Sound as Geometry.

Sound, in this system, is not accompaniment. It is a fourth rendering layer that shares one truth table with the body, the light, and the stage. Four systems each govern one dimension of that table:

聲音在這套系統裡不是配樂，而是與身體、燈光、舞台共用同一張真值表的第四個渲染層。四個系統各自負責這張表的一個維度：

Sound's task is to render these four dimensions back into spatial geometry — point, line, plane, volume — so that it can be described, triggered, and answered in the same language as the body and the light.

聲音的任務，是把這四個維度還原為空間幾何——點、線、面、體——使其能與身體、燈光以同一種語言被描述、被觸發、被回應。

The four geometries are not timbral categories. They are ways of existing in time. A point is a momentary event — it begins, it ends, it does not persist. A line is a point drawn quickly through space, a trajectory that gives rise to direction. A plane is a texture built from many lines — heard not as a sound but as a field. A volume occupies space with no edge.

四種聲音幾何不是音色分類，而是時間中的存在方式。點是瞬間事件——有開始、有結束，沒有持續。線是點在空間中被迅速划開所留下的軌跡，方向由此而生。面是許多條線鋪陳而成的紋理——聽感上是「一片」，而非「一個聲音」。體占據空間，沒有邊界。

Set against Laban's three effort factors, a clean structure emerges: geometry is fully determined by Time × Space, polarity entirely by Weight — the two axes are orthogonal.

與拉班力效的三個因子對照，會看到一個乾淨的結構：幾何類別完全由時間×空間兩位決定，陰陽完全由重量一位決定——兩軸正交。

Light = Dab, Glide, Flick, Float. Strong = Punch, Press, Slash, Wring. Sound geometry is not a metaphor bolted onto the system — it is a projection that already exists inside the body's own quality table. Any effort combination yields its point / line / plane / volume identity directly from its Time + Space bits, with polarity superimposed independently.

輕 = 點拍、滑抹、弹拂、漂浮；重 = 冲打、推压、劈砍、拧絞。聲音幾何不是外掛的比喻層，它是身體質感真值表本來就存在的一個投影：任何一個力效組合，直接從其時間＋空間位就能讀出對應的點／線／面／體，陰陽獨立疊加其上。

The instrument itself uses the eight doors in their home positions — Rest/Kan, Death/Kun, Injury/Zhen, Blocking/Xun, Opening/Qian, Fear/Dui, Life/Gen, Scenery/Li — with no attachment to any single hour's chart, so the skeleton can be reused across works. In performance, a given hour's Qimen chart decides which cells activate, and at what intensity.

樂器本身使用八門的本位表——坎/休、坤/死、震/傷、巽/杜、乾/開、兌/驚、艮/生、離/景——不綁定任何具體時辰盤，骨架得以跨作品復用。演出時，由該時辰的奇門格局決定哪些格子被激活、以何種強度被激活。

Eight streams (Float, Glide, Flick, Dab, Wring, Press, Slash, Punch) × eight doors = 64 cells, isomorphic to the 64 hexagrams. Each cell carries two independent attributes — the geometry of its stream, and the geometry of its door. Where the two coincide, the cell reads as pure; where they cross, it reads as fused, carrying friction. This distinction is what determines which cells serve as stable texture and which serve as sites of anomaly or resistance.

八流（漂浮、滑抹、弹拂、點拍、拧絞、推压、劈砍、冲打）× 八門 ＝ 64格，與六十四卦同構。每一格同時攜帶兩個獨立屬性——該流本身的幾何，與該門的幾何。二者重合為本體格，聽感更純；二者交叉為融合／張力格，聽感更有摩擦。這個區分，決定了哪些格子適合作為穩定質感層，哪些適合作為異常／抵抗層。

Section 2 named the diagonal of the 8×8 matrix — where stream and door coincide — as the axis separating pure cells from fused ones. The matrix carries a second, independent axis: the pair of cells sitting at antipodal positions through the matrix's center, where every governing factor (space, weight, time) is inverted at once, not partially crossed. We mark this relation 極反 — "polar reversal." Unlike the pure/fused distinction, which concerns a single cell's internal coherence, antipodal pairing concerns a relation between two cells across the whole structure, and marks the matrix's points of maximum contrast.

第二節已指出8×8矩陣的對角線——流與門重合之處——是區分本體格與融合格的軸線。矩陣內部還存在第二條、與之獨立的軸線：透過矩陣中心彼此對稱的兩格，其間所有支配因子（空間、重量、時間）並非部分交叉，而是同時、完整地翻轉。我們將這組關係標記為「極反」。與本體／融合的區分不同，本體／融合關心的是單一格自身的內部一致性，極反關心的是貫穿整個結構、兩格之間的關係，標記出矩陣裡對比最劇烈的幾個點。

This structure was arrived at independently, from the matrix's own symmetry — but it corresponds closely to a training practice already established within Laban's own system: the Diagonal Scale (also called the "Diagonal Scale with Action Drive Affinities"), in which a practitioner moves along the cube's four space diagonals, from one corner directly to its opposite corner — for instance, from Floating (light, indirect, sustained) to Punching (strong, direct, quick) — with all three motion factors reversing at once, rather than shifting one or two factors at a time along an edge or a face. This is, by description, the same geometric relation the matrix's antipodal pairing formalizes: the two are not the same claim, but they pick out the same structural feature of the underlying cube from two independent directions — one arrived at through body training pedagogy, the other through the symmetry of a symbolic matrix.

這一結構是我們從矩陣自身的對稱性中獨立推得的——但它與拉班體系內部早已確立的一項訓練法高度對應：對角線量表（Diagonal Scale，亦稱「附帶動作驅力親緣性的對角線量表」）。練習者沿立方體的四條空間對角線移動，從立方體一角直接移至其正對角——例如從漂浮（輕、間接、緩慢）移至沖打（重、直接、快速）——三個運動因子同時全部翻轉，而非像沿棱邊或沿面移動那樣，僅逐次改變一到兩個因子。就描述而言，這正是矩陣極反關係所形式化的同一種幾何關係：兩者並非同一項主張，而是分別從兩個獨立方向——一個源自身體訓練教學法，一個源自符號矩陣的對稱性——指向了同一個立方體結構裡的同一項特徵。

The practical implication is straightforward: antipodal transitions are, by both traditions' independent accounting, the matrix's points of maximum transformation, and a performer already trained in the Diagonal Scale brings a directly transferable body vocabulary to them — no translation layer required. We flag this correspondence rather than treat it as proof of anything beyond itself: it does not validate the deterministic-generator framework argued for elsewhere in this research, nor does the framework depend on it. It is offered here because a body of practice already exists for exactly the transitions this matrix marks as most extreme, and that practice is worth naming.

這一發現的實務意涵很直接：無論依哪一套系統各自的判定，極反過渡都是矩陣裡轉換幅度最劇烈的節點，一名已受過對角線量表訓練的表演者，面對這些節點時能直接調用一套現成、不需額外轉譯的身體語彙。我們在此標記這一對應關係，但不將其當作證明本研究其餘部分之外任何主張的依據——它既不驗證本研究論證的確定性發生器框架，該框架也不依賴於它成立。之所以在此提出，是因為這套矩陣標記為最劇烈的過渡節點，恰好已有一套現成的訓練實踐與之對應，值得被指出。

Materials within a single palace are not placed by dividing bars evenly. They follow the ratios generated by San Fen Sun Yi (三分損益) — an ancient method of pitch generation — walking the Luoshu palace order (Kan → Kun → Zhen → Xun → Qian → Dui → Gen → Li), alternating "subtract a third" (×2/3) and "add a third" (×4/3) from a root.

同一宮內的多個素材，不用等分小節的方式排列，而是使用三分損益法生成的比值——一套古老的生律方法——按洛書宮位順序（坎→坤→震→巽→乾→兌→艮→離），從根音起交替「損一」（×2/3）與「益一」（×4/3）。

Bar offset = (1 − cumulative ratio r) × total bars of the clip

Because the ratio oscillates rather than decreasing monotonically, the order of generation and the order in time diverge. Sorted by time — Kan (0), Zhen (7), Qian (13), Gen (19), Kun (21), Xun (26), Dui (30), Li (34) — every material generated by "adding" clusters in the first half of the clip, and every material generated by "subtracting" clusters in the second half. This bisection is not designed by hand; it is an emergent product of the alternation rule itself, giving every 64-bar clip a hidden two-part form.

因損、益交替、比值震盪而非單調遞減，生成順序與時間順序並不相同。按時間排列——坎(0)、震(7)、乾(13)、艮(19)、坤(21)、巽(26)、兌(30)、離(34)——全部由「益」生成的素材聚集在clip前半，全部由「損」生成的素材聚集在後半。這個二分不是手動設計的，是交替規則本身的emergent產物，讓每條64小節clip天然帶有隱藏的二段體結構。

The five voices of any palace do not arrive together. They layer in from the abstract toward the specific — Spirit first (the most abstract layer, "existence" itself), Door second (the concrete layer of space), Star third (the concrete agent), Heavenly Stem fourth, Earthly Stem last (the finest layer of ganzhi relation). The order of entrance is an order of attention: from cosmology toward mechanism, surfacing gradually rather than arriving as a single chord.

任一宮的五個聲部並非同時進入，而是按「抽象→具體」的順序依次疊加——神先進（最抽象的「存在」層），門次之（具體的空間層），星再次（具體的行動者），天干、地干殿後（最細節的干支關係層）。進入順序即注意力引導順序：從宇宙論到具體機制，逐層浮現，而非和弦式的一次性呈現。

Each palace's complete timeline is built from two segments: a "still" version (64 bars, the full five-voice build) and a "moving" version (16 bars, a strict four-times compression of the same build). Together they run 80 bars — five minutes twenty seconds at 60 BPM, 4/4. The moving version is not a redesigned contrast; it is the still version rescaled — entrance points and the proportion of full-texture time are held constant across scale. This self-similarity is what allows the system to reproduce its own structure at a different resolution, and is the clearest expression of its claim to determinism.

每一宮的完整時間軸由兩段構成：「靜」版本（64小節，完整五聲部漸進build）與「動」版本（16小節，同一build結構的嚴格四倍壓縮），合計80小節——60 BPM、4/4下為五分二十秒。「動」版本不是重新設計的對比結構，而是「靜」版本的等比例縮放——聲部進入時間點、全聲部齊奏佔比，在兩個尺度上保持一致。這一自相似關係，讓系統能在不同解析度上復現自身結構，是「確定性系統」這一主張最直接的體現。

The relation between heaven-stem and earth-stem across the nine palaces falls into three states, each answered by an independent sound treatment — not a single "block-on-conflict" logic.

九宮的天干地干關係分為三種，各自對應獨立的聲音處理邏輯，而非單一的「克→切斷」。

The same nine-palace system admits three distinct readings, each serving a different dramaturgical function.

同一套九宮系統對應三種不同的「讀取方式」，分別服務不同的戲劇功能。

Choosing a route is choosing how dramatic tension is distributed: Route I keeps the work in a continuous state of accord; Routes II and III guarantee that the work passes through its one point of real conflict — and it is only in those two routes that the sound's blocking mechanism carries genuine structural meaning.

路線的選擇即戲劇張力分布的選擇：路線一讓作品始終處於協和狀態；路線二、三則讓作品必然經歷唯一的克戰宮——聲音的阻滯機制，也只有在後兩條路線中才具有真實的結構意義。

What this gives the work is a sound that no longer illustrates the body from outside, but is generated by the same machine, reading the same chart, at the same moment. The geometry was never a metaphor borrowed from painting — it was already sitting inside the quality table, waiting to be read as sound.

這給予作品的，是一種不再從外部為身體配樂、而是由同一台機器、讀著同一張盤、在同一個時刻生成的聲音。這套幾何從來不是從繪畫裡借來的比喻——它本來就坐在質感真值表裡，等著被讀作聲音。