CHORD LANGUAGE

和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUAGE (First name:Equal Temperament Logic and Equal Temperament Painting) 和弦语言 （首发名：平均律逻辑与平均律绘画） (English and Chinese version) （中，英文对照版） Li Xiaohong;李晓虹 Email:[email protected] ISBN:9781370273348 ASIN: B0919JJ3R7 DOI:10.13140/RG.2.2.25415.65440 作者：李晓虹 Author:LI Xiaohong 版权 2016.李晓虹 Copyright 2016 LI Xiaohong Work registration information, copyright reservation;作品注册信息，版权保留 《量子人看宇宙》NAME OF AUTHOR：XIAOHONG LI；For a Literary Work UNITED STATES COPYRIGHT OFFICE TXu 635-761； 《十二平均色律——量子人看宇宙》NAME OF AUTHOR：XIAOHONG LI；For a Literary Work UNITED STATES COPYRIGHT OFFICE TXu 777-504； 《十二平均色律——量子人看宇宙》作者或著作权人：李晓虹登记号：21-1996-A-(0183)-0146 中国.四川省版权局。 *本书部分章节为 24-25 届世界哲学大会论文。 * Some chapters of this book are papers from the 24th and 25th World Congress of Philosophy. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Overview Of Chord Language；和弦语言综述 25 届世界哲学大会论文 ； Papers of the XXV World Congress of Philosophy 和弦语言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），共现宇宙结构。 Chord language uses a quantized spectrum as its encoding structure, encompassing 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), and life (meridians), distributed as chord fields (quantum fields), cooccurring in the structure of the universe. 在这些研究中，我们首次在人体与绘画中定量观测到与音乐同构的和弦结构及运行法则，由此共现 和弦时空——量子化的时空结构。 In these studies, we have for the first time quantitatively observed chord structures and operating rules that are isomorphic to music in the human body and painting, thereby co-occurring chord spacetime—a quantized spacetime 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），5、半音阶和弦（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 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 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)，5. Chromatic chords (membrane strings) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 关键词 ； 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（量子时空 场），音乐（时间域）、绘画（空间域）是其常见形式。 Chord (tonal) spacetime: using quantized spectra as the encoding structure, mapped to a spatiotemporal semantic set, generating a chord spacetime field (quantum spacetime 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 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 组离散的频率/能量结构。 Chord spectrum: The chord spectrum is essentially the same as the quantum of energy. Both are based on a reference frequency f and generate a set of discrete frequency/energy structures under the control of an integer n. 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——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=19=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 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 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. 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，其生成域为：纯时间（音乐）与纯空间（绘画），共现时空的物理结 构。 Chords encompass quantization and string space, and their generation domains are: pure time (music) and pure space (painting), co-occurring the physical structure of spacetime. Chord space-Reface to Chord Painting；和弦空间-《和弦绘画》序言 《和弦绘画》是和弦语言体系的视觉分支与实验基础。它揭示出一个事实：绘画中的离散色彩分 布，本质上是一种和弦几何结构。 在此结构中，和弦编码（量子化频谱）分别生成音乐的时间域与绘画的空间域，两者呈现镜像对称 关系：-7,-4,0 ↔0,4,7 (mod 12) *Chord Painting* is the visual branch and experimental foundation of the chord language system. It reveals that the discrete color distribution in painting is essentially a chordal geometric structure. In this structure, chord encoding (quantized spectrum) generates the temporal domain of music and the spatial domain of painting, respectively, exhibiting a mirror-symmetric relationship: -7, -4, 0 ↔ 0, 4, 7 (mod 12). 这种对称性使得音乐与绘画成为同一和弦系统的两种展开方式。 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 和弦编码不仅描述频率比例，也携带几何语义： 开弦（Open String）：对应小三和弦 (−7,−3,0) mod 12，为分面线结构； 闭弦（Closed String）：对应大三和弦 (−7,−4,0) mod 12，为轮廓线结构； 膜弦（Membrane String）：对应等比和弦，如减七 (0,3,6,9)、全音阶 (0,2,4,6,8,10)、增三 (0,4,8) mod 12，代表非线性空间的连续面。 This symmetry makes music and painting two ways of unfolding the same chord system. Chord encoding not only describes frequency ratios but also carries geometric semantics: Open String: Corresponds to a minor triad (−7,−3,0) mod 12, with a faceted structure; Closed String: Corresponds to a major triad (−7,−4,0) mod 12, with a contour structure; Membrane String: Corresponds to proportional chords, such as diminished seventh (0,3,6,9), whole tone (0,2,4,6,8,10), augmented triad (0,4,8) mod 12, representing a continuous surface in nonlinear space. 三和弦（开弦与闭弦）定义了等比和弦（膜弦）的边界——即空间的生成线。由此，和弦几何框架 得以确立： 和弦的几何语义（弦）决定空间结构，而和弦的频谱语义（和弦）定义其调性关系。 两者共同构成和弦空间（Chord Space）——一个连接音乐与绘画的统一结构场。 这些结果并非理论假设，而源自于绘画中的独立观察与实验。在色彩的离散分布、形态的空间排列 中，可以反复验证上述和弦几何特征。 Triads (open and closed chords) define the boundaries of equal-ratio chords (membrane strings)— that is, the generating lines of space. Thus, the geometric framework of chords is established: The geometric semantics of a chord (the string) determines the spatial structure, while the spectral semantics of a chord (the chord itself) defines its tonal relationships. Both together constitute the Chord Space—a unified structural field connecting music and painting. These results are not theoretical assumptions, but rather stem from independent observations and experiments in painting. The aforementioned chord geometric characteristics can be repeatedly verified through the discrete distribution of colors and the spatial arrangement of forms. 因此，《和弦绘画》不仅是一部艺术专著，更是一份关于和弦空间的实验报告： 它展示了如何从视觉中测得音乐的几何结构，如何以绘画为观测仪器，揭示生命与宇宙的调性秩 序。绘画在此被重新定义： 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 它不再是主观表现，而是和弦的可见生成。 每一幅作品，都是一次频谱的空间展开； 每一条线、每一个色面，都是和弦在时空中的几何显现。 《和弦绘画》由此成为和弦语言体系的支柱之一——它提供了观测、验证与应用的可视基础， 让和弦从音乐的时间流中，转化为绘画的空间形。 Therefore, *Chord Painting* is not only an art monograph but also an experimental report on chordal space: It demonstrates how to measure the geometric structure of music visually, and how to use painting as an observational instrument to reveal the tonal order of life and the universe. Painting is redefined here: It is no longer a subjective expression but the visible generation of chords. Each work is a spatial unfolding of the spectrum; Every line, every color plane, is a geometric manifestation of a chord in space and time. *Chord Painting* thus becomes one of the pillars of the chordal language system—it provides a visual foundation for observation, verification, and application, transforming chords from the temporal flow of music into the spatial form of painting. Li, X. H. (2020). Chord Painting. ResearchGate. https://www.researchgate.net/publication/340492620_Chord_Painting Li, X. H. (2024). Chord Language. Zenodo. https://zenodo.org/records/11817631 Chord Biology；和弦生命 人类有两种生命观察者：和弦（调性）观察者与非和弦（无调性）观察者，分别观察两种生命形 式：和弦包（量子化频谱，场）与生物体（细胞，分子等），生命是两者的二层结构。 Humans have two types of life observers: chord (tonal) observers and non-chord (atonal) observers. They respectively observe two types of life forms: chord packages (quantized spectra, fields) and organisms (cells, molecules, etc.). Life is the two-layer structure of these two types. 在人体中，和弦（chord）表现为经络（或脉轮）系统。初步观察表明，十二经络系统展现受激频 谱响应，其频率分布可近似为几何级数： 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 该式通过对数变换可切换为泛音频线性谱 ( n f )，并与量子化假设 ( n f h )（能量离散结构）数学一 致。 这暗示音乐（时间域）、绘画（空间域）、经络（生命域）及量子化假设共享统一的离散数学框架。 In the human body, chords manifest as a meridian (or chakra) system. Preliminary observations indicate that the twelve meridian systems exhibit an excited spectral response, the frequency distribution of which can be approximated as a geometric series: fn=H^n⋅f0, where H=2^(1/12)≈1.059463, n∈Z. This equation can be transformed into a linear overtone spectrum (nf) through logarithmic transformation, and is mathematically consistent with the quantization hypothesis (nfh) (discrete energy structure). This suggests that music (temporal domain), painting (spatial domain), meridians (life domain), and the quantization hypothesis share a unified discrete mathematical framework. Natural Spirit；自然精神 和弦语言是和弦结构（第三人称观察）与和弦语义（第一人称观察）的共现，是自然编码（量子化 频谱）语言，存在自身的生成方式。 Chord language is a co-occurrence of chord structure (third-person observation) and chord semantics (first-person observation). It is a natural encoding (quantized spectrum) language with its own generation method. 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 人的认识来源于两种观察者：和弦观察者与非和弦观察者。 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 Human cognition originates from two types of observers: chord observers and non-chord observers. 和弦观察者（Chord Observer） 依托于 和弦观察系统（Chord Observation System）。在此系统中， 和弦表现为物理、数学与自然语义的统一，精神与物理实在的统一。在和弦观察中，心与物、主与客的 界限消解，第一人称观察与第三人称观察紧密耦合。在此，精神是和弦的物理属性之一。 The Chord Observer is based on the Chord Observation System. In this system, chords are represented as a unity of physics, mathematics, and natural semantics, and a unity of spirit and physical reality. In chord observation, the boundaries between mind and matter, subject and object, dissolve, and first-person and third-person observations are tightly coupled. Here, spirit is one of the physical properties of chords. 非和弦观察者（Non-Chord Observer） 则屏蔽了和弦系统的共振结构。其观察以符号命名（主体） 与经验对象（客体）的分离为特征：主体反映客体，客体独立于主体。这类观察依赖外部工具与测量， 以排除观察者影响，实现可重复、可验证的客观性。 Non-chord observers, on the other hand, shield the resonant structure of the chord system. Their observation is characterized by the separation of symbolic naming (subject) and experiential object (object): the subject reflects the object, and the object is independent of the subject. This type of observation relies on external tools and measurements to eliminate the influence of the observer and achieve repeatable and verifiable objectivity. 两种认识的形式，分别对应于：自然精神系统（Natural-Spiritual System） —— 主客合一的内在共 振性认知；人类工具系统（Human Instrumental System） —— 主客分离的外在表征性认知。 The two forms of cognition correspond to: The Natural-Spiritual System – an internally resonant cognition that unites subject and object; and the Human Instrumental System – an externally representational cognition that separates subject and object. 两种观察者的根本区别还在于其世界显现方式： 和弦（调性）观察者 所见之宇宙，是一个基于和弦框架而展开的整体性场域。在此框架中，时空、 生命与精神共享同一和弦结构与数学模型，万象共振、层层对应，构成连续而自洽的整体。 非和弦（无调性）观察者 所见则是割裂的宇宙。在缺乏和弦框架的情况下，现象呈现为随机、孤立 的事件，整体被分解为离散的经验碎片，缺乏内在的调性与共鸣。 The fundamental difference between the two types of observers lies in their mode of world perception: 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 Overtone Sequence；泛音数列 图1-1.1、泛音频谱 Figure 1-1.1 Overtone spectrum 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——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=19=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. 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 Equal Temperament Sequence；平均律数列 公式：H^n-1*f（H= half-step= 12√2=1.059463，n=序数，f=频率） 首项指数 1-1=0，默认首项指数=0，可用：H^n*f 将平均律数列的指数放入集合：{-11，-10，-9，-8，-7，-6，-5，-4，-3，-2，-1， 0，1，2，3， 4，5，6，7，8，9，10，11 } mod 12，可以显示其数学结构并进行群运算。 Formula: H^n-1*f (H = half-step = 12√2 = 1.059463, n = ordinal number, f = frequency) The leading exponent 1-1 = 0. The default leading exponent is 0. You can use: H^n*f Put the exponents of the equal-tempered series into the set: {-11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} mod 12 to display its mathematical structure and perform group operations. 十二平均律的音高分布是严格的等比数列： fn=f0⋅2^n/12。 十二平均律形成半音阶，它既是一个和弦（无调性特征和弦），也是所有等比和弦的生成基础： 减七和弦（小三度等距，公比=H^3≈1.189207） 全音阶和弦（大二度等距，公比= H^2≈1.122462） 增三和弦（大三度等距，公比= H^4≈1.259921） The pitch distribution of the twelve-tone equal temperament is a strict geometric sequence: fn = f0 ⋅ 2^n/12. The twelve-tone equal temperament forms a chromatic scale, which is both a chord (an atonal characteristic chord) and the basis for generating all geometric chords: Diminished seventh chord (equal minor third interval, common ratio = H^3 ≈ 1.189207) Die-tone chord (equal major second interval, common ratio = H^2 ≈ 1.122462) Augmented triad (equal major third interval, common ratio = H^4 ≈ 1.259921) 等比和弦（geometric chords）的几何语义是大于一维的非线空间，是和弦空间的生成基础之一； 十二平均律虽来自数学，却契合几何法则。 The geometric semantics of geometric chords is a non-linear space greater than one dimension, which is one of the generation bases of chord space; although the twelve-tone equal temperament comes from mathematics, it conforms to the laws of geometry. 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 1-2. 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. 半音阶和弦（Chromatic chords）、公比=H≈1.059463，小二度（minor second）数列，{ 0，1， 2，3，4，5，6，7，8，9，10，11 } Chromatic chords, common ratio H ≈ 1.059463, minor second sequence: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 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），4、半音阶和 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), 4. Chromatic chords (membrane strings) * ◆=positive note, ●=negative note, color=color charge 等比和弦（Geometric chords）是不同音阶系统：七声音阶，爵士音阶，爵士五声音阶，无调性体 系的构成基础。 Geometric chords are the foundation of different scale systems: the heptatonic scale, the jazz scale, the jazz pentatonic scale, and the atonal system. Triad；三和弦 三和弦是非对称和弦，包含纯五度，大三度或小三度。纯五度是是其特征音程（不存在于等比和弦 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。 Triads + Geometric chords make up the scale, key, more on this later section. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 三和弦重叠等比和弦，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 traditional 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 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 2-2.± Note Distribution In Triads；三和弦中的±音符分布 三和弦（triad）由三个离散频率值组成，在音乐中分别称为：根音（Root）， 三度（Third）， 五度 （Fifth）本文仍沿用音乐中的术语。 A triad is composed of three discrete frequency values, which are called the root, third, and fifth in music. This article still uses the terminology in music. 三和弦又可分为大三和弦（Major triad）和小三和弦（Minor triad），这两种和弦的区别取决于它们 的根色与三度（Third）的音程，大三度（major third）为大三和弦，小三度（minor third）为小三和 弦，两种和弦在几何语义上有着重要的区别，在后面章节有详细的介绍。 Triads can be divided into major triads and minor triads. The difference between these two chords depends on their root color and the interval of the third. The major third is the major triad, and the minor third is the minor triad. The two chords have important differences in geometric semantics, which will be introduced in detail in the following chapters. 分别以 12 个色做根色（Root color），构成 24 个三和弦，12 个大三和弦，12 个小三和弦，包含了 所有三和弦的±音符分布形式。 Use 12 colors as the root color, respectively, to form 24 triads, 12 major triads, and 12 minor triads, including the ± note distribution of all triads. 图2-4.1：大三和弦表（菱形=+音符，圆形=-音符） Figure 2-4.1: Major chord table(Diamond=+note, circle=-note) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图2-4.2：小三和弦表（菱形=+音符，圆形=-音符） Figure 2-4.2: Minor chord table(Diamond=+note, circle=-note) 忽略表中的频率分布，保留正-负值分布，共有六种组合： Ignoring the frequency distribution in the table and retaining the positive-negative value distribution, there are six combinations: （+，+，+），（ -，-，-），（ -，-，+），（+，+，-），（ -，+，+），（+，-，-） 六种组合在和弦语义上有重要的区别，涉及：开弦，闭弦，正-负电荷等。 The six combinations have important differences in chord semantics, involving: open strings, closed strings, positive-negative charges, etc. 六种组合可以是大-小三和弦，这里涉及以下规则： The six combinations can be major-minor triads, where the following rules are involved: （1）、 +根三和弦（+，x，x）倾向生成大三和弦，-根三和弦（-，x，x）倾向生成小三和弦。 (1) + root triads (+, x, x) tend to generate major triads, while - root triads (-, x, x) tend to generate minor triads. （2）、 标准三和弦（Standard triads）：+根大三和弦（+，x，x）与 -根小三和弦（-，x，x）可充 当调系统中的主和弦。 (2) The positive root major triad (+, ±, ±) and the negative root minor triad (-, ±, ±) act as the main chords in the tuning system. （3）、非标准三和弦（Non-standard triads）：+根小三和弦（+，x，x）与-根大三和弦（-，x， x），不能充当调系统中的主和弦。 (3) Non-standard triads: + minor triad (+, x, x) and - major triad (-, x, x) cannot serve as the main chords in the key system. 标准三和弦又可分为两种： 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 There are two types of standard triads: 纯三和弦（pure triad），如：纯大三和弦（+，+，+），纯小三和弦（-， -， -）。 pure triad, such as pure major triad (+,+,+), pure minor triad (-, -, -). 混合三和弦（Mixed triad ）：混合大三和弦（+，x，-）；混合小三和弦（-，x，+）。 Mixed triad: Mixed major triad (+, x, x); Mixed minor triads (-, x, x). 两种标准三和弦在调群中涉及以下规则： The two standard triads involve the following rules in key groups: 纯三和弦（pure triad）在调群中充当主调的主和弦 A pure triad acts as the main chord of the main key in a key group 混合三和弦（Mixed triad）在调群中充当副调的主和弦。 Mixed triad are tonic chords that act as secondary keys in a key group. 上面规则适用于七声音阶系统，在爵士音阶系统中有一些区别，在后面相关章节分别介绍。 The above rules apply to the heptachord scale system, and there are some differences in the jazz scale system, which are described in the relevant sections later. 2-3.±Note Distribution In 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），4、半音阶和 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), 4. Chromatic chords (membrane strings) * ◆=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 positive-negative 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），5、半音阶和弦（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)，5. Chromatic chords (membrane strings) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, 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 Spectral coordinates: MOD12 group 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; non-line 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-dimensional volumes. Chord space is the result of line chords defining membrane chords, undefined membrane 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 These respectively represent the geometric duality of chordal time and chordal space. This mirror symmetry relationship indicates that time and space can be mutually mapped through geometric structures in the language of chords. (See: 1-3.1. Mirror Symmetry) Within a chordal package: Triads act as boundary operators, generating spacetime boundaries: Time dimension: Define temporal boundaries (starting point, ending point). Space dimension: Define spatial boundaries (contour lines, Facet lines). Geometric chords act as field filling: Through geometric frequency distributions (diminished seventh chords, whole-tone chords, augmented triads), they permeate the spacetime continuum inside and outside the boundaries, functioning similarly to the ether field in classical physics or the background field in quantum field theory. The chordal package (Chordal Package) can be formally defined as: Chordal Package=Triads (Boundary)+Geometric chords (Field Filling)Chordal Package=Triads (Boundary)+Geometric chords (Field Filling) Here, "+" denotes symmetry-breaking coupling, ultimately generating a stable chordal spacetime manifold. In the language of chords, chordal packages are also referred to as "keys"—including major keys, minor keys, diatonic scales, jazz scales, etc.—each expressing different spacetime meanings, which will be gradually introduced in later chapters. 4-1.Chord Space Packet ； 和弦空间包 一个和弦空间包必须包含两种和弦：线和弦（三和弦）与等比和弦（膜和弦），和弦空间包=线和弦 +导音膜和弦，线和弦构成轮廓线、分面线，产生空间定义（图-底关系等），膜和弦充满所有非线空 间，类似“以太”，和弦空间包是和弦空间的基本单元。 A chord space packet must contain two kinds of chords: line chords (triads) and Geometric chords (membrane chords), chord space packet = line chords + membrane chords, line chords form contour lines, Facet line, and produce space definitions (Figure-ground relationship, etc.), membrane chords fill all non-linear spaces, similar to "ether", chord space packet is the basic unit of chord space. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4.1、1、七声音阶和弦空间包；2-3、爵士音阶和弦空间包 Figure 4.1, 1. Heptachord scale chord space packet; 2-3. Jazz scale chord space packet 三和弦的几何语义是：线（开弦，闭弦），等比和弦（Geometric chords）的几何语义是：非线膜， 线和弦对膜和弦作边界定义（轮廓线，分面线），产生和弦空间包。 The geometric semantics of triads are: lines (open string, closed string), and the geometric semantics of Geometric chords are: non-linear membranes, line chords define boundaries (contours, Facet line) to membrane chords, resulting in Chord Space Packet. 一个完整的和弦空间包只含一个膜和弦，但通常需要两个线和弦：大三和弦（闭弦）与小三和弦 （开弦），分别构成轮廓线与分面（分形）线。 A complete chord space packet contains only one membrane chord, but usually requires two line chords: a major triad (closed string) and a minor triad (open string), which form the contour line and the facet (fractal) line respectively. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4.2、七声音阶 C大调-升f小调，大三和弦生成图形轮廓线，小三和弦生成分面线，减七和弦填 充所有 M维空间。 Figure 4.2. heptachord C major f-sharp, major triads generate figure contour lines, minor triads generate Facet line lines, and diminished 7th fill all M-dimensional spaces. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4.3、爵士音阶，升 f小调，大三和弦生成图形轮廓线，小三和弦生成分面线，全音阶和弦填充 所有非线空间。 Figure 4.3. Jazz scale f-sharp minor, major triads generate figure outlines, minor triads generate Facet line line, and diatonic chords fill all non-linear spaces. 4-1.2.Figure-Ground Relation ； 图-底关系 图-底关系（figure-ground relation）是空间知觉的基本模式，“背景空间”与“图形空间”是产生空 间知觉的必要条件；两种空间都与音符-和弦的正-负属性相关，正音符-和弦具有背景（远）倾向，负音 符-和弦具有图形（近）倾向，图-底关系与“景深”相关。 The figure-ground relation is the basic mode of spatial perception, and "background space" and "figure space" are necessary conditions for spatial perception; both spaces are related to the positivenegative properties of note-chords, and the positive Note-chords have background (far) tendencies, negative note-chords have figure (near) tendencies, and the figure-ground relationship is related to "depth of field". 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图4-2、七声音阶，升 f小调-C 大调图-底关系 Figure 4-2. Heptachord scale f-sharp minor,C major figure-ground relationship 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图-底关系包括：三和弦图-底关系与等比和弦图-底关系。 The figure-ground relationship includes: triad figure-ground relationship and geometric chord figureground relationship. 三和弦与图-底关系：图-底关系与三和弦相关，表现为：小调的图形（近）倾向，大调的背景 （远）倾向，（参见：2-4、和弦中的±音符规则；3-3、正-负闭弦与开弦）。 Triads and Figure-Ground Relations: The figure-ground relationship is related to triads and is manifested as: minor keys tend to have a figure (closer) tendency, while major keys tend to have a background (farther) tendency (see: 2-4, ± note rules in chords; 3-3, positive-negative closed strings and open strings). 等比和弦与图-底关系：等比和弦（Geometric chords）中的负音符具有图形（近）的倾向，正音符 具有背景（远）的倾向。两种音符分别构成正音符集合与负音符集合，具有相对独立性。 Geometric chords and figure-ground relationship: In geometric chords, negative notes tend to be more figure (near), while positive notes tend to be more background (far). The two types of notes form the positive and negative note sets respectively, and are relatively independent. 下面例图中包含两种图-底关系。 The following example diagram contains two figure-ground relationships. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图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。 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 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. 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），5、半音阶和弦（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)，5. Chromatic chords (membrane strings) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 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 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 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 semantic differences, which are also the main content of the following chapters. 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.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. 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. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图5-2.2、七声音阶，含平行大小调；C大调，降 e小调，f#小调，A大调 Figure 5-2.2. heptachord scale, including parallel major and minor scales; C major, E flat minor, F# minor, A major 绝对图底关系（figure-ground relation）可以包含相对图底关系（figure-ground relation），共同构 成空间系统：纯大调与纯小调构成绝对图底关系，纯大调与其关系小调，纯小调与其关系大调构成其中 的相对图-底关系。 Absolute figure-ground relations can include relative figure-ground relations, together forming a spatial system: pure major and pure minor constitute absolute figure-ground relations, while pure major and its relative minor, and pure minor and its relative major, constitute the relative figure-ground relations within it. 5-1.3.dim7 调群 完整的七声音阶空间系统包含两种图底关系，四个调，共享同一导音减七和弦：称之为：同导音减 七和弦的调群，或：dim7 调群，和弦系统共有三个 dim7 调群，分别以减七和弦中的音符命名：C 调 群，D 调群，E调群。 The complete heptachord scale space system contains two figure-ground relationships, four keys, sharing the same leading tone diminished seventh chord: it is called: key group with the same leading tone 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 diminished seventh chord, or: dim7 key group. There are three dim7 key groups in the chord system, named after the notes in the diminished seventh chord: C key group, D key group, and E key group. 图13-1.1、D，E，C调群 Figure 13-2.1, D，E，C keys group 5-2. Same Root Major Minor ； 同根大-小调 根音符相同的大-小三和弦构成同根大-小调（Same Root Major Minor），同根大-小调只用于在同调 中产生轮廓线与分面线，不产生图-底关系，其中的大三和弦生成轮廓线（闭弦），小三和弦生成分面线 （开弦）。 Major-minor triads with the Same Root note form the Same Root Major Minor, which is only used to produce contours and Facet line in the homology, and does not produce a figrue-ground relationship, where the major triads generate contours (closed strings) and the minor triads generate Facet line (open strings). 同根大-小调中，主和弦是标准三和弦。 In the same root major-minor key, the main chord is the standard triad. 图9-2.1、同根大-小三和弦，大-小调。 Figure 9-2.1, same root major - minor triad, major - minor. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-2.1、同根音符大-小三和弦，大-小调。 same root major - minor triad, major - minor. 图9-2.1、同根音符大-小三和弦，大-小调。 Figure 9-2.1, same root major - minor triad, major - minor. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 5-3、Solution ； 解决 七声音阶中，膜和弦具有寻找线和弦倾向，从而达到稳定，这一属性称作解决（solution）倾向。 膜和弦中各音符具有不同的解决倾向，与主和弦根音符为小二度关系的音符具有最强的解决倾向， 该音符称作：导音。 在图-底调群中，各调都包含导音，系统具有多个导音，由此产生图-底调群的系统特征。 In the heptatonic scale, the membrane chord has a tendency to seek resolution towards the line chord, thereby achieving stability. This property is known as the resolution tendency. Within the membrane chord, each note possesses a different resolution tendency. The note that has the strongest resolution tendency, being a minor second interval from the root note of the tonic chord, is called the leading tone. In the figure-ground tonality group, each key contains a leading tone, and the system has multiple leading tones, which gives rise to the systemic characteristics of the figure-ground tonality group. 5-4.Omit Chord ；省略和弦 省略减七和弦主要用于产生空间景深变化，无调性兼容性，跨音阶兼容性，常见的省略形式如下： The omitted diminished seventh chord is mainly used to produce changes in spatial depth of field, atonal compatibility, and inter-scale compatibility. Common forms of omission are as follows: 图5-4，减七和弦的常见省略形式 Figure 5-4, common ellipsis of the diminished 7th 1）省略正或负音符、减七和弦被省略正或负音符后，空间景深会发生改变——正音符具有背景 （远）倾向，负音符具有图形（近）倾向。 1) When the positive or negative notes are omitted, the spatial depth of field will change - the positive 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 notes have a background (far) tendency, the negative notes have a graphic (near) tendency. 下图中的减七和弦省略了正音符，空间系统系统表现出向前靠近的倾向。 The diminished 7th in the image below omits positive notes, and the spatial system system shows a tendency to approach forward. 图7-3、省略了正音符的减七和弦 2）导音增四度（leading note augmented fourth）是减七和弦，全音阶和弦共同省略形式，减七和 弦省略为导音增四度（leading note augmented fourth）音程时，七声音阶-爵士音阶的膜和弦没有区 别。 下图中的减七和弦（Diminished 7th）省略为增四度（augmented fourth）音程，七声音阶音阶的确 定性消失。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图7-4、减七和弦的省略形式：导音增四度（leading note augmented fourth） Figure 7-4. The omitted form of the Diminished 7th: leading note augmented fourth 3）省略三和弦、当七声音阶中的三和弦省略 1-2 音符后，其和弦语义的确定性降低，可以兼容更 多的空间状态。 When 1-2 notes are omitted for triads in the heptachord scale, the certainty of the chord semantics is reduced and more spatial states are compatible. 6.Heptachord T-D-S Triad；七声音阶 T-D-S 三和弦 前面介绍了七声音阶（heptachord）和弦包（调）的基础结构：主和弦+导音减七和弦，在主和弦 （tonic）的 5度音符上生成属和弦（dominant chord），4度音符上生成下属和弦（subordinate chord），系统中便有了三个三和弦，称作：T-D-S 三和弦，音乐理论中称为：正三和弦（Primary triad），用于表达调内分离图形与分面的亮度关系。 Earlier we introduced the basic structure of the heptachord chord package (key): tonic chord + diminished seventh chord. The dominant chord is generated on the 5th note of the tonic, and the 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 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。 The T-D-S luminance relation of major key expresses the relative figure of different luminance. The TD-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 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 ； 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. 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 #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。 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. 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 图8.4、{C#,Bb,G,E}，闭合-开放兼容图形 Figure 8.4, {C#,Bb,G,E}, closed-open compatible figure {C#,Bb,G,E}可表达轮廓线闭合图形，也可表达轮廓线开放图形，兼容两种闭合状态，我们将这种空 间特征称作：次闭合性。 {C#,Bb,G,E} can express contour closed figure and contour open figure, and is compatible with two Close states. We call this spatial feature: sub Close. 综合以上观察，对三个减七和弦的闭合性规则总结如下： Based on the above observations, the closure rules for the three diminished seventh chords are summarized as follows: 减七和弦 Diminished 7th 闭合倾向-稳定性 Closing tendency-stability {B,Ab,F,D}，B dim7 高；High {C#,Bb,G,E}，C# dim7 中；Medium, {A,F#,Eb,C}，A dim7 低；low ⚫ 三个减七和弦具有不同的闭合倾向，由此形成闭合倾向-稳定性层级，它在和弦空间中具有重 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 要意义。 ⚫ The three diminished seventh chords have different closing tendencies, thus forming a closing tendency-stability hierarchy, which is of great significance in the chord space. ⚫ 主-次秩序：空间系统同时存在三个减七和弦时，会依照减七和弦的闭合倾向-稳定性产生主-次 秩序，高-中-低对应：主-次-最次，形成自然解决倾向：由低向高解决。 ⚫ Major-minor order: When there are three diminished seventh chords in a spatial system at the same time, a major-minor order will be generated according to the closing tendency-stability of the diminished seventh chord, with high-middle-low corresponding to: major-minor-least, forming a natural solution tendency: from low to high. ⚫ 这一法则可投射到以其为导音膜和弦的三和弦，三和弦可以继承其导音减七和弦的闭合倾向， 即使在其导音减七和弦缺位的状态下。 ⚫ This rule can be projected to the triad with it as the leading membrane chord. The triad can inherit the closing tendency of its leading tone diminished seventh chord even when its leading tone diminished seventh chord is absent. ⚫ 在爵士音阶，无调性状态下，以上秩序失效，主次秩序可以发生逆转。 ⚫ In the jazz scale and atonal state, the above order becomes invalid and the primary and secondary order can be reversed. 8-2.The Close level of T-D-S ；T-D-S 的闭合级别 T-D-S 三和弦也包含闭合状态：主和弦（Tonic），属和弦（Dominant），下属和弦（Subdominant）， 都存在闭合状态差异，这种差异来自三和弦所属的导音减七和弦调群。 T-D-S triads also contain Close states: Tonic, Dominant, and Sub-dominant, all have Close state differences, which come from the leading diminished seventh chord group to which the triad belongs. T-D-S 三和弦所在的和弦包中，闭合性较高的图形处于主体地位，闭合性较低的图形处于从属地 位。 There are differences in Close between T-D-S triads, the figure with higher Close is in the dominant position, and the figure with lower Close is in the subordinate position. T-D-S 三和弦的闭合状态差异，以及由此产生的主体-从属关系与恒星，行星的秩序相关。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Close state differences of the T-D-S triad, and the resulting subject-subordination relationship is related to the order of stars, planets. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 9. Jazz Scale；爵士音阶 爵士音阶是弱调性系统，它屏蔽了七声音阶的部分和弦语义，并具有无调性兼容性，常见于一些现 代音乐形式。 The jazz scale is a weak tonality system, which shields part of the chord semantics of the heptachord scale and has atonal compatibility. It is common in some modern forms of music. 爵士音阶的特征和弦是全音阶和弦（Diatonic chord），其中包含正-负两个增三和弦（Augmented triad），三和弦+全音阶和弦构成爵士音阶和弦包，三和弦+增三和弦构成爵士五声音阶和弦包。 The characteristic chords of the jazz scale are the Diatonic chord, which contains two Augmented triads, positive and negative; triads + diatonic chords form the jazz scale chord package; triads + augmented triads form the Jazz pentatonic chord package. 图9-1、爵士音阶特征和弦，1、全音阶和弦（Diatonic chord）， 2、增三和弦（Augmented triad） （◆=正音符，●=负音符，色彩=色荷） Figure 9-1. Characteristic chords of the jazz Scale, 1. Diatonic chord, 2. Augmented triad (◆=+note, ●=-note) 爵士音阶的主要特征如下： The main features of the jazz Scale are as follows: ⚫ 爵士音阶由主和弦+导音等比和弦（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 figureground relation, and the constituent forms are: augmented fourth major-minor figure-ground relation and positive and negative augmented triad figure-ground relation respectively. 爵士音阶与七声音阶的图-底关系既有联系，也有区别，参阅：5-1. Figure-Ground Relation 图-底关 系。 The figure-ground relationship between the jazz scale and the heptatonic scale is both related and different. See: 5-1. Figure-Ground Relation. 爵士音阶中的图-底关系（figure-ground relation）由增四度大-小调群构成——两调的主音为增四度 （Augmented fourth）关系，共享同一个导音全音阶和弦（Leading note diatonic Chords），大调表达背 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 景，小调表达图形。 The absolute figure-ground relation in the jazz scale is composed of the augmented fourth majorminor group - the tonics of the two keys are in an augmented fourth relationship, sharing the same leading note diatonic chords, the major key expresses the background, and the minor key expresses the figure. 图9-1.1、爵士音阶中的增四度大-小调群 Figure 9-1.1. Augmented fourth major-minor group in jazz scales 爵士音阶的增四度大-小调及三和弦不区别相对图底关系与绝对图底关系，可用于两种图底关系。 The augmented fourth major-minor scale and triads of the jazz scale do not distinguish between relative figure-ground relationships and absolute figure-ground relationships, and can be used for both figure-ground relationships. 图9-1.3、爵士音阶 C大调，f#小调，绝对图-底关系 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Figure 9-1.3, jazz scale C major, f# minor, Absolute figure-ground relationship 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. 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9-1.5、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 图9-1.6、爵士音阶 C大调，升f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 9-1.6, 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 Figure 9-1.7, Jazz Scale C# Major, G Minor, Relative Figure-ground Relationship 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). 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. 图9-2.2.、同根大-小三和弦，大-小调。 Figure 9-2.2, same root major - minor triad, major - minor. 9-3. Augmented Triad ； 增三和弦 增三和弦可看作全音阶和弦的正-负音符集合，服从以下规则： An augmented triad can be viewed as a set of positive and negative notes for a diatonic chord, and it 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图9-5.3，爵士音阶 f#十一和弦 Figure 9-5.3, jazz scale f# eleventh chord 图9-5.4，爵士音阶 f#十三和弦 Figure 9-5.3, jazz scale f# eleventh chord 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 10.Atonal；无调性 无调性体系的特征和弦是半音阶和弦，向无彩色（噪音）解决。 The characteristic chords of the atonal system are chromatic chords that resolve to achromatic (noise). 基本和弦表：1-1、大三和弦（闭弦），1-2、小三和弦（开弦）,2、减七和弦（膜弦），3、全音阶和 弦（膜弦），4、增三和弦（膜弦），5、半音阶和弦（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)，5. Chromatic chords (membrane strings) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 无调性体系不含三和弦（开弦，闭弦），其特征和弦（半音阶）向和弦无彩色（噪音）解决，包 括：线性，非线性解决。不能形成调性和弦包。 Atonal systems do not contain triads (open strings, closed strings). Their characteristic chords (chromatic scales) resolve to chords with achromatic (noise) resolution, including linear and nonlinear resolutions. They cannot form tonal chord packages. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图10-1，无调性体系 Figure 10-1, Atonal System 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图10-2，无调性体系，省略形式 Figure 10-2, Atonal System, Abbreviated Form 图10-3，无彩色解决形式 Figure 10-3, Solution without color. 半音阶和弦越完整，无彩色解决倾向越强。半音阶和弦常用省略形式，削弱无调性（无彩色）倾 向，省略半音阶和弦仍需要保持半音阶形式。（参见：9-1.2，） The more complete a chromatic chord is, the stronger its tendency towards atonal resolution. Chromatic chords are often abbreviated to reduce their atonal (atonal) tendency; however, even when a chromatic chord is omitted, it is still necessary to maintain the chromatic form. See also: 9-1.2, overlapping chords; 9-4, lonely key. 非和弦（无调性）系统是和弦（调性）系统的反过程，它屏蔽了调性系统的语义逻辑，主要由亮度 变化来产生视觉空间。 和弦（调性）与非和弦（无调性）是不同的认知方式，甚至是不同的宇宙观。 The atonal (non-chordal) system is the reverse process of the chordal (tonal) system. It shields the semantic logic of the tonal system and primarily generates visual space through variations in brightness. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Chords (tonality) and atonal (non-chordal) systems represent different ways of cognition, and even different worldviews. 10-2、Figure-Ground Relationship；图底关系 无调性体系中只有等比和弦，服从以下规则： The atonal system contains only geometric chords, which follow these rules: 等比和弦与图-底关系：等比和弦（Geometric chords）中的负音符具有图形（近）的倾向，正音符 具有背景（远）的倾向。两种音符分别构成正音符集合与负音符集合，具有相对独立性。 Geometric chords and figure-ground relationship: In geometric chords, negative notes tend to be more figure (near), while positive notes tend to be more background (far). The two types of notes form the positive and negative note sets respectively, and are relatively independent. 10-3, Atonal Resolution of Jazz Scales；爵士音阶的无调性解决 爵士音阶具有一定的无调性兼容性， 主要表现在重叠和弦中，如：主七和弦，主九和弦，主 11 和 弦，主 13 和弦等。爵士音阶的重叠和弦最多可达到八个音符；其中包含了 1-4 个半音程，可视作爵士 音阶与无调性体系的中间形式。 参见：9-1.2，重叠和弦；9-4，孤调（Lonely key）。 Jazz scales possess a degree of atonal compatibility, primarily manifested in overlapping chords, such as the tonic seventh, ninth, eleventh, and thirteenth chords. Overlapping chords in jazz scales can reach up to eight notes, encompassing 1-4 semitones, and can be considered an intermediate form between jazz scales and the atonal system. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 11.Melody Of Color；色彩旋律 前面的讨论和弦语句是以“和弦”为单位，本章讨论的旋律语句则以音符（色）为单位，两者既有 联系，又有相对独立性。 The chord statement discussed above is in the unit of "chord", while the melodic statement discussed in this chapter is in the unit of note (color), which are both related and relatively independent. 旋律在音乐中表现为非同时组织，而在和弦绘画中则表现为同时性组织。 Melody is not synchronic organization in music, but synchronic organization in chord painting. 色彩旋律发生在一个空间包之内，不同空间包则视作不同的旋律段落。 Color melody occurs within a space packet, and different space packets are treated as different melodic paragraphs. 按旋律的语义作用，色彩旋律可分为三种形式：M-L 旋律，分面旋律，点旋律。 According to the semantic function of melody, color melody can be divided into three forms: M-L melody, faceted melody and dot melody. 11-1.M-L Melody；M-L 旋律 M-L 旋律是膜和弦+线和弦语句的省略形式，语句中的和弦被省略为音符，产生 M-L 旋律进行 （melodic progression）。 The M-L melody is an abbreviated form of the Membrane chords + line chord sentence. The chords in the sentence are omitted as notes, resulting in an M-L melody progression. M-L 旋律发生在膜和弦与线和弦之间，膜和弦具有寻找线和弦形成空间包的倾向，这种倾向称为： 膜和弦解决（solve）。 The M-L melody occurs between the Membrane chords and the line chord. The Membrane chords has a tendency to find the line chord to form a space packet. This tendency is called: Membrane chords solve. 在七声音阶（Heptachord）中，减七和弦（Diminished 7th）向主和弦解决（solve）。 In the Heptachord, the Diminished 7th is resolved to the tonic. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 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（root-note）、 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 图11.4、平均律色环 Figure 11.4, equal temperament color circle 分面旋律分为：正序旋律与反序旋律。 Faceted melody is divided into: Positive order melody and reverse order melody. 正序旋律：相对高频色在亮部，相对低频色在暗部。 Positive order melody: relatively high frequency colors are in the bright part, and relatively low frequency colors are in the dark part. 反序旋律：相对高频色在暗部，相对低频色在亮部。 Reverse melody: relatively high frequency colors are in the dark part, and relatively low frequency colors are in the bright part. 正序旋律具有图形（近）倾向，反序旋律具有背景（远）倾向，这一特征可表现在调性，无调性体 系中。 The positive sequence melody has a figure (near) tendency, and the reverse sequence melody has a background (far) tendency, which can be manifested in the tonality and atonal system. 调性系统中，正序旋律通常出现在构成图形的小调上，反序进行旋律通常出现在构成背景的大调 上，也出现可在同一个调中，表现相对图-底关系，见下图： In the tonal system, the Positive order melody usually appears on the minor key that constitutes the figure, and the reverse order melody usually appears on the major key that constitutes the background. It 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 spatial depth of field is generated, similar to music: pedal point, Vorhalt, anticipation. 图12.4、爵士音阶 A大调 Figure 12.4, Weak Tonal System A major 空间区域偏移通常发生在线和弦与膜和弦之间，其它形式有待观察。 The spatial region offset usually occurs between the online chord and the Membrane chords, other forms are to be seen. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 13. Multilayer Tone Group；多层调群 一个和弦空间系统包含多个和弦包（调），称为：调群，它是以和弦包（调）为单位的组织形式。 A chord space system contains multiple Chord packets (key), called: key group, which is an organizational form of Chord packets (key) as a unit. 和弦语言中包含多种调群：增四度大-小调（Augmented Fourth Major-Minor），平行大小调 （Parallel Major-Minor）， C-D-E 调群，T-D-S 调群，前两种共享同导音减七和弦（Leading note diminished 7th），是同层空间系统，称：同层调群，后两种包含多个导音减七和弦（Leading note diminished 7th），分别具有不同的闭合状态，是多层空间系统；称：多层调群。 The chord language includes many key groups: Augmented Fourth Major-Minor, Parallel Major-Minor, C-D-E key group, T-D-S key group. The first two share the same leading note diminished 7th chord and are the same-layer space system, called: same-layer key group. The last two contain multiple leading note diminished 7th chords, each with different Close states, and are multi-layer space systems, called: multilayer key groups. 多层调群（Key group）存在主-次秩序。 The multi-layer Key group has a primary-secondary order. 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 fractal-facet relationship of different brightness in the spatial system; it has a higher certainty than the T-D-S triad. T-D-S 调群是七声音阶（heptachord）调群，其中的属和弦（Dominant）、下属和弦 （Subdominant）分别转为属调（dominant key）、下属调（Subdominant Key）。 The T-D-S key group is a heptachord Key group, in which the Dominant and Subdominant chords are converted to the dominant key and Subdominant Key respectively. 图13-2.T-D-S 调集团 ； Figure 13-2.T-D-S tone group; 大调的属调（dominant key）、下属调（Subdominant Key）表达不同亮度的分离图形；小调的属调 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 （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 chord-subdominant chord + leading tone diminished seventh chord. 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 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13-2.4. 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-DE 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: 导音减七和弦 Leading note Diminished 7th 天体 Celestial Bodies 闭合性权重 Close Weight 对称生命 Symmetrical Life {B,Ab,F,D} 星系核 Galactic nucleus 高 High 神 God {C#,Bb,G,E} 恒星系 Star system 中 Medium 人 Man {A,F#,Eb,C} 行星，星尘 低 魔 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 Planets, stardust Low Demon 恒星系（太阳系）模型 Model of the star system (solar system) 导音减七和弦 天体 Celestial Bodies 闭合性权重 Close Weight 对称生命 Symmetrical Life {B,Ab,F,D} 恒星 Star 高 High 神 God {C#,Bb,G,E} 恒星系背景 Star system background 中 Medium 人 Man {A,F#,Eb,C} 行星 planet 低 Low 魔 Demon 以上结果来自和弦观察，方法包括：音乐，绘画（和弦时空），经络感知。 The above results are from chord observation, and the methods include: music, painting (chord time and space), and meridian perception. 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 packets. 图15-3.2 与下面的照片比较。 Figure 15-3.2 is compared with the following photos. 图14-2.3、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.3. Iron atoms taken by aperture grating microscope (picture from Internet) 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) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 14-2.1.Electric Charge And Magnetic Charge；电荷与磁荷 音符具有正负属性，由此产生和弦的正负属性，正和弦的根音符为正音符，负和弦的根音符为负音 符，通常：正和弦为大三和弦（闭弦），负和弦为小三和弦（开弦）。见图：14-2.1 The notes have positive and negative properties, resulting in the positive and negative properties of the chord, the root note of the positive chord is a positive note, the root note of the negative chord is a negative note, generally: the positive chord is a major triad (closed string), and the negative chord is a minor triad (open string). See Figure 14-2.1 【电荷】下图和弦包中包括正和弦（大三和弦，闭弦）与 负和弦（小三和弦，开弦），闭弦构成轮 廓线，开弦构成分面线，膜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 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 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, closed 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 string), showing a tendency to exclude each other. 上面的视觉实验中，和弦空间包的表现类似电场效应，两种和弦之间存在库伦力，合理的解释是： 正-负电荷来自正-负和弦。 In the above visual experiment, the chord space package behaves like an electric field effect, there is a coulomb force between the two chords, and the reasonable explanation is that the positive-negative charge comes from the positive-negative chord. 大三和弦（闭弦、正电荷）用于构成轮廓线，封闭、束缚空间包，不能脱离和弦空间包，小三和弦 （开弦、负电荷）可以自由的出现在和弦空间包的内-外。 Positive major triads (closed strings, positive charges) are used to form contour lines, closed and bound space packet, and cannot be separated fromembrane chords space packet, minor triads (open strings, negative charges) can freely appear inside-outside of the chord space packet . 【磁荷】爵士音阶和弦包的膜和弦是全音阶和弦，全音阶和弦包含六个音符，各音符分别具有正-负 属性与色荷，所有色荷混合产生白色。 【Magnetic charge】The membrane chord of the chord packet of the jazz Scale is the diatonic chord. 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 negative notes 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 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. 和弦包成分及作用： 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 package components and functions: 和弦包成分 Chord Packet Components 几何语义 Geometric semantics 物理属性 Physical properties 可能的物理含义 Possible physical implications 音符 Note 点 Point ±，色荷 ±, Color charge 基本粒子 Elementary particles 等比和弦 Geometric chords 膜弦 Membrane strings 磁场，±磁荷 Magnetic field, ±magnetic charge 磁子，夸克 Magnetons, quarks 大三和弦 Major 闭弦 Closed String 正电荷 Positive Charge 束缚和弦包，强力 Bound Chord Packet, Powerful 小三和弦 Minor 开弦 Open String 负电荷 Negative charge 分面，增维 Faceting, adding dimension 无彩色 Neutral colour 线，膜 Line, Membrane 中性 Neutral 待观察 To be seen 上面讨论的只是和弦基本形式，和弦还有许多变化形式，包括正开弦，负闭弦等，在本书其它章节 中有介绍。 What is discussed above is only the basic form of chords. There are many variations of chords, including positive open chords, negative closed chords, etc., which are introduced in other chapters of this book. 14-2.2.Chord Packet Spectrum；和弦包光谱 和弦空间的基本单位为和弦空间包，各调的和弦空间包都有其特征光谱。 The basic unit of chord space is the chord space packet, and the chord space packet of each key has its characteristic spectrum. 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14-2.13：C大调、f#小调和弦包特征光谱 Figure 14-2.13: C major, f# minor chord packet characteristic spectrum 将和弦空间包的特征光谱与原子光谱进行比较，或是个好主意。 It may be a good idea to compare the characteristic spectrum of the chord space Packet with the spectrum of atoms. 图14-2.14、元素光谱 Figure 14-2.14, element spectrum （计算方法见：和弦（量子）数学） (For the calculation method, see: 1. Chord Mathematical; Chord Math) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Pure time vs. pure space: Bach and Monet’s comparison In Bach’s music, we can only observe the time changes of chords and melodies, and cannot perceive any geometric shapes or positions. In the pure time state, spatial properties cannot be observed, and spatial positions are in a superposition state. If you want to observe spatial properties in Bach’s music, the only way is to convert chord time into its mirror-symmetric form - chord space. 结论：巴赫的音乐是和弦时间，莫奈的绘画是和弦空间。在纯时间状态下，空间位置的概念是无意 义的，相当于所有位置的叠加。 Conclusion: Bach’s music is chord time, and Monet’s paintings are chord space. In the pure time state, the concept of spatial position is meaningless, which is equivalent to the superposition of all positions. 图14-3.3、巴赫手稿 Figure 14-4.2. Bach manuscript 3. 莲花的时空二相性：莫奈 vs. 莫扎特 莫奈的莲花（绘画）是空间表达，具有定域性，即它不能同时出现在卢浮宫和奥赛博物馆。 莫扎特的莲花（音乐）是时间表达，具有非定域性，可以处于任意空间位置的叠加态，包括卢浮宫 和奥赛。 3. The space-time duality of the lotus: Monet vs. Mozart 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Monet's lotus (painting) is a spatial expression with locality, that is, it cannot appear in the Louvre and the Musee d'Orsay at the same time. Mozart's lotus (music) is a temporal expression with non-locality, and can be in a superposition state of any spatial position, including the Louvre and the Musee d'Orsay. 这意味着，莲花同时具有莫奈（空间）-莫扎特（时间）二相性，类似于波粒二象性： 作为绘画（莫奈）时，它是粒子，位置固定。 作为音乐（莫扎特）时，它是波动，位置可叠加。 结论： 莲花在“莫奈-莫扎特”二相性中展现了时空结构的波粒二象性。 从和弦时间到和弦空间的转换，与量子测量导致波函数坍缩的过程类似。 This means that the lotus has both the Monet (space) and Mozart (time) duality, similar to the waveparticle duality: As a painting (Monet), it is a particle with a fixed position. As music (Mozart), it is a wave with superimposable positions. Conclusion: The lotus shows the wave-particle duality of the space-time structure in the "Monet-Mozart" duality. The conversion from chord time to chord space is similar to the process of wave function collapse caused by quantum measurement. 图14-3.4：莫奈-莫扎特二相性。 Figure 14-3.4: Monet-Mozart duality. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 14-4.Chord Spacetime Concept Framework；和弦时空概念框架 和弦时空由和弦（量子化频谱）构成，时间与空间是能量的不同形式，由此有： E=t+s 和弦时空中存在 纯时间（s=0）与纯空间（t=0），这需要与其适应的时空框架。 时间能量（T）：非定域性，类似量子态，不依赖外部时钟。 空间能量（S）：定域性，具有几何属性，如形状、位置等，质量依赖定域性。 Chord spacetime is composed of chords (quantized spectrum). Time and space are different forms of energy, so: E=t+s In chord spacetime, there is pure time (s=0) and pure space (t=0), which requires a spacetime framework that adapts to it. Time energy (T): non-local, similar to quantum state, does not depend on external clocks. Space energy (S): local, has geometric properties, such as shape, position, etc., and quality depends on locality. 1、时间与空间的互补关系： 设和弦时-空的总能量归一化为 1，则： S+T=1 其中： S 代表和弦空间的能量占比。 T 代表和弦时间的能量占比。 当 S=0（纯时间）时，无空间信息，时间完全非定域。 当 T=0（纯空间）时，无时间信息，空间完全定域。 结论：时间和空间是互补变量，它们的分布决定了和弦时空的性质。 1.The complementary relationship between time and space: Assume that the total energy of chord space-time is normalized to 1, then: S+T=1 Where: S represents the energy proportion of chord space. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 T represents the energy proportion of chord time. When S=0 (pure time), there is no spatial information and time is completely non-local. When T=0 (pure space), there is no time information and space is completely local. Conclusion: Time and space are complementary variables, and their distribution determines the properties of chord space-time. 2. 速度的定义：由于速度是时间（非定域性）与空间（定域性）的叠加，时间能与空间能的比值 v=T/S+T=T 由于 S+T=1，我们有： v=1−S 这表明： 当 S=0（纯时间），v=1（无空间状态，时间完全非定域）。 当 T=0（纯空间），v=0（无时间状态，空间完全定域）。 速度 v 是时间能量的占比，独立于外部参考系，仅由和弦时空内部状态决定。 结论： 速度 v 不是外部测量的运动速度，而是时间能量的占比。 在和弦时空中，时间能量越高（越非定域），速度越大；空间能量越高（越定域），速度越小。 这类似于量子力学中的“不确定性关系”——时间越模糊，空间信息越清晰，反之亦然。 2. Definition of speed: Since speed is the superposition of time (non-locality) and space (locality), the ratio of time energy to space energy v=T/S+T=T Since S+T=1, we have: v=1−S This shows that: When S=0 (pure time), v=1 (no space state, time is completely non-local). When T=0 (pure space), v=0 (no time state, space is completely local). Speed v is the proportion of time energy, independent of the external reference system, and only determined by the internal state of the chord spacetime. Conclusion: 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Speed v is not the speed of movement measured externally, but the proportion of time energy. In chord spacetime, the higher the time energy (the more non-local), the greater the speed; the higher the space energy (the more local), the smaller the speed. This is similar to the "uncertainty relationship" in quantum mechanics-the more vague the time, the clearer the spatial information, and vice versa. 3. 和弦时空的不连续性 和弦时间（T）与和弦空间（S）互为反和弦（镜像对称），可数学转换。 在纯时间中（S=0），空间信息完全消失。 在纯空间中（T=0），时间信息完全消失。 这表明： 和弦时空可以是不连续的，即时间和空间可以在某些状态下完全分离。 当 S→0 或 T→0 时，和弦时空表现出类似“量子跃迁”的行为，即从一种完全状态跳跃到另一种完 全状态，而不是连续变化。 3. Discontinuity of chord spacetime Chord time (T) and chord space (S) are antichords (mirror symmetry) and can be mathematically transformed. In pure time (S=0), spatial information disappears completely. In pure space (T=0), time information disappears completely. This shows that: Chord spacetime can be discontinuous, that is, time and space can be completely separated in certain states. When S→0 or T→0, chord spacetime exhibits a behavior similar to a "quantum jump", that is, jumping from one complete state to another complete state, rather than changing continuously. 4. 质量的测量问题 时间无法测量质量， 质量必须在定域的空间状态（S>0）下才能被测量。 在纯时间状态（S=0）下，质量无法定义，因为没有空间参考。 质量仅能在具有几何结构的区域内被测量，这意味着质量是空间定域性的表现。 数学表达： 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 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 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。 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 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, 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。 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. ± 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). 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 15.Chord Biology；和弦生命 人类有两种生命观察者：和弦（调性）观察者与非和弦（无调性）观察者，分别观察两种生命形 式：和弦包（量子化频谱，场）与生物体（细胞，分子等），生命是两者的二层结构。 Humans have two types of life observers: chord (tonal) observers and non-chord (atonal) observers. They respectively observe two types of life forms: chord packages (quantized spectra, fields) and organisms (cells, molecules, etc.). Life is the two-layer structure of these two types. 在人体中，和弦（chord）表现为经络（或脉轮）系统。初步观察表明，十二经络系统展现受激频 谱响应，其频率分布可近似为几何级数： fn=H^n⋅f0，其中 H=2^(1/12)≈1.059463，n∈Z 该式通过对数变换可切换为泛音频线性谱 ( n f )，并与量子化假设 ( n f h )（能量离散结构）数学一 致。 这暗示音乐（时间域）、绘画（空间域）、经络（生命域）及量子化假设共享统一的离散数学框架。 In the human body, chords manifest as a meridian (or chakra) system. Preliminary observations indicate that the twelve meridian systems exhibit an excited spectral response, the frequency distribution of which can be approximated as a geometric series: fn=H^n⋅f0, where H=2^(1/12)≈1.059463, n∈Z. This equation can be transformed into a linear overtone spectrum (nf) through logarithmic transformation, and is mathematically consistent with the quantization hypothesis (nfh) (discrete energy structure). This suggests that music (temporal domain), painting (spatial domain), meridians (life domain), and the quantization hypothesis share a unified discrete mathematical framework. 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），5、半音阶和弦（膜弦） 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 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)，5. Chromatic chords (membrane strings) Chord spectrum formula: n*f, H^n*f, (H=1.059463, n∈Z) Symbols: ◆=+ note, ●=- note, note color = color charge Spectral coordinates: MOD12 group 关键词：和弦生物学，经络，中医，频谱 Keywords: Chord Biology, Meridians, Traditional Chinese Medicine, Spectrum 5-1.Qualitative And Dimensional；定性与量纲 十二正经（Twelve regular meridians）是经络系统的主体，每一经络都具有特征频率与正-负（阴阳）属性，这是本节的要点。 Twelve regular meridians are the main body of the meridian system. Each meridian has a characteristic frequency and positive-negative attributes. This is the main point of this section. 本文数据来自对人体经络系统（和弦编码系统）的自观察：经络对乐音-色光的受激反应；不同的频 率的乐音-色光在不同经络上诱发受激反应，表现为经络线路区域出现相应体觉——循经传感 （Propagated sensation along the channels），特定经络的受激反应与乐音-色光的频率相关。 The data in this article comes from the Self-observation of the human body meridian system (chord coding system): the stimulated response of the meridian to the music tone-color light; the different frequency of the music-color light induces the stimulated response on the different meridians, which is expressed as the meridian Corresponding somatosensory emerges in the line area—Propagated sensation along the channels. The stimulated response of a specific meridian is related to the frequency of music tone-color light. 上述观察得到如下结果： The above observations have the following results: