CHORD LANGUAGE

和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUAGE (First name:Equal Temperament Logic and Equal Temperament Painting) 和弦语言 （首发名：平均律逻辑与平均律绘画） (English and Chinese version) （中，英文对照版） Li Xiaohong;李晓虹 Email:[email protected] ISBN:9781370273348 ASIN: B0919JJ3R7 DOI:10.13140/RG.2.2.25415.65440 作者：李晓虹 Author:LI Xiaohong 版权 2016.李晓虹 Copyright 2016 LI Xiaohong Work registration information, copyright reservation;作品注册信息，版权保留 《量子人看宇宙》NAME OF AUTHOR：XIAOHONG LI；For a Literary Work UNITED STATES COPYRIGHT OFFICE TXu 635-761； 《十二平均色律——量子人看宇宙》NAME OF AUTHOR：XIAOHONG LI；For a Literary Work UNITED STATES COPYRIGHT OFFICE TXu 777-504； 《十二平均色律——量子人看宇宙》作者或著作权人：李晓虹登记号：21-1996-A-(0183)-0146 中国.四川省版权局。 *本书部分章节为 24-25 届世界哲学大会论文。 * Some chapters of this book are papers from the 24th and 25th World Congress of Philosophy. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Overview Of Chord Language；和弦语言综述 25 届世界哲学大会论文 ；Papers of the XXV World Congress of Philosophy 和弦语言是量子化频谱（n·f ，1.05946^n·f ）的编码与作用机制。 每一个和弦对应其专属的特征频谱，并据此映射至特定的和弦语义集合。基于这一映射关系，和弦 编码并生成一个统一的现象域，包括：时间（和弦进行—音乐）、空间（膜–弦结构—绘画）与生命 （经络系统），呈现为跨尺度的相干和弦场。 我们在人体与绘画中定量观察到与音乐同构的和弦结构与组织方式，由此扩展了和弦的定义： 和弦是涵盖时空，生命与精神领域的一致性结构与普遍机制。 量子化与和弦是离散物理量的不同观察者视角：前者是第三人称视角，后者是第一人称视角。 Chord language is the encoding and functioning mechanism of a quantized spectrum (n·f, 1.05946^n·f). Each chord corresponds to its own characteristic frequency spectrum, and based on this, it is mapped to a specific set of chord semantics. Based on this mapping relationship, chords are encoded and generate a unified phenomenal domain, including: time (chord progression—music), space (membrane– string structure—painting), and life (meridian system), presenting as a cross-scale coherent chord field. We have quantitatively observed in the human body and in painting chord structures and organizational methods that are isomorphic with music, thereby expanding the definition of chords: Chords are a consistent structure and universal mechanism that encompass the realms of spacetime, life, and spirit. Quantization and chords are different observer perspectives on discrete physical quantities: the former is a third-person perspective, while the latter is a first-person perspective. 基本和弦表：1-1、大三和弦（闭弦），1-2、小三和弦（开弦）,2、减七和弦（膜）， 3、全音阶和弦 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 （膜）， 4、增三和弦（膜）， 5、半音阶和弦（膜） 和弦频谱公式：n*f，H^n*f ,（H=1.059463，n∈Z） 符号：◆=+音符，●=-音符，音符色=色荷 频谱坐标：mod12 群 Basic chord table: 1-1, major triad (closed string), 1-2, minor triad (open string), 2, diminished 7th (membrane), 3, diatonic chord (membrane), 4, augmented Triads (membrane)，5. Chromatic chords (membrane) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 关键词：时空，音乐，绘画，生命，经络，量子化，膜-弦 Keywords: spacetime, music, painting, life, meridians, quantization, membrane-string Chord Spacetime；和弦时空 时空是宇宙的一致性结构，是一切现象的共同生成域。 Spacetime is the consistent structure of the universe and the common domain of generation of all phenomena. 人类有两类时空观察者：和弦（调性）观察者与非和弦（无调性）观察者，分别观察到两种时空： Humans have two types of spacetime observers: chordal (tonal) observers and non-chordal (atonal) observers, who observe two different types of spacetime respectively: 和弦（调性）时空：以量子化频谱为编码结构，映射到时空语义集合，量子化地生成和弦时空；音 乐（时间域）与绘画（空间域）是其常见形式。 非和弦（无调性）时空：屏蔽了时空的和弦（量子化频谱）结构，只保留几何（图-底）与运动的 纯粹关系性描述，从外部参考系统（如时钟、尺子、参照物）获得定量，常用于经典物理学框架中，也 是日常的时空经验。 Chord (tonal) spacetime: Encoded with a quantized spectrum, it is assigned to a set of spacetime semantics, generating chordal spacetime in a quantized manner; music (time domain) and painting (spatial domain) are common forms. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Non-chord (atonal) spacetime: It shields the chordal (quantized spectrum) structure of spacetime, retaining only the purely relational descriptions of geometry (figure-ground) and motion. Quantitative information is obtained from external reference systems (such as clocks, rulers, reference objects), and is often used within the framework of classical physics, as well as in everyday spacetime experience. 量子化与和弦化：和弦频率与量子能量在本质上具有同构性，二者均基于一个基准频率 f，通过整 数n的调控生成离散的频率谱或能量谱： 和弦频谱通式：𝑓 𝑛= 𝑛 ⋅ 𝑓，其中 𝑛 ∈ ℤ，f为基频。 量子化假设形式：𝐸𝑛= 𝑛 ⋅ 𝑓 ⋅ ℎ，其中 ，n同样为整数。 从数学结构上看，二者均表现为 𝑛 ⋅ 𝑓 的线性离散序列，区别仅在于物理维度的转换（频率→能 量）。这种整数 n调控的离散性是构成和谐音程与基础和弦的数学根源。 例如，取 n为连续整数可构造常见和弦的音高结构： n = 1, 2, 3, 4, 5, 6 → 对应频率比 4:5:6 → 大三和弦 n = 1, 2, 3, 4, 5, 6, 7 → 频率比 4:5:6:7 → 大七和弦 n = 1, 2, 3, 4, 5, 6, 7, 8, 9 → 频率比 4:5:6:7:9 → 大九和弦 n = 1 至11 的选择 → 频率比 4:5:6:7:9:11 → 大十一和弦 若以整数比 𝑛: 𝑚 表示频率间的和谐关系，上述和弦可统一表达为： 大三和弦：4 : 5 : 6 大七和弦：4 : 5 : 6 : 7 大九和弦：4 : 5 : 6 : 7 : 9 大十一和弦：4 : 5 : 6 : 7 : 9 : 11 由此可见，整数序列生成的离散频率结构同时支撑了量子能级与和弦构成。在此视角下，量子化可 视为物理世界的“频谱和弦化”，而和弦化亦可视为音乐领域的“频率量子化”。二者共同揭示了一种基于 整数生成与离散对称的普遍结构原理。 Quantization and Chordification: Chord frequencies and quantum energy are essentially isomorphic, both based on a fundamental frequency f, and generated as discrete frequency or energy spectra through the modulation of integer n: General formula for chord spectrum: fn = n⋅f, where n ∈ Z and f is the fundamental frequency. Quantization hypothesis form: E_n = n⋅f⋅ h, where n is also an integer. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Mathematically, both represent linear discrete sequences of n⋅ f, differing only in the transformation of the physical dimension (frequency → energy). This discreteness, modulated by integer n, is the mathematical root of harmonious intervals and fundamental chords. For example, taking n as consecutive integers allows us to construct the pitch structures of common chords: n = 1, 2, 3, 4, 5, 6 → Corresponding frequency ratio 4:5:6 → Major triad n = 1, 2, 3, 4, 5, 6, 7 → Frequency ratio 4:5:6:7 → Major seventh chord n = 1, 2, 3, 4, 5, 6, 7, 8, 9 → Frequency ratio 4:5:6:7:9 → Major ninth chord n = choices from 1 to 11 → Frequency ratio 4:5:6:7:9:11 → Major eleventh chord If we use the integer ratio n:m to represent the harmonious relationship between frequencies, the above chords can be uniformly expressed as: Major triad: 4 : 5 : 6 Major seventh chord: 4 : 5 : 6 : 7 Major ninth chord: 4 : 5 : 6 : 7 : 9 Major 11th chord: 4 : 5 : 6 : 7 : 9 : 11 Thus, it can be seen that the discrete frequency structure generated by integer sequences simultaneously supports both quantum energy levels and chord formation. From this perspective, quantization can be seen as the "spectral chordification" of the physical world, while chordification can be seen as the "frequency quantization" of the music field. Together, they reveal a universal structural principle based on integer generation and discrete symmetry. 泛音是一维震荡模式，高维震荡模式涉及到平均律：(1.059463)^n · f₀，两种模式可以切换——前 者满足协和性，后者满足对称性，形成对称-破缺结构。 将 n 切换为 (1.059463)^n，引入指数型量子化能级：Eₙ=h·1.059463^{n}·f₀，通过模 12 群 ℤ₁₂ 的结 构，实现和弦的系统生成。 Overtones are one-dimensional oscillation modes. Higher-dimensional oscillation modes involve equal temporality: (1.059463)^n · f₀. These two modes can be switched—the former satisfies consonance, and the latter satisfies symmetry, forming a symmetry-broken structure. Switching n to (1.059463)^n introduces an exponential quantized energy level: 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Eₙ=h·1.059463^{n}·f₀. Through the structure of the modulo 12 group ℤ₁₂, a systematic generation of chords is achieved. 时空二相性：和弦时间与和弦空间镜像对称：{-7,-4,0} ↔ {0,4,7} mod 12（互为反和弦，反调），可 数学转换；空间具有定域性，时间具有非定域性，共同表现为时空二相性（定域-非定域二相性），类似 波粒二象性。 Spacetime duality: Chord time and chord space are mirror symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 (they are inverse chords, inverse keys), which can be mathematically transformed; space is local and time is nonlocal, which together manifests as spacetime duality (local-nonlocal duality), similar to wave-particle duality. 和弦几何：和弦编码包含几何语义：开弦，闭弦，膜，可生成所有空间状态，也是绘画空间的生成 基础。 Chord geometry: Chord encoding contains geometric semantics: open strings, closed strings, membrane, which can generate all spatial states and are also the basis for the generation of painting space. 和弦是先验的量子化时空结构，经验现象是：时空在音乐，绘画中被量子化。 Chords are a priori quantized spacetime structures, and empirical phenomena show that spacetime is quantized in music and painting. Chord Geometry - Space And Chord Painting; 和弦几何-空间与和弦绘画 在和弦空间系统中，和弦表现为量子化的色彩频谱，映射到特定的几何结构（膜-弦），生成和弦空 间，其本质是先验的量子化空间结构，绘画是其经验现象，它同样存在于欧几里得几何与膜-弦理论的架 构中。 In the chord space system, chords are represented as quantized color spectra, which are mapped onto specific geometric structures (membrane-string) to generate chord space. Its essence is a priori quantized spatial structure, and painting is its empirical phenomenon. It also exists in the framework of Euclidean geometry and membrane-string theory. 核心机制：时空镜像对称 和弦编码（量子化频谱）是时空生成的统一基底：它在时间域展开为音乐，在空间域凝结为绘画。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 两者展现出内在的镜像对称关系：-7,-4,0 ↔0,4,7 (mod 12)。这种对称性使得音乐与绘画成为同一和弦系 统的两种展开方式。 Core Mechanism: Spacetime Mirror Symmetry Chord encoding (quantized spectrum) is the unified basis for spacetime generation: it unfolds as music in the time domain and condenses into painting in the spatial domain. The two exhibit an inherent mirror symmetry: -7, -4, 0 ↔ 0, 4, 7 (mod 12). This symmetry makes music and painting two ways of unfolding the same chord system. 和弦编码的几何语义 和弦编码不仅描述频率比例，也携带几何语义（膜-弦），从而决定空间结构： 开弦（Open String）：对应小三和弦 (−7,−3,0) mod 12，为分面线结构； 闭弦（Closed String）：对应大三和弦 (−7,−4,0) mod 12，为轮廓线结构； 膜（Membrane）：对应对称和弦（Symmetrical Chords），如减七 (0,3,6,9)、全音阶 (0,2,4,6,8,10)、 增三 (0,4,8)，半音阶和弦（0,1,2,3,4,5,6,7,8,9,10,11）mod12 代表非线性空间的连续面。 The Geometric Semantics of Chord Encoding Chord encoding not only describes frequency ratios but also carries geometric semantics (membrane -strings), thus determining the spatial structure: Open String: Corresponds to a minor triad (−7,−3,0) mod 12, representing a faceted structure; Closed String: Corresponds to a major triad (−7,−4,0) mod 12, representing a contour structure; Membrane: Corresponds to symmetrical chords, such as diminished seventh (0,3,6,9), whole tone (0,2,4,6,8,10), augmented third (0,4,8), and chromatic chords (0,1,2,3,4,5,6,7,8,9,10,11) mod 12, representing continuous surfaces in nonlinear space. 和弦几何框架 三和弦（开弦与闭弦）定义了对称和弦（膜）的边界，即空间的生成线。由此，和弦几何框架得以 确立：和弦的几何语义（膜-弦）决定空间结构，而和弦的频谱语义（和弦）定义其调性关系。两者共同 构成和弦空间（Chord Space）——一个连接音乐与绘画的统一结构场。 Chord Geometry Framework: Triads (open and closed chords) define the boundaries of symmetrical chords (membrane), i.e., the generating lines of space. Thus, the chord geometry framework is established: the geometric semantics of 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 a chord () determines the spatial structure, while the spectral semantics of a chord (the chord itself) defines its tonal relationships. Together, they constitute the Chord Space—a unified structural field connecting music and painting. 实验验证 这些结果并非理论假设，而源自于绘画中的独立观察与实验。在色彩的离散分布、形态的空间排列 中，可以反复验证上述和弦几何特征。因此，《和弦绘画》不仅是一部艺术专著，更是一份关于和弦空 间的实验报告。 它展示了如何从视觉中测得音乐的几何结构，如何以绘画为观测仪器，揭示生命与宇宙的调性秩 序。绘画在此被重新定义：它不再是主观的感知再现，而是和弦结构的可见生成。 每一幅作品，都是一次频谱的空间展开；每一条线、每一个色面，都是和弦在时空中的几何显现。 《和弦绘画》由此成为和弦语言体系的支柱之一——它提供了观测、验证与应用的可视基础，让和弦从 音乐的时间流中，转化为绘画的空间形。 Experimental Verification These results are not theoretical assumptions, but rather stem from independent observation and experimentation in painting. The discrete distribution of color and the spatial arrangement of forms repeatedly verify the aforementioned chordal geometric characteristics. Therefore, *Chord Painting* is not only an art monograph, but also an experimental report on chordal space. It demonstrates how to measure the geometric structure of music visually, and how to use painting as an observational instrument to reveal the tonal order of life and the universe. Painting is redefined here: it is no longer a subjective representation of perception, but a visible generation of chordal structures. Each work is a spatial unfolding of the spectrum; every line, every color plane, is a geometric manifestation of a chord in space and time. *Chord Painting* thus becomes one of the pillars of the chordal language system—it provides a visual foundation for observation, verification, and application, allowing chords to transform from the temporal flow of music into the spatial form of painting. Li, X. H. (2020). Chord Painting. ResearchGate. https://www.researchgate.net/publication/340492620_Chord_Painting Li, X. H. (2024). Chord Language. Zenodo. https://zenodo.org/records/11817631 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Chord Biology；和弦生命 人类有两种生命观察者：和弦（调性）观察者与非和弦（无调性）观察者，分别观察两种生命形 式：和弦包（量子化频谱，场）与生物体（细胞，分子等），生命是两者的二层结构。 Humans have two types of life observers: chord (tonal) observers and non-chord (atonal) observers. They respectively observe two types of life forms: chord packages (quantized spectra, fields) and organisms (cells, molecules, etc.). Life is the two-layer structure of these two types. 在人体中，和弦（chord）表现为经络（或脉轮）系统。初步观察表明，十二经络系统展现受激频 谱响应，其频率分布可近似为几何级数： fn=H^n⋅f0，其中 H=2^(1/12)≈1.059463，n∈Z 该式通过对数变换可切换为泛音频线性谱 ( n f )，并与量子化假设 ( n f h )（能量离散结构）数学一 致。 这暗示音乐（时间域）、绘画（空间域）、经络（生命域）及量子化假设共享统一的离散数学框架。 In the human body, chords manifest as a meridian (or chakra) system. Preliminary observations indicate that the twelve meridian systems exhibit an excited spectral response, the frequency distribution of which can be approximated as a geometric series: fn=H^n⋅f0, where H=2^(1/12)≈1.059463, n∈Z. This equation can be transformed into a linear overtone spectrum (nf) through logarithmic transformation, and is mathematically consistent with the quantization hypothesis (nfh) (discrete energy structure). This suggests that music (temporal domain), painting (spatial domain), meridians (life domain), and the quantization hypothesis share a unified discrete mathematical framework. Natural Spirit；自然精神 和弦语言是和弦结构（第三人称观察）与和弦语义（第一人称观察）的共现。 Chord language is the co-occurrence of chord structure (third-person observation) and chord semantics (first-person observation). 人类存在两套语言系统：符号语言（后天语言）与和弦语言（先天语言）；前者是人工信息系统， 基于语音符号，如：自然语言；后者是自然信息系统，基于和弦（量子化频谱），如：音乐、绘画，经 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 15-2.Chord Distribution On The Human body；人体上的和弦分布 162 15-3.Chord Life Packet；和弦生命包 166 15-4. Levels of Life；生命层次 167 15-5. Life-Death and Modulation；生死与转调 172 15-7.Chord Medicine；和弦医学 175 Appendix；附录 177 16.NATURAL SPIRIT;自然精神 182 16-2.Compile；编译 184 16-3.Observer；观察者 186 16-1.Two Language；两种语言 188 Conclusion；结语 190 CONCLUSION；结语 192 Disclaimer；免责声明 192 REFERENCES；参考文献 194 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 1.Chord Mathematics-1；和弦数学-1 和弦是量子化频谱的结构性子集与编码机制，声-光等信号被编码为和弦之后，获得明确的语法—语 义结构与内在生成性。和弦数学是其数学工具，并关联其物理属性。它涵盖音乐数学，并扩展至和弦绘 画（和弦空间）与和弦生命（经络）领域的观察结果。作为一种有关波动，频谱的数学框架，它应该适 用于所有涉及波动与频率的现象和事件。 Chords are a structural subset and encoding mechanism of the quantized spectrum. Signals such as sound and light, after being encoded into chords, acquire a clear grammatical-semantic structure and inherent generative nature. Chord mathematics is its mathematical tool and is related to its physical properties. It encompasses music mathematics and extends to observations in the fields of chordal painting (chord space) and chordal life (meridians). As a mathematical framework concerning fluctuations and the spectrum, it should be applicable to all phenomena and events involving fluctuations and frequencies. 关键词：和弦，波动，频率，色谱，±音符，镜像对称 Keywords: chord, wave, frequency, color spectrum, ± note, Mirror Symmetry 1-1.Temperament Systems ；律制 和弦数学具有离散数学结构，其取值的数学方法称为：律制（Temperament systems），如：五度相 生律（Circle-of-fifths system），纯律（Just intonation）， 十二平均律（Equal Temperament）等。 Chord mathematics has a discrete mathematical structure, and the mathematical methods for determining their values are called tempera systems, such as the circle-of-fifths system, just intonation, and equal tempera. 所有律制（Temperament systems）基于两个数列集合：泛音数列 {n*f，n∈Z+ }（等差数列）与平 均律数列 {H^n*f，H=1.059463, n∈Z }（等比数列），泛音满足协和，平均律满足对称，大三和弦与对称 和弦分别是两者的子集。 All temperament systems are based on two sets of sequences: the overtone sequence {n*f，n∈Z+ } (arithmetic sequence) and the equal temperament sequence {H^n*f, H=1.059463, n∈Z} (geometric sequence). Overtones satisfy consonance, and equal temperament satisfies symmetry. Major triads and 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 symmetric chords are subsets of both. 倍频数列{2^n*f n=序数} 是 {泛音} 与 { 平均律 } 的交集，这是和弦语言保持统一的基础。 The octave series {2^n*f n= ordinal} is the intersection of {overtone} and { equal temperament }, which is the basis for chord language to remain unified. Overtone Sequence；泛音数列 图1-1.1、泛音频谱 Figure 1-1.1 Overtone spectrum 量子化与和弦化：和弦频率与量子能量在本质上具有同构性，二者均基于一个基准频率 f，通过整 数n的调控生成离散的频率谱或能量谱： 和弦频谱通式：𝑓 𝑛= 𝑛 ⋅ 𝑓，其中 𝑛 ∈ ℤ，f为基频。 量子化假设形式：𝐸𝑛= 𝑛 ⋅ 𝑓 ⋅ ℎ，其中 ，n同样为整数。 从数学结构上看，二者均表现为 𝑛 ⋅ 𝑓 的线性离散序列，区别仅在于物理维度的转换（频率→能 量）。这种整数 n调控的离散性是构成和谐音程与基础和弦的数学根源。 例如，取 n为连续整数可构造常见和弦的音高结构： n = 1, 2, 3, 4, 5, 6 → 对应频率比 4:5:6 → 大三和弦 n = 1, 2, 3, 4, 5, 6, 7 → 频率比 4:5:6:7 → 大七和弦 n = 1, 2, 3, 4, 5, 6, 7, 8, 9 → 频率比 4:5:6:7:9 → 大九和弦 n = 1 至11 的选择 → 频率比 4:5:6:7:9:11 → 大十一和弦 若以整数比 𝑛: 𝑚 表示频率间的和谐关系，上述和弦可统一表达为： 大三和弦：4 : 5 : 6 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 大七和弦：4 : 5 : 6 : 7 大九和弦：4 : 5 : 6 : 7 : 9 大十一和弦：4 : 5 : 6 : 7 : 9 : 11 由此可见，整数序列生成的离散频率结构同时支撑了量子能级与和弦构成。在此视角下，量子化可 视为物理世界的“频谱和弦化”，而和弦化亦可视为音乐领域的“频率量子化”。二者共同揭示了一种基于 整数生成与离散对称的普遍结构原理。 Quantization and Chordification: Chord frequencies and quantum energy are essentially isomorphic, both based on a fundamental frequency f, and generated as discrete frequency or energy spectra through the modulation of integer n: General formula for chord spectrum: fn = n⋅f, where n ∈ Z and f is the fundamental frequency. Quantization hypothesis form: E_n = n⋅f⋅ h, where n is also an integer. Mathematically, both represent linear discrete sequences of n⋅ f, differing only in the transformation of the physical dimension (frequency → energy). This discreteness, modulated by integer n, is the mathematical root of harmonious intervals and fundamental chords. For example, taking n as consecutive integers allows us to construct the pitch structures of common chords: n = 1, 2, 3, 4, 5, 6 → Corresponding frequency ratio 4:5:6 → Major triad n = 1, 2, 3, 4, 5, 6, 7 → Frequency ratio 4:5:6:7 → Major seventh chord n = 1, 2, 3, 4, 5, 6, 7, 8, 9 → Frequency ratio 4:5:6:7:9 → Major ninth chord n = choices from 1 to 11 → Frequency ratio 4:5:6:7:9:11 → Major eleventh chord If we use the integer ratio n:m to represent the harmonious relationship between frequencies, the above chords can be uniformly expressed as: Major triad: 4 : 5 : 6 Major seventh chord: 4 : 5 : 6 : 7 Major ninth chord: 4 : 5 : 6 : 7 : 9 Major 11th chord: 4 : 5 : 6 : 7 : 9 : 11 Thus, it can be seen that the discrete frequency structure generated by integer sequences simultaneously supports both quantum energy levels and chord formation. From this perspective, quantization can be seen as the "spectral chordification" of the physical world, while chordification can be 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 seen as the "frequency quantization" of the music field. Together, they reveal a universal structural principle based on integer generation and discrete symmetry. 泛音是一维震荡模式，高维震荡模式涉及到平均律：(1.059463)^n · f₀，两种模式可以切换——前 者满足协和性，后者满足对称性，形成对称-破缺结构。 将 n 切换为 (1.059463)^n，引入指数型量子化能级：Eₙ=h·1.059463^{n}·f₀，通过模 12 群 ℤ₁₂ 的结 构，实现和弦的系统生成。 Overtones are one-dimensional oscillation modes. Higher-dimensional oscillation modes involve equal temporality: (1.059463)^n · f₀. These two modes can be switched—the former satisfies consonance, and the latter satisfies symmetry, forming a symmetry-broken structure. Switching n to (1.059463)^n introduces an exponential quantized energy level: Eₙ=h·1.059463^{n}·f₀. Through the structure of the modulo 12 group ℤ₁₂, a systematic generation of chords is achieved. Equal Temperament Sequence；平均律数列 公式：H^n-1*f（H= half-step= 12√2=1.059463，n=序数，f=频率） 首项指数 1-1=0，默认首项指数=0，可用：H^n*f 将平均律数列的指数放入集合：{-11，-10，-9，-8，-7，-6，-5，-4，-3，-2，-1， 0，1，2，3， 4，5，6，7，8，9，10，11 } mod 12，可以显示其数学结构并进行群运算。 Formula: H^n-1*f (H = half-step = 12√2 = 1.059463, n = ordinal number, f = frequency) The leading exponent 1-1 = 0. The default leading exponent is 0. You can use: H^n*f Put the exponents of the equal-tempered series into the set: {-11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} mod 12 to display its mathematical structure and perform group operations. 十二平均律的音高分布是严格的等比数列： fn=f0⋅2^n/12。 十二平均律形成半音阶，它既是一个和弦（无调性特征和弦），也是所有对称和弦的生成基础： 减七和弦（小三度等距，公比=H^3≈1.189207） 全音阶和弦（大二度等距，公比= H^2≈1.122462） 增三和弦（大三度等距，公比= H^4≈1.259921） The pitch distribution of the twelve-tone equal temperament is a strict geometric sequence: fn = f0 ⋅ 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 2^n/12. The twelve-tone equal temperament forms a chromatic scale, which is both a chord (an atonal characteristic chord) and the basis for generating all Symmetrical Chords: Diminished seventh chord (equal minor third interval, common ratio = H^3 ≈ 1.189207) Die-tone chord (equal major second interval, common ratio = H^2 ≈ 1.122462) Augmented triad (equal major third interval, common ratio = H^4 ≈ 1.259921) 对称和弦（Symmetrical Chords）的几何语义是大于一维的非线空间，是和弦空间的生成基础之 一；十二平均律虽来自数学，却契合几何法则。 The geometric semantics of Symmetrical Chords is a non-linear space greater than one dimension, which is one of the generation bases of chord space; although the twelve-tone equal temperament comes from mathematics, it conforms to the laws of geometry. 1-2. Symmetrical and Asymmetrical Chords；对称与非对称和弦 和弦分为对称和弦与非对称和弦，对称和弦基于平均律，如：减七和弦，全音阶和弦，增三和弦； 非对称和弦基于泛音频谱，如：大三和弦，整体表现为：对称-破缺。 Chords are divided into symmetrical chords and asymmetric chords, and symmetrical chords are based on the equal temperament, such as: diminished seventh chord, diatonic chord, increased triad; Asymmetrical chords are based on the overtone spectrum, such as the major triad, and the overall performance is: symmetry-broken. Symmetrical Chords；对称和弦 等比数列（Geometric sequence）和弦是对称和弦，基于平均律的数学框架（mod12 群），共有四 种： Symmetrical Chords are symmetrical chords based on the mathematical framework of equal temperament (mod12 group). There are three types: 减七和弦、公比=H^3≈1.189207；小三度数列，{0,3,6,9}；七声音阶（Heptachord）特征和弦。 Diminished 7th, common ratio =H^3≈1.189207; Minor third series, {0,3,6,9}; Heptachord characteristic chords. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 全音阶和弦、公比= H^2≈1.122462；全音阶数列，{0,2,4,6,8,10}，爵士音阶特征和弦。 Diatonic chord, common ratio = H^2≈1.122462; Diatonic series, {0,2,4,6,8,10}, characteristic chords of the jazz scale. 增三和弦（augmented triad）、 公比= H^4≈1.259921，大三度（Major third）数列，{0，4，8}， 爵士五声音阶特征和弦。 augmented triad, common ratio = H^4≈1.259921, Major third series, {0,4,8}, characteristic chord of the jazz pentatonic scale. 半音阶和弦（Chromatic chords）、公比=H≈1.059463，小二度（minor second）数列，{ 0，1， 2，3，4，5，6，7，8，9，10，11 } Chromatic chords, common ratio H ≈ 1.059463, minor second sequence: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 对称和弦表：1、减七和弦（膜）、 2、全音阶和弦（膜）， 3、增三和弦（膜），4、半音阶和弦 （膜） *◆=正音符，●=负音符，色彩=色荷 Symmetrical Chords table: 1, diminished 7th chord (membrane), 2, diatonic chord (membrane), 3, augmented Triads (membrane), 4. Chromatic chords (membrane) * ◆=positive note, ●=negative note, color=color charge 对称和弦（Symmetrical Chords）是不同音阶系统：七声音阶，爵士音阶，爵士五声音阶，无调性 体系的构成基础。 Symmetrical Chords are the foundation of different scale systems: the heptatonic scale, the jazz scale, the jazz pentatonic scale, and the atonal system. Triad；三和弦 三和弦是非对称和弦，包含纯五度，大三度或小三度。纯五度是是其特征音程（不存在于对称和弦 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 中）。 Triads are asymmetrical chords that contain a perfect fifth, a major third, or a minor third. The perfect fifth is their characteristic interval (not present in geometric progression chords). 大三和弦是泛音频谱的 f1-f6，两者存在自然联系。 The major triad is f1-f6 of the overtone spectrum, and there is a natural connection between the two. 大三和弦（Major triad），{0,4,7}。 Major triad , {0,4,7}. 小三和弦（Minor triad），{0,3,7} Minor triad , {0,3,7} 三和弦+对称和弦组成音阶，调，在后面部分有更多介绍。 Triads + Symmetrical Chords make up the scale, key, more on this later section. 三和弦重叠对称和弦，或三和弦重叠三和弦还可产生众多的重叠和弦，它们是基本和弦的衍生形 式，放在后面的章节介绍。 Triad overlap Symmetrical Chords or triad overlap Triads can also produce numerous overlapping chords, which are derivative forms of the basic chords and are described in later sections. Mirror Symmetry；镜像对称 三和弦（Triad）有升序与降序两种组织方式，音乐（时间域）采用升序方式，绘画（空间域）采用 降序方式形式，数学形式为镜像对称（互为反和弦-反调）。 Triads can be organized in two ways: ascending and descending. Music (time domain) uses ascending order, and painting (space domain) uses descending order. The mathematical form is mirror symmetry (antichords - anti-tones). 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图1-3、大三和弦-小三和弦的升序，降序，镜像对称形式。Y=平均律数列的指数 Figure 1-3, Major triad - minor triad ascending, descending, mirror-symmetric form. Y= exponents of the equal temperament series. 大三和弦，升序：{0，4，7}，大三和弦，降序：{-7，-4，0} （mod 12） Major triad, ascending: {0,4,7}, Major triad, descending: {-7，-4，0}（mod 12） 小三和弦，升序：{0，3，7}，大三和弦，降序：{-7，-3，0} （mod 12） Minor triad, ascending: {0,3,7}, Major triad, descending: {-7，-3，0}（mod 12） 图1-3.2、大三和弦-小三和弦的升序，降序，镜像对称形式。七声音阶（Heptachord）， C大调，关 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 系小调。 Figure 1-3.2. Ascending, descending, mirror-symmetric forms of Major - minor triads. Heptachord, C major, relation minor. Formula；公式： C大三和弦（升序）=H^0,4,7.C C major chord, (ascending)= H ^ 0,4,7.C a小三和弦（升序）=H^0,3,7.a a minor triad (ascending)=H^0,3,7.a C大三和弦（降序）=H^0,-4,-7.C C major chord(descending)= H ^ 0, -4, -7.C Eb 小三和弦（降序）=H^0,-3,-7.Eb Eb minor triad (descending)=H^0,-3,-7.Eb 镜像对称产生了反和弦，反调，这是和弦数学的重要概念。 Mirror symmetry produces the antichord, the antikey, which is an important concept in chord mathematics. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Common Formula；常用公式 Chord=H^n1,n2,n3,nx*f0；（ H=1.05946，n=序数） Chord = H ^ n1, n2, n3, nx * f0; ( H=1.05946, n= ordinal) 大三和弦（Major Chord）=H^0,4,7.f0 小三和弦（Minor chord）=H^0,3,7.f0 大三和弦（降序）=H^0,-4,-7.f0 major chord(descending)= H ^ 0, -4, -7.f0 小三和弦（降序）=H^0,-3,-7.f0 minor triad (descending)=H^0,-3,-7.f0 减七和弦（Diminished 7th）=H^0,3,6,9.f0（Geometric sequence；等比数列） 增三和弦（Augmented triads）=H^0,4,8.f0（Geometric sequence；等比数列） 全音阶和弦（Diatonic chord）=H^0,2,4,6,8,10,12.f0（Geometric sequence；等比数列） 半音阶（Chromatic chord）= H ^ 0,1,2,3,4,5,6,7,8,9,10,11,12,13.f0（Geometric sequence；等比数 列） 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 2.Chord Mathematics-2；和弦数学-2 和弦数学是波动与频率的自然法则映射，依赖和弦的物理属性。它涵盖音乐数学，并扩展至和弦绘 画（和弦空间）与和弦生命（经络）领域的观察结果。作为一种理论框架，和弦数学应适用于所有涉及 波动与频率的现象和事件。 Chord mathematics is a mapping of natural laws of wave motion and frequency, relying on the physical properties of chords. It encompasses the mathematics of music and extends to observations in the fields of chord painting (chord space) and chord life (meridians). As a theoretical framework, chord mathematics should apply to all phenomena and events involving wave motion and frequency. 关键词：和弦，波动，频率，色谱，±音符，镜像对称 Keywords: chord, wave, frequency, color spectrum, ± note, Mirror Symmetry 和弦由三个以上的特定离散频率构成，基本分类为三和弦与对称和弦（Symmetrical Chords），两者 的结合产生和弦语句，表达和弦语义。 Chords are composed of three or more specific discrete frequencies, and are basically classified into triads and Symmetrical Chords. The combination of the two produces chord statements and expresses chord semantics. 平均律数列（Equal temperament series）是和弦的常用取值范围，其中的每个音符都具有频率值与 正-负值，两者是和弦的基本编码元素，前者构成离散频率值分布，后者构成正、负值分布，所有和弦都 包含这两种分布，并由此决定和弦的时空语义以及其它属性。 The Equal temperament series is a commonly used range of values for chords. Each note in the series has a frequency value and a positive-negative value. These two are the basic encoding elements of chords. The former constitutes a discrete frequency value distribution, and the latter constitutes a positivenegative value distribution. All chords contain these two distributions, which determine the spatiotemporal semantics and other properties of the chord. 和弦的频率值分布在前面已经介绍（1、和弦数学-1），本章主要介绍和弦的正-负值分布及编码、语 义规则，涉及和弦，调，调群的构成规则。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 The frequency value distribution of chords has been introduced before (1. Chord Mathematics-1). This chapter mainly introduces the positive-negative value distribution, encoding and semantic rules of chords, involving the composition rules of chords, keys and key groups. 基本和弦表：1-1、大三和弦（闭弦），1-2、小三和弦（开弦）,2、减七和弦（膜）， 3、全音阶和弦 （膜）， 4、增三和弦（膜）， 5、半音阶和弦（膜） 和弦频谱公式：n*f，H^n*f ,（H=1.059463，n∈Z 符号：◆=+音符，●=-音符，音符色=色荷 频谱坐标：mod12 群 Basic chord table: 1-1, major triad (closed string), 1-2, minor triad (open string), 2, diminished 7th (membrane), 3, diatonic chord (membrane), 4, augmented Triads (membrane)，5. Chromatic chords (membrane) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group ±音符是频率的物理属性，继承自经络学，这里有未知的自然法则，我们只能通过观察它在和弦语 言中的作用及数学规律，确定其真实性。（参见：15.和弦生命） ± notes are the physical properties of frequency, inherited from meridians. There are unknown natural laws here. We can only determine its authenticity by observing its role in chord language and mathematical laws. (See: 15. Chord life) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 平均律（Equal Temperament）元素对应表 Equal Temperament element correspondence table 1列：音名（pitch names）。 Line 1: Pitch names. 2列：色荷 Column 2: Color Charge 3列：受激-反应经络及阴-阳（±）属性。 3 columns: stimulus-response meridians and yin-yang(±) properties. *注：经络具有正、负（阴-阳）属性，并会传递给同一行中的声、光频率，这是频率的物理属性； 也是最重要的和弦编码元素，涉及后面的所有章节。 *Note: Meridians have positive and negative (yin-yang) properties and will be transmitted to the sound and light frequencies in the same line. This is the physical property of frequency; it is also the most important chord coding element, involving all subsequent chapters. 上面表中的对应关系基于经络的受激反应特征频率，在本书第 15 章还有专门的介绍。（15.Chord Biology;和弦生命） The corresponding relationship in the above table is based on the characteristic frequency of the stimulated response of the meridian, which is specifically introduced in Chapter 15 of this book. (15.Chord Biology;和弦生命) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 2-2.± Note Distribution In Triads；三和弦中的±音符分布 三和弦（triad）由三个离散频率值组成，在音乐中分别称为：根音（Root）， 三度（Third）， 五度 （Fifth）本文仍沿用音乐中的术语。 A triad is composed of three discrete frequency values, which are called the root, third, and fifth in music. This article still uses the terminology in music. 三和弦又可分为大三和弦（Major triad）和小三和弦（Minor triad），这两种和弦的区别取决于它们 的根色与三度（Third）的音程，大三度（major third）为大三和弦，小三度（minor third）为小三和 弦，两种和弦在几何语义上有着重要的区别，在后面章节有详细的介绍。 Triads can be divided into major triads and minor triads. The difference between these two chords depends on their root color and the interval of the third. The major third is the major triad, and the minor third is the minor triad. The two chords have important differences in geometric semantics, which will be introduced in detail in the following chapters. 分别以 12 个色做根色（Root color），构成 24 个三和弦，12 个大三和弦，12 个小三和弦，包含了 所有三和弦的±音符分布形式。 Use 12 colors as the root color, respectively, to form 24 triads, 12 major triads, and 12 minor triads, including the ± note distribution of all triads. 图2-4.1：大三和弦表（菱形=+音符，圆形=-音符） Figure 2-4.1: Major chord table(Diamond=+note, circle=-note) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图2-4.2：小三和弦表（菱形=+音符，圆形=-音符） Figure 2-4.2: Minor chord table(Diamond=+note, circle=-note) 忽略表中的频率分布，保留正-负值分布，共有六种组合： Ignoring the frequency distribution in the table and retaining the positive-negative value distribution, there are six combinations: （+，+，+），（ -，-，-），（ -，-，+），（+，+，-），（ -，+，+），（+，-，-） 六种组合在和弦语义上有重要的区别，涉及：开弦，闭弦，正-负电荷等。 The six combinations have important differences in chord semantics, involving: open strings, closed strings, positive-negative charges, etc. 六种组合可以是大-小三和弦，这里涉及以下规则： The six combinations can be major-minor triads, where the following rules are involved: （1）、 +根三和弦（+，x，x）倾向生成大三和弦，-根三和弦（-，x，x）倾向生成小三和弦。 (1) + root triads (+, x, x) tend to generate major triads, while - root triads (-, x, x) tend to generate minor triads. （2）、 标准三和弦（Standard triads）：+根大三和弦（+，x，x）与 -根小三和弦（-，x，x）可充 当调系统中的主和弦。 (2) The positive root major triad (+, ±, ±) and the negative root minor triad (-, ±, ±) act as the main chords in the tuning system. （3）、非标准三和弦（Non-standard triads）：+根小三和弦（+，x，x）与-根大三和弦（-，x， x），不能充当调系统中的主和弦。 (3) Non-standard triads: + minor triad (+, x, x) and - major triad (-, x, x) cannot serve as the main chords in the key system. 标准三和弦又可分为两种： 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 There are two types of standard triads: 纯三和弦（pure triad），如：纯大三和弦（+，+，+），纯小三和弦（-， -， -）。 pure triad, such as pure major triad (+,+,+), pure minor triad (-, -, -). 混合三和弦（Mixed triad ）：混合大三和弦（+，x，-）；混合小三和弦（-，x，+）。 Mixed triad: Mixed major triad (+, x, x); Mixed minor triads (-, x, x). 两种标准三和弦在调群中涉及以下规则： The two standard triads involve the following rules in key groups: 纯三和弦（pure triad）在调群中充当主调的主和弦 A pure triad acts as the main chord of the main key in a key group 混合三和弦（Mixed triad）在调群中充当副调的主和弦。 Mixed triad are tonic chords that act as secondary keys in a key group. 上面规则适用于七声音阶系统，在爵士音阶系统中有一些区别，在后面相关章节分别介绍。 The above rules apply to the heptachord scale system, and there are some differences in the jazz scale system, which are described in the relevant sections later. 2-3.±Note Distribution In Symmetrical Chords；对称和弦中的±音符分布 对称和弦（Symmetrical Chords）的离散频率分布为等比数列（Geometric sequence），这类和弦在 音乐中称作：不协和弦（Dissonant chords），对称和弦有：减七和弦，全音阶和弦，增三和弦，分别是 不同音阶系统的特征和弦，在前面的章节已有介绍。（参见：1.Chord Mathematical;和弦数学）。 The discrete frequency distribution of Symmetrical Chords is a geometric sequence. This type of chord is called dissonant chords in music. Symmetrical Chords include diminished seventh chords, diatonic chords, and augmented triads, which are characteristic chords of different scale systems and have been introduced in the previous chapters. (See: 1. Chord Mathematical). 下图是对称和弦表，请注意各和弦中的±音符比例。 The figure below is a Symmetrical Chords table, please pay attention to the proportion of ± notes in each chord. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 对称和弦表：1、减七和弦（膜）、 2、全音阶和弦（膜）， 3、增三和弦（膜），4、半音阶和弦 （膜） *◆=正音符，●=负音符，色彩=色荷 Symmetrical Chords table: 1, diminished 7th chord (membrane), 2, diatonic chord (membrane), 3, augmented Triads (membrane), 4. Chromatic chords (membrane) * ◆=positive note, ●=negative note, color=color charge 忽略表中频率分布，只保留正-负值分布，可以记为以下组合： Ignoring the frequency distribution in the table, only keeping the positive-negative value distribution, it can be recorded as the following combination: （+，+，-，-），（+，-，+，-，+，-），（+，+，+），（ -，-，-） 其中，减七和弦（diminished 7sh）与全音阶和弦（diatonic chord）表现出正-负对称性，增三和弦 是全音阶和弦的包含部分。 对称和弦中的正-负音符可以构成正-负集合，在表现空间景深，大-小调性时具有重要的作用，因此 具有相对的独立性，是对称和弦的特殊形式。 Among them, diminished 7th chords (diminished 7th) and diatonic chords exhibit positive-negative symmetry, and augmented triads are included within diatonic chords. Positive and negative notes in Symmetrical Chords can form positive and negative sets, which play an important role in expressing spatial depth and major-minor tonality. Therefore, they have relative independence and are a special form of Symmetrical Chords. Reference；参考 三和弦的正-负音符分布与中国古代易经中的八卦图有些相似，但是我无法证明它们是或不是同一对 象，放在下面仅供参考。 The distribution of the positive and negative notes of the triad is somewhat similar to the Eight 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 diagrams in the ancient Chinese Book of Changes, but I cannot prove that they are or are not the same object, which is placed below for reference only. （+，+，+），（ -，-，-），（ -，-，+），（+，+，-），（ -，+，+），（+，-，-） 乾（☰）、坎（☵）、艮（☶）、震（☳）、巽（☴）、离（☲）、坤（☷）、兑（☱） 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 3.Chord Geometry；和弦几何 和弦语言是时空语言，包含空间的语义表达：由和弦编码结构（量子化频谱）包含的几何语义集合 {开弦|闭弦|膜} 生成“和弦空间”，是量子化的空间结构。 Chord language is a spatiotemporal language that contains the semantic expression of space: the geometric semantic set {open string|closed string|membrane} contained in the chord encoding structure (quantized spectrum) generates the "chord space", which is a quantized spatial structure. 在音乐中，基本频率单位是“音符”（机械波）。然而，和弦绘画的定量基础基于色彩频率（光，电磁 波）。因此，我们需要扩充定义：音符 = 频符（Frequency Note）：包含所有频率的广义概念。其中，色 彩频率可特称为色荷（Chromatic Charge）。 In music, the fundamental unit of frequency is the "note" (a mechanical wave). However, the quantitative basis of polyphonic painting is based on color frequencies (light and electromagnetic waves). Therefore, we need to expand the definition: note = frequency symbol: a broad concept that encompasses all frequencies. Color frequencies can be specifically called chromatic charges. 本文涉及两个关键术语：“和弦”与“弦”。 和弦：由三个以上离散频率构成的和弦编码，以量子化频谱为编码结构。 弦：和弦编码包含的几何语义，是和弦信息（或量子信息），也是方便区别于“和弦”的概念。 关系：和弦是弦的编码形式，弦是和弦的几何语义。两者是一体两面，分别从编码结构和几何语义 的角度进行描述。 Chords: Chord codes composed of three or more discrete frequencies, using a quantized spectrum as their encoding structure. Strings: The geometric semantics contained in chord codes represent chord information (or quantum information), and are also a convenient way to distinguish them from "chords." Relationship: Chords are the encoding form of strings, and strings are the geometric semantics of chords. The two are two sides of the same coin, described from the perspectives of encoding structure and geometric semantics, respectively. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 后，确定性降低，空间语义也会相应的发生变化。 Both major and minor triads possess definitive geometric semantics: closed strings represent contour lines, while open strings correspond to facet lines. However, when a triad omits 1-2 notes, its determinacy diminishes, and the spatial semantics undergo corresponding transformations. 点空间： 所有音符都可以知觉为点空间，但是有图形意义的点空间是三和弦（线和弦）的省略、收缩形式。 将三和弦省略，只剩下一色，三和弦的线空间（1维）便会收缩为“点空间”（0维），点空间是线 和弦的省略引起线空间收缩的结果。见图 3.1，图 3.2 在图例中、墙上的挂钩为点状空间，使用小三和弦（开弦）的根色；正方体的分面线为小三和弦， 根色出现在各个转角的点上。 Point Space: "All notes can be perceived as point spaces, but point spaces with graphical significance are abbreviated and contracted forms of triads (line chords). By omitting the notes of a triad, leaving only one color, the line space (1-dimensional) of the triad contracts into a 'point space' (0-dimensional). The point space is the result of the line space contracting due to the omission of the line chord. See Figure 3.1 and Figure 3.2. In the illustrations, the wall hooks serve as point spaces, using the root color of a minor triad (open chord); the facet lines of the cube are minor triads, with the root color appearing at the points of each corner." 不确定线： 开和弦（开弦）与闭和弦（闭弦）的区别在和弦的三度（大三度与小三度），如果省略和弦三度， 两者的区别便消失，产生不确定的线空间。 Uncertainty line: The difference between an open chord (open string) and a closed chord (closed string) is in the third of the chord (major and minor third), and if the chord third is omitted, the difference between the two disappears, creating an uncertain line space. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 3-4、Overlapping Chords ； 重叠和弦 重叠和弦由同调中的不同和弦重叠构成，常见形式之一是：三和弦叠加对称和弦（Symmetrical Chords）。 Overlapping chords are composed of overlapping chords in the same key. One of the common forms is triads superimposed on Symmetrical Chords. 图3-5、常见重叠和弦 Figure 3-5. Common Overlapping Chords 重叠和弦模糊了三和弦（线和弦）与对称和弦（膜和弦）的区别，能兼容线-膜两种空间语义，并产 生更加丰富，复杂的空间语义变化。 重叠和弦涉及的内容比较多，放在后面的章节分别介绍。 Overlapping chords blur the distinction between triads (linear chords) and Symmetrical Chords (membrane chords), can accommodate both linear and membrane spatial semantics, and produce more rich and complex spatial semantic changes. Overlapping chords involve a lot of content and will be introduced separately in the following chapters. 3-5、Time Chord ； 时间和弦 时间和弦与空间和弦互为反和弦，两者在数学形式上表现为：镜像对称——这表明两者相互依存， 联系。（参见：1-5. Mirror Symmetry；镜像对称） Time chord and space chord are opposite to each other. The two are shown in mathematical form: mirror symmetry-which shows that the two are interdependent and connected. (Refer to: 1-5. Mirror Symmetry) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图3-6、平均律镜像坐标，七声音阶（Heptachord）， C大调的三和弦与音阶 Figure 3-6, the equal temperament mirror coordinates, Heptachord, C major triad and scale 和弦时间用频率与振幅等能量变化产生时间表达。 Chord time is expressed in terms of time generated by energy changes such as frequency and amplitude. 和弦时间包的基本单元是“时段”，主和弦构成时段边界，对称和弦填充主和弦之外的时间。 The basic unit of the chord time Packet is the "period", the tonic forms the boundary of the period, and the Symmetrical Chords fills the time outside the tonic. 时间与空间的边界都需要由三和弦定义，没有三和弦定义的膜和弦没有确定的时-空状态。 The boundaries of time and space need to be defined by triads, and membrane chords without triads have no definite space-time state. 时间和弦不含几何语义，没有空间状态，可以处于任意空间位置的叠加态（非定域性）；反之，空 间和弦不含时间语义，没有时间状态，只能表达静止的空间（定域性）；定域性与非定域性产生了“时 空二相性”（波粒二相性）。 Time chord does not contain geometric semantics, no space state, can be in any space position superposition state (non-locality); On the contrary, spatial chord has no time meaning, no time state, can only express the static space (locality); Locality and non-locality produce "space-time duality" (waveparticle duality). 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 4. Chord Packages；和弦包 在和弦时空中，孤立的三和弦（非对称和弦）与对称和弦（对称和弦）均无法独立构成完整的时空 表达。只有通过将三和弦（非对称和弦）与对称和弦（对称和弦）组合为“和弦包”，并形成对称-破缺 （Symmetry Breaking）结构，才能完整地表达时空。 和弦包分为和弦时间包与和弦空间包。两者的核心三和弦（triad）满足镜像对称关系： {−7,−4,0}↔{0,4,7}mod 12 分别表征和弦时间与和弦空间的几何对偶性。这一镜像对称关系（Mirror Symmetry）表明，时间 和空间在和弦语言中可以通过几何结构相互映射。（参见：1-3.1.镜像对称） 在一个和弦包中： 三和弦作为边界算子，生成时空边界： 时间维度：定义时段边界（起始点、终止点）。 空间维度：定义空间边界（轮廓线、分面线）。 对称和弦作为场填充（Field Filling）： 通过等比频率分布（减七和弦，全音阶和弦，增三和弦）渗透边界内外的时空连续体，其作用类似 于经典物理中的以太场（Ether Field）或量子场论中的背景场（Background Field）。 和弦包（Chordal Package）可形式化定义为： 和弦包 = 三和弦（边界） + 对称和弦（场填充） 其中，“+”表示对称-破缺耦合，最终生成稳定的和弦时空流形。 和弦语言中，和弦包又称为：调——包括大调，小调，及七声音阶，爵士音阶等，分别表达不同的 时空含义，在后面章节将会逐步介绍。 In chordal spacetime, isolated triads (asymmetric chords) and Symmetrical Chords (symmetric chords) cannot independently constitute a complete expression of spacetime. Only by combining triads (asymmetric chords) with Symmetrical Chords (symmetric chords) to form a "chordal package," and establishing a symmetry-breaking structure, can spacetime be fully expressed. Chordal packages are divided into chordal time packages and chordal space packages. The core triads (triads) of the two satisfy a mirror symmetry relationship: {−7,−4,0}↔{0,4,7}mod 12 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 These respectively represent the geometric duality of chordal time and chordal space. This mirror symmetry relationship indicates that time and space can be mutually mapped through geometric structures in the language of chords. (See: 1-3.1. Mirror Symmetry) Within a chordal package: Triads act as boundary operators, generating spacetime boundaries: Time dimension: Define temporal boundaries (starting point, ending point). Space dimension: Define spatial boundaries (contour lines, Facet lines). Symmetrical Chords act as field filling: Through geometric frequency distributions (diminished seventh chords, whole-tone chords, augmented triads), they permeate the spacetime continuum inside and outside the boundaries, functioning similarly to the ether field in classical physics or the background field in quantum field theory. The chordal package (Chordal Package) can be formally defined as: Chordal Package=Triads (Boundary)+Symmetrical Chords (Field Filling)Chordal Package=Triads (Boundary)+Symmetrical Chords (Field Filling) Here, "+" denotes symmetry-breaking coupling, ultimately generating a stable chordal spacetime manifold. In the language of chords, chordal packages are also referred to as "keys"—including major keys, minor keys, diatonic scales, jazz scales, etc.—each expressing different spacetime meanings, which will be gradually introduced in later chapters. 4-1.Chord Space Packet ； 和弦空间包 一个和弦空间包必须包含两种和弦：线和弦（三和弦）与对称和弦（膜和弦），和弦空间包=线和弦 +导音膜和弦，线和弦构成轮廓线、分面线，产生空间定义（图-底关系等），膜和弦充满所有非线空 间，类似“以太”，和弦空间包是和弦空间的基本单元。 A chord space packet must contain two kinds of chords: line chords (triads) and Symmetrical Chords (membrane chords), chord space packet = line chords + membrane chords, line chords form contour lines, Facet line, and produce space definitions (Figure-ground relationship, etc.), membrane chords fill all non-linear spaces, similar to "ether", chord space packet is the basic unit of chord space. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4.1、1、七声音阶和弦空间包；2-3、爵士音阶和弦空间包 Figure 4.1, 1. Heptachord scale chord space packet; 2-3. Jazz scale chord space packet 三和弦的几何语义是：线（开弦，闭弦），对称和弦（Symmetrical Chords）的几何语义是：非线 膜，线和弦对膜和弦作边界定义（轮廓线，分面线），产生和弦空间包。 The geometric semantics of triads are: lines (open string, closed string), and the geometric semantics of Symmetrical Chords are: non-linear membrane, line chords define boundaries (contours, Facet line) to membrane chords, resulting in Chord Space Packet. 一个完整的和弦空间包只含一个膜和弦，但通常需要两个线和弦：大三和弦（闭弦）与小三和弦 （开弦），分别构成轮廓线与分面（分形）线。 A complete chord space packet contains only one membrane chord, but usually requires two line chords: a major triad (closed string) and a minor triad (open string), which form the contour line and the facet (fractal) line respectively. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4.2、七声音阶 C大调-升f小调，大三和弦生成图形轮廓线，小三和弦生成分面线，减七和弦填 充所有 M维空间。 Figure 4.2. heptachord C major f-sharp, major triads generate figure contour lines, minor triads generate Facet line lines, and diminished 7th fill all M-dimensional spaces. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4.3、爵士音阶，升 f小调，大三和弦生成图形轮廓线，小三和弦生成分面线，全音阶和弦填充 所有非线空间。 Figure 4.3. Jazz scale f-sharp minor, major triads generate figure outlines, minor triads generate Facet line line, and diatonic chords fill all non-linear spaces. 4-1.2.Figure-Ground Relation ； 图-底关系 图-底关系（figure-ground relation）是空间知觉的基本模式，“背景空间”与“图形空间”是产生空 间知觉的必要条件；两种空间都与音符-和弦的正-负属性相关，正音符-和弦具有背景（远）倾向，负音 符-和弦具有图形（近）倾向，图-底关系与“景深”相关。 The figure-ground relation is the basic mode of spatial perception, and "background space" and "figure space" are necessary conditions for spatial perception; both spaces are related to the positivenegative properties of note-chords, and the positive Note-chords have background (far) tendencies, negative note-chords have figure (near) tendencies, and the figure-ground relationship is related to "depth of field". 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4-2、七声音阶，升 f小调-C 大调图-底关系 Figure 4-2. Heptachord scale f-sharp minor,C major figure-ground relationship 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图-底关系包括：三和弦图-底关系与对称和弦图-底关系。 The figure-ground relationship includes: triad figure-ground relationship and geometric chord figureground relationship. 三和弦与图-底关系：图-底关系与三和弦相关，表现为：小调的图形（近）倾向，大调的背景 （远）倾向，（参见：2-4、和弦中的±音符规则；3-3、正-负闭弦与开弦）。 Triads and Figure-Ground Relations: The figure-ground relationship is related to triads and is manifested as: minor keys tend to have a figure (closer) tendency, while major keys tend to have a background (farther) tendency (see: 2-4, ± note rules in chords; 3-3, positive-negative closed strings and open strings). 对称和弦与图-底关系：对称和弦（Symmetrical Chords）中的负音符具有图形（近）的倾向，正音 符具有背景（远）的倾向。两种音符分别构成正音符集合与负音符集合，具有相对独立性。 Symmetrical Chords and figure-ground relationship: In Symmetrical Chords, negative notes tend to be more figure (near), while positive notes tend to be more background (far). The two types of notes form the positive and negative note sets respectively, and are relatively independent. 下面例图中包含两种图-底关系。 The following example diagram contains two figure-ground relationships. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图5-1.2.相对图-底关系 Figure 5-1.2. Relative figure-ground relationship 对称和弦与图-底关系：对称和弦（Symmetrical Chords）中的负音符具有图形（近）的倾向，正音 符具有背景（远）的倾向。两种音符分别构成正音符集合与负音符集合，具有相对独立性。 Symmetrical Chords and figure-ground relationship: In Symmetrical Chords, negative notes tend to be more figure (near), while positive notes tend to be more background (far). The two types of notes form the positive and negative note sets respectively, and are relatively independent. 5-1.1. Absolute Figure-Ground Relationship；绝对图底关系 七声音阶（heptachord）中的绝对图-底关系（figure-ground relation）由纯大调与纯小调构成，两 调的主音为增四度（Augmented fourth）关系，拥有相同的导音减七和弦（Leading note diminished 7th）， 纯大调表达绝对背景，纯小调表达绝对图形。（参见：2-2） The absolute figure-ground relation in heptachord is composed of pure major key and pure minor key, and the tonic of the two keys is an Augmented fourth relation. With the same Leading note diminished 7th, 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 the pure major expresses the absolute background and the pure minor expresses the absolute figure. (See: 2-2) 图5-1.1、七声音阶（Heptachord）中的±纯三和弦（和弦 1、3）构成图-底大小调。 Figure 5-1.1.The ± Pure triads (chords 1, 3) in the Heptachord constitute a figure-ground relational key. 图5-1.2、七声音阶，增四度大-小调 Figure 5-1.2, Heptatonic scale, Augmented fourth major-minor 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图5-1.2、七声音阶，增四度大-小调 Figure 5-1.2, Heptatonic scale, Augmented fourth major-minor 5-1.2. Relative Figure-Ground Relationship；相对图底关系 七声音阶中的相对图-底关系由平行大-小调（Parallel Major-Minor）表达。 The relative figure-ground relationship in the heptatonic scale is expressed by Parallel Major-Minor. 平行大小调（Parallel Major-Minor）中的两个调分为：主调（first key）与副调（Second key），主 调（First key）的主和弦（Tonic）是纯三和弦，副调（Second key）的主和弦（Tonic）是混合三和弦， 两调的主音为小三度关系，拥有相同的导音减七和弦（Leading note diminished 7th）。 The two keys in Parallel Major-Minor are divided into: The first key and the Second key, the Tonic of the First key is a pure triad, the Tonic of the Second key is a mixed triad, and the tonic of the two keys is a minor third. It has the same Leading note diminished 7th. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图5-2.1、上图中，和弦 1、3为纯三和弦；和弦 2、4为混合三和弦。（菱形=+音符，圆形=-音 符） In Figure 5-2.1 and above, chords 1 and 3 are pure triads; Chords 2 and 4 are mixed triads. (Diamond =+ note, circle = -note) 下图中的部分图-底关系具有相对性，采用平行大-小调。 Some of the figure-ground relationships in the figure below are relative, using parallel major-minor scale. 图5-2.2、七声音阶，含平行大小调；C大调，降 e小调，f#小调，A大调 Figure 5-2.2. heptachord scale, including parallel major and minor scales; C major, E flat minor, F# minor, A major 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图5-2.2、七声音阶，含平行大小调；C大调，降 e小调，f#小调，A大调 Figure 5-2.2. heptachord scale, including parallel major and minor scales; C major, E flat minor, F# minor, A major 绝对图底关系（figure-ground relation）可以包含相对图底关系（figure-ground relation），共同构 成空间系统：纯大调与纯小调构成绝对图底关系，纯大调与其关系小调，纯小调与其关系大调构成其中 的相对图-底关系。 Absolute figure-ground relations can include relative figure-ground relations, together forming a spatial system: pure major and pure minor constitute absolute figure-ground relations, while pure major and its relative minor, and pure minor and its relative major, constitute the relative figure-ground relations within it. 5-1.3.dim7 调群 完整的七声音阶空间系统包含两种图底关系，四个调，共享同一导音减七和弦：称之为：同导音减 七和弦的调群，或：dim7 调群，和弦系统共有三个 dim7 调群，分别以减七和弦中的音符命名：C 调 群，D 调群，E调群。 The complete heptachord scale space system contains two figure-ground relationships, four keys, sharing the same leading tone diminished seventh chord: it is called: key group with the same leading tone 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 diminished seventh chord, or: dim7 key group. There are three dim7 key groups in the chord system, named after the notes in the diminished seventh chord: C key group, D key group, and E key group. 图13-1.1、D，E，C调群 Figure 13-2.1, D，E，C keys group 5-2. Same Root Major Minor ； 同根大-小调 根音符相同的大-小三和弦构成同根大-小调（Same Root Major Minor），同根大-小调只用于在同调 中产生轮廓线与分面线，不产生图-底关系，其中的大三和弦生成轮廓线（闭弦），小三和弦生成分面线 （开弦）。 Major-minor triads with the Same Root note form the Same Root Major Minor, which is only used to produce contours and Facet line in the homology, and does not produce a figrue-ground relationship, where the major triads generate contours (closed strings) and the minor triads generate Facet line (open strings). 同根大-小调中，主和弦是标准三和弦。 In the same root major-minor key, the main chord is the standard triad. 图9-2.1、同根大-小三和弦，大-小调。 Figure 9-2.1, same root major - minor triad, major - minor. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-2.1、同根音符大-小三和弦，大-小调。 same root major - minor triad, major - minor. 图9-2.1、同根音符大-小三和弦，大-小调。 Figure 9-2.1, same root major - minor triad, major - minor. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 5-3、Solution ； 解决 七声音阶中，膜和弦具有寻找线和弦倾向，从而达到稳定，这一属性称作解决（solution）倾向。 膜和弦中各音符具有不同的解决倾向，与主和弦根音符为小二度关系的音符具有最强的解决倾向， 该音符称作：导音。 在图-底调群中，各调都包含导音，系统具有多个导音，由此产生图-底调群的系统特征。 In the heptatonic scale, the membrane chord has a tendency to seek resolution towards the line chord, thereby achieving stability. This property is known as the resolution tendency. Within the membrane chord, each note possesses a different resolution tendency. The note that has the strongest resolution tendency, being a minor second interval from the root note of the tonic chord, is called the leading tone. In the figure-ground tonality group, each key contains a leading tone, and the system has multiple leading tones, which gives rise to the systemic characteristics of the figure-ground tonality group. 5-4.Omit Chord ；省略和弦 省略减七和弦主要用于产生空间景深变化，无调性兼容性，跨音阶兼容性，常见的省略形式如下： The omitted diminished seventh chord is mainly used to produce changes in spatial depth of field, atonal compatibility, and inter-scale compatibility. Common forms of omission are as follows: 图5-4，减七和弦的常见省略形式 Figure 5-4, common ellipsis of the diminished 7th 1）省略正或负音符、减七和弦被省略正或负音符后，空间景深会发生改变——正音符具有背景 （远）倾向，负音符具有图形（近）倾向。 1) When the positive or negative notes are omitted, the spatial depth of field will change - the positive 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 notes have a background (far) tendency, the negative notes have a graphic (near) tendency. 下图中的减七和弦省略了正音符，空间系统系统表现出向前靠近的倾向。 The diminished 7th in the image below omits positive notes, and the spatial system system shows a tendency to approach forward. 图7-3、省略了正音符的减七和弦 2）导音增四度（leading note augmented fourth）是减七和弦，全音阶和弦共同省略形式，减七和 弦省略为导音增四度（leading note augmented fourth）音程时，七声音阶-爵士音阶的膜和弦没有区 别。 下图中的减七和弦（Diminished 7th）省略为增四度（augmented fourth）音程，七声音阶音阶的确 定性消失。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图7-4、减七和弦的省略形式：导音增四度（leading note augmented fourth） Figure 7-4. The omitted form of the Diminished 7th: leading note augmented fourth 3）省略三和弦、当七声音阶中的三和弦省略 1-2 音符后，其和弦语义的确定性降低，可以兼容更 多的空间状态。 When 1-2 notes are omitted for triads in the heptachord scale, the certainty of the chord semantics is reduced and more spatial states are compatible. 6.Heptachord T-D-S Triad；七声音阶 T-D-S 三和弦 前面介绍了七声音阶（heptachord）和弦包（调）的基础结构：主和弦+导音减七和弦，在主和弦 （tonic）的 5度音符上生成属和弦（dominant chord），4度音符上生成下属和弦（subordinate chord），系统中便有了三个三和弦，称作：T-D-S 三和弦，音乐理论中称为：正三和弦（Primary triad），用于表达调内分离图形与分面的亮度关系。 Earlier we introduced the basic structure of the heptachord chord package (key): tonic chord + diminished seventh chord. The dominant chord is generated on the 5th note of the tonic, and the 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 8. Closure；闭合性 七声音阶中，和弦空间包具有闭合倾向，即：图形轮廓线的闭合倾向，这是减七和弦的内禀属性， 包含减七和弦的和弦包都具有闭合倾向。 In the heptachord, the chord space package has a tendency to be closed, that is, the graphic contour line tends to be closed. This is an inherent property of the diminished seventh chord. The chord package containing the diminished seventh chord has a tendency to be closed. 减七和弦是七声音阶特征膜和弦，三个减七和弦各有不同的闭合倾向（Closure tendency），由此产 生了七声音阶和弦包的闭合梯度（Closed gradient）与空间秩序。 The diminished seventh chord is the characteristic membrane chord of the heptatonic scale. The three diminished seventh chords have different closure tendencies, which produces the closed gradient and spatial order of the heptatonic scale chord package. 不同闭合倾向的减七和弦包含不同的和弦语义，包括：几何语义，生命语义，自然道德语义；这是 和弦语言中最难理解之处。 Diminished seventh chords with different closure tendencies contain different chord semantics, including: geometric semantics, life semantics, and natural moral semantics; this is the most difficult part of the chord language to understand. 图8.1、减七和弦表：1、{B,Ab,F,D}-高闭合性，2、{C#,Bb,G,E}-中闭合性，3、{A,F#,Eb,C} -低闭合 性 Fig. 8.1 Table of minus seventh chords: 1, {B,Ab,F,D} - high closure, 2, {C#,Bb,G,E} - medium closure, 3, {A,F#,Eb,C} - low closure 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 也可使用缩写形式：B dim7，C# dim7，A dim7。 Abbreviations can also be used: B dim7，C# dim7，A dim7。 三和弦+导音减七和弦（Liading note diminished 7th）生成调，一个减七和弦可生成四个调，即： 同导音减七和弦调群，调群中的三和弦可继承其导音减七和弦的闭合性。 A triad + ligating note diminished 7th chord generates a key. A diminished seventh chord can generate four keys, namely: a key group with the same ligating note diminished seventh chord. The triads in the key group can inherit the closure of the ligating note diminished seventh chord. 图8-1.2、导音减七和弦生成的调群：{B,Ab,F,D}-{C#,Bb,G,E}-{A,F#,Eb,C} Fig. 8-1.2 The key group generated by the leading note diminished 7th: {B,Ab,F,D}-{C#,Bb,G,E}- {A,F#,Eb,C} 8-1.Close level ； 闭合层级 三个减七和弦的数学表达相同（Diminished 7th={0,3,6,9} mod12），但是它们有着不同的闭合状态 及空间规则，请看下面例图。 The mathematical expressions of the three diminished 7th are the same (Diminished 7th ={0,3,6,9} ), but they have different Close states and space rules. Please see the following examples. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图8.2：{B,Ab,F,D}，闭合图形 Figure 8-2: {B,Ab,F,D}, closed figure {B,Ab,F,D}只能表现轮廓弦闭合的图形，我们将这种空间特征称作：闭合性。 {B,Ab,F,D} can only express figures with closed contour. We call this space feature: Close. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图8.3、{A,F#,Eb,C} 、开放图形 Figure 8-3. {A,F#,Eb,C} , Open figure {A,F#,Eb,C} 只能表现轮廓线开放的图形，但是轮廓线仍有闭合倾向，我们将这种空间属性称作：弱 闭合性。 {A,F#,Eb,C} can only express figure with open contours, but the contours still have a tendency to close. We call this space attribute: weak Close. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图8.4、{C#,Bb,G,E}，闭合-开放兼容图形 Figure 8.4, {C#,Bb,G,E}, closed-open compatible figure {C#,Bb,G,E}可表达轮廓线闭合图形，也可表达轮廓线开放图形，兼容两种闭合状态，我们将这种空 间特征称作：次闭合性。 {C#,Bb,G,E} can express contour closed figure and contour open figure, and is compatible with two Close states. We call this spatial feature: sub Close. 综合以上观察，对三个减七和弦的闭合性规则总结如下： Based on the above observations, the closure rules for the three diminished seventh chords are summarized as follows: 减七和弦 Diminished 7th 闭合倾向-稳定性 Closing tendency-stability {B,Ab,F,D}，B dim7 高；High {C#,Bb,G,E}，C# dim7 中；Medium, {A,F#,Eb,C}，A dim7 低；low ⚫ 三个减七和弦具有不同的闭合倾向，由此形成闭合倾向-稳定性层级，它在和弦空间中具有重 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 要意义。 ⚫ The three diminished seventh chords have different closing tendencies, thus forming a closing tendency-stability hierarchy, which is of great significance in the chord space. ⚫ 主-次秩序：空间系统同时存在三个减七和弦时，会依照减七和弦的闭合倾向-稳定性产生主-次 秩序，高-中-低对应：主-次-最次，形成自然解决倾向：由低向高解决。 ⚫ Major-minor order: When there are three diminished seventh chords in a spatial system at the same time, a major-minor order will be generated according to the closing tendency-stability of the diminished seventh chord, with high-middle-low corresponding to: major-minor-least, forming a natural solution tendency: from low to high. ⚫ 这一法则可投射到以其为导音膜和弦的三和弦，三和弦可以继承其导音减七和弦的闭合倾向， 即使在其导音减七和弦缺位的状态下。 ⚫ This rule can be projected to the triad with it as the leading membrane chord. The triad can inherit the closing tendency of its leading tone diminished seventh chord even when its leading tone diminished seventh chord is absent. ⚫ 在爵士音阶，无调性状态下，以上秩序失效，主次秩序可以发生逆转。 ⚫ In the jazz scale and atonal state, the above order becomes invalid and the primary and secondary order can be reversed. 8-2.The Close level of T-D-S ；T-D-S 的闭合级别 T-D-S 三和弦也包含闭合状态：主和弦（Tonic），属和弦（Dominant），下属和弦（Subdominant）， 都存在闭合状态差异，这种差异来自三和弦所属的导音减七和弦调群。 T-D-S triads also contain Close states: Tonic, Dominant, and Sub-dominant, all have Close state differences, which come from the leading diminished seventh chord group to which the triad belongs. T-D-S 三和弦所在的和弦包中，闭合性较高的图形处于主体地位，闭合性较低的图形处于从属地 位。 There are differences in Close between T-D-S triads, the figure with higher Close is in the dominant position, and the figure with lower Close is in the subordinate position. T-D-S 三和弦的闭合状态差异，以及由此产生的主体-从属关系与恒星，行星的秩序相关。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Close state differences of the T-D-S triad, and the resulting subject-subordination relationship is related to the order of stars, planets. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 9. Jazz Scale；爵士音阶 爵士音阶是弱调性系统，它屏蔽了七声音阶的部分和弦语义，并具有无调性兼容性，常见于一些现 代音乐形式。 The jazz scale is a weak tonality system, which shields part of the chord semantics of the heptachord scale and has atonal compatibility. It is common in some modern forms of music. 爵士音阶的特征和弦是全音阶和弦（Diatonic chord），其中包含正-负两个增三和弦（Augmented triad），三和弦+全音阶和弦构成爵士音阶和弦包，三和弦+增三和弦构成爵士五声音阶和弦包。 The characteristic chords of the jazz scale are the Diatonic chord, which contains two Augmented triads, positive and negative; triads + diatonic chords form the jazz scale chord package; triads + augmented triads form the Jazz pentatonic chord package. 图9-1、爵士音阶特征和弦，1、全音阶和弦（Diatonic chord）， 2、增三和弦（Augmented triad） （◆=正音符，●=负音符，色彩=色荷） Figure 9-1. Characteristic chords of the jazz Scale, 1. Diatonic chord, 2. Augmented triad (◆=+note, ●=-note) 爵士音阶的主要特征如下： The main features of the jazz Scale are as follows: ⚫ 爵士音阶由主和弦+导音对称和弦（全音阶和弦，增三和弦）构成，与七声音阶 （heptachord）不同的是：爵士音阶的三和弦与导音对称和弦有重叠音符，所有三和弦都是重 叠和弦，并且允许主七和弦，主九和弦，主十一和弦等和弦形式，这是其独有特征。 ⚫ The jazz scale is composed of the tonic chord + the leading tone Geometric Chord (diatonic chord, augmented triad). Unlike the heptatonic scale (heptachord), the triads of the jazz scale have overlapping notes with the leading tone Symmetrical Chords. All triads are overlapping 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 chords, and chord forms such as the tonic seventh chord, the tonic ninth chord, and the tonic eleventh chord are allowed. This is its unique feature. ⚫ 爵士音阶中的对称和弦（Geometric Chord）可向无彩色（neutral colors）解决，构成无调性解 决。 ⚫ Symmetrical Chords in the jazz scale can be resolved towards neutral colors, constituting atonal solutions. ⚫ 全音阶和弦，增三和弦没有闭合倾向，可以表达任意闭合状态的图形。（参见：8、闭合性） ⚫ Diatonic chords and augmented triads have no tendency to close and can express any closed state. (See: 8. Closure) ⚫ 爵士音阶常在多层调群（Multi-Layer Key Group）中充当从属调（参见：13、多层调群）；七声 音阶调群中的爵士音阶可以保留闭合语义，这来自三和弦隐含的导音减七和弦。 ⚫ The jazz Scale often acts as a sub-key in the Multi-Layer Key Group (see: 13, Multi-Layer Key Group); the jazz Scale in the heptatonic key group can retain the Close semantics, which comes from Triads implicitly leading note diminished 7th chords. 9-1. Figure-Ground Relation ；图-底关系 图-底关系（figure-ground relation）由图形与背景构成，是空间知觉的基本模式，图-底关系包括： 绝对图-底关系与相对图-底关系，构成形式分别为：增四度大-小调图底关系与正负增三和弦图底关系。 The figure-ground relation is composed of figure and background and is the basic pattern of spatial perception. The figure-ground relation includes: absolute figure-ground relation and relative figureground relation, and the constituent forms are: augmented fourth major-minor figure-ground relation and positive and negative augmented triad figure-ground relation respectively. 爵士音阶与七声音阶的图-底关系既有联系，也有区别，参阅：5-1. Figure-Ground Relation 图-底关 系。 The figure-ground relationship between the jazz scale and the heptatonic scale is both related and different. See: 5-1. Figure-Ground Relation. 爵士音阶中的图-底关系（figure-ground relation）由增四度大-小调群构成——两调的主音为增四度 （Augmented fourth）关系，共享同一个导音全音阶和弦（Leading note diatonic Chords），大调表达背 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 景，小调表达图形。 The absolute figure-ground relation in the jazz scale is composed of the augmented fourth majorminor group - the tonics of the two keys are in an augmented fourth relationship, sharing the same leading note diatonic chords, the major key expresses the background, and the minor key expresses the figure. 图9-1.1、爵士音阶中的增四度大-小调群 Figure 9-1.1. Augmented fourth major-minor group in jazz scales 爵士音阶的增四度大-小调及三和弦不区别相对图底关系与绝对图底关系，可用于两种图底关系。 The augmented fourth major-minor scale and triads of the jazz scale do not distinguish between relative figure-ground relationships and absolute figure-ground relationships, and can be used for both figure-ground relationships. 图9-1.3、爵士音阶 C大调，f#小调，绝对图-底关系 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-3.2 增三和弦 Figure 9-3.2. Augmented triad 9-3.2.独立增三和弦 增三和弦单独构成空间系统时，具有全局的景深属性。 When the augmented triad constitutes a spatial system alone, it has a global depth of field property. 图9-3.3.增三和弦 Figure 9-3.3. Augmented triad 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-3.4.增三和弦 Figure 9-3.4. Augmented triad 9-4、Overlapping Chord；重叠和弦 爵士音阶的调结构为：三和弦+导音对称和弦（Leading note Symmetrical Chords）——全音阶和 弦。 The key structure of the jazz scale is: triad + leading note Symmetrical Chords - diatonic chords. 在爵士音阶中，三和弦（线和弦）与导音对称和弦（膜和弦）有重叠音符。 In jazz scales, triads (line chords) and leading-tone Symmetrical Chords (membrane chords) have overlapping notes. 大调（Major）： {0，4，7}，{1，3，5，7，9，11} 小调（Minor）： {6，9，1}，{1，3，5，7，9，11} 重叠和弦的音符不限于三个，原理上，三和弦+导音对称和弦（Leading note Symmetrical Chords） 包含的音符都是取值范围。常见的有：主七和弦，主九和弦等。 Overlapping chords aren't limited to three notes. In principle, triads and leading note Symmetrical 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Chords all contain notes within a range of values. Common examples include the tonic seventh and tonic ninth chords. 重叠和弦削弱了三和弦的几何语义（线），常用于模糊的图-底关系。 Overlapping chords weaken the geometric semantics (line) of triads and are often used to ambiguous figure-ground relationships. 爵士音阶的重叠和弦中包含了半音程，加强了无调性兼容性与解决倾向，是常用的无调性结构， 如：如：主七和弦，主九和弦，主十一和弦，主十三和弦等。 The overlapping chords of the jazz scale contain semitones, which enhance the atonal compatibility and resolution tendency. It is a commonly used atonal structure, such as: the tonic seventh chord, the tonic ninth chord, the tonic eleventh chord, the tonic thirteenth chord, etc. 爵士音阶中的重叠和弦在后面章节（10.无调性）还有专门的介绍。 The overlapping chords in jazz scales are specially introduced in the following chapters (10. Atonality). 9-5．Lonely key；孤调 爵士音阶都是以正-负增四度关系成对出现，当系统中只有一个调时，调性减弱，无调性解决倾向加 强。 Jazz scales always appear in pairs with a positive-negative augmented fourth relationship. When there is only one key in the system, the tonality is weakened, and the tendency for atonal resolution is strengthened. 孤调（Lonely key）系统通常采用重叠和弦构成，如：主七和弦，主九和弦，主十一和弦，主十三 和弦，其中包含的半音越多，越接近无调性体系的结构。 参见：10、无调性 The lonely key system typically employs overlapping chords, such as the tonic seventh, ninth, eleventh, and thirteenth chords. The more semitones it contains, the closer it is to an atonal system. See also: 10. Atonality 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-5.1，爵士音阶 f#七和弦 Figure 9-5.1, Jazz scale F# seventh chord 图9-5.2，爵士音阶 f#九和弦 Figure 9-5.2, Jazz scale F# ninth chord 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-5.3，爵士音阶 f#十一和弦 Figure 9-5.3, jazz scale f# eleventh chord 图9-5.4，爵士音阶 f#十三和弦 Figure 9-5.3, jazz scale f# eleventh chord 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 10.Atonal；无调性 无调性体系的特征和弦是半音阶和弦，向无彩色（噪音）解决。 The characteristic chords of the atonal system are chromatic chords that resolve to achromatic (noise). 基本和弦表：1-1、大三和弦（闭弦），1-2、小三和弦（开弦）,2、减七和弦（膜）， 3、全音阶和弦 （膜）， 4、增三和弦（膜）， 5、半音阶和弦（膜） 和弦频谱公式：n*f，H^n*f ,（H=1.059463，n∈Z 符号：◆=+音符，●=-音符，音符色=色荷 频谱坐标：mod12 群 Basic chord table: 1-1, major triad (closed string), 1-2, minor triad (open string), 2, diminished 7th (membrane), 3, diatonic chord (membrane), 4, augmented Triads (membrane)，5. Chromatic chords (membrane) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 无调性体系不含三和弦（开弦，闭弦），其特征和弦（半音阶）向和弦无彩色（噪音）解决，包 括：线性，非线性解决。不能形成调性和弦包。 Atonal systems do not contain triads (open strings, closed strings). Their characteristic chords (chromatic scales) resolve to chords with achromatic (noise) resolution, including linear and nonlinear resolutions. They cannot form tonal chord packages. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图10-1，无调性体系 Figure 10-1, Atonal System 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图10-2，无调性体系，省略形式 Figure 10-2, Atonal System, Abbreviated Form 图10-3，无彩色解决形式 Figure 10-3, Solution without color. 半音阶和弦越完整，无彩色解决倾向越强。半音阶和弦常用省略形式，削弱无调性（无彩色）倾 向，省略半音阶和弦仍需要保持半音阶形式。（参见：9-1.2，） The more complete a chromatic chord is, the stronger its tendency towards atonal resolution. Chromatic chords are often abbreviated to reduce their atonal (atonal) tendency; however, even when a chromatic chord is omitted, it is still necessary to maintain the chromatic form. See also: 9-1.2, overlapping chords; 9-4, lonely key. 非和弦（无调性）系统是和弦（调性）系统的反过程，它屏蔽了调性系统的语义逻辑，主要由亮度 变化来产生视觉空间。 和弦（调性）与非和弦（无调性）是不同的认知方式，甚至是不同的宇宙观。 The atonal (non-chordal) system is the reverse process of the chordal (tonal) system. It shields the semantic logic of the tonal system and primarily generates visual space through variations in brightness. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Chords (tonality) and atonal (non-chordal) systems represent different ways of cognition, and even different worldviews. 10-2、Figure-Ground Relationship；图底关系 无调性体系中只有对称和弦，服从以下规则： The atonal system contains only Symmetrical Chords, which follow these rules: 对称和弦与图-底关系：对称和弦（Symmetrical Chords）中的负音符具有图形（近）的倾向，正音 符具有背景（远）的倾向。两种音符分别构成正音符集合与负音符集合，具有相对独立性。 Symmetrical Chords and figure-ground relationship: In Symmetrical Chords, negative notes tend to be more figure (near), while positive notes tend to be more background (far). The two types of notes form the positive and negative note sets respectively, and are relatively independent. 10-3, Atonal Resolution of Jazz Scales；爵士音阶的无调性解决 爵士音阶具有一定的无调性兼容性， 主要表现在重叠和弦中，如：主七和弦，主九和弦，主 11 和 弦，主 13 和弦等。爵士音阶的重叠和弦最多可达到八个音符；其中包含了 1-4 个半音程，可视作爵士 音阶与无调性体系的中间形式。 参见：9-1.2，重叠和弦；9-4，孤调（Lonely key）。 Jazz scales possess a degree of atonal compatibility, primarily manifested in overlapping chords, such as the tonic seventh, ninth, eleventh, and thirteenth chords. Overlapping chords in jazz scales can reach up to eight notes, encompassing 1-4 semitones, and can be considered an intermediate form between jazz scales and the atonal system. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 11.Melody Of Color；色彩旋律 前面的讨论和弦语句是以“和弦”为单位，本章讨论的旋律语句则以音符（色）为单位，两者既有 联系，又有相对独立性。 The chord statement discussed above is in the unit of "chord", while the melodic statement discussed in this chapter is in the unit of note (color), which are both related and relatively independent. 旋律在音乐中表现为非同时组织，而在和弦绘画中则表现为同时性组织。 Melody is not synchronic organization in music, but synchronic organization in chord painting. 色彩旋律发生在一个空间包之内，不同空间包则视作不同的旋律段落。 Color melody occurs within a space packet, and different space packets are treated as different melodic paragraphs. 按旋律的语义作用，色彩旋律可分为三种形式：M-L 旋律，分面旋律，点旋律。 According to the semantic function of melody, color melody can be divided into three forms: M-L melody, faceted melody and dot melody. 11-1.M-L Melody；M-L 旋律 M-L 旋律是膜和弦+线和弦语句的省略形式，语句中的和弦被省略为音符，产生 M-L 旋律进行 （melodic progression）。 The M-L melody is an abbreviated form of the Membrane chords + line chord sentence. The chords in the sentence are omitted as notes, resulting in an M-L melody progression. M-L 旋律发生在膜和弦与线和弦之间，膜和弦具有寻找线和弦形成空间包的倾向，这种倾向称为： 膜和弦解决（solve）。 The M-L melody occurs between the Membrane chords and the line chord. The Membrane chords has a tendency to find the line chord to form a space packet. This tendency is called: Membrane chords solve. 在七声音阶（Heptachord）中，减七和弦（Diminished 7th）向主和弦解决（solve）。 In the Heptachord, the Diminished 7th is resolved to the tonic. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图11.8、并行旋律 Figure 11.8, Parallel Melody 上图的衬布上有三组分面旋律，有正序旋律，也有反序旋律，称为：并行旋律。 There are three-group faceted melody on the lining cloth of the above picture, there are positive melody and reverse melody, called: parallel melody. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 12.Non-Chord Tone；和弦外色 和弦外音（non-chord tone）， 调内的和弦之外的色，在和弦绘画中通常有两种用途：1、产生亚旋 律；2、削弱色相、和弦的确定性，在和弦绘画中常用的有：邻音（Neighbor note），非离散（nondiscrete）， 持续音（pedal point）、延留音（Vorhalt）、先现音（Anticipation）等。 Non-chord tone, the color outside the chord within the key, usually has two uses in chord painting: 1. Produce sub-melody; 2. Weaken the certainty of hue and chord. Commonly used in chord painting are: neighbor note, non-discrete, pedal point, vorhalt, anticipation, etc. 和弦外色（non-chord color）有几种常见形式： There are two common forms of non-chord color: 和弦的频率偏移，如：邻音（Neighbor note），非离散（non-discrete）。 The frequency offset of the chord, such as: Neighbor note, Glide. 和弦空间区域偏移，如：持续音（pedal point）、延留音（Vorhalt）、先现音（Anticipation）。 The chord space area offset, such as: continuous tone (pedal point), sustained tone (Vorhalt), anticipation (Anticipation). 12-1.Frequency Offset；频率偏移 和弦频率偏移的形式很多，按照用途可归入两类：1、产生亚旋律，2、削弱和弦内色的色相确定 性。 There are many forms of chord frequency offset, which can be classified into two categories according to their purposes: 1. to generate sub-melody, 2. to weaken the hue certainty of the colors in the chord. 邻音（Neighbor note）：用于产生分面亚旋律，通常是膜和弦的和弦外色。 Neighbor note: used to produce faceted sub-melody, usually the chord outer color of the Membrane chords. 下图为增三和弦构成的无调性系统，图形上与背景上都有由邻音（Neighbor note）产生的亚旋律， 图形上用于表现分面，背景上用于表现投影。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 The figure below shows an Atonal system composed of augmented triads. There are sub-melody generated by Neighbor notes on the figure and on the background. The figure is used to express facet, and the background is used to express projection. 邻音（Neighbor note）可以改变音符的正-负属性，正音符具有背景（远）的倾向，负音符具有图 形（近）的倾向，常用于改变特定空间区域的景深。 Neighbor notes can change the positive-negative properties of notes, positive notes have a background (far) tendency, and negative notes have a figure (near) tendency, often used to change the depth of field in a specific spatial area. 图12.1、邻音（Neighbor note）产生的景深 Figure 12.1. Depth of field generated by Neighbor note 非离散（non-discrete）， 和弦系统基于特定离散值，采用了非离散处理后，和弦特征削弱，可以削 弱色相的确定性，表达色相不确定的对象，如：水、玻璃等。 non-discrete: The chord system is based on specific discrete values. After the non-discrete treatment is adopted, the chord features will be weakened, which can weaken the certainty of the hue and express 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 the objects with uncertain hue, such as water and glass. 下图的水面使用了非离散（non-discrete）处理，削弱了水面的色相的确定性。 The water surface below uses non-discrete treatment, which reduces the certainty of the hue of the water surface. 图12.2、爵士音阶 C大调 Figure 12.2, Weak Tonal System C major 12-2.Space Region Offset；空间区域偏移 和弦空间区域偏移通常表现为：线和弦与膜和弦互相跨界，进入对方的空间区域，类似音乐中的持 续音（pedal point）、 延留音（Vorhalt）、先现音（Anticipation）， 通常用于表达空间系统所需要的模糊 性。 The offset of the chord space area is usually expressed as: the line chord and the membrane chord cross each other and enter the space area of Used to express the ambiguity required by spatial systems. 在下图中的天空部分，主和弦（线和弦）与全音阶和弦（膜和弦）互相越界，导致和弦结构与和弦 语义含混，并产生空间景深，类似音乐中的：持续音（pedal point），延留音（Vorhalt），先现音 （Anticipation）。 In the sky part in the picture below, the tonics ( line chords) and the Diatonics (membrane chords) cross each other, resulting in the chord structure and the chord semantics being ambiguous, and the 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 spatial depth of field is generated, similar to music: pedal point, Vorhalt, anticipation. 图12.4、爵士音阶 A大调 Figure 12.4, Weak Tonal System A major 空间区域偏移通常发生在线和弦与膜和弦之间，其它形式有待观察。 The spatial region offset usually occurs between the online chord and the Membrane chords, other forms are to be seen. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 13. Multilayer Tone Group；多层调群 一个和弦空间系统包含多个和弦包（调），称为：调群，它是以和弦包（调）为单位的组织形式。 A chord space system contains multiple Chord packets (key), called: key group, which is an organizational form of Chord packets (key) as a unit. 和弦语言中包含多种调群：增四度大-小调（Augmented Fourth Major-Minor），平行大小调 （Parallel Major-Minor）， C-D-E 调群，T-D-S 调群，前两种共享同导音减七和弦（Leading note diminished 7th），是同层空间系统，称：同层调群，后两种包含多个导音减七和弦（Leading note diminished 7th），分别具有不同的闭合状态，是多层空间系统；称：多层调群。 The chord language includes many key groups: Augmented Fourth Major-Minor, Parallel Major-Minor, C-D-E key group, T-D-S key group. The first two share the same leading note diminished 7th chord and are the same-layer space system, called: same-layer key group. The last two contain multiple leading note diminished 7th chords, each with different Close states, and are multi-layer space systems, called: multilayer key groups. 多层调群（Key group）存在主-次秩序。 The multi-layer Key group has a primary-secondary order. 对称和弦 Symmetrical Chords 闭合状态 Close state 主-次权重 Primary-Secondary Weight {B,Ab,F,D}，B dim7 闭合 Closed 高 High, {C#,Bb,G,E}，C# dim7 闭合-半闭合 Closed-semi-closed 中 medium {A,F#,Eb,C}，A dim7 半闭合，弱闭合 Semi-closed, weakly Close 低 low 参见：8-1.闭合级别 See: 8-1.Close level 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 13-1.C-D-E Key Group；C-D-E 调群 C-D-E 是三个减七和弦 C dim7，D dim7，E dim7 的缩写，分别表示三个导音减七和弦调群，C-D-E 是由调群组成的群，是和弦系统的全局调群。参见：5-1.3.dim7 调群 C-D-E is the abbreviation of three diminished seventh chords C dim7, D dim7, E dim7, which represent three leading tone diminished seventh chord key groups. C-D-E is a group composed of key groups, which is the global key group of the chord system. See: 5-1.3.dim7 key group 图13-1.1、C-D-E 调群 Figure 13-2.1, C-D-E keys group C-D-E 调群中包含不同闭合状态的图形，涉及不同的导音减七和弦，各个图形具有共同的连续背 景，并共享主调群的导音减七和弦。 The C-D-E key group contains figures of different Close states, involving different leading diminished seventh chords, each figure has a common continuous background, and shares the leading diminished seventh chords of the main key group. C-D-E 调群具有主-次权重（自然解决倾向）。参见：8-1.闭合层级。 The C-D-E tone group has a primary-secondary weight (natural solution tendency). See: 8-1. Close levels. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图13-1.2. C-D-E 调群 Figure 13-1.2. C-D-E key group 图13-1.3. B-C 调群 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Figure 13-1.3. C-D-E key group 爵士音阶和弦包的主-次权重低于所有七声音阶（heptachord）和弦包，当闭合层级较高的和弦包转 为爵士音阶，解决方向发生逆转。 The major-minor weight of the jazz scale chord package is lower than that of all heptachord chord packages. When the chord package with a higher Close level is converted to a jazz scale, the solution direction is reversed. 图13.1.4.爵士音阶和弦包向七声音阶和弦包解决。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 13-2.T-D-S Key Group；T-D-S 调群 T-D-S 调群是 T-D-S 三和弦的转调形式，用于表达空间系统中不同亮度的分形-分面关系；较 T-D-S 三和弦具有更高的确定性。 The T-D-S keys groups is a transition form of the T-D-S triad, which is used to express the fractal-facet relationship of different brightness in the spatial system; it has a higher certainty than the T-D-S triad. T-D-S 调群是七声音阶（heptachord）调群，其中的属和弦（Dominant）、下属和弦 （Subdominant）分别转为属调（dominant key）、下属调（Subdominant Key）。 The T-D-S key group is a heptachord Key group, in which the Dominant and Subdominant chords are converted to the dominant key and Subdominant Key respectively. 图13-2.T-D-S 调集团 ； Figure 13-2.T-D-S tone group; 大调的属调（dominant key）、下属调（Subdominant Key）表达不同亮度的分离图形；小调的属调 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 If we use the integer ratio n:m to represent the harmonious relationship between frequencies, the above chords can be uniformly expressed as: Major triad: 4 : 5 : 6 Major seventh chord: 4 : 5 : 6 : 7 Major ninth chord: 4 : 5 : 6 : 7 : 9 Major 11th chord: 4 : 5 : 6 : 7 : 9 : 11 Thus, it can be seen that the discrete frequency structure generated by integer sequences simultaneously supports both quantum energy levels and chord formation. From this perspective, quantization can be seen as the "spectral chordification" of the physical world, while chordification can be seen as the "frequency quantization" of the music field. Together, they reveal a universal structural principle based on integer generation and discrete symmetry. 泛音是一维震荡模式，高维震荡模式涉及到平均律：(1.059463)^n · f₀，两种模式可以切换——前 者满足协和性，后者满足对称性，形成对称-破缺结构。 将 n 切换为 (1.059463)^n，引入指数型量子化能级：Eₙ=h·1.059463^{n}·f₀，通过模 12 群 ℤ₁₂ 的结 构，实现和弦的系统生成。 Overtones are one-dimensional oscillation modes. Higher-dimensional oscillation modes involve equal temporality: (1.059463)^n · f₀. These two modes can be switched—the former satisfies consonance, and the latter satisfies symmetry, forming a symmetry-broken structure. Switching n to (1.059463)^n introduces an exponential quantized energy level: Eₙ=h·1.059463^{n}·f₀. Through the structure of the modulo 12 group ℤ₁₂, a systematic generation of chords is achieved. 时空二相性：和弦时间与和弦空间镜像对称：{-7,-4,0} ↔ {0,4,7} mod 12（互为反和弦，反调），可 数学转换；空间具有定域性，时间具有非定域性，共同表现为时空二相性（定域-非定域二相性），类似 波粒二象性。 Spacetime duality: Chord time and chord space are mirror symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 (they are inverse chords, inverse keys), which can be mathematically transformed; space is local and time is nonlocal, which together manifests as spacetime duality (local-nonlocal duality), similar to wave-particle duality. 和弦几何：和弦编码包含几何语义：开弦，闭弦，膜，可生成所有空间状态，也是绘画空间的生成 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 基础。 Chord geometry: Chord encoding contains geometric semantics: open strings, closed strings, membrane, which can generate all spatial states and are also the basis for the generation of painting space. 和弦是先验的量子化时空结构，经验现象是：时空在音乐，绘画中被量子化。 Chords are a priori quantized spacetime structures, and empirical phenomena show that spacetime is quantized in music and painting. Chord Space And Chord Painting; 和弦空间与和弦绘画 在和弦空间系统中，和弦表现为色彩频谱，映射到特定几何结构（膜-弦），生成和弦空间，其本质 是先验的量子化空间结构，绘画是其经验现象，它同样存在于欧几里得几何与膜-弦理论的架构中。 In the chord space system, chords manifest as a color spectrum, mapped onto a specific geometric structure (membrane-string), generating the chord space. Its essence is an a priori quantized spatial structure, and painting is its empirical phenomenon. It likewise exists within the frameworks of Euclidean geometry and membrane-string theory. 核心机制：时空镜像对称 和弦编码（量子化频谱）是时空生成的统一基底：它在时间域展开为音乐，在空间域凝结为绘画。 两者展现出内在的镜像对称关系：-7,-4,0 ↔0,4,7 (mod 12)。这种对称性使得音乐与绘画成为同一和弦系 统的两种展开方式。 Core Mechanism: Spacetime Mirror Symmetry Chord encoding (quantized spectrum) is the unified basis for spacetime generation: it unfolds as music in the time domain and condenses into painting in the spatial domain. The two exhibit an inherent mirror symmetry: -7, -4, 0 ↔ 0, 4, 7 (mod 12). This symmetry makes music and painting two ways of unfolding the same chord system. 和弦编码的几何语义 和弦编码不仅描述频率比例，也携带几何语义（弦），从而决定空间结构： 开弦（Open String）：对应小三和弦 (−7,−3,0) mod 12，为分面线结构； 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 闭弦（Closed String）：对应大三和弦 (−7,−4,0) mod 12，为轮廓线结构； 膜（Membrane）：对应对称和弦（Symmetrical Chords），如减七 (0,3,6,9)、全音阶 (0,2,4,6,8,10)、 增三 (0,4,8)，半音阶和弦（0,1,2,3,4,5,6,7,8,9,10,11）mod12 代表非线性空间的连续面。 The Geometric Semantics of Chord Encoding Chord encoding not only describes frequency ratios but also carries geometric semantics (strings), thus determining the spatial structure: Open String: Corresponds to a minor triad (−7,−3,0) mod 12, representing a faceted structure; Closed String: Corresponds to a major triad (−7,−4,0) mod 12, representing a contour structure; Membrane: Corresponds to symmetrical chords, such as diminished seventh (0,3,6,9), whole tone (0,2,4,6,8,10), augmented third (0,4,8), and chromatic chords (0,1,2,3,4,5,6,7,8,9,10,11) mod 12, representing continuous surfaces in nonlinear space. 和弦几何框架 三和弦（开弦与闭弦）定义了对称和弦（膜）的边界，即空间的生成线。由此，和弦几何框架得以 确立：和弦的几何语义（弦）决定空间结构，而和弦的频谱语义（和弦）定义其调性关系。两者共同构 成和弦空间（Chord Space）——一个连接音乐与绘画的统一结构场。 Chord Geometry Framework: Triads (open and closed chords) define the boundaries of symmetrical chords (membrane), i.e., the generating lines of space. Thus, the chord geometry framework is established: the geometric semantics of a chord (the string) determines the spatial structure, while the spectral semantics of a chord (the chord itself) defines its tonal relationships. Together, they constitute the Chord Space—a unified structural field connecting music and painting. 实验验证 这些结果并非理论假设，而源自于绘画中的独立观察与实验。在色彩的离散分布、形态的空间排列 中，可以反复验证上述和弦几何特征。因此，《和弦绘画》不仅是一部艺术专著，更是一份关于和弦空 间的实验报告。 它展示了如何从视觉中测得音乐的几何结构，如何以绘画为观测仪器，揭示生命与宇宙的调性秩 序。绘画在此被重新定义：它不再是主观的感知再现，而是和弦结构的可见生成。 每一幅作品，都是一次频谱的空间展开；每一条线、每一个色面，都是和弦在时空中的几何显现。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 《和弦绘画》由此成为和弦语言体系的支柱之一——它提供了观测、验证与应用的可视基础，让和弦从 音乐的时间流中，转化为绘画的空间形。 Experimental Verification These results are not theoretical assumptions, but rather stem from independent observation and experimentation in painting. The discrete distribution of color and the spatial arrangement of forms repeatedly verify the aforementioned chordal geometric characteristics. Therefore, *Chord Painting* is not only an art monograph, but also an experimental report on chordal space. It demonstrates how to measure the geometric structure of music visually, and how to use painting as an observational instrument to reveal the tonal order of life and the universe. Painting is redefined here: it is no longer a subjective representation of perception, but a visible generation of chordal structures. Each work is a spatial unfolding of the spectrum; every line, every color plane, is a geometric manifestation of a chord in space and time. *Chord Painting* thus becomes one of the pillars of the chordal language system—it provides a visual foundation for observation, verification, and application, allowing chords to transform from the temporal flow of music into the spatial form of painting. Li, X. H. (2020). Chord Painting. ResearchGate. https://www.researchgate.net/publication/340492620_Chord_Painting Li, X. H. (2024). Chord Language. Zenodo. https://zenodo.org/records/11817631 14-2.Chord Packet；和弦包 和弦空间由和弦表达，基本单元是：和弦空间包（调），在前面章节已有介绍，本节主要讨论和弦 空间包的物理含义。 The chord space is expressed by chords, and its basic unit is the chord space package (key), which has been introduced in the previous chapter. This section mainly discusses the physical meaning of the chord space package. 本章的讨论默认采用爵士音阶，下面分析一个典型的和弦空间包。 The discussion in this chapter uses the jazz Scale by default, and a typical chord space package is analyzed below. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 三和弦（开弦，闭弦）定义全音阶和弦（膜）的边界（轮廓线，分面线等），生成爵士音阶的和弦 空间包，下面以 C大调，F#小调为例： Triads (open chords, closed chords) define the boundaries (contours, Facet line, etc.) of diatonic chords (membrane), and generate the chord space packet of the jazz Scale. The following takes C major and F# minor as examples: 图14-2.1、爵士音阶和弦包：1、C大三和弦（闭弦），2、F#小三和弦（开弦），3、全音阶和弦 （膜）（◆=正音符，●=负音符，色彩=色荷） Figure 14-2.1, jazz Scale chord package: 1,C major triad (closed string), 2,F# minor triad (open string), 3,diatonic chord (membrane) (◆=positive note, ●=negative note, color=color charge) 图14-2.2、爵士音阶，C大调，f#小调空间包 Figure 14-2.2, jazz Scale C major ,f# minor space packet 实验 1：C 大三和弦（闭弦），构成了图形的闭合轮廓线，全音阶和弦（膜）填充所有非线空间，包 括图形与背景。 Experiment 1: The C major triad (closed string) forms the closed contour of the figure, and the 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 diatonic chord (membrane) fills all non-linear Spaces, including the figure and background. 空间包的轮廓线由大三和弦（闭弦）构成，用于束缚空间包，轮廓线（闭弦）的内部由全音阶和弦 （膜）充实，线和弦与膜和弦分别构成和弦空间包的外层与内核。 The contour of the space packet is composed of major triads (closed strings), which are used to bind the space packet. The interior of the contour line (closed strings) is enriched by diatonic chords (membrane), and the line chord and membrane chord form the outer and inner core of the chord space packet respectively. 和弦包是和弦时空的基本单位；那么原子，星体是和弦包吗？合理的回答是：如果原子，星体是和 弦时空中的空间单位，其形式就只能是和弦包。 The chord packet is the basic unit of chord space-time ; So are atoms, stars a chord packet? The reasonable answer is that if atoms and stars are spatial units in chord space-time, their form can only be chord packets. 图15-3.2 与下面的照片比较。 Figure 15-3.2 is compared with the following photos. 图14-2.3、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.3. Iron atoms taken by aperture grating microscope (picture from Internet) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-2.4、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.4. Iron atoms taken by aperture grating microscope (picture from Internet) 14-2.1.Electric Charge And Magnetic Charge；电荷与磁荷 音符具有正负属性，由此产生和弦的正负属性，正和弦的根音符为正音符，负和弦的根音符为负音 符，通常：正和弦为大三和弦（闭弦），负和弦为小三和弦（开弦）。见图：14-2.1 The notes have positive and negative properties, resulting in the positive and negative properties of the chord, the root note of the positive chord is a positive note, the root note of the negative chord is a negative note, generally: the positive chord is a major triad (closed string), and the negative chord is a minor triad (open string). See Figure 14-2.1 【电荷】下图和弦包中包括正和弦（大三和弦，闭弦）与 负和弦（小三和弦，开弦），闭弦构成轮 廓线，开弦构成分面线，膜充满所有非线空间。 [Charge] The chord package in the figure below includes positive chords (major triads, closed strings) and negative chords (minor triads, open strings). Closed strings form contour lines, open strings form Facet line, and membrane fill all non-linear spaces. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-2.5、和弦空间包的构成 Figure 14-2.5, the composition of the chord space packet 下面是一组和弦空间包相互作用的视觉实验。 Below is a visual experiment of a set of chord space packages interacting with each other. 图14-2.6、左右两个和弦空间包均含有正和弦（大三和弦，闭弦），负和弦（小三和弦，开弦），表 现为稳定状态。 Figure 14-2.6. Both the left and right chord space packages contain positive chords (major triad, closed string) and negative chords (minor triad, open string), which are represented as stable states. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-2.7、左图含大三和弦（正和弦，闭弦），右图含小三和弦（负和弦，开弦），分别为正、负和 弦空间包，表现出相互吸引的倾向。 Figure 14-2.7, the left picture contains the major triad (positive chord, closed string), the right picture contains the minor triad (negative chord, open string), respectively, positive and negative chord space packages, showing a tendency to attract each other. 图14-2.8、左，右两个和弦包都含同种三和弦（小三和弦，负和弦，开弦），表现出相互排斥的倾 向。 Figure 14-2.8. Both left and right chord packages contain the same triad (minor triad, negative chord, 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 open string), showing a tendency to exclude each other. 图14-2.9、左，右两个和弦包都含同种三和弦（大三和弦，正和弦，闭弦），表现出相互排斥的倾 向。 Figure 14-2.9, left and right chord packages contain the same triad (major triad, normal chord, closed string), showing a tendency to exclude each other. 上面的视觉实验中，和弦空间包的表现类似电场效应，两种和弦之间存在库伦力，合理的解释是： 正-负电荷来自正-负和弦。 In the above visual experiment, the chord space package behaves like an electric field effect, there is a coulomb force between the two chords, and the reasonable explanation is that the positive-negative charge comes from the positive-negative chord. 大三和弦（闭弦、正电荷）用于构成轮廓线，封闭、束缚空间包，不能脱离和弦空间包，小三和弦 （开弦、负电荷）可以自由的出现在和弦空间包的内-外。 Positive major triads (closed strings, positive charges) are used to form contour lines, closed and bound space packet, and cannot be separated fromembrane chords space packet, minor triads (open strings, negative charges) can freely appear inside-outside of the chord space packet . 【磁荷】爵士音阶和弦包的膜和弦是全音阶和弦，全音阶和弦包含六个音符，各音符分别具有正-负 属性与色荷，所有色荷混合产生白色。 【Magnetic charge】The membrane chord of the chord packet of the jazz Scale is the diatonic chord. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-5.1、闭弦，开弦，膜的空间作用 Figure 14-5.1. The space effect of closed strings, open strings, and membrane 空间相互作用有两种方式：电磁作用与非电磁作用：和弦（调性）空间的相互作用是闭弦（正电 子），开弦（负电子），膜（磁场）的作用，是电磁作用；非和弦（无调性）空间不含闭弦（正电子）、 开弦（负电子），磁极，是非电磁作用。 There are two ways of space interaction: electromagnetic and non-electromagnetic interaction: Chord (tonality) Space interaction is closed string (positron), open string (negative electron), membrane (magnetic field), is electromagnetic action; Non-chord (atonal) space does not contain closed strings (positrons), open strings (negative electrons), magnetic poles, and non-electromagnetic interactions. 图14-5.2、屏蔽和弦后的无调性空间作用 Figure 14-5.2: Atonal spatial effect after shielding chords 空间相互作用包括七声音阶与爵士音阶两种方式，七声音阶和弦包用于生命、天体表达，是时空的 宏观形式。 Spatial interaction includes two modes: the heptachord and the jazz scale. The heptachord and chord package are used to express life and celestial bodies and are the macroscopic form of space-time. 在七声音阶中，和弦空间包的结合力与闭合梯度相关，并由此产生空间的主-次秩序，解决倾向，引 力中心。参见：8.Close;闭合性，13.Multi-Layer Key Group;多层调群。 In the heptachord, the cohesion of the chord space package is related to the Close gradient, which 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 produces the major-minor order of space, the tendency of resolution, and the center of gravity. See: 8. Close, 13. Multi-Layer Key Group. 和弦包相互作用（引力，斥力等），涉及调内，调群，三和弦，重叠和弦，以及不同音阶系统等， 具有多样性，复杂性，涉及对不同和弦结构的具体分析。 The chords package interactions (attraction, repulsion, etc.), involving intra-key, key groups, triads, overlapping chords, and different scale systems, etc., are diverse and complex, and involve specific analysis of different chord structures. 14-2.4.Integrity；整体性 整体性：和弦系统具有整体性，其中的所有元素（音符，和弦，和弦包）在全局系统的控制下保持 相互关联状态，与空间距离、尺度无关。 Holism: A chord system possesses a holistic nature, where all elements (notes, chords, and chord packages) remain interconnected under the control of the global system, independent of spatial distance or scale. Poplar forest, Jazz Scale A major；白杨林、爵士音阶，A大调 上面图例由爵士音阶 A大调发挥整体控制作用，将该图放大，缩小到任何尺度，其中的音符，和弦 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 的关联保持不变。 The jazz scale A major plays an overall controlling role in the above diagram. Whether the diagram is enlarged or reduced to any scale, the relationship between the notes and chords remains unchanged. 14-3. Space-Time Duality；时-空二相性 和弦语言包含时间表达与空间表达，前面部分介绍了和弦的空间表达，本节将讨论时-空关系。 Chord language includes time expression and space expression. The previous section introduced the spatial expression of chords. This section will discuss the time-space relationship. 和弦语言包含时间语义（始-末，进行）与空间语义（线，膜），分别表达时间与空间。 和弦时间与和弦空间镜像对称： {-7,-4,0} ↔ {0,4,7} mod 12 The chord language contains time semantics (beginning-end, progression) and space semantics (line, membrane), which express time and space respectively. Chord time and chord space are mirror-symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 两者互为反结构：反和弦，反调，可以数学转换。 空间具有定域性，时间具有非定域性，整体表现为时空二相性（定域-非定域二相性），类似波粒二 相性。 The two are inverse structures of each other: anti-chords, anti-keys, and can be converted mathematically. Space is localized, time is non-localized, and the overall performance is space-time duality (localnonlocal duality), similar to wave-particle duality. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-3.1、大三和弦-小三和弦的升序，降序，镜像对称形式。Y=平均律数列的指数 Figure 1-3, Major triad - minor triad ascending, descending, mirror-symmetric form. Y= exponents of the equal temperament series. 大三和弦，升序：{0，4，7}，大三和弦，降序：{-7，-4，0}（mod 12） Major triad, ascending: {0,4,7}, Major triad, descending: {-7，-4，0}（mod 12） 小三和弦，升序：{0，3，7}，大三和弦，降序：{-7，-3，0}（mod 12） Minor triad, ascending: {0,3,7}, Major triad, descending: {-7，-3，0}（mod 12） 图14-3.2、和弦镜像：和弦时间（上），和弦空间（下）互为反和弦。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Figure 14-3.2, Chord mirror image: Chord time (top) and chord space (bottom) are each other's antichords. 图1-3.2、大三和弦-小三和弦的升序，降序，镜像对称形式。七声音阶（Heptachord）， C大调，关 系小调。 Figure 1-3.2. Ascending, descending, mirror-symmetric forms of Major - minor triads. Heptachord, C major, relation minor. Formula；公式： C大三和弦（升序）=H^0,4,7.C C major chord, (ascending)= H ^ 0,4,7.C a小三和弦（升序）=H^0,3,7.a a minor triad (ascending)=H^0,3,7.a C大三和弦（降序）=H^0,-4,-7.C C major chord(descending)= H ^ 0, -4, -7.C Eb 小三和弦（降序）=H^0,-3,-7.Eb Eb minor triad (descending)=H^0,-3,-7.Eb 和弦时间与和弦空间具有相反的数学结构，甚至还有相反的物理属性：定域性与非定域性。 和弦时间不含几何语义，没有空间状态；和弦空间不含时间语义，没有时间状态。两者整体表现为 时空二相性，类似于量子力学中的波粒二象性。 Chord time and chord space have opposite mathematical structures and even opposite physical properties: locality and non-locality. Chord time does not contain geometric semantics and has no spatial state; chord space does not contain temporal semantics and has no temporal state. The two as a whole show the duality of space and time, which is similar to the wave-particle duality in quantum mechanics. 纯时间 vs. 纯空间：巴赫与莫奈的对比 在巴赫的音乐中，我们只能观察到和弦与旋律的时间变化，无法感知任何几何形状或位置。 纯时间状态下，空间属性无法被观察，空间位置处于叠加态（Superposition State）。 如果要在巴赫的音乐中观察到空间属性，唯一的方式是将和弦时间转换为其镜像对称形式——和弦 空间。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Pure time vs. pure space: Bach and Monet’s comparison In Bach’s music, we can only observe the time changes of chords and melodies, and cannot perceive any geometric shapes or positions. In the pure time state, spatial properties cannot be observed, and spatial positions are in a superposition state. If you want to observe spatial properties in Bach’s music, the only way is to convert chord time into its mirror-symmetric form - chord space. 结论：巴赫的音乐是和弦时间，莫奈的绘画是和弦空间。在纯时间状态下，空间位置的概念是无意 义的，相当于所有位置的叠加。 Conclusion: Bach’s music is chord time, and Monet’s paintings are chord space. In the pure time state, the concept of spatial position is meaningless, which is equivalent to the superposition of all positions. 图14-3.3、巴赫手稿 Figure 14-4.2. Bach manuscript 3. 莲花的时空二相性：莫奈 vs. 莫扎特 莫奈的莲花（绘画）是空间表达，具有定域性，即它不能同时出现在卢浮宫和奥赛博物馆。 莫扎特的莲花（音乐）是时间表达，具有非定域性，可以处于任意空间位置的叠加态，包括卢浮宫 和奥赛。 3. The space-time duality of the lotus: Monet vs. Mozart 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Monet's lotus (painting) is a spatial expression with locality, that is, it cannot appear in the Louvre and the Musee d'Orsay at the same time. Mozart's lotus (music) is a temporal expression with non-locality, and can be in a superposition state of any spatial position, including the Louvre and the Musee d'Orsay. 这意味着，莲花同时具有莫奈（空间）-莫扎特（时间）二相性，类似于波粒二象性： 作为绘画（莫奈）时，它是粒子，位置固定。 作为音乐（莫扎特）时，它是波动，位置可叠加。 结论： 莲花在“莫奈-莫扎特”二相性中展现了时空结构的波粒二象性。 从和弦时间到和弦空间的转换，与量子测量导致波函数坍缩的过程类似。 This means that the lotus has both the Monet (space) and Mozart (time) duality, similar to the waveparticle duality: As a painting (Monet), it is a particle with a fixed position. As music (Mozart), it is a wave with superimposable positions. Conclusion: The lotus shows the wave-particle duality of the space-time structure in the "Monet-Mozart" duality. The conversion from chord time to chord space is similar to the process of wave function collapse caused by quantum measurement. 图14-3.4：莫奈-莫扎特二相性。 Figure 14-3.4: Monet-Mozart duality. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 14-4.Chord Spacetime Concept Framework；和弦时空概念框架 和弦时空由和弦（量子化频谱）构成，时间与空间是能量的不同形式，由此有： E=t+s 和弦时空中存在 纯时间（s=0）与纯空间（t=0），这需要与其适应的时空框架。 时间能量（T）：非定域性，类似量子态，不依赖外部时钟。 空间能量（S）：定域性，具有几何属性，如形状、位置等，质量依赖定域性。 Chord spacetime is composed of chords (quantized spectrum). Time and space are different forms of energy, so: E=t+s In chord spacetime, there is pure time (s=0) and pure space (t=0), which requires a spacetime framework that adapts to it. Time energy (T): non-local, similar to quantum state, does not depend on external clocks. Space energy (S): local, has geometric properties, such as shape, position, etc., and quality depends on locality. 1、时间与空间的互补关系： 设和弦时-空的总能量归一化为 1，则： S+T=1 其中： S 代表和弦空间的能量占比。 T 代表和弦时间的能量占比。 当 S=0（纯时间）时，无空间信息，时间完全非定域。 当 T=0（纯空间）时，无时间信息，空间完全定域。 结论：时间和空间是互补变量，它们的分布决定了和弦时空的性质。 1.The complementary relationship between time and space: Assume that the total energy of chord space-time is normalized to 1, then: S+T=1 Where: S represents the energy proportion of chord space. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 T represents the energy proportion of chord time. When S=0 (pure time), there is no spatial information and time is completely non-local. When T=0 (pure space), there is no time information and space is completely local. Conclusion: Time and space are complementary variables, and their distribution determines the properties of chord space-time. 2. 速度的定义：由于速度是时间（非定域性）与空间（定域性）的叠加，时间能与空间能的比值 v=T/S+T=T 由于 S+T=1，我们有： v=1−S 这表明： 当 S=0（纯时间），v=1（无空间状态，时间完全非定域）。 当 T=0（纯空间），v=0（无时间状态，空间完全定域）。 速度 v 是时间能量的占比，独立于外部参考系，仅由和弦时空内部状态决定。 结论： 速度 v 不是外部测量的运动速度，而是时间能量的占比。 在和弦时空中，时间能量越高（越非定域），速度越大；空间能量越高（越定域），速度越小。 这类似于量子力学中的“不确定性关系”——时间越模糊，空间信息越清晰，反之亦然。 2. Definition of speed: Since speed is the superposition of time (non-locality) and space (locality), the ratio of time energy to space energy v=T/S+T=T Since S+T=1, we have: v=1−S This shows that: When S=0 (pure time), v=1 (no space state, time is completely non-local). When T=0 (pure space), v=0 (no time state, space is completely local). Speed v is the proportion of time energy, independent of the external reference system, and only determined by the internal state of the chord spacetime. Conclusion: 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Speed v is not the speed of movement measured externally, but the proportion of time energy. In chord spacetime, the higher the time energy (the more non-local), the greater the speed; the higher the space energy (the more local), the smaller the speed. This is similar to the "uncertainty relationship" in quantum mechanics-the more vague the time, the clearer the spatial information, and vice versa. 3. 和弦时空的不连续性 和弦时间（T）与和弦空间（S）互为反和弦（镜像对称），可数学转换。 在纯时间中（S=0），空间信息完全消失。 在纯空间中（T=0），时间信息完全消失。 这表明： 和弦时空可以是不连续的，即时间和空间可以在某些状态下完全分离。 当 S→0 或 T→0 时，和弦时空表现出类似“量子跃迁”的行为，即从一种完全状态跳跃到另一种完 全状态，而不是连续变化。 3. Discontinuity of chord spacetime Chord time (T) and chord space (S) are antichords (mirror symmetry) and can be mathematically transformed. In pure time (S=0), spatial information disappears completely. In pure space (T=0), time information disappears completely. This shows that: Chord spacetime can be discontinuous, that is, time and space can be completely separated in certain states. When S→0 or T→0, chord spacetime exhibits a behavior similar to a "quantum jump", that is, jumping from one complete state to another complete state, rather than changing continuously. 4. 质量的测量问题 时间无法测量质量， 质量必须在定域的空间状态（S>0）下才能被测量。 在纯时间状态（S=0）下，质量无法定义，因为没有空间参考。 质量仅能在具有几何结构的区域内被测量，这意味着质量是空间定域性的表现。 数学表达：