waiting for a “resolution” in some direction. This difference does not depend on whether the melody is complex; even if a few notes are simply pressed together, most people can immediately distinguish which combinations “hold their ground” and which “need to move on.”

This shows that when the relationship between notes changes from “sequential” to “simultaneous,” music enters a new structural level. More importantly, this stability and instability are not accidental.

If we return to the familiar scale structure, taking C natural major as an example, the seven notes formed by the white keys already contain a clear and uneven distribution of intervals. When certain notes among them are selected simultaneously, the distance relationships between them naturally create blend, tension, or tendency in our hearing. In other words,not all “simultaneously occurring notes” are equivalent。

In practice, people quickly discovered that certain combinations are used and accepted repeatedly, while others rarely exist as points of rest. It is precisely on the basis of such practice that those combinations of notes within the same scale thatsound stable, have a clear structure, and are easily perceived as a wholewere gradually distinguished and became an independent and important structural unit in music. What we call “chords” today is precisely the summary and naming of this phenomenon.

From this perspective, chords are not concepts “invented” out of thin air, nor are they rules artificially imposed on scales. They stem from a very simple fact:when multiple notes in a scale are used simultaneously, our hearing actively filters them.

Therefore, chords are not the opposite of scales, but rather the natural unfolding of scales in another dimension—if scales describe how notes are arranged in time, then chords discuss how these notes cooperate with each other at the same moment. Understanding this, the subsequent topics regarding the composition of triads, functional tendencies, and even more complex harmonic progressions are merely further refinements and extensions of this basic fact.

2 Why “Three Notes”: The Most Stable Vertical Structure

In the previous section, we have already seen a very crucial phenomenon: when multiple notes are played simultaneously, our hearing does not perceive them as a “cluttered superposition,” but instead actively judges which combinations are more stable and which carry tension. Thus, a natural question arises:Exactly how many notes are needed to form a relatively complete vertical structure that can be independently recognized by our hearing?

Starting from the simplest case: when two notes appear simultaneously, the core focus of our hearing is still theinterval relationshipWhether it is a perfect fifth, a perfect fourth, or a major third, a minor third, it is essentially still “the distance between one note and another.” This combination can, of course, be stable or unstable, but it still remains at the level of “relationship” rather than “structure.” In other words,two notes are more about describing tension rather than establishing a sense of belongingThey can serve melody or counterpoint well, but it is difficult for them to independently assume the role of a “landing point” or “center.”

When a third note is added, the situation changes fundamentally. Three notes are no longer just a superposition of distances between pairs, but begin to form aself-consistent wholeAt this point, our hearing no longer tracks each note individually, but automatically integrates them into a unified auditory object. Taking C natural major as an example, when the three notes C, E, and G appear simultaneously:

we barely perceive their individual pitches anymore, but instead directly hear a “firmly standing whole” that both clearly points to C and does not force our hearing to continue moving forward. This point is very crucial:Three notes, for the first time, allow our hearing to simultaneously obtain a “sense of center” and a “sense of completeness.”

Structurally, this is because the three-note combination is already able to satisfy three conditions simultaneously: the existence of a clear reference note (tonic or root), the existence of a note that determines the color (major or minor third), and a note used for support and expansion (fifth). Even without using any theoretical terminology, our hearing will naturally make this judgment: “This combination is complete; it can stop here.”

In contrast, if we continue to increase the number of notes, such as adding the seventh or ninth, our hearing does not become more stable as a result; instead, it often introduces new tension and directionality. These notes are not useless, but they are more like adding decoration, driving the direction, or creating suspense on top of an already established structure.

Therefore, from the perspective of long-term musical practice, three notes happen to constitute a minimal yet sufficiently complete vertical structural unit. It is neither a makeshift combination barely holding together nor an overly complex stack, but rather achieves a very natural balance among stability, clarity, and recognizability. Precisely because this structure is sufficiently complete to our hearing, the combination of three notes has been used repeatedly and has gradually become the most fundamental building block in vertical sound organization.

However, it is important to note that “complete” is not equivalent to “identical.” Even if they consist of the same number of notes, these three-note structures are not perceived in the same way in actual listening.

When they are placed back into a specific scale context, some are naturally heard as “places to stop,” while others seem to possess an inherent sense of direction, pointing toward a landing point that has not yet appeared.It is precisely this difference that makes structures composed of three notes no longer just abstract, stable combinations, but instead begin to assume different musical roles.

Next, we need to look further into how these roles are created.

3 Also Three Notes, Why Do They Sound Different?

In the previous section, we established one point: a structure composed of three notes is the smallest, yet already sufficiently complete, vertical unit in auditory perception. However, this does not mean that all three-note structures are perceptually equivalent.

If we still use C natural major as the background and stack the notes of the scale upward in thirds, we will get multiple combinations of three notes. Structurally, they all meet the condition of “three notes,” but in actual listening, they exhibit distinctly different tendencies.

For example, when the three notes C, E, and G sound simultaneously, most people will have a very clear feeling: this sound can stop here, with no need to continue forward. Even if the melody ends here, the listener will not feel suspense or discomfort. This sense of stability is not because there are more notes or because they are louder, but because this combination highly coincides with the scale's center of gravity.

But if we apply the same method to another set of notes, such as G, B, and D, the situation changes. Although these are also three notes from the same scale and the structure is perfectly valid, the listener often gets a feeling of “not yet finished.” This combination seems to point to a landing point that has not yet appeared, rather than becoming the ending itself.

If we switch to another set of notes, such as F, A, and C, the perception will be different again. It neither has a strong sense of finality like C–E–G, nor does it urgently demand resolution like G–B–D; instead, it presents a state somewhere in between, capable of pausing temporarily while retaining room for further development.

These differences are not coincidences of subjective perception, but stem directly from their positional relationships within the scale. Although the three-note structure is already vertically complete, its distance from the tonic and its degree of association with the scale's center of gravity still quietly influence auditory judgment.

Because of this, the ear does not treat all three-note combinations equally, but naturally assigns them different “roles.” Some are more like points of arrival, some are more like driving forces, and others assume the function of transition and connection.

Precisely because of these perceptual differences among three-note structures, the ear does not view them as equivalent units that can be swapped at will. Even though they are structurally complete, in actual experience, they naturally exhibit different tendencies: some are more easily perceived as points of arrival, while others seem to push the listener forward.

It must be emphasized that this difference is not an acquired rule, but the result of a judgment spontaneously formed by the ear when facing different scale positions. It is also at this level that we are able to distinguish for the first time:Structures that are equally composed of three notes do not assume the same auditory roles.

Up to this point, we are still at the level of “individual structures,” discussing the tendencies and characteristics they each present. Only when these structures with different tendencies are placed in time and connected to one another do they further form a more complex overall progression.

4 Diatonic Chords: The Unfolding of the Three-Note Structure in the Scale

In the previous sections, we have confirmed one thing: chords are not just random piles of notes, but stable vertical forms built within a scale, with the “three-note structure” at their core. So, the next question becomes—If we stand within a specific key, in what way will these three-note structures appear?

To avoid introducing extra complexity, here we will use the most intuitive and most frequently referenced C natural major as an example.

The scale of C major is: C – D – E – F – G – A – B. If we strictly follow the rules discussed earlier:stacking three notes within the scale by “taking every other note”, we will get a set of triads derived entirely from within that key. Starting from each degree of the scale, we can build in turn:

• With C as the root: C–E–G
• With D as the root: D–F–A
• With E as the root: E–G–B
• With F as the root: F–A–C
• With G as the root: G–B–D
• With A as the root: A–C–E
• With B as the root: B–D–F

As we can see, these chords are not “a set of combinations artificially designed,” butthe natural result derived from the scale structure itself. As long as you stay within a fixed key and stick to stacking thirds, these seven chords will almost inevitably appear.

Further observation reveals that although they appear similar in form, their degree of stability is not exactly the same—some sound bright and stable, some are softer, and others are noticeably tense and unstable. This difference is not accidental, but stems from the different interval relationships contained within each chord. Because of this, in tonal music, these chords have gradually been assigned different “positions” and “roles,” rather than existing merely as isolated vertical structures.

However, for now, we need not rush into discussing “how they should be used” or “where they should go.” The focus of this section is simply to let the reader clearly see that when three-note structures are fully integrated into a scale, chords are no longer scattered concepts, but unfold naturally along the scale in a systematic way. From this moment on, “chords” are no longer just a matter of individual stable structures, but officially become a part of the tonal system. And when these diatonic chords begin to relate to one another, creating a sense of direction and momentum, we truly enter the realm of “harmony.”

4 Harmony: When Structure Begins to Move

1 When Chords Begin to Point to One Another

In the previous chapter, we saw that even though they are also composed of three notes, different three-note structures are not aurally equivalent. Due to their differing relationships with the tonic, they naturally exhibit different tendencies, such as stability, drive, or transition.

But so far, our discussion has still been about what these structures “individually look like.” In other words, as long as these structures are only understood as “existing in isolation,” what we perceive aurally is merely a momentary state, rather than the movement of the music itself. What truly gives music a sense of direction is not any single three-note structure itself, but the overall relationship formed when they appear sequentially in time and relate to one another—this is precisely where “harmony” begins to play its part。

Harmony can be understood in this way:Along the timeline, the continuous change of vertical structures (chords) and their relationships to one another is harmony itself. In other words, harmony is concerned not with what a single chord is, but with how these chords unfold in time, point to one another, generate tension and release, and ultimately shape the music's sense of direction.

When a three-note structure with a stable tendency appears, the ear often defaults to treating it as a temporary resting point; when a structure with a driving tendency appears, the ear instinctively anticipates the arrival of the next structure. This expectation does not come from the melody itself, but from the implicit directional relationships between the vertical structures.

For example, when a structure centered on G–B–D appears, even if the melody has not yet clearly resolved to C, the ear already begins to “wait” for some kind of return to occur. This sense of anticipation does not depend on the number of notes or the loudness, but stems from the structure's position in the scale and its unresolved relationship with the tonic.

Therefore, harmony is not describing “what is heard at this moment,” but ratherwhat kind of space the current structure leaves for the structure that might follow。

From this perspective, chords are more like static components, while harmony is the way these components are organized in time. The former answers “what is it,” while the latter answers “where is it going.” When multiple chords are placed in different positions and appear in a specific order, they form a series of relationships—such as tension, release, return, and deviation—which are precisely the musical movement perceived by the ear.

Because of this, even if two pieces of music use the exact same chords, as long as the order of arrangement or the timing of staying and transitioning differs, the final overall feeling they project can be completely opposite. Harmony is never concerned with isolated materials, but with the paths formed between them.

When we realize this, we find that the so-called “sense of harmony” is essentially an ability to judge structural direction. It does not require the listener to be able to name the chords accurately, yet it allows them to clearly perceive that “it's not over yet,” “it has returned,” or “it is turning elsewhere.”

In this text, the “harmony” we refer to isConcepts used in modern vocal and music theory to describe chords and their vertical relationships—that is, a system that analyzes how pitch, intervals, and triadic structures interact over time to generate tension and resolution. This is not entirely the same as the everyday understanding of “harmony”: in daily singing, when the lead vocalist sings the melody and backing vocalists sing different notes, we also call that harmony.

The connection between the two lies in the fact that the different notes sung by backing vocalists are often precisely the chord tones analyzed in theoretical harmony; their arrangement and progression actually manifest the stability, tension, and sense of direction in harmonic theory. In other words, backing harmony can be seen as an intuitive manifestation of theoretical harmony, but theoretical harmony focuses on structure and function, rather than just the heard layering of multiple voices.

2 What Is Harmony Doing While the Melody Progresses?

In everyday listening experiences, we tend to naturally focus our attention on the melody. The melody is “in the foreground”: it is the line that is sung, remembered, and most easily hummed. Therefore, when we talk about the direction of a piece of music, it is easy to intuitively attribute feelings of “progression,” “pause,” and “resolution” entirely to the melody itself.

But if we pay a little closer attention, we find an intriguing phenomenon: the same melody, against different backgrounds, often feels quite different—sometimes it sounds firmly settled in one place, while other times it seems suspended in mid-air; sometimes a note can naturally be perceived as an ending, while in other cases, that same note seems to be just “passing through.”

The issue does not lie in the melodic note itself, but in thevertical environmentin which it is situated. Melody is essentially a horizontally unfolding line. It presents only one note at a time, and a single note does not inherently carry information like “this is the end” or “this is the beginning.” Whether a note is heard as stable or unstable is often not because of its absolute pitch, but because ofthe kind of relationship it has with the current vertical structure。

It is precisely at this level that harmony begins to play its role. When a chord (or more accurately, a vertical structure) is in the background, it provides an implicit frame of reference for the current moment. Every note in the melody is automatically placed into this framework by our hearing to be judged: is this note part of the structure, or a deviation from it? Is it reinforcing the current state of stability, or is it creating tension and pointing toward the next change?

Therefore, harmony does not need to be fully “heard” to have an effect. Even if it is only faintly present, or simplified in the accompaniment, it is already quietly influencing how our hearing interprets the melody.

To give an intuitive example: when the note G appears in a melody, if the background structure clearly points to C as the center, this G is often heard as a stable but not fully closed state; however, if the background structure itself is already in an unstable position, the same G may be perceived as a force driving things further forward. The note has not changed, and the direction of the melody has not changed, butthe auditory expectation of “what will happen next” has already become significantly different。

From this perspective, the melody is not isolated in “carrying the music forward.” It is more like moving within an already laid-out force field, and this force field is precisely what is constructed by the harmony.

And because of this, when we listen to music, we often have a very clear yet hard-to-explain feeling: in some places, “singing up to here is enough,” while in others, “it feels like it hasn't ended yet, no matter what.” This judgment is not arrived at step-by-step by analyzing the intervals of the melody, but is an overall intuition formed by our hearing simultaneously integrating the horizontal lines and vertical structures.

It can be said thatmelody is responsible for speaking, while harmony is responsible for defining whether this statement is making a declaration, asking a question, or waiting for a response. Melody tells us what is happening, while harmony quietly decides in the background: whether these sounds have found stable footing, are still suspended, or are pointing toward a resolution that has yet to appear.

Once we realize this, we will find that the so-called “sense of melody” and “sense of harmony” are not two separate abilities. The former is hearing lines in time, while the latter is perceiving direction in structure. A truly mature listening experience happens precisely in the continuous interaction between the two.

3 Harmonic Progression: How Structure Forms a Path in Time

In the previous two sections, we have gradually shifted our perspective away from “individual structures” and begun to focus on the relationships between these structures over time. As the melody progresses, different vertical structures constantly appear and disappear in the background, quietly shifting the auditory center of gravity and expectations. But if we only view these changes as a series of “passive backdrops,” it is still insufficient to explain a more crucial phenomenon:Why the sequential order of certain structures feels natural and logical, while other sequences seem stiff, abrupt, or even unsettling.—This is precisely the dimension that “harmonic progression” aims to describe.

What is called harmonic progression is not a listing of “which chords can be used,” but rather a discussion of:how different vertical structures, appearing in succession, connect in our hearing to form a path with a sense of direction.This path does not appear out of thin air, but is built upon a core fact that has been repeatedly mentioned—that different structures themselves already carry different tendencies toward stability.

When a relatively stable structure appears, the listener naturally tends to perceive it as a temporary resting point; whereas when a structure with a sense of propulsion or incompleteness appears, the listener begins to anticipate the next development. Importantly, this anticipation is not generated after the structure disappears, but is already activated the very moment it appears. That is to say,the moment certain structures appear, they are already “implying” what is more likely to follow, and what is highly unlikely to follow.

It is precisely through the continuous accumulation of these implications that harmony begins to exhibit a “direction.” When the directional relationships between structures connect with one another, the listener no longer merely perceives one momentary state after another, but begins to perceive a continuous process of motion: from relative stability to instability, from tension to resolution, and from departure to return.

It is worth noting that the “path” here is not an absolutely fixed rule, let alone a mechanical formula. It is more like a consensus gradually formed through long-term listening experience:the reason certain directions feel natural is not because they are uniquely correct, but because they move along with auditory expectations.And when music deliberately violates these expectations, the resulting tension is established precisely on the premise of “it should have been so, but was not.”

From this perspective, harmonic progression does not dictate “how music should be written,” but rather describes “how music is usually understood.” It does not focus on the name or composition of a single structure, but rather on:where the appearance of this structure at this moment will push the listener, and when the next structure appears, whether it continues this direction or deliberately alters it.

Because of this, even if two pieces of music use the exact same set of structures, as long as the order of appearance, the duration of stay, and the avoided or emphasized nodes differ, the final overall direction presented can be completely opposite. What the listener perceives is not “what materials were used,” but “what kind of route these materials form in time.”

Understanding this, we can view harmonic progression as a kind of “path design”: some paths are clear and direct, while others constantly detour, delay, and create suspense. But no matter which approach is chosen, they all rely on a common premise—the listener is constantly tracking the directional relationships between structures, and continuously adjusting expectations for the music to follow based on this.

4 Why Does Deviating from the Path Create Tension?

In the previous section, we understood harmonic progression as a “path”: different vertical structures appear in succession over time, forming an aurally trackable direction through their respective directional relationships. When this path unfolds along existing expectations, the listener feels it is natural and smooth, and even before it ends, already “knows” roughly what will happen next.

So, where does tension come from? The answer is not complicated:Tension is precisely what arises at the moment when the path does not continue forward as expected.

When a structure appears, it is not merely stating its own condition, but is also sending an implicit directional hint to the listener. Through long-term experience, the listener has become accustomed to which structures are more likely to follow certain other structures, and is used to the idea that certain incomplete states ultimately need to be “completed.” It is against this backdrop that once subsequent developments do not unfold along this implicit path, the listener immediately senses a deviation.

This deviation is not equivalent to “error” or “chaos.” On the contrary, it is built precisely on the premise that the path has already been understood. If the listener has not yet formed any expectations, then the so-called deviation cannot even be spoken of.Only when the path is clear enough will deviation be perceived as tension.

From the perspective of listening experience, this tension often manifests as a state of “suspense” or “indecision”: the music seems to pause temporarily in a place where it shouldn't, or continues forward in a direction that is not the destination. At this point, the listener does not lose their sense of direction; instead, they focus even more intently on the upcoming changes, trying to judge whether this path will be pulled back or veer further elsewhere.

Importantly, tension is not created by a single structure itself, but bythe relationships between structures being temporarily suspended or twisted.triggered by. The same vertical structure, if it appears on a logical path, might go almost unnoticed; but if it appears in a position where it “should not appear,” its instability will immediately be magnified by the ear.

And precisely because of this, deviating from the path does not endlessly accumulate tension. If the music continues to wander in a direction that is completely untrackable, the ear will instead gradually give up its expectation of the path, and the tension will also lose its effect. In other words,tension relies on order, rather than chaos. It requires an already established sense of direction to serve as a reference point for deviation.

When deviation occurs, the music usually unfolds between two possibilities: one is to re-establish a new path through further turning; the other, through return or correction, is to bring the ear back to the originally expected position. Whichever it is, the deviation itself will not become the end point; it is merely a stage in the evolutionary process of the path.

From this perspective, tension is not an “extra effect” in music, but rather a natural byproduct of path awareness. When hearing has learned to track the directional relationships between structures, any delay, avoidance, or reversal of this relationship will be perceived as a state that needs to be resolved.

Understanding this, it is not difficult to see that the so-called “tension” and “release” are not abstract emotional labels, but rather a dynamic judgment experienced by hearing in the process of a path being deviated from and then reconfirmed.

5 When the Path Is Redefined: Mode Change / Modulation

In the previous section, we discussed a situation where the path still exists, but music chooses to temporarily deviate from it, thus creating tension; subsequently, through return or correction, the path is reconfirmed. No matter how far the deviation, hearing always defaults to—This path is still the original one。

But music does not always turn back; sometimes, what music does is not “deviating and then returning,” but rather a more thorough step:Directly redefining the path itselfWhen this moment occurs, hearing does not wait to return to the original center, but rather is guided to accept a new point of stability. This is precisely the experience brought about by mode changes or modulation.

From the perspective of hearing, modulation is not “changing a set of note names,” but rather something more fundamental happening:The reference frame originally used to judge direction has been entirely replacedThose structures previously used to create tension and drive forward no longer hold their directional meaning; new stable relationships take effect, and a new “route home” is quietly established.

This process works precisely because hearing is already sensitive enough to the path. When music begins to repeatedly emphasize a new point of stability and develops a series of self-consistent directional relationships around it, hearing will gradually abandon the old center and shift the “sense of destination” to the new position. This shift does not need to be explicitly announced, but rather is slowly confirmed over time.

And because of this, successful modulation is often not an abrupt rupture, but rather ashift of gravityBefore the shift is complete, music often experiences an ambiguous state: the attraction of the old path has not completely disappeared, and the stability of the new path has not yet fully taken hold. During this time, hearing will retain two sets of judgment criteria simultaneously, and this “swaying back and forth” experience is precisely the most tense part of the modulation process.

Structurally, modulation is fundamentally different from the “deviation” discussed earlier. Deviation still creates suspense within the same path, defaulting to an unchanged destination; whereas modulation tells hearing:The original destination is no longer the destinationOnce this is confirmed, all previously unresolved tension will be reinterpreted, rather than “resolved.”

This is also why, after modulation is complete, music often gives people a sense of “opening up the horizon.” It is not because there are more notes or they have become more difficult, but rather because the reference frame of hearing has been refreshed. Originally familiar structures may acquire completely different meanings under the new path; while originally inconspicuous combinations may suddenly become the new stable core.

It must be emphasized that mode changes do not necessarily have to stay far away from the original pitch material. Even if a large number of the same notes are used, as long as the point of stability shifts, hearing will still perceive the reconstruction of the path. This is highly consistent with our experience of discussing relative major and minor keys earlier: the set of notes can remain unchanged, but once the question of “where to go” changes, the overall feeling will flip accordingly.

From this perspective, modulation is not a decorative technique, but rather an act of replanning the path. What it decides is not whether a certain moment is tense, but ratherwhat the entire next section of music will revolve around。

5 Afterword: What This Article Deliberately Left Unsaid

At this point, to be quite frank:The chords and harmony introduced in this article deliberately remain at a very basic level. Throughout the process, we have revolved almost exclusively around a few of the simplest yet most core concepts: the structure of scales, vertical combinations of three notes, the auditory tendencies of different structures, and how they point to each other in time to form paths. To this end, we have avoided a large number of professional classifications that are common and indeed exist in music theory.

For example, in a more complete theoretical system, chords do not stop at “triads” composed of three notes. On top of the three-note structure, one can continue to stack upwards in thirds, forming seventh chords with four notes, ninth chords with five notes, and even more complex extended forms.

Triads are named by thenumber of notes—three notes stacked to form a basic chord, and when we continue to stack more notes, such as seventh chords, ninth chords, and eleventh chords, the naming method is no longer based solely on the number of notes: the names of these chords reflect theinterval difference from the root note to the top note(for example, a seventh chord indicates a span of a seventh from the root note to the top note), rather than just the number of notes.

This difference in naming is mainly due to historical convention, so there is no need to get bogged down in it.

Even looking only at triads themselves, they can be further distinguished into major triads, minor triads, diminished triads, and augmented triads based on different internal interval relationships; and in harmonic analysis, more detailed tools such as function, inversion, and voice leading are often introduced to describe how these structures function in time.

These contents are not unimportant; on the contrary, they constitute an indispensable part of a complete harmonic theory system. But in this article, they have beendeliberately set aside for the time beingThe reason is also very simple: the goal of this article is not to make readers learn to “analyze,” but rather to first solve a more fundamental and easily overlooked question—On what basis, after all, do we feel the stability, tension, and sense of return in music?

If a large number of terms and classifications are introduced directly before auditory intuition is established, it is easy to create an illusion: as if these feelings in music exist only because we “remembered the rules.” In fact, the exact opposite is true; it is precisely because these feelings are first repeatedly heard and verified that theories are gradually summarized to describe them. If, after reading, you begin to realize that when listening to music, you can more clearly feel “it's not over yet,” “it's turning here,” and “it's finally back here,” then the purpose of this article has actually been achieved.

As for the temporarily omitted content—more complex chord forms, finer functional divisions—they are not rejected, but rather left for other occasions. Perhaps in subsequent articles, or perhaps slowly emerging when you begin to actively deconstruct your favorite music. Music theory is not a knowledge system that must be learned all at once. In many cases,understanding never begins with “completeness,” but rather with “just enough.”

If this article can help you build a little more of such understanding in front of music, then the restraint it chooses is already worth it in itself.