Chapter Fifteen: Musical Pitch — The Correspondence of the Forest Bell

I. The Twelve Pitches and the Twelve Months: Uniting Musical Pitch and Calendar

In pre-Qin cosmology, musical pitch bore a profound and precise correspondence to the calendar and to the yin-yang of the four seasons — this is the concept of "uniting musical pitch and calendar" (lüli heyi). The twelve pitches (Huangzhong, Dalü, Taicu, Jiazhong, Guxian, Zhonglü, Ruibin, Linzhong, Yize, Nanlü, Wuyi, Yingzhong) correspond one-to-one with the twelve months, each month possessing its own pitch that holds sway.

The sixth month (the Month of Wei), in which Minor Heat falls, corresponds to the pitch "Linzhong" (the Forest Bell). The "Monthly Ordinances" of the Book of Rites states explicitly, regarding the month of late summer: "The pitch corresponds to Linzhong." The "Record of Late Summer" of the Springs and Autumns of Lü Buwei likewise states: "The pitch corresponds to Linzhong." This means that, in the ancients' cosmology, the vibration of heaven-and-earth's qi in the sixth month resonates with the frequency of this pitch, Linzhong.

II. Interpreting "Linzhong": The Pitch of Yin Energy Beginning to Flourish

What is the meaning of the name "Linzhong"$2 The ancients offered various explanations of the names of the twelve pitches, discussed in such texts as the "Treatise on Pitch" (Lüshu) of the Records of the Grand Historian and the "Treatise on Pitch and Calendar" (Lüli Zhi) of the Book of Han (Hanshu). It is generally held that the character "lin" (林, forest) in "Linzhong" carries the sense of "abundant, luxuriant" — in the sixth month, plants and trees grow as luxuriant as a forest; at the same time, "Linzhong" occupies, within the sequence of yin-yang waxing and waning, the position where yin energy has begun to grow and flourish.

Examined still more deeply, the twelve pitches are divided, according to yin and yang, into the "six lü" (yang pitches: Huangzhong, Taicu, Guxian, Ruibin, Yize, Wuyi) and the "six lü tonal category" — properly the six tong or lü in the narrower sense (yin pitches: Dalü, Jiazhong, Zhonglü, Linzhong, Nanlü, Yingzhong). Linzhong belongs to this latter, yin category of pitches. This is exceedingly significant: the sixth month's correspondence to Linzhong (a yin pitch) precisely matches the sixth month's correspondence to the hexagram Dun (two yin lines gradually growing) — the yin-yang configuration of yin energy steadily growing! The yin quality of the musical pitch (Linzhong belonging to the yin category) confirms the yin quality of the solar term (the hexagram Dun's two growing yin lines) — this is precisely a vivid embodiment of "uniting musical pitch and calendar," the precise correspondence between musical pitch and yin-yang.

From the fifth month's Ruibin (a yang pitch, corresponding to the hexagram Gou's one yin line born, yet still answered by a yang pitch, because yang energy remains at its height at the Summer Solstice) to the sixth month's Linzhong (a yin pitch, corresponding to the hexagram Dun's two growing yin lines), this transition from yang pitch to yin pitch marks precisely the critical turning point at which heaven-and-earth's qi turns from the height of yang toward the growth of yin. Linzhong's status as a yin pitch is precisely the exact correspondence, at the level of musical pitch, of Minor Heat's "yang energy concealing itself, two yin lines gradually growing."

III. The Method of Thirds: The Generative Law of the Pitches

The generation of the twelve pitches follows the "method of thirds" (sanfen sunyi fa, literally "the method of losing and gaining by thirds") — the most important law for generating musical pitches in ancient China, and also the key link connecting musical pitch to number and to cosmic order.

What is called the "method of thirds" takes the length of a foundational pitch-pipe (Huangzhong) as its basis, and through the alternating operations of "losing a third" (subtracting one-third of the length) and "gaining a third" (adding one-third of the length), successively generates the remaining pitches in turn. Such texts as the "Land Officers" (Diyuan) chapter of the Guanzi and the "Musical Pitch" (Yinlü) chapter of the Springs and Autumns of Lü Buwei record this law. Specifically: Huangzhong, losing a third, generates Linzhong; Linzhong, gaining a third, generates Taicu; and so the process of losing and gaining continues in mutual generation until all twelve pitches are produced.

It is worth noting that Huangzhong (the eleventh month, the Winter Solstice, when one yang line is born), through "losing a third," generates precisely Linzhong (the sixth month, after the Summer Solstice, when yin energy grows). Huangzhong and Linzhong — one corresponding to the Winter Solstice (one yang line born, the beginning of yang), the other to the sixth month (yin energy growing) — stand in a direct relationship of mutual generation within the sequence of the method of thirds (Huangzhong generates Linzhong). This direct connection in the generation of musical pitch once again confirms the profound correspondence between the Winter Solstice and the Summer Solstice, between the birth of yang and the growth of yin — they are the two poles of this same single process of yin-yang waxing and waning, and they are closely linked as well within the numerical structure of musical pitch.

The "method of thirds" grounds the generation of musical pitch in precise mathematical ratios (two-thirds, four-thirds), making musical pitch a kind of "calculable cosmic order." This embodies an exceedingly profound conviction held by the ancients — that everything between heaven and earth (musical pitch, the calendar, yin and yang, the four seasons) follows one and the same set of laws expressible through number. The pitch Linzhong is precisely the concrete embodiment, in the sixth month, at Minor Heat, of this cosmic order that "threads through heaven and earth by means of number."

IV. Between Zhi and Gong: The Transition of Musical Pitch at the Juncture of Fire and Earth

As discussed earlier in the chapter on the Five Phases, the month of late summer has "its note is zhi" (the note of Fire), while "Central Earth" has "its note is gong" (the note of Earth). This constitutes a subtle feature of late summer's musical correspondence — it belongs both to "zhi" (Fire) and is linked to "gong" (Earth).

Within the system of the Five Notes (gong, shang, jue, zhi, yu), the zhi note is stirring and high-pitched (the sound of Fire), while the gong note is resonant and steady (the sound of Earth, the sound of the sovereign, the ruler of the five notes). The sixth month of late summer stands precisely at the transitional season of "Fire withdrawing as Earth rises," and its musical correspondence likewise displays a corresponding transition from zhi (Fire) toward gong (Earth) — from stirring and high-pitched toward resonant and steady; from unrestrained outward expression toward centered settledness.

This transition between zhi and gong, together with the turning point of Linzhong's status as a yin pitch among the twelve pitches, together form a complete picture of Minor Heat (late summer) at the level of musical pitch — whether it is the turning of the Five Notes from zhi to gong (Fire turning to Earth), or the turning of the twelve pitches from yang to yin (Ruibin turning to Linzhong), both speak of the same core theme: the height of flourishing about to turn, the great transition from Fire to Earth, from yang to yin, from high summer toward autumn's Metal, is quietly unfolding at this juncture of Minor Heat, within the vibration of heaven-and-earth's qi (musical pitch). Through the pitch Linzhong and the turning between zhi and gong, the ancients set this profound transition to music, composing it into the score of heaven and earth.