Whenever a given lü is established as gong, then although each of the other four degrees may separately form a mode, all of them remain governed by that parent gong, and all take the gong-tone as the principal modal tone. Therefore a mode must contain a gong-tone. If it did not, then how could one identify it as one of the four derived modes belonging to that particular gong?

For example, if Huangzhong is taken as gong, then even if Linzhong serves as the zhi-mode, and even if the piece begins and ends on zhi, the piece must still contain, subtly within it, the gong-tone of Huangzhong as the hidden master of the mode. Otherwise, how could it be called a zhi-mode piece of ¸Huangzhong-gong?

The same applies when any other lü is taken as gong. Someone might object: “Take the third string, for instance. In ¸Zhong-gong it is Zhonglü, and on the third string in Wuyi it is also Zhonglü. Since the pitch-name is the same, how can it count as zhi?” The answer is that when, in Wuyi, the fifth string is tightened by one lü and made the gong, the relative ordering of the five tones in pitch is thereby altered. So although the third string is Zhonglü in both cases, it cannot in both cases be treated as gong.

Another objection might be: “If the five strings are already assigned to the five tones, how could there ever be a mode without gong?” That too is not correct. A mode may indeed lack an open-string gong-tone; but if no gong-tone appeared among the stopped or harmonic tones either, then how could the mode hold together as a mode at all?

Notes to me from Chat GPT5.4

The above paragraph was the strongest evidence yet that this subsection has something that may hint at your modern analysis.

The key phrases are:

1. 皆本宮所統
“All are governed by the parent gong.”
This is strongly hierarchical language. It suggests that even when another degree becomes the overt modal degree, that degree remains subordinate to a governing parent center.

2. 皆以宮聲爲主調
“All take the gong-tone as the principal mode.”
This is especially important. It suggests that the gong-tone is not just a classificatory label but the real governing tone.

3. 雖林鍾為徵調，曲首尾皆用徵……黃鍾宮聲隱然爲曲調之主
This is very close to what you are looking for. The piece may be classed as a zhi-mode, and may begin and end on zhi, yet still have gong as its hidden governing center. That is not yet a full theory of “primary” and “secondary” tonal centers in modern terms, but it is very compatible with such a reading. One tone has overt formal prominence; another remains the deeper governing center.

4. 調中固有無散絃宮聲者矣
This is also useful. It shows that the gong need not always be available as an open-string pitch. In other words, the governing tone need not always be the most obvious or most immediately exposed pitch in the tuning layout. That also fits rather well with your kind of structural analysis.

As for 律 lü, here I think your instinct is good: it should not always be heard as “absolute pitch standard” in a rigid acoustical sense. In this passage it often works more like “lü-position within a relational tuning system,” though still framed in traditional lü terminology.

Whatever pitch in a pitch-standard (relative tuning) is considered as gong, then although each of its other four other relative pitches could separately form a mode, here they are all considered in relation to that parent-tone, gong, and all take gong as the principal mode-tone (tonal center?). Therefore, within the mode there must necessarily be a gong-tone. If there were no gong-tone, then by what means could one determine that it belonged to the four modes of that particular gong? For example, if Huangzhong is taken as gong, then although Linzhong may serve as the zhi-mode, and although the piece may begin and end on zhi, yet within the piece there must still be, subtly present, the gong-tone of Huangzhong as the hidden master of the mode. Otherwise, how could it be a zhi-mode piece under Huangzhong-gong? When other pitch-standards are taken as gong, all follow this same principle.

Someone might object: “Take the third string, for example. In Zhong-gong, the third string is Zhonglü; but in Wuyi, the third string is also Zhonglü. Since the pitch is the same, how can one case count as zhi?” The answer is that when, in Wuyi, the fifth string is tightened by one pitch-standard and taken as gong, then the relative order of the five tones in highness and lowness is naturally no longer the same. Thus, although the third string is in both cases Zhonglü, it cannot in both cases count as gong.

Another objection might be raised: “If the five strings are already divided among the five tones, how could there ever be a case with no gong?” That too is not so. It is certainly possible in a mode for there to be no open-string gong-tone; but if among the stopped and harmonic tones there were none either, then how could the mode be constituted?

Whenever one and the same pitch-standard serves as this gong and this mode, and also as another gong and another mode, then if its pitch is the same and its sound is also the same, wherein lies the difference between one mode and another? For example, in Zhonglü-gong, Huangzhong serves as zhi, whereas in Wuyi-gong, Huangzhong serves as shang. The pitch of Huangzhong is indeed the same in both cases, but because the string-methods under the different gongs are already different, the places at which modal tones and sonic resonances turn and shift, and the order in which they do so, naturally also differ. From this, the modes and pitch-relations of the other gong-systems may likewise be understood. Whenever one composes a modal prelude or a piece, its first tone ought in principle to use the tone of the root pitch-standard. Yet among pieces composed both ancient and modern, many freely mix in the various pitch-tones belonging to the parent gong, and this too is permissible. But when one comes to the conclusion of a prelude or piece, its final tone always ends only on the tone of the root pitch-standard, never on some other tone. As for the kind of tone employed, there is no restriction to open, stopped, or harmonic tones: all three may be used. This is because the open tones are the regular forms of the five tones, while the sixth and seventh strings provide the clear tones; stopped tones, as level tones and responsive tones, together with harmonic tones, all correspond to the same values as the open tones.

A given lü may serve as one degree in one gong-system and mode, yet serve as a different degree in another gong-system and mode. Since the lü-name is the same and the sound itself is also the same, wherein lies the difference between these modes? For example, in Zhonglü-gong Huangzhong functions as zhi, whereas in Wuyi-gong Huangzhong functions as shang.

The answer is that although the sounded pitch of Huangzhong is the same, the string-methods belonging to the different gong-systems are different. Therefore the places at which modal tones and resonant contours turn and shift, and the sequence in which those changes occur, are naturally not the same. From this one may understand the corresponding relations in the other gong-systems and lü-modes as well.

Notes to me from Chat GPT5.4

This paragraph is highly relevant to your concerns, though in a somewhat different way.

The crucial phrase is:

其為調聲韻轉換處先後自有不同者矣
“The places where the modal tones and sonic contours turn and shift, and the order of those changes, naturally differ.”

This is important because it suggests that mode is not defined only by the inventory of pitch-names. It also depends on:

string-method / tuning setup,
functional placement of tones,
and the ordering of modal shifts and resonant turns within the piece.

That is quite congenial to your own analytical method, which is based not merely on scale content but on the hierarchy and behavior of tones within melodic motion.

In other words, the passage says something close to this: the same pitch-name can function differently in different modal and tuning frameworks because what matters is not only the pitch itself, but how it behaves within that framework.

That is not yet a direct statement about secondary tonal centers, but it is a strong hint that the author understands mode dynamically and relationally, not as a fixed list of notes.

You might even find this paragraph especially useful when arguing against overly static understandings of Ming modal theory.

When composing a prelude or a piece in a given mode, the first tone ought, in principle, to use the tone of the root lü. In actual compositions, however, both ancient and recent, one often finds the opening mixed with other lü-tones belonging to the parent gong, and that is acceptable as well.

But when one comes to the ending of such a prelude or piece, the final tone always returns to the tone of the root lü and not to any other tone.

As for the form that tone may take, it need not be restricted to open-string, stopped, or harmonic sound: any of the three is acceptable. Open-string tones are the regular forms of the five tones, while the sixth and seventh strings provide the clear tones; stopped tones, whether level or responsive, and harmonic tones as well, are treated as equivalent in function to the corresponding open-string tones.

Notes to me from Chat GPT5.4

This paragraph is also quite useful for your inquiry.

The strongest phrase here is:

其末聲却皆止是用本律之聲，無用他聲者。
“At the end, the final tone always uses the root lü, never another.”

That is strong evidence for a privileged tone of return and closure. Even if the opening may vary, the end is much stricter. This sounds very much like a structural center or finalis.

That does not by itself prove your distinction between primary and secondary centers, but it does support the idea that one tone has a superior cadential authority.

The opening is looser:

其第一聲皆合用本律聲……多雜用本宮諸律聲，亦無不可。
The first tone should ideally use the root lü, but in practice pieces often begin with other tones of the parent gong, and that is allowed.

So here the hierarchy seems to be:

opening: somewhat flexible;
ending: much stricter;
final return: to 本律.

That is the sort of evidence that could support your idea that while several tones may be active or prominent in a mode, one remains the principal governing point of return.

As for 本律, in this paragraph I think “root lü” or “governing lü” is better than “pitch standard” if you want to avoid overly absolute language. “Root pitch” might sound too modern and acoustical; “root lü” keeps the Chinese framework visible while still suggesting structural priority.

Whenever one composes a song with text, a prelude, or a piece, one chooses one of the twelve lü as gong and uses the five lü governed by it as the five degrees of the mode. Each of the twelve lü governs a different set. Thus, if Huangzhong is taken as gong, the five corresponding lü serving as the five tones are Huangzhong, Taicu, Guxian, Linzhong, and Nanlü. If Dalü is taken as gong, the corresponding five are Dalü, Jiazhong, Zhonglü, Ruibin, and Wuyi. The same principle holds for the other lü: what each governs is different.

Once the open-string sounds of the first five strings have been assigned to these five lü as gong, shang, jue, zhi, and yu, then the sixth and seventh strings become the clear-tone forms of the first and second strings. The stopped and harmonic tones are likewise taken as proper lü wherever they correspond to, and match, the open-string sounds of those same five lü. Tones that fall outside these five lü may occasionally be borrowed incidentally as auxiliary responsive tones in order to complete a piece, but in the end they do not possess full correctness.

As for altered gong and altered zhi, these too are found among the stopped and harmonic tones, and one does encounter them from time to time, but they are used only rarely. In the other musical traditions there are only the five tones, the two altered tones, and the clear tones. The qin, however, beyond its proper lü and clear tones, also has stopped and harmonic tones, and within the thirteen hui there are many fine gradations of ascent and descent. In this respect the qin possesses resources beyond those of the other musics.

Thus the variety in the number of sounds can extend beyond the basic five. Yet in their turnings, inflections, and final points of return, that by which a mode is actually constituted goes no further than the five tones. If one can confine oneself to the proper open, stopped, and harmonic tones belonging to these five lü, and avoid all the remaining mixed or miscellaneous tones, the result will be purer still.

Notes to me from Chat GPT5.4

This paragraph is very important for your question, though in a somewhat different way from the earlier one about Huangzhong and Linzhong.

The central claim comes near the end:

故其聲數之變，有出於五者之外；然其委折歸宿，所以爲調，不過五聲而巳。
“Thus the variety in the number of sounds may go beyond the five; yet in their turnings and final return, that by which a mode is constituted does not go beyond the five tones.”

This is extremely suggestive. The author is explicitly saying that, although the actual sounded resources of the qin are more numerous than five, the underlying modal logic still comes back to five principal tones. That is very congenial to your analytical approach, because it distinguishes between:

1. the full audible surface of the music, with many possible pitches and inflections; and
2. the deeper modal framework, which remains grounded in the five principal degrees.

That does not yet state “primary” and “secondary” tonal centers, but it does support the idea that the melodic surface can be much richer than the underlying modal structure.

Another especially important phrase is:

其委折歸宿
literally something like “its winding turns and points of return.”

This language is dynamic, not static. It suggests that mode is defined not merely by scale membership but by how tones move, turn, and finally come to rest. That, again, is quite sympathetic to your way of hearing Ming qin melodies.

The phrase

所以爲調，不過五聲而巳
“that by which a mode is constituted does not go beyond the five tones”

is also crucial. It suggests that however many extra pitches, stopped tones, harmonics, altered tones, or fine gradations may appear, they do not overturn the basic modal identity. The real basis of the mode remains the five principal tones.

That may be useful to you if you want to argue that many apparent extra pitches in qin music are ornamental, coloristic, or situational, rather than constituting independent modal centers.

The discussion of 變宮 and 變徵 is also interesting. The author acknowledges them, but immediately says they are used only rarely. So although the system allows for them, he does not give them equal status with the main five-tone framework.

The phrase

其有在五律之外者……然終不得其正矣
“those outside the five lü … in the end do not obtain full correctness”

is especially strong. It suggests a clear hierarchy:

the five governing lü are proper and normative;
tones outside them may occur; but
they are not fully regular or fully proper.

That hierarchy may help support a reading in which some tones are structurally central, while others are secondary, auxiliary, or merely decorative.

So, in relation to your tonal-center question, I would say this paragraph supports your approach in three ways:

First, it insists on an underlying five-tone modal framework even when the actual sounded material is more abundant.

Second, it defines mode through motion and return, not merely through a static pitch collection.

Third, it clearly ranks some tones as proper and central, while treating others as marginal or auxiliary.

All of that seems compatible with your effort to distinguish between deeper governing tones and other less central but still important focal tones.

On one point of wording, I think 委折歸宿 deserves special care. I would not flatten it into something too abstract. It seems to refer to the actual course of melodic motion: its bends, turnings, and eventual place of return or settlement. That phrase may be one of the most useful in the whole section for your purposes.

(After this section the essay seems to move away from defining the five-tone framework itself and more toward explaining how that framework is actually realized in composition: how phrases end, how returns to the governing lü are handled, how local contrast and motion are shaped, and how a piece can vary richly without losing modal identity.)

In composing a piece, the concluding tone at the end of each section should be one that accords with the governing lü. In the final section of all, there must be a harmonic-tone ending that brings the music back into the mode. And not only the harmonic cadence itself, but also the open-string or stopped tones above it where the section comes to rest, should accord with the governing lü. One should not suppose that it is enough for the harmonic ending alone to return to the benlü, while the open and stopped tones at sectional endings may be ignored.

Notes to me from Chat GPT5.4

This paragraph strongly continues the earlier emphasis on return to the 本律.

The key phrase is:

每叚結處一聲，合用本律
“At each sectional ending, the concluding tone should accord with the benlü.”

That is important because it extends the earlier principle of final return beyond the end of the whole piece to the close of each section. In other words, structural return is not only global but also local.

The phrase

最末後一叚，必有入調泛聲結
“in the very last section there must be a harmonic-tone ending that enters the mode”

is also interesting. "入調" here seems to suggest not merely stopping, but settling properly back into modal identity. That gives the final harmonic cadence a specifically modal function.

The last sentence makes Chen’s point even stronger: it is not enough for the final harmonic tone alone to reflect the benlü; the open and stopped tones associated with the cadence must also do so. So the governing tone is not just an abstract terminal idea, but something that should be reflected across the whole cadential complex.

For your purposes, this looks like further support for a governing structural center. It does not speak directly of secondary centers, but it does show that sectional and final closure are repeatedly measured against the 本律.

When composing a piece, the manner in which its ending returns to the mode should depend on the kind of character the piece is meant to embody. If the piece values elegance and restraint, it should end on a proper middle tone, around the tenth hui. If it values clarity and harmony, it should end on a half-tone, around the seventh hui. If it values sharp urgency, it should end on a still narrower tone, around the sixth hui. Broadly speaking, the main possibilities fall within these three categories.

Music marked by elegance and restraint tends to evoke thoughts that are deep and far-reaching; music marked by clarity and harmony tends to evoke cheerful and joyful feelings; music marked by sharp urgency tends to evoke sorrow and emotional poignancy. A cultivated person, in handling sound and composing music, must surely understand what kind of quality is being sought.

Notes to me from Chat GPT5.4

This paragraph is somewhat different from the others, because here Chen is not mainly defining the modal framework itself, but discussing types of cadence according to expressive character.

The most important phrase is:

其結末歸調處，各隨其曲所尚何如
“the place where, at the ending, it returns to the mode should in each case follow what the piece esteems.”

So 歸調 (“returning to the mode”) remains the basic issue; but the precise sonority of that return varies according to style and affect.

The three categories are:

雅淡 — elegant, plain, restrained;
清和 — clear, harmonious, gentle;
峭急 — sharp, urgent, tense.

And each is associated with a different cadential region or sonority: "正中聲", "半聲", and "半半聲", placed roughly at the tenth, seventh, and sixth hui respectively.

I would be cautious here about translating these three too dogmatically into modern acoustical terms, because Chen seems to be speaking from within qin technique and sonority rather than abstract interval theory alone. Still, the basic point is clear: different expressive aims call for different kinds of return.

This passage may matter for your larger analysis because it shows that modal return is not mechanically fixed in one surface form. The governing framework remains, but the audible manner of cadence can differ quite a bit according to aesthetic intention.

So if paragraph 5 stresses the necessity of returning to the 本律, here paragraph 6 adds that the color and placement of that return may vary with the expressive type of the piece.

That too fits well with your general approach: a piece may preserve the same deeper modal logic while presenting it through differing surface behaviors and cadential emphases.

Whenever a passage runs successively across a number of strings, then at any point where a definite lü-value must be identified, it is the last sounded note that should be taken as the relevant lü. Thus, if one brushes from the first string through to the seventh, the seventh-string sound is taken as the lü; if one rolls from the seventh back to the first, the first-string sound is taken as the lü. The intervening strings are not counted for this purpose.

Notes to me from Chat GPT5.4

This is a short but useful practical rule. Chen is explaining how to determine the operative lü in a gesture that passes across several strings.

The key phrase is:

即合以末聲爲律
“one should take the last sounded tone as the lü.”

So in this context the structurally relevant pitch is not the first tone struck, nor the whole sweep taken collectively, but the terminal one. That fits well with the broader tendency in this section to give special weight to points of arrival and settling.

This paragraph is therefore less about defining the modal system in the abstract than about identifying which note counts functionally in actual performance gestures.

For your interests, it may matter because it again suggests that not every sounded pitch in a figure has equal structural weight. In a string-sweep, the final pitch is the one that counts as the effective reference-point.

Whenever a passage begins from a plucked stopped tone and a definite lü-value must be assigned, the relevant lü is the stopped note produced under the named finger after the pluck.

Notes to me from Chat GPT5.4

This is another practical rule for identifying the operative pitch in performance. The important phrase is:

取名指按聲爲律
“take the stopped sound under the named finger as the lü.”

So just as in paragraph 7 the last tone of a string-sweep is treated as decisive, here in a stopped-note gesture the note actually fixed by the indicated left-hand finger is the one that counts.

Again, this implies a hierarchy among sounded events: the relevant structural pitch is determined by function within the gesture, not merely by the fact that several sounds may be present.

These two short paragraphs, 7 and 8, seem almost like applied clarifications of the larger theory. Chen has been insisting throughout that beginnings, endings, and sectional returns must accord with the governing lü; here he explains, in specific technical situations, exactly which sounded note should be treated as that meaningful pitch.

So although these paragraphs do not directly discuss gong, zhi, or host and guest, they do continue the same general concern: in actual playing and composition, one must know which note is functionally decisive.

In composing a piece, each mode contains five tones, which take turns acting as host and guest. If one tone is treated as host, another becomes guest; if that other tone becomes host, then the first becomes guest. When the host-tone is set forth at the opening, the mode has coherence and governing order; when the host-tone gathers the music in at the end, the mode has a point of return and repose. But if the host-tone is not established at the outset, then the host-tone at the end stands there in isolation, without anything corresponding to it, and the musical line is not continuous.

Someone might object: earlier it was said that the opening sound may perfectly well mix in various lü-tones belonging to the parent gong; why does the present passage seem to say otherwise? The answer is that by “setting it forth at the opening” I mean that the closing tone of the opening section should accord with the benlü; I do not mean the very first note of the very first phrase. This may be verified by examining the Yupu.

Notes to me from Chat GPT5.4

This is one of the most important paragraphs in the whole section. The crucial phrase is:

一調有五音，迭爲主客
“In one mode there are five tones, which alternately serve as host and guest.”

This is very significant for your interests. It shows explicitly that Chen does not regard the five tones within a mode as functionally identical. They may exchange roles, and the distinction between zhu and ke, host and guest, is clearly a hierarchy of function.

I would still be cautious about equating 主客 directly with your “primary and secondary tonal centers,” because Chen’s formulation is more flexible and relational: tones alternate in role. But it is certainly close in spirit to the idea that not all tones are equal, and that some can become structurally dominant while others are subordinate.

The phrases

以主聲倡之於首 and
以主聲收之於尾

are also very important. They say, in effect, that the host-tone should frame the piece or section: it should be made manifest at the beginning and should gather the music in at the end. That gives the piece both coherence (統紀) and final return (歸宿).

For your purposes, this is probably one of the strongest passages in the section for arguing that Ming qin theory recognized differentiated tonal functions within a mode.

The clarification in the second half is also important: Chen is careful to say that this does not mean the first literal note must always be the governing one. Rather, what matters is the structurally significant close of the opening section. That is quite subtle, and again it fits your kind of analysis rather well: structural prominence need not coincide with the very first sounded pitch.

In composing a piece, open-string and stopped tones should be interspersed with one another, while the clear-tone sonorities should be supplied through harmonics. Xu said that this achieves the middle way; to lean too far to one side is not appropriate.

Notes to me from Chat GPT5.4

This paragraph is brief, but it states an important aesthetic principle: balance.

The phrase 得中道 “to attain the middle way” suggests that Chen or the Xu he quotes is not recommending an exclusively open-string style, nor an excessively stopped-note style, nor an overreliance on harmonics. A good piece balances these resources.

This paragraph is thus less directly about mode or tonal return, and more about textural and technical proportion.

Still, it fits the section’s larger tendency: proper composition is neither shapeless freedom nor rigid narrowness, but balanced use of available means within an ordered framework.

When composing a piece, one must first determine a particular gong and lü as its mode. At the beginning, the ending, and the sectional divisions, one should keep to the governing lü as the proper norm. Between these points, however, in broken phrases and within individual phrases, there may be calls, responses, pauses, single tones, paired tones, winding turns, and various transformations, each with its own distinct rhythmic and sonic character. The essential thing is to understand these inwardly and test them by ear, adapting them to the piece at hand while always watching how they return and come to rest, so that they do not contradict one another or depart from the mode and lü. If that is achieved, then the composition is successful.

Notes to me from Chat GPT5.4

This paragraph is almost a summary of the entire theoretical position.

The opening statement,

先定以某宮某律爲調
first determine a certain gong and lü as the mode,

makes clear that modal identity is prior. One does not compose first and infer the mode afterwards; one establishes the modal framework first.

The next phrase is especially important:

其起畢及段落處守律爲正
“At beginnings, endings, and sectional places, one keeps to the lü as the proper norm.”

That strongly reinforces what you have been noticing throughout this section: the structurally important points are governed by the lü.

But Chen then contrasts those fixed points with the freer interior:

喚, 應, 間歇, 單聲, 比聲, 委曲轉換.

So the internal movement of the music may be varied and subtle, but this variety must still cohere and must return properly.

The phrase 視其歸宿何如 (“watch what sort of return and resting-place it has”) is especially important for your interests. It suggests that the ultimate test of these interior motions is where and how they come to rest.

This paragraph is therefore very congenial to your broader argument: a piece may contain much local variety, but that variety is judged in relation to structurally privileged points of return.

In composing a piece, endings often use repeated tones, such as gong-gong or zhi-zhi. Openings, by contrast, have no fixed rule. Within phrases and at their endings there may be rises and falls and graceful turns, yet the underlying tone may remain the same, and one need not be too rigid about these details. What matters is that at the points of call, lift, and response the music should in the end return to the governing lü.

Notes to me from Chat GPT5.4

This paragraph again contrasts relative freedom in the interior with stronger control at points of closure.

The phrase 畢調處多疊聲 (“at points where the mode is concluded, repeated tones are common”) suggests a cadential strengthening or reinforcement. Repetition of the governing tone, whether gong or zhi in a particular case, helps articulate closure.

The next contrast is also important: 起調處却無定 (“at openings there is no fixed rule.”)

So openings are less rigidly prescribed than endings. This matches what Chen said earlier.

The last clause is perhaps the most important: 終歸於律爲善 (It is best that in the end it return to the lü.)”

Once again, return to the governing lü is the decisive criterion. That recurring emphasis is one of the strongest threads running through the section.

In composing a piece, its sonic movement may incline upward or downward. With open strings, movement from the outer strings inward counts as upward motion, while movement from the inner strings outward counts as downward motion. Calls that lead upward likewise count as upward motion, while answering phrases that settle downward count as downward motion. There are also cases in which an upward tendency is answered with another high response, or a downward tendency with another low one, while in other cases one is high and the other low. These patterns of variation are many and cannot be reduced to a single form; they must be grasped intuitively.

Notes to me from Chat GPT5.4

This paragraph is more about directional shaping and registral behavior than about modal identity as such.

The key distinction is: 向高 / 向沉: “tending upward” / “tending downward.”

Chen is describing contour and response-pattern: some motions rise, some settle downward, and they may be answered in matching or contrasting ways.

This may matter for your interests because it shows that Chen pays close attention to functional movement within the phrase, not only to static pitch categories. The music’s behavior includes directional tendencies, calls and answers, and contrasting registral responses.

The closing phrase, 當以意會可也 “it should be grasped by intuitive understanding,” is also notable. It shows that not every aspect of composition can be codified mechanically. Some of it depends on a cultivated musical apprehension.

So these paragraphs, taken together, continue the same pattern seen throughout the section: the governing framework is fixed, especially at beginnings, endings, and returns, but within that framework the music may display a great deal of subtle internal variation.

In composition, one must as a matter of principle never depart from the twelve lü and the five tones; their distinctions are fixed. Yet once they are woven together into actual musical form, the possibilities of variation are inexhaustible, and elegant, well-ordered music has always arisen in this way. It is like the game of yi: the board has only nineteen lines each way, yet even transcendent or wise minds cannot exhaust all its calculations, and wondrous strategies and brilliant moves keep appearing anew. If one truly understands this, then one sees that the real principles of composition also include matters that lie beyond any mere list of general rules, though they still cannot be violated. How could such things be fully covered by verbal explanation alone? They must be grasped inwardly for oneself.

Notes to me from Chat GPT5.4

This is the summative close of this section.

The first sentence restates the normative framework very strongly:

不可違十二律五聲 “one must not violate the twelve lü and the five tones.”

So Chen ends where he began: there is a fixed underlying order.

But immediately after that he balances fixity with inexhaustible variety:

及經緯之以成文，變化無盡 “once they are woven into actual patterned composition, the transformations are endless.”

This is an important final statement of his whole method. The framework is fixed, but the realized music is infinitely various.

The comparison with the board game is apt: a limited set of elements generates limitless combinations.

The most important interpretive phrase may be: 製曲真例又有在於凡例之外而罔可違者 “the true principles of composition also include matters lying beyond the general rules, yet not to be violated.”

That is very revealing. Chen is saying that there are truths of composition that cannot be reduced to explicit rule-lists, but they are nonetheless real and binding.

Then comes the final conclusion: 豈惟說所能該備？當自得之可也。 “How could verbal explanation alone fully encompass them? One must grasp them for oneself.”

In context, I think this means not simply “words are inadequate” in a vague sense, but more specifically: beyond the formal rules lies a level of musical understanding that can only be apprehended through cultivated practice and insight.

So as a close to the whole of Section 4, paragraph 16 says:

the modal and tonal framework is fixed;
actual musical realization is endlessly varied;
good composition cannot be reduced to formulas alone; and
true understanding must be attained inwardly.

For your larger question, this is useful because it gives you a principled reason why Chen does not simply spell out everything in a rigid theoretical scheme. His own conclusion is that some of the most important truths of composition lie beyond exhaustive verbal statement.

So if you find hints rather than explicit declarations of differentiated tonal functions, temporary reorientations, and return to a governing center, that is actually quite consistent with the way this section ends.