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） 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 引言：和弦编码时空，生命，精神，宇宙基于和弦。 Introduction: Chord coding of space-time, life, spirit, and the universe is based on chords. 和弦语言以量子化频谱为编码结构，涵盖和弦几何（开、闭、膜弦）与和弦数学（代数结构、 群作 用）。每个和弦都有唯一的特征频谱，映射至特定的和弦语义集合，生成：时间（音乐），空间（绘 画），生命（经络），分布为和弦场（量子场）。 Chord language uses a quantized spectrum as its encoding structure, encompassing both chord geometry (open, closed, and membrane strings) and chord mathematics (algebraic structure and group action). Each chord has a unique characteristic spectrum, mapped to a specific set of chord semantics, generating: time (music), space (painting), life (meridians), and distributed as a chord field (quantum field). 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（膜弦）、3、全音阶 和弦（膜弦），4、增三和弦（膜弦） ⚫ 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 string), 3, diatonic chord (membrane string), 4, augmented Triads (membrane strings) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) 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 Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 关键词 ； Keywords： 时空，音乐，绘画，生命，经络，量子化，弦 Space-time, music, painting, life, meridians, quantization, strings Chord Spacetime；和弦时空 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： Spacetime is the "structure" or "framework" of the universe and the foundation of all physical processes. Humans have two types of spacetime observers: harmonic (tonal) observers and nonharmonic (atonal) observers, who observe two types of spacetime: 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，生成和弦时空场，音乐（时 间域）、绘画（空间域）是其常见形式。 Chord (tonality) space-time: Using the quantized spectrum as the encoding structure, it is mapped to the space-time semantic set to generate the chord space-time field. Music (time domain) and painting (space domain) are its common forms. 非和弦（无调性）时空：屏蔽了时空的和弦结构，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。 Non-chordal (atonal) spacetime : It blocks the chordal structure of spacetime, retains only the purely relational description of geometry (figure-ground) and motion, obtains quantification from external reference systems (such as clocks, rulers, reference objects), is often used in the framework of classical physics, and is also the daily experience of spacetime. 和弦频谱：和弦频谱与能量量子本质相通，均以一个基准频率 f 为单位，在整数 n 的调控下生成一 组离散的频率/能量结构。 泛音频谱公式：n*f ，N∈Z，f=频率 量子化假设：n*f*h（h=6.626×10^−34）N∈Z 两个公式结构一致，当：n=1-6=大三和弦，n=1-7=大7和弦，n=1-9=大9和弦，n=1-11=大十一 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——量子化基于和弦结构。 泛音是一维震荡模式，大于一维的震荡模式涉及到平均律：(1.059463)^n · f₀，两种模式可以切换。 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。 Overtone spectrum formula: n*f, N∈Z, f=frequency Quantization assumption: n*f*h (h=6.626×10^−34)N∈Z The two formulas have the same structure when: n=1-6=major triad, n=1-7=major 7th chord, n=1-9=major 9th chord, n=1-11=major 11th chord - quantization is based on chord structure. Overtones are one-dimensional oscillation patterns. Oscillation patterns larger than one dimension involve equal temperament: 1.059463)^n·f₀. these two modes can be switched. Switching n to (1.059463)^n introduces exponential quantized energy levels: Eₙ=h·1.059463^{n}·f₀. Through the structure of the module 12 group ℤ₁₂, 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；波粒二象性只能在和弦（调 性）时空中成立。 Space-time duality : Chord time and chord space are mirror-symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 (they are anti-chords and anti-tones), which can be mathematically converted; Space is local and time is non-local, which together manifest as the space-time duality. The wave-particle duality can only hold true in chord (tonal) space-time. 和弦几何：和弦编码（量子化频谱）包含几何语义：开弦，闭弦，膜弦，可生成所有空间状态，也 是绘画空间的生成基础。 Chord geometry: Chord encoding (quantized spectrum) contains geometric semantics: open strings, closed strings, membrane strings, which can generate all spatial states and are also the basis for the generation of painting space. ±音符：音符具有±属性，这是频率的物理属性，应涉及所有波动、频率，也可以解释物理学中普 遍存在的±属性。 ±Notes: notes have ± properties, which are physical properties of frequency and should involve all waves and frequencies. They can also explain the ubiquitous ± properties in physics. 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 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: The chord system has wholeness, where all elements (notes, chords, chord bundles) remain interrelated under the control of the global system, regardless of spatial distance or scale. 和弦涵盖量子化与弦空间，时间（音乐）与空间（绘画）构成其生成域，也是时空自然法则的显 现。 Chords encompass quantization and string space, with time (music) and space (painting) forming their generative domain, and they are also manifestations of the natural laws of space and time. Chord Space；和弦空间 和弦编码（量子化频谱）分别生成音乐（时间域）与绘画（空间域），两者镜像对称：{-7,-4,0} ↔ {0,4,7} mod 12，可数学转换。 Chord encoding (quantized spectrum) generates music (time domain) and painting (space domain) respectively, which are mirror-symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 and can be mathematically converted. 和弦编码（量子化频谱）包含和弦几何语义 {开弦，闭弦，膜弦} 并构成和弦几何框架，以此定义和 弦空间结构。 The chord encoding (quantized spectrum) contains the chord geometry semantics {open string, closed string, membrane string } and constitutes a chord geometry framework to define the chord space structure. “弦”是“和弦”的几何语义，“和弦”是“弦”的特征频谱。不同和弦映射到不同的几何语义： "String" is the geometric semantics of "chord", and "chord" is the characteristic spectrum of "strings". Different chords map different geometric semantics: 大三和弦 (−7,−4,0)mod 12 ↔ 闭弦（轮廓线） 小三和弦 (−7,−3,0)mod 12 ↔ 开弦（分面线） 等比和弦：减七和弦 (0,3,6,9) mod 12，全音阶和弦 (0,2,4,6,8,10)mod 12，增三和弦 (0,4,8) mod 12 ↔ 膜弦（非线性空间） 三和弦（开弦，闭弦）定义等比和弦（膜弦）的边界（轮廓线，分面线），生成所有空间状态及相 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 互作用。 Major triad (−7,−4,0)mod 12 ↔ closed string (contour line) Minor triad (−7,−3,0)mod 12 ↔ open string (Facet line) Geometric chords: diminished seventh chord (0,3,6,9) mod 12, diatonic chord (0,2,4,6,8,10)mod 12, augmented triad (0,4,8) mod 12 ↔ membrane chord (nonlinear space) The triads (open strings,closed stirngs) define the boundaries (contours, facets) of the geometric chords (membrane strings), generating all spatial states and interactions. 以上结果来自和弦绘画中的独立观察，在绘画中可重复，并有视觉实验支持。 The above results come from independent observations in chord painting, are repeatable in painting, and are supported by visual experiments. 和弦空间是和弦语言的重要支柱与核心部分，绘画是其主要观察基础与应用领域。 Chord space is an important pillar and core part of chord language, and painting is its main observation basis and application field. 观察、实验案例：Observation and experimental cases: 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 Griffiths, D. J. (2005). Introduction to Quantum Mechanics. Pearson. Chord Biology；和弦生命 人类有两种时空-生命观察者：和弦（调性）观察者与非和弦（无调性）观察者，分别观察两种时空 -生命形式：和弦包（基于量子化频谱，弦）与生物体（基于细胞），生命包含和弦与形态两个层。 Humans have two kinds of space-time-life observers: chord (tonality) observers and non-chord (atonality) observers, who respectively observe two kinds of space-time-life forms: chord packages (based on quantized spectrum, strings) and organisms (based on cells). Life contains two layers: chords and forms. 在人体中，和弦表现为经络（脉轮）系统，观察表明：十二经络系统具有受激频谱响应，其分布可 近似为： 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 fn=H^n⋅f0 其中 H=2^1/12≈1.059463, n∈Z In the human body, the chords are manifested as the meridian (chakra) system. Observations show that the twelve meridian systems have a stimulated spectrum response, and their distribution can be approximated as follows: fn=H^n⋅f0 其中 H=2^1/12≈1.059463, n∈Z 这说明音乐（时间域）、绘画（空间域）与经络（生命域）共享同一组量子化频谱结构，是和弦场 （Chord Field）在不同感知维度中的体现。 This shows that music (time domain), painting (space domain) and meridians (life domain) share the same set of quantized spectrum structures, which are the manifestation of the chord field in different perceptual dimensions. 纯小三和弦+导音减七和弦构成生命和弦包——生命的和弦编码形式；在特定状态下，生命和弦包 可独立于生物体，不依赖生物体，具有灵魂的性质。 Pure minor triads + leading tone diminished seventh chords constitute the life chord package - the chord coding form of life; under certain conditions, the life chord package can be independent of the organism, not dependent on the organism, and has the nature of a soul. 和弦（经络）是生命的物理（离散频谱）编码结构。 Chords (meridians) are the physical (discrete spectrum) encoded structures of life. Natural Spirit；自然精神 和弦语言是自然编码（量子化频谱）语言。 The chord language is a natural coding (quantized spectrum) language. 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 络等——精神是符号与和弦二层存有。 Humans possess two language systems: symbolic language (acquired language) and chord language (innate language). The former is an artificial information system based on phonetic symbols, such as natural language; the latter is a natural information system based on 1 chords (quantized spectra), such as music, painting, meridians, etc. Spirit is a dual existence of symbols and 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 人的认识来自两个观察者系统：和弦（调性）观察者与非和弦（无调性）观察者，前者是和弦系统 的内部观察，依赖观察者的和弦系统，即：和弦系统观察和弦系统，不能区别主观-客观，如：和声学 （音乐、绘画）， 经络（脉轮）等，或许还有量子-波粒二象性；后者屏蔽了和弦系统，主体与客体分 离，无关；通常可用观察工具代替人类观察者，如：常规的科学。 Human cognition comes from two observer systems: the chord (tonal) observer and the nonchord (atonal) observer. The former is the internal observation of the chord system and depends on the chord system of the observer, that is, the chord system observes the chord system and cannot distinguish between subjective and objective, such as: harmony (music, painting), meridians (chakras), etc., and perhaps also quantum-wave-particle duality; the latter shields the chord system, and the subject and object are both isolated systems. The object has nothing to do with the subject, and observation tools can usually be used to replace human observers, such as: conventional science. 两种观察者的重要区别还在于： 和弦（调性）观察者所见是一个基于和弦框架的整体：时空，生命，精神共享和弦结构与数学模 型。非和弦（无调性）观察者所见是随机，孤立事件，宇宙被割裂为碎片——任何观察都与观察者有 关。 Another key difference between the two types of observers is this: The chordal (tonal) observer sees a whole based on a chordal framework: spacetime, life, and mind share a chordal structure and mathematical model. The non-chordal (atonal) observer sees random, isolated events, a universe fragmented into pieces—any observation is relative to the observer. 和弦语义无法完全进入自然语言，具有不可言说的本体特征。 Chord semantics cannot be fully incorporated into natural language and has an unexpressible ontological characteristic. ◼ 和弦语言出版物有：《和弦语言》与《和弦绘画》，前者介绍和弦语言的语法、语义规则及数学 模型，侧重和弦空间语言。后者是和弦绘画（和弦空间）的视觉实验案例。 ◼ Chord language publications include "Chord Language" and "Chord Painting." The former introduces the grammar, semantic rules, and mathematical models of chord language, focusing on the language of chord space. The latter provides visual experimental cases of chord painting (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 Directory；目录 OVERVIEW OF CHORD LANGUAGE；和弦语言综述 2 CHORD SPACETIME；和弦时空 3 CHORD SPACE；和弦空间 5 CHORD BIOLOGY；和弦生命 6 NATURAL SPIRIT；自然精神 7 DIRECTORY；目录 9 1.CHORD MATHEMATICS-1；和弦数学-1 13 1-1.TEMPERAMENT SYSTEMS ；律制 13 1-2. SYMMETRICAL AND ASYMMETRICAL CHORDS；对称与非对称和弦 16 1-3. MOD12 NOTATION；MOD12 记谱法 20 1-4. EQUAL TEMPERAMENT CHROMATOGRAPHY；平均律色谱 23 1-5.±NOTES；±音符 25 REFERENCE；参考 26 2.CHORD MATHEMATICS-2；和弦数学-2 27 2-2.± NOTE DISTRIBUTION IN TRIADS；三和弦中的±音符分布 30 2-3.±NOTE DISTRIBUTION IN GEOMETRIC CHORDS；等比和弦中的±音符分布 32 REFERENCE；参考 33 3.CHORD GEOMETRY；和弦几何 35 3-1.GEOMETRIC SEMANTICS OF CHORD ；和弦的几何语义 36 3-2.LINE AND MEMBRANE CHORDS；线和弦与膜和弦 39 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 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. Geometric Chords；等比和弦 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），共有三 种： Geometric 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. 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. 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 等比和弦表：1、减七和弦（膜弦）、2、全音阶和弦（膜弦），3、增三和弦（膜弦） *◆=正音符，●=负音符，色彩=色荷 Geometric chords table: 1, diminished 7th chord (membrane chord), 2, diatonic chord (membrane chord), 3, augmented Triads (membrane chord) * ◆=positive note, ●=negative note, color=color charge 三种等比和弦（Geometric chords）是三种音阶：七声音阶，爵士音阶，爵士五声音阶的构成基 础。 The three Geometric chords are the basis of three scales: the heptatonic scale, the jazz scale, and the jazz pentatonic scale. 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（不存在于等比和弦 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+等比和弦组成音阶，调，在后面部分有更多介绍。 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 Triads + Geometric chords make up the scale, key, more on this later section. 三和弦重叠等比和弦，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 Geometric 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). 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） 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1-3.2、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 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 1-3. mod12 notation；mod12 记谱法 图1-3、mod12 记谱与 mod12 群，上下表为镜像反转。 Figure 1-3, mod12 notation and mod12 group, the upper and lower tables are mirror inversion. 1. 结构概述 在绘画（空间域）中，和弦结构是音乐（时间域）的镜像反转。然而，传统五线谱难以完整表达这 一结构。 Mod 12 记谱法以半音（小二度）为基本单位，构建对称、可计算的音高系统，并支持 mod 12 变 换运算，提供更精准的和弦分析和调式变换工具。 1. Structure Overview In painting (spatial domain), chord structure is the mirror inversion of music (temporal domain). However, traditional musical notation struggles to fully express this structure. Mod 12 notation uses the semitone (minor second) as the basic unit, constructing a symmetrical, calculable pitch system. It supports mod 12 transformation operations, providing more precise tools for chord analysis and modal transformation. 2. 记谱方式 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 音高表示 音高以整数表示（mod 12），即： (−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,7,…)mod 12 0 代表 C（或可定义其他调性起点），作为锚点，上下可自由加线扩展音域。 整数映射到音高：每个音高以 mod 12 进行归约，使音程关系计算更为直观。 谱表设计 均匀分布的音程体系： 相邻的线与空格均为 小二度（半音） 关系，确保音程分布均匀且对称完整。 示例： 线：0, 2, 4, 6, 8, 10, 0, 2, 4, 6, 8, 10 空格：1, 3, 5, 7, 9, 11, 1, 3, 5, 7, 9, 11 数学统一性：适用于和弦分析、调式变换、T/I 群变换等数学运算，使得音乐理论可以直接映射到 数学结构中。 2. Notation Method Pitch Representation Pitches are represented by integers (mod 12), as follows: (−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,7,…)mod 12 0 represents C (or another defined tonal starting point), serving as an anchor point. Lines can be freely added above and below to extend the range. Integer Mapping to Pitches: Each pitch is reduced by mod 12, making the calculation of interval relationships more intuitive. Staff Design Evenly Distributed Intervals: Adjacent lines and spaces are all in a minor second (semitone) relationship, ensuring that the intervals are evenly distributed and symmetrically complete. Example: Lines: 0, 2, 4, 6, 8, 10 Spaces: 1, 3, 5, 7, 9, 11 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 Mathematical Unity: Suitable for mathematical operations such as chord analysis, modal transformation, and T/I group transformation, allowing music theory to be directly mapped into mathematical structures. 3. 兼容五线谱 保留传统五线谱的节奏、力度、连线、指法等符号，确保音乐家能够快速适应。 兼容现有音乐软件与 MIDI 处理，支持计算机辅助作曲和 AI 生成音乐。 3. Compatibility with Traditional Notation Retains traditional symbols for rhythm, dynamics, slurs, fingering, etc., ensuring that musicians can adapt quickly. Compatible with existing music software and MIDI processing, supporting computer-aided composition and AI-generated music. 4. 主要优势 图形化的 mod 12 群表示 → 能完整呈现音乐与绘画的数学结构。 数学对称性强，支持 mod 12 计算 → 适用于调式变换、对称和弦分析、T/I 群运算。 适用于计算机音乐、AI 作曲、音高变换计算 → 推动音乐科技、电子音乐的发展。 4. Main Advantages Graphical representation of the mod 12 group → can fully represent the mathematical structure of music and painting. Strong mathematical symmetry, supports mod 12 calculation → suitable for modal transformation, symmetrical chord analysis, and T/I group operations. Applicable to computer music, AI composition, and pitch transformation calculation → promotes the development of music technology and electronic music. 总结 Mod 12 记谱法通过均匀的半音分布体系，打破传统五线谱的局限，使和弦、调式和音程变换更加 数学化、对称化，并且能更好地与计算机音乐和 AI 结合。这种方法不仅能够提供更清晰的音高关系， 还能拓展音乐与绘画的数学连接，为现代音乐理论和科技音乐提供新的工具。 Summary Mod 12 notation, through its evenly distributed semitone system, breaks the limitations 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 traditional notation. It makes chord, mode, and interval transformations more mathematical and symmetrical, and can be better integrated with computer music and AI. This method not only provides clearer pitch relationships but also expands the mathematical connection between music and painting, providing new tools for modern music theory and technology. 1-4. Equal Temperament Chromatography；平均律色谱 平均律色谱（Equal Temperament Chromatography）包含 12 个色荷，是和弦空间语言与和弦绘画 的基本定量，量纲。 Equal Temperament Chromatography contains 12 color charges and is the basic quantitative and dimension of chord space language and chord painting. 可见光的波长与频率对照表 Visible light wavelength and frequency comparison table 色彩名称（Color name），波长（Wavelength：nm），频率（frequency：MHz） 紫光（Purple）、 400~435；790-680 蓝光（Blue）、 450~480；680-620 青光（Cyan-blue）、 480~490；600-620 绿光（Green）、 500~560；600-530 黄光（Yellow）、 580~595；530-510 橙光（Orange）、 595~605；510-480 红光、（Red）605~700；480-405 采用：红≈410 作为初始值，用平均律（Equal Temperament）公式：Fn=H^n.F（H=1.05946，n= 序数，F=初始频率）计算，得出平均律（Equal Temperament）色谱。 Using red = 410 as the initial value, using the equal temperament formula: Fn = H ^ n.F (H = 1.05946, n = ordinal number, F = initial frequency) to calculate the equal temperament chromatogram: 红（Red）：410 朱红（Rot-orange）≈434.3827 橙（Orange）≈460.1094922 橙-黄（Orange-yellow）≈487.472106 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 黄（Yellow）≈516.4620658 黄-绿（Yellow-green）≈547.1759951 绿（Green）≈579.7164508 绿兰（Green blue）≈614.1921343 兰（Blue）≈650.7181042 青紫（Indigo）≈691.5352454 紫（Violet）≈732.6607983 紫红（Surplish red）≈776.2320318 将平均律（Equal Temperament）色谱记入下表，并与音符，经络的频率关联。 Record the Equal Temperament chromatogram in the table below and associate it with the frequency of the notes and meridians. 平均律（Equal Temperament）元素对应表 Equal Temperament element correspondence table 1列：音名（pitch names）。 Line 3: Pitch names. 2列：色荷 Column 4: Color Charge 3列：受激-反应经络及阴-阳属性。 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 columns: stimulus-response meridians and yin-yang properties. 1-5.±Notes；±音符 和弦语言基于一系列频率值，定量单位为“音符”，这里需要扩充定义：在本书中，音符=频符 （Frequency note），包括声-光等所有频率。 Chord language is based on a series of frequency values, and the unit of quantification is "notes". Here we need to expand the definition: in this book, note = frequency note, including all frequencies such as sound and light. 和弦语言中，所有音符都具有正-负属性，它是频率的物理属性，不是数学中的正-负数。 In the chord language, all notes have a positive-negative attribute, which is a physical attribute of frequency, not a positive-negative number in mathematics. 音符的正-负属性继承自经络的阴-阳属性，由中医经典记载。（参见：和弦数学-2）。 The positive-negative properties of musical notes are inherited from the Yin-Yang properties of meridians, as documented in the classics of Chinese medicine (see: Chord Mathematics-2). 图1-5、±音符表：椭圆=负音符，菱形=正音符。 Figure 1-5, ± note table: oval = negative note, diamond = positive note. 音符（频率）的正、负是重要的物理属性与和弦编码元素，涉及的内容比较多，放在后面章节（和 弦数学-2）专门介绍。 The positive and negative values of notes (frequencies) are important physical properties and chord encoding elements. There is a lot of content involved, so it will be introduced in the following chapter (Chord Mathematics-2). 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 Geometric chords；等比和弦中的±音符分布 等比和弦（Geometric 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），等比和弦有：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 Geometric chords is a geometric sequence. This type of chord is called dissonant chords in music. Geometric 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). 下图是等比和弦表，请注意各和弦中的±音符比例。 The figure below is a Geometric 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 等比和弦表：1、减七和弦（膜弦）、2、全音阶和弦（膜弦），3、增三和弦（膜弦） *◆=正音符，●=负音符，色彩=色荷 Geometric chords table: 1, diminished 7th chord (membrane chord), 2, diatonic chord (membrane chord), 3, augmented Triads (membrane chord) * ◆=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。 等比和弦中的正-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，是等比和弦的特殊形式。 Among them, diminished 7th chords (diminished 7th) and diatonic chords exhibit positivenegative symmetry, and augmented triads are included within diatonic chords. Positive and negative notes in Geometric 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 Geometric 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|膜弦} 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 string} 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 和弦空间的研究以和弦绘画为观察基础，以视觉实验为主要研究方法，采用代数、模 12 群（Mod 12）等数学工具，其观察表明：空间由和弦编码（量子化频谱）包含的几何语义集合生成，具有量子化 特征，为认识空间与视觉艺术都提供了新的视角。 The study of chord space is based on the observation of chord painting, with visual experiments as the main research method, and uses mathematical tools such as algebra and Mod 12. The observation shows that the space is generated by the geometric semantic set contained in the chord code (quantized spectrum) and has quantized characteristics, providing a new perspective for understanding space and visual art. 3-1.Geometric semantics Of Chord ；和弦的几何语义 和弦以量子化频谱为编码形式，包含两个基本类型：对称和弦与非对称和弦，整体表现为对称-破缺 结构。 The chords are encoded in the quantized spectrum and contain two basic types: symmetric chords and asymmetric chords, and the overall performance is symmetry-broken structure. 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（膜弦）、3、全音阶 和弦（膜弦），4、增三和弦（膜弦） *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 *本文使用 mod12 记谱法 Basic chord table: 1-1, major triad (closed string), 1-2, minor triad (open string), 2, diminished 7th (membrane string), 3, diatonic chord (membrane string), 4, augmented Triads (membrane strings) * Chord spectrum formula: n*f, H^n*f (H=1.059463，n∊Z) * Symbol: ◆=+ note, ●=- note, note color = color charge ** This article uses mod12 notation 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 基本和弦表中的和弦按照几何语义可分为：1、线和弦与膜和弦；2、开和弦与闭和弦。 The chords in the basic chord table can be divided into: 1. line chords and membrane chords; 2. open chords and closed chords. 图：3.1：和弦几何语义图例，开和弦，闭和弦，膜和弦，点空间（线图） Figure: 3.2: Semantic legend of chord space, open chord, closed chord, membrane chord, point space 说明：上面几何图形中的线有几种作用：1、用于构成图形边界（轮廓线），产生图形-背景关系； 2、用于分面，如：分面线（绘画中称为：明暗交界线），4、点空间。 The line in the above geometric figure has several functions: 1. It is used to form the figure boundary (contour line) and produce the figure-ground relationship; 2, used for faceted, such as: Facet line (painting called: light and dark Facet line), 4, point 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：3.2：和弦几何语义图例，开和弦，闭和弦，膜和弦，点空间（详细图例） Figure: 3.2: Semantic legend of chord space, open chord, closed chord, membrane chord, point space (detailed legend) 上图中出现的和弦及几何语义： The chords and geometric semantics that appear in the picture above: 闭和弦具有闭合（闭合）倾向，用于构成图形空间的轮廓线，产生图-底关系（Figure-ground relation）。 Closed chords have a tendency to close (Close) and are used to form the contours of the figure space, resulting in a figure-ground relation. 2、开和弦没有闭合（闭合）倾向，用于非轮廓线，如：分面线，线状空间等。 2, open chord has no closing (Close) tendency, used for non-contour lines, such as: faceted lines, linear Spaces, etc. 3、点空间：点空间包括端点，角点，独立点空间，用线和弦中的音符表达，它是线和弦的特殊形 式。 3. Point space: Point space includes end points, corner points, and independent point space, expressed by the notes in the line chord, which is a special form of the line chord. 4、膜和弦充满所有非线（点）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 4. Membrane chords fill all non-linear (point) spaces. 3-2.Line And Membrane Chords；线和弦与膜和弦 和弦按几何语义分为两类：线和弦与膜和弦，分别表达两种空间状态“线”与“非线膜”；非线膜 没有边界限定，无法用“维”进行描述，它是和弦空间特有的空间状态。 Chord are divided into two categories according to geometric semantics: line chords and membrane chords, which express two spatial states "line" and "non-line membrane" respectively; nonline membrane has no boundary limit and cannot be described by "dimensions", it is a chord space unique spatial state. 三和弦（大三和弦，小三和弦）的几何语义是“线”，表达“线空间”，称作：线和弦。见图 3-1。 The geometric semantics of triads (major triads, minor triads) is "line", which expresses "line space" and is called: line chord,. See Figure 3-1. 等比和弦（减七和弦、全音阶和弦，增三和弦）的几何语义为：非线膜，称作“膜和弦”。 The geometric semantics of Geometric chords (diminished 7th, diatonic chords, augmented triads,) are: non-linear membrane, called "membrane chord". 见图 3-1、和弦空间图例：膜和弦充满所有非线空间，线和弦（轮廓线、分面线）之外的空间都由 膜和弦占据。 See Figure 3-1, chord space legend: membrane chords fill all non-linear spaces, and the space outside of linear chords (contours, Facet line) is occupied by membrane chords. 非线膜和弦只有在被线和弦限定边界后，才能形成二维，三维空间；膜和弦与线和弦相互依赖，孤 立的线和弦与膜和弦都处于不稳定状态。 The Membrane chords can form a two-dimensional and three-dimensional space only after it is defined by the line chords; the Membrane chords and the line chords are interdependent, and the isolated L and Membrane chords are in an unstable state. 和弦空间由线和弦+膜和弦构成：线和弦定义膜和弦，产生轮廓线与分面线，形成二维面与三维体 积，和弦空间是线和弦定义膜和弦的结果，未经定义的膜和弦处于任意维度。 The chord space is composed of line chords + membrane chords: line chords define membrane chords, generate contour lines and Facet line, and form two-dimensional surfaces and three- 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 dimensional volumes. Chord space is the result of line chords defining membrane chords, undefined membrane chords are in arbitrary dimensions. 3-3.Closed And Open Chords ； 闭和弦与开和弦 线和弦分为两种：大三和弦与小三和弦，其几何语义分别为：闭和弦（闭弦）与开和弦（开弦）， （见图 3.1）。 line chords are divided into two types: major triads and minor triads. Their Geometric semantics are: closed chords (closed strings) and open chords (opened strings), (see Figure 3.1). 大三和弦具有闭合性（闭合性），几何语义是闭弦，表达图形与背景交界处的轮廓线，产生图-底关 系（Figure-ground relation）。 The major triad has closure (Close), and the geometric meaning is a closed string, which expresses the contour line at the junction of the Figure and the background, and generates a figure-ground relation. 小三和弦没有闭合性（闭合性），几何语义是开弦，表达开放的线空间，常用于三维体上的分面 线。 Minor triads do not have closure (Close), and the geometric meaning is open string, expressing Facet line space, often used for faceted lines on a three-dimensional body. 两者的基本区别是：闭和弦（闭弦）表达轮廓线，开和弦（开弦）表达分面线。 The basic difference between the two is: closed chords (closed string) express contour lines, and open chords (open string) express Facet line. Positive-Negative Closed And Open Strings ； 正-负闭弦与开弦 大三和弦（闭弦）构成轮廓线，小三和弦（开弦）构成分面线，两种和弦分别包含正-负两种形式： 正大三和弦 {+，x，x} 负大三和弦 {-，x，x} 正大三和弦在图底关系（figure-ground relation）中构成背景侧的轮廓线，负大三和弦在图底关系 （figure-ground relation）中构成图形侧的轮廓线。 负小三和弦 {-,x,x} 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 正小三和弦 {+,x,x} 负小三和弦构成凸分面线，正小三和弦构成凹分面线。 正大三和弦构成背景轮廓线，负大三和弦生成图形轮廓线；负小三和弦生成凸分面线，正小三和弦 生成凹分面线。 Major Triads (Closed Chords) form contour lines, while minor triads (open chords) form facet lines. Both types of chords include positive and negative forms: Positive Major Triad: {+, x, x} Negative Major Triad: {-, x, x} In a figure-ground relation, positive major triads create contour lines on the background side, and negative major triads create contour lines on the figure side. Negative Minor Triad: {-, x, x} Positive Minor Triad: {+, x, x} Negative minor triads form convex facet lines, and positive minor triads form concave facet lines. Positive major triads form background contour lines, negative major triads form figure contour lines; negative minor triads form convex facet lines, and positive minor triads form concave facet lines. 图3.3.正-负、大-小三和弦 Figure 3.3. Positive - negative, major - minor 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，等比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 Geometric 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" (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 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 4-1.2.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 图-底关系包括：三和弦图-底关系与等比和弦图-底关系。 The figure-ground relationship includes: triad figure-ground relationship and geometric chord figure-ground relationship. 三和弦图-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）。 Figure-ground relationship of triads: The figure-ground relationship is related to triads, which is manifested as: figure (near) tendency in minor keys, background (far) tendency in major keys (see: 2-4, ± note rule in chords; 3-3, positive-negative closed and open strings). 等比和弦图-底关系：等比和弦中的负音符具有图形（近）倾向，正音符具有背景（远）倾向。 Figure-ground relationship of geometric chords: The negative notes in a geometric chord have a figure (near) tendency, and the positive notes have a background (far) tendency. 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4-2.2、七声音阶 E大调，降b小调 Figure 4-2.2, Heptachord scale E major, b-flat minor 4-2. Chord Time Packet ； 和弦时间包 和弦时间包与和弦空间包的区别在于其中的三和弦，两者互为反和弦（镜像对称）。（参见：15.Mirror Symmetry；镜像对称） The difference between the chord time packet and the chord space packet is the triads in them, which are antichords (mirror-symmetrical) of each other. (See: 1-5.Mirror Symmetry) 和弦时间的进行由音符-和弦及强度（振幅）的变化产生，和弦时间的基本单位是时间包。 The progression of chord time is produced by changes in note-chord and intensity (amplitude), and the basic unit of chord time is the time packet. 和弦时间包构成“时段”，主和弦构成时段边界（开始与结束），等比和弦充满边界之外的时间。 The chord time packets make up the "periods", the tonic chords form the period boundaries (start and end), and the Geometric chords fill the time outside the boundaries. 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 人类对时间的观察比对空间的观察少很多，和弦时间（音乐）是一个还需要更多关注的部分。 Humans observe a lot less of time than space, and chord time (music) is an area that needs more attention. 4-3.Scale System ； 音阶系统 和弦语言中有三种基本的等比和弦：减七和弦，全音阶和弦，增三和弦，等比和弦是不同音阶系统 的特征和弦。 There are four basic geometric progression chords in the chord language: diminished seventh chords, diatonic chords, augmented triads, and diatonic chords. Geometric progression chords are the characteristic chords of different scale systems. 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（膜弦）、3、全音阶 和弦（膜弦），4、增三和弦（膜弦） *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 *本文使用 mod12 记谱法 Basic chord table: 1-1, major triad (closed string), 1-2, minor triad (open string), 2, diminished 7th (membrane string), 3, diatonic chord (membrane string), 4, augmented Triads (membrane strings) * Chord spectrum formula: n*f, H^n*f (H=1.059463，n∊Z) * Symbol: ◆=+ note, ●=- note, note color = color charge ** This article uses mod12 notation 减七和弦向三和弦解决，产生七声音阶（heptachord）；全音阶和弦与增三和弦向三和弦解决，产 生爵士音阶，不同音阶系统有着重要的和弦语义差别，也是后面章节的主要内容。 The diminished seventh resolves to the triad, producing heptachord; Diatonic chords and augmented triads solve to triads, producing jazz scales. Different scale systems have important 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 semantic differences, which are also the main content of the following chapters. Reference, Prompt ； 参考、提示 *本书的 1-4 章是和弦语言的基础部分，请在完全熟悉之后再进入后面的内容。 *Tip: Chapters 1-4 of this book are the basic part of the chord language. Please enter the following content after you are fully familiar with it. Bibliography；参考书目 Basic Theory Of Music；音乐基础理论 Harmony；和声学 Chord Painting；和弦绘画 General Physics；普通物理学 5.Heptachord；七声音阶 和弦语言包含三种和弦包：七声音阶（Heptachord）， 爵士音阶，无调性体系，七声音阶是其中的 主系统，也是典型的调性体系。 The chord language contains three chord packet: Heptachord, jazz scale, and Atonal system, of which the heptatonic scale is the main system and a typical tonal system. 减七和弦（Diminished 7th）是七声音阶（Heptachord）的特征膜和弦，它是产生七声音阶系统的 必须条件。 Close: Close is related to closed string, Diminished 7th, space packet interaction is related to Close, the higher the Close, the greater the binding force (gravity), which can produce cosmic order, such as: galaxies, stars, etc. See also: 8.Close; Close, 13.Multi-Layer Key Group; Multilayer tone group. 七声音阶（Heptachord）和弦包的基本语句形式是：三和弦（主和弦）+导音减七和弦（Leading note diminished 7th），在音乐中被称为：和声小音阶与和声大音阶。 The basic sentence form of the Heptachord is: triad (main chord) + leading note diminished 7th to form a heptachord chord packet, which is called in music: harmonic minor scale and Harmonic major scale. 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、七声音阶基本型（和声大-小音阶），1、C大三和弦、2、降 e小三和弦，3、升 f小三和 弦，4、A大三和弦，5、导音减七和弦（Leading note diminished 7th）。 Figure 5.1. Basic type of heptachord (harmonic major-minor scale), 1, C major triad, 2, e flat-minor triad, 3, f-sharp minor triad, 4, A major triad, 5, Leading note diminished 7th. 图6.1 中，1、2、3、4是主和弦（线和弦），用于定义减七和弦（膜弦）。 In the figure, 1, 2, 3, 4 are the tonics ( line chords), used to define the Diminished 7th (membrane chords). 减七和弦中的四个色分别充当导音，可产生四个调，称为：同导音减七和弦调群（same leading note diminished 7th keys group），四个调具有相同的闭合性。（参见：8、闭合性） Each of the four colors in the diminished 7th chord acts as a leading note, resulting in four tones, known as the same leading note diminished 7th keys group, all of which have the same Close. (See: 8, Close) 只有纯大调（主和弦为纯大三和弦），纯小调（主和弦为纯小三和弦）才能充当七声音阶系统的主 调。参见：2-4、和弦中的±音符规则。 Only pure major (the tonic is a pure major triad) and pure minor (the tonic is a pure minor triad) can act as the tonic of the heptachord system. See: 2-4, ±note rule in chords. 七声音阶服从和弦中的±音符规则。参见：2-4、和弦中的±音符规则。 The heptachord obeys the ± note rule of the chord, see: 2-4, The ± Note Rule In Chord. 5-1. Figure-Ground Relation ； 图-底关系 图-底关系由图形与背景构成，是空间知觉的基本元素。 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-ground relation is composed of figure and background, which is the basic element of spatial perception. 图-底关系（figure-ground relation）包括两种类型：绝对图-底关系与相对图-底关系；前者的图形 与背景均具有确定性，绝对性；后者的图形与背景具有相对性。 There are two types of figure-ground relation: absolute figure-ground relation and relative figureground relation. In the former, both the figure and the ground are definite and absolute; in the latter, the figure and the ground are relative. 下面例图中，石膏模型是绝对图形，墙面是绝对背景，两者构成绝对图-底关系。 In the example picture below, the plaster model is the absolute figure and the wall is the absolute background, and the two form an absolute figure-ground relationship. 图5-1.绝对图-底关系 Figure 5-1. Absolute Figure – Ground Relationship 下面例图中，部分图形-背景具有相对性，是相对图-底关系。 In the example below, some figure-backgrounds are relative; they have a relative 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 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 positive 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. 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 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 subordinate chord is generated on the 4th note. There are three triads in the system, called T-D-S triads, which are called primary triads in music theory. They are used to express the brightness relationship between separated figures and facets within the key. 图6.1、T-D-S 三和弦 Figure 7.1, T-D-S triad T-D-S 三和弦中，主和弦（Tonic），属和弦，下属和弦具有不同的亮度（亮，暗，中），由此产生 TD-S 亮度关系，大调，小调具有不同的 T-D-S 亮度关系。 Among the T-D-S triads, the Tonic, the dominant chord, and the subordinate chords have different brightness (bright, dark, medium), resulting in the T-D-S brightness relationship, and the major and minor keys have different T-D-S brightness relationships. 大调的 T-D-S 亮度关系表达不同亮度的相对图形；小调的 T-D-S 亮度关系表达图形上不同亮度的分 面。 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 T-D-S luminance relation of major key expresses the relative figure of different luminance. The T-D-S luminance relation in a minor key expresses the different luminance facets of the figure. 属和弦与下属和弦共享主和弦的导音减七和弦。 The dominant and subordinate chords share the leading note diminished seventh chord of the tonic chord. 调-和弦 key-chord 亮度 brightness 空间语义 Spatial semantics 大调主和弦 Major Tonic Chord 中 Middle 系统背景 System Background 大调属和弦 Major dominant chord 暗 Dark 背景相对图形 Background relative figure 大调下属和弦 Major subordinate chord 亮 Bright 背景相对图形 Background relative figure 小调主和弦 Minor Tonic Chord 中 Middle 图形 figure 小调属和弦 Minor dominant chord 亮 Bright 图形亮面 Figure highlight 小调下属和弦 Minor subordinate chord 暗 Dark 图形暗面 Figure dark surface; 图6-1.T-D-S 三和弦的亮度关系表 Luminance relationship table for T-D-S 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6.2、C大调、#F 小调的 T-D-S 三和弦 Figure 6.2, T-D-S triad in C major, #F minor C大调（背景）、暗色挂盘=C 大调属和弦，亮色挂盘=C 大调下属和弦，中间色背景=C 大调主和 弦。 C major (background), dark hanging plate = C major dominant chord, bright hanging plate = C major subordinate chord, mid-color background = C major tonic. 纯大调的属和弦与下属和弦可以构成背景上的相对图形。 The dominant and subdominant chords in the pure major scale can form relative figures on the background. #F 小调（石膏正方性）、正方体上有三个不同亮度的分面，亮面=#F 小调属和弦，暗面=#F 小调下 属和弦，中间色=#F 小调主和弦。 #F minor (plaster squareness), there are three facet of different brightness on the cube, bright side = #F minor dominant chord, dark side = #F minor subdominant chord, middle color = #F minor tonic. 背景上的挂盘与墙面产生调内图-底关系：主和弦构成背景，属和弦，下属和弦构成图形。 The hanging plate on the background and the wall produce an figure-ground relationship within the key: the main chord forms the background, the dominant chord, and the subordinate chord form the figure. 同根音符大-小调转换，可以产生不同图形，不同分面的转换，但服从主调的 T-D-S 亮度级关系。 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 The same root note major to minor conversion, can produce different figures, different facets of conversion, but obey the main key T-D-S brightness level relationship. Reference ；参考 Basic Theory Of Music；音乐基础理论 Harmony；和声学 Chord Painting；和弦绘画 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 7.Overlapping Chords；和弦的重叠 三和弦+导音等比和弦（leading note geometric chords）构成和弦包，这两种和弦是基本和弦。不 同和弦的重叠，如：三和弦重叠等比和弦，三和弦重叠三和弦，还可产生大量的重叠和弦，重叠和弦可 模糊基本和弦的几何语义，生成更多的空间状态。 The triad + leading note geometric chords constitute the chord package, and these two chords are basic chords. The overlap of different chords, such as triads overlapping geometric chords and triads overlapping triads, can also generate a large number of overlapping chords. Overlapping chords can blur the geometric semantics of basic chords and generate more spatial states. 重叠和弦的形式非常多，如：扩展和弦（Extended Chords），挂留和弦（Sus Chords），附加音和 弦（Added-Tone Chords）等，本文不逐一介绍，只讨论其一般构成原理。 There are many forms of overlapping chords, such as Extended Chords, Sus Chords, Added-Tone Chords, etc. This article will not introduce them one by one, but only discuss their general composition principles. 三和弦重叠三和弦只出现在七声音阶（heptachord）中，是较简单的形式；三和弦重叠等比和弦 （Geometric Chords）则较复杂，可出现在七声音阶与爵士音阶中，下面将重点讨论。 Overlapping triads only appear in the heptachord, which is a simpler form; overlapping triads and geometric chords are more complex and can appear in the heptachord and jazz scales, which will be discussed in detail below. 一个调中只能包含一个等比和弦（geometric chords），每个调都有其唯一的关联等比和弦 （Related geometric chords）。 A key can only contain one geometric chord (membrane chord), and each key has its own unique related geometric chords. T-D-S 三和弦与关联等比和弦（Related geometric chords）的关系包括以下三种情况： The relationship between the T-D-S triad and related geometric chords includes the following three situations: 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 主和弦-关联等比和弦（Related geometric chords）， {0，4，7}，{2，5，8，11}，三和弦与关联等 比和弦（Related geometric chords）不重叠。 Main chords - Related geometric chords, {0, 4, 7}, {2, 5, 8, 11}, triads and related geometric chords do not overlap. 属和弦-关联等比和弦（Related geometric chords）， {7，11，2}，{2，5，8，11} ，三和弦的 3-5 音符与关联等比和弦（Related geometric chords）重叠，非根音重叠。 Dominant chords - Related geometric chords, {7, 11, 2}, {2, 5, 8, 11}, the 3-5 notes of the triad overlap with the Related geometric chords, and the non-root notes overlap. 下属和弦-关联等比和弦（Related geometric chords）， {5，9，0}，{2，5，8，11}，三和弦根音符 与关联等比和弦（Related geometric chords）重叠，根音重叠。 Subdominant chords - Related geometric chords, {5, 9, 0}, {2, 5, 8, 11}, the root notes of the triad overlap with the related geometric chords, and the root notes overlap. 属和弦，下属和弦都是重叠和弦，即：三和弦重叠关联等比和弦（Related geometric chords）。 Dominant chords and subdominant chords are overlapping chords, that is, triads overlapping related geometric chords. 重叠和弦的音符也不限于三个，原理上，三和弦+关联等比和弦（Related geometric chords）包含 的音符都是取值范围，如：属和弦也可以是：{7，11，2，5}，下属和弦也可以是：{5，9，0，2}。 The notes of overlapping chords are not limited to three. In principle, the notes contained in triads + related geometric chords are all value ranges, such as: dominant chords can also be: {7, 11, 2, 5}, and subdominant chords can also be: {5, 9, 0, 2}. 属和弦与下属和弦也可以重叠关联等比和弦（Related geometric chords）之外的其它等比和弦，这 就包含了暧昧的转调。 The dominant and subdominant chords can also overlap other geometric chords besides related geometric chords, which includes ambiguous modulations. 一些重叠和弦有专用名称，如：属七和弦（Dominant Seventh）、下属七和弦（Subdominant seventh），属九和弦（Dominant ninth），下属九和弦（Subordinate nine chords）等；但重叠和弦的形 式很多，难以全部命名，只需要理解其生成原理，在应用中更多依赖直觉。 Some overlapping chords have special names, such as: Dominant Seventh, Subdominant Seventh, 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 tendencystability of the diminished seventh chord, with high-middle-low corresponding to: majorminor-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. Reference ； 参考 Basic Theory Of Music；音乐基础理论 Harmony；和声学 Chord Painting；和弦绘画 General Physics；普通物理学 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+导音等比和弦（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等比和弦有重叠音符，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 Geometric 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. ⚫ 爵士音阶中的等比和弦（Geometric Chord）可向无彩色（neutral colors）解决，构成无调性 解决。 ⚫ Geometric 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 figure-ground 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. 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 9-1.1. Augmented fourth Figure-Ground Relationship；增四度图-底关系 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. 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9-1.3、爵士音阶 C大调，f#小调，绝对图-底关系 Figure 9-1.3, jazz scale C major, f# minor, Absolute 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9-1.4、爵士音阶 C#大调，g小调，绝对图-底关系 Figure 9-1.4, Jazz scale C# major, g minor, Absolute figure-ground relationship 将增四度大-小调中的三和弦转换为重叠和弦形式，如：主七和弦，主九和弦，可表达相对图底关 系。 Converting the triads in the augmented fourth major-minor key into overlapping chord forms, such as the tonic seventh chord and the tonic ninth chord, can express the relative figure-ground relationship. 图9-1.5、爵士音阶 C大调，升f小调，相对图底关系 Figure 9-1.5, Jazz scale C major, F sharp minor, relative 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9-1.6、爵士音阶 C大调，升f小调，相对图底关系 Figure 9-1.6, Jazz scale C major, F sharp minor, relative figure-ground relationship 图9-1.7,爵士音阶 C#大调，g小调，相对图底关系 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 Figure 9-1.7, Jazz Scale C# Major, G Minor, Relative Figure-ground Relationship 9-1.2、Overlapping Chord；重叠和弦 爵士音阶的调结构为：三和弦+导音等比和弦（Leading note geometric chords）——全音阶和 弦。 The key structure of the jazz scale is: triad + leading note geometric chords - diatonic chords. 在爵士音阶中，三和弦（线和弦）与导音等比和弦（膜和弦）有重叠音符。 In jazz scales, triads (line chords) and leading-tone geometric 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+导音等比和弦（Leading note geometric 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 geometric 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). 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 9-2、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). 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. 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. 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、单一色 Figure 10-2. Monochrome 此外，还有一些频谱分布结构具有无调性特征。 In addition, there are some spectral distribution structures that have atonal characteristics. 半音阶：半音阶具有无彩色兼容性与解决倾向。 频域收窄：色彩频域收窄也可以削弱，消除和弦-调性。 上面两个条件是和弦-调性的阻断机制。 Chromatic scale: Chromatic scales have achromatic compatibility and resolution tendencies. Narrowing of the frequency domain: Narrowing of the color frequency domain can also weaken and eliminate chord-tonality. The above two conditions are the blocking mechanisms of chord-tonality. 全音阶和弦（爵士特征和弦）具有轻度无彩色兼容性与解决倾向，在插入半音后，无调性倾向被加 强，如：重叠和弦（主七和弦，主九和弦，主 11 和弦，主 13 和弦等），其极端形式是半音阶——爵士 音阶是常见的无调性组织框架。 Whole tone chords (jazz characteristic chords) have a mild achromatic compatibility and resolution 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 tendency. After the semitone is inserted, the atonality tendency is strengthened, such as: reduplicated chords (major seventh chord, major ninth chord, major 11th chord, major 13th chord, etc.), and their extreme form is the chromatic scale - the jazz scale is a common atonality organizational framework. 相对无调性结构，1，C 13 和弦，2，Eb 9 和弦，3，f# 9 和弦，4，A 13 和弦，5，半音阶 Relatively atonal structures, 1, C 13 chords, 2, Eb 9 chords, 3, f# 9 chords, 4, A 13 chords, 5, chromatic scales 半音阶具有无彩色解决倾向，并依赖无彩色，如频域收窄，则产生单一色倾向。 The chromatic scale has a tendency to resolve achromatic colors and relies on achromatic colors. If the frequency domain is narrowed, a single color tendency will be produced. 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10-3.半音阶 Figure 10-3. Chromatic scale 图10-4.半音阶 Figure 10-4. Chromatic scale 爵士音阶中的重叠和弦包含 1-4 个半音程，具有无彩色解决倾向与兼容性。参见：9-4、重叠和弦 The overlapping chords in jazz scales contain 1 to 4 semitones and have a tendency for achromatic resolution and compatibility. See: 9-4, Overlapping 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 图10-5. 爵士 A9 和弦 Figure 10-5. jazz C9 chord 图10-5. 爵士 f# 9 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 10-5. jazz f# 9 chord 图10-5. 爵士 C 9 和弦 Figure 10-5. jazz C 9 chord 非和弦（无调性）系统是和弦（调性）系统的反过程，它屏蔽了和弦系统的所有编码，语义逻辑， 主要由亮度变化来产生视觉空间。 The non-chord (atonal) system is the inverse process of the chord (tonal) system, which blocks out all the coding, semantic logic of the chord system, and produces visual space mainly by brightness changes. 和弦（调性）与非和弦（无调性）具有不同的语义逻辑，是不同的宇宙观。 Chord (tonality) and non-chord (atonality) have different semantic logic and different cosmological views. Reference ；参考 调性·无调性·泛调性、作者: [奥] 鲁道夫·雷蒂，人民音乐出版社，1992-8， ISBN: 9787103010778。 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 无调性音乐的结构、作者: 艾伦•福特 ，译者: 罗忠镕，上海音乐出版社-2009-10，ISBN： 9787807515593 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. 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 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. 在爵士音阶系统中，全音阶和弦向主和弦解决。 In the Weak Tonal System, the Diatonic is resolved toward the tonic. 主和弦为大三和弦（闭和弦）时，膜和弦向着轮廓线解决。 When the tonic is a major triad (closed chord), the Membrane chords is resolved toward the contour line. 主和弦为小三和弦（开和弦）时，膜和弦向着分面线解决。 When the tonic is a minor triad (open chord), the Membrane chords is resolved toward the Facet line. 和弦解决语句中，和弦省略为音符（色）时，表现为色彩旋律，产生色相知觉。 In the chord resolved sentence, when the chord is omitted as a note (color), it is expressed as a color melody and produces a sense of hue. 膜和弦各音符（色）都可以向线和弦各音符（色）解决，但以下形式比较常见： Each note (color) of the Membrane chords can be solved by the note (color) of the line chord, but the following forms are more common: 导音（leading note）-主音（key-note）语句：导音（leading note）是与主音（key-note）相邻的 膜和弦音符（色），具有最强的解决（solve）倾向。 Leading note-key-note sentence: Leading note is the Membrane chords note (color) adjacent to the key-note, which has the strongest tendency to solve. 与主和弦的三度，五度相邻的膜和弦音符（色），可向着主和弦三度，五度解决，见下图： The Membrane chords note (color) adjacent to the third and fifth degrees of the tonic can be solve toward the third and fifth of the tonic, as shown in the figure below: 图11.1、M-L 解决语句 Figure 11.1, M-L resolved statement 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11.2、系统背景上，减七和弦（Diminished 7th）的两个色分别向主和弦上的根音（rootnote）、五度（fifth）作 M-L 解决。 Figure 11.2. On the background of the system, the two colors of Diminished 7th are resolved by M-L to the root-note and fifth of the tonic. 11-2.Facet Melody；分面旋律 分面旋律是最常见的色彩旋律进行（melodic progression）， 用于在空间包上产生不同亮度的分 面，不同亮度的分面由不同音符（色）构成，称为：分面旋律。 Faceted melody is the most common color melody progression (melodic progression), which is used to produce facet of different brightness on the space packet. The faceg of different brightness are composed of different notes (colors), called: faceted 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 图11.3、分面旋律表达的明-暗分面 Figure 11.3: Light-dark Facet line expressed by faceted melody 分面旋律只适用膜和弦，大调的分面旋律只发生在一个膜和弦内，小调的分面旋律可发生在多个膜 和弦之间。 The faceted melody only applies to the Membrane chords, the faceted melody of the major key only occurs in one Membrane chords, and the faceted melody of the minor key can occur between multiple Membrane chords. 正序旋律与反序旋律：在平均律（Equal Temperament）色环中，红色（E）的能量级最低，紫红色 （bE）的能量级最高，其它色的频率高-低是相对的，如：绿色相对黄色，绿色频率更高。 Positive order melody and reverse order melody: In the Equal Temperament color circle, red (E) has the lowest energy level, magenta (bE) has the highest energy level, and the high-low frequencies of other colors are relative, such as : Green is relatively yellow, and green has a higher frequency. 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 treatment is adopted, the chord features will be weakened, which can weaken the certainty of the hue and express 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）。 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 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 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 MajorMinor, 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: multi-layer key groups. 多层调群（Key group）存在主-次秩序。 The multi-layer Key group has a primary-secondary order. 等比和弦 Geometric 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 fractalfacet 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; 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 （dominant key）、下属调（Subdominant Key）表达同一图形上不同亮度的分面。 The dominant key and subdominant key of the major key express fractal figure of different brightness;the dominant key and the subdominant key of minor key express the facet of different brightness on the same figure. T-D-S 调群组成部分 T-D-S tone group components 亮度 Brightness 空间语义 Spatial semantics 大调主调 Major main key 中 middle 系统背景 System Background 大调属调 Major Dominant key 暗 dark 背景相对图形 Background Relative figure 大调下属调 Major subdominant key 亮 Bright 背景相对图形 Background Relative figure 小调主调 Minor main key 中 middle 图形 Figure 小调属调 Minor Dominant key 亮 Bright 图形亮分面 Graphics bright facet 小调下属调 Minor subdominant key 暗 dark 图形暗分面 Graphic dark facets 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 13-2.2、#F 小调、C大调 T-D-S 调群 13-2.2, #F minor, C major T-D-S key group #f 小调（石膏图形），亮面=#f 小调-属调（dominant key）；暗面=#f 小调-下属调（Subdominant Key），中间色=#f 小调主和弦。 #f minor (gypsum graphics), bright side = #f minor-dominant key; dark side = #f minorsubdominant key, middle color = #f minor major chord. C大调（背景）：墙上的白色挂盘=C 大调的属调（dominant key）；墙上的黑色挂盘=C 大调的下属 调（Subdominant Key）。中间色背景=C 大调主和弦。 C major (background): the white hanging plate on the wall = the dominant key of C major; the black hanging plate on the wall = the subdominant key of A major. Mid-color background = C major major chord. 13-2.1. Mixed Key Group；混合调群 T-D-S 调群中的属调与下属调可以采用爵士音阶形式：三和弦+导音全音阶和弦，其分离强度低于 属和弦-下属和弦+导音减七和弦。 The dominant and subdominant keys in the T-D-S key group can take the form of a jazz scale: triad + leading tone diatonic chord, which has a lower separation intensity than the dominant chordsubdominant chord + leading tone diminished seventh 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13-2.3. 基于 T-D-S 的混合调群 Figure 13-3.2. Hybrid tone group based on T-D-S 图13-2.4. 基于 T-D-S 的混合调群 Figure 13-2.4. Hybrid tone group based on T-D-S 13-4. Chord Celestial Model；和弦天体模型 多层调群可构成天体解释模型，其中，C-D-E 调群为星系（银河系）模型，T-D-S 调群为恒星系 （太阳系）模型。 Multi-layer tuning groups can constitute a celestial body interpretation model, among which the C-D-E tuning group is the galaxy (Milky Way) model, and the T-D-S tuning group is the star system (solar system) model. 星系（银河系）模型： Galaxy (Milky Way) Model: 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 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 Griffiths, D. J. (2005). Introduction to Quantum Mechanics. Pearson. 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. 三和弦（开弦，闭弦）定义全音阶和弦（膜和弦）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 chords), 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 （膜弦）（◆=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 string) (◆=positive note, ●=negative note, color=color charge) 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14-2.2、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（膜弦）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 diatonic chord (membrane string) 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 （膜弦）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 strings), 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。 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 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) 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 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 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，膜弦充满所有非线空间。 [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 strings fill all non-linear spaces. 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. 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14-2.6、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. 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 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 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, 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, 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 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 positivenegative 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. The diatonic chord contains six notes, and each note has positive-negative attributes and color charges, and all color charges are mixed to produce white. 图14-2.10、1、全音阶和弦；2、增三和弦（◆=正音符，●=负音符，色彩=色荷） Figure 14-2.10, 1. Diatonic chords; 2. Augmented triads ( ◆=positive note, ●=negative note, color=color charge) 全音阶和弦充满所有非线空间——包括空间系统的图形与背景，背景上的全音阶和弦表现出如下特 征：其中的正-负音符分别倾向于在图形两端的对立位置聚集，形成正极与负极，类似磁场中的±磁荷分 布形态。 Diatonic chords fill all non-linear Spaces, including the figure and background of the spatial system. Diatonic chords on the background show the following characteristics: the positive 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 negative notes tend to gather at opposite positions at both ends of the figure, forming positive and negative poles, similar to the distribution of ± magnetic charges in a magnetic field. 图14-2.11a、全音阶和弦中的±音符分布表现出类似±磁荷的特征 FIG. 14-2.11a. the ± notes in diatonic chords show characteristics similar to ± Magnetic charge 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14-2.11b、全音阶和弦中的±音符分布表现出类似±磁荷的特征 FIG. 14-2.11b. the ± notes in diatonic chords show characteristics similar to ± Magnetic charge 以上观察表明：电荷来自三和弦，磁荷来自膜和弦，大三和弦（正和弦）带正电荷，小三和弦（负 和弦）带负电荷，膜和弦中的正-负音符产生正-负磁荷。 The above observations show that the charge comes from the triad, the magnetic charge comes from the membrane chord, the major triad (closed string) has a positive charge, the minor triad (open string) has a negative charge, and the positive-negative notes in the membrane chord produce a positive-negative magnetic charge. 图14-2.12、爵士音阶和弦包：1、C大三和弦（闭弦，正电荷），2、F#小三和弦（开弦，负电 荷），3、全音阶和弦（膜弦，磁荷）（◆=正音符，●=负音符，色彩=色荷） 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 14-2.12. The chord packet of the jazz Scale: 1, C major triad (closed string, positive charge), 2. F# minor triad (open string, negative charge), 3, diatonic chord (membrane string, Magnetic charge) ( ◆=positive note, ●=negative note, color=color charge) 大三和弦（闭弦），小三和弦（开弦），等比和弦（膜弦）产生电荷，磁荷，电磁场。 Major triads (closed strings), minor triads (open strings), and isometric series chords (membrane strings) generate electric charges, magnetic charges, and electromagnetic fields. 上面观察表明：±电荷，±磁荷来自±音符。 The above observation shows that ± charge, ± magnetic charge comes from ± note. 大三和弦（闭弦，正电子）与其束缚在内部的膜和弦（膜弦）不能分离，两者共同表现为质子，带 正电荷。 The major triad (closed string, positron) cannot be separated from its bound membrane chord (membrane string), which together appear as a proton and are positively charged. 膜弦中的各音符被大三和弦（闭弦，正电子）束缚在和弦包中，类似夸克禁闭与强相互作用。 Each note in the membrane string is bound in a chord package by a major triad (closed string, positron), similar to quark confinement and strong interaction. 开弦在和弦包中产生分离作用：包括分面与图形分裂。 Open strings produce separation effects in the chord package: including faceting and figure splitting. 膜和弦在无调性解决（solution）时，和弦包不含三和弦（正-负电子），表现为不带电荷的中性和弦 包（中子）。 Membrane chords In the atonal solution, the chord package contains no triads (positive-negative electrons) and appears as a neutral chord package with no charge (neutrons). 增三和弦（augmented triads）只含有正音符或负音符，不能表现出±磁荷。 augmented triads contain only positive or negative notes and cannot show ± magnetic charges. 天体与原子都是和弦空间包（调），但前者是七声音阶系统，后者是爵士音阶系统，两者具有很大 的区别。 Both celestial bodies and atoms are chord space packages (keys), but the former is a heptachord system, the latter is a jazz scale system, and the two have a big difference. 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 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，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, similar to wave-particle duality. 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） 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14-3.2、和弦镜像：和弦时间（上），和弦空间（下）互为反和弦。 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 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 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。 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. 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14-3.3、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 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 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 wave-particle 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. 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: 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 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. 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： 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 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: 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。 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 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： 设质量 m 依赖于空间定域性 S，则： m=MS 其中 M 为某个常数。 当 S=0（纯时间），则 m=0，即纯时间状态下无法测量质量。 当 S=1（纯空间），m=M，即质量完全在空间中表现。 由此得出质量-速度关系： m+t=1 能量，质量，速度关系为：E=s+t=m+t=1 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 结论： 质量只存在于和弦空间，而不存在于和弦时间。 4. Measurement of quality Time cannot measure mass, and mass must be measured in a localized spatial state (S>0). In a pure time state (S=0), mass cannot be defined because there is no spatial reference. Mass can only be measured in a region with a geometric structure, which means that mass is a manifestation of spatial locality. Mathematical expression: Assume that mass m depends on spatial locality S, then: m=MS Where M is a constant. When S=0 (pure time), m=0, that is, mass cannot be measured in a pure time state. When S=1 (pure space), m=M, that is, mass is completely manifested in space. From this, the mass-speed relationship is: m+t=1 The relationship between energy, mass, and speed is: E=s+t=m+t=1 Conclusion: Mass only exists in chord space, not in chord time. 5. 总结： 时间能（T）和空间能（S）满足归一化关系：S + T = 1。 速度 v = T，决定于时间能量的占比，而不是外部参考系。 在纯时间状态（T = 1, S = 0），空间信息消失；在纯空间状态（S = 1, T = 0），时间信息消失。 和弦时空的不连续性表明，时间和空间可以完全分离，表现出类似量子跃迁的行为。 质量只存在于和弦空间，在纯时间状态下无法测量质量。 5. Summary: Time energy (T) and space energy (S) satisfy the normalization relationship: S + T = 1. Speed v = T, determined by the proportion of time energy, not the external reference frame. In the pure time state (T = 1, S = 0), spatial information disappears; in the pure space state (S = 1, 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 = 0), time information disappears. The discontinuity of chord spacetime shows that time and space can be completely separated, showing quantum jump-like behavior. Mass only exists in chord space and cannot be measured in the pure time state. 14-5.Chord Space-Time Measurement；和弦时空测量 在和弦时空的观察、测量中，一些和弦语言特征可能被观察到。 In the observation and measurement of chord space -time, some chord language features may be observed. 1、离散性：和弦时-空由和弦表达，可测量到一系列频率（能量）值，不是任何频率（能量）都能 进入和弦系统，系统只接受和弦法则允许的一系列离散值（C=H^n*f, H=1.059463），表现为和弦频谱。 1, discrete: chord space-time is expressed by the chord, can be measured to a series of frequency (energy) values, not any frequency (energy) can enter the chord system, the system only accepts a series of discrete values allowed by the chord law (C=H^n*f, H=1.059463), expressed as the chord spectrum. 2、和弦几何语义：和弦空间由和弦表达，和弦按几何语义分为：开弦，闭弦，膜弦。（参见：3、 和弦与弦） 2. Chord Geometric semantics: Chord space is expressed by chords, and chords are divided into open strings, closed strings, and membrane strings according to geometric semantics. (See: 3, Chords and Strings) 3、±对称：和弦时-空的“基本粒子”是±音符；和弦属性都涉及±音符及对称性。 3. ± symmetry: The "elementary particles" of chord space-time are ± notes; all chord properties involve ± notes and symmetry. 4、时-空二相性：时间和弦与空间和弦互为反和弦，数学形式为：镜像对称，和弦时间具有非定域 性，和弦空间具有定域性，在观察中会表现出“时空二相性”（波粒二相性）。 4. Time-space duality: time chord and space chord are antichords to each other, and the mathematical form is: mirror image and symmetry. Chord time has non-locality, chord space has locality, and the observation will show "space-time duality" (wave-particle duality).