Chord Spacetime

和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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、Chord Spacetime;和弦时空 24 届世界哲学大会会议论文 Papers of the of 24th World Congress of Philosophy Xiaohong Li；李晓虹 时空是宇宙的一致性结构，是一切现象的共同生成域。 Spacetime is the consistent structure of the universe and the common domain of generation of all phenomena. 人类有两类时空观察者：和弦（调性）观察者与非和弦（无调性）观察者，分别观察到两种时空： Humans have two types of spacetime observers: chordal (tonal) observers and non-chordal (atonal) observers, who observe two different types of spacetime respectively: 和弦（调性）时空：以量子化频谱为编码结构，映射到时空语义集合，生成和弦时空场——时空被 量子化；音乐（时间域）、绘画（空间域）是其常见形式。 非和弦（无调性）时空：屏蔽了时空的和弦结构，只保留几何（图-底）与运动的纯粹关系性描 述，从外部参考系统（如时钟、尺子、参照物）获得定量，常用于经典物理学框架中，也是日常的时空 经验。 Chord (tonal) spacetime: Encoded with a quantized spectrum, it maps to a set of spacetime semantics, generating a chordal spacetime field—spacetime is quantized; music (time domain) and painting (spatial domain) are common forms. Non-chord (atonal) spacetime: It shields the chordal structure of spacetime, retaining only purely relational descriptions of geometry (figure-ground) and motion. Quantitative information is obtained from external reference systems (such as clocks, rulers, reference objects), and is often used within the framework of classical physics, as well as in everyday spacetime experience. 先验的频谱结构：和弦频谱与能量量子本质相通，均以一个基准频率 f 为单位，在整数 n 的调控下 生成一组离散的频率/能量结构： 泛音频谱公式：n*f ，N∈Z，f=频率 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 量子化假设：n*f*h（h=6.626×10^−34）N∈Z 两者在数学结构上呈现高度一致性。 这种 n 调控的离散性是生成主要和弦的基础。例如： 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。 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。 The a priori spectral structure: Chord spectra and energy quanta are essentially interconnected, both using a reference frequency *f* as the unit, and generating a discrete frequency/energy structure under the control of an integer *n*: Overtone spectrum formula: *n*f, N∈Z, *f* = frequency Quantization assumption: *n*f*h (*h* = 6.626 × 10^−34), N∈Z Both exhibit a high degree of consistency in mathematical structure. This discreteness of *n* control is the basis for generating major chords. For example: *n=1-6=major triad, *n=1-7=major seventh chord, *n=1-9=major ninth chord, *n=1-11=major eleventh chord. Overtones are one-dimensional oscillation modes; oscillation modes larger than one dimension involve equal temperament: (1.059463)^n · *f*, and the two modes can switch. By switching n to (1.059463)^n and introducing an exponential quantized energy level: Eₙ=h·1.059463^{n}·f₀, a systematic generation of chords can be achieved through the structure of the modulo 12 group ℤ₁₂. 因此：和弦结构并非文化建构，而是量子化振动体系的普遍数学属性。此属性在声学、光学、膜-弦 理论、固体物理、原子跃迁谱等众多领域均得到验证。 Therefore: chord structures are not a cultural construct, but a universal mathematical property of quantized vibration systems. This property has been verified in many fields, including acoustics, optics, membrane-string theory, solid-state physics, and atomic transition spectra. 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 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 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，类似波粒二象性。 Spatiotemporal duality: Chord time and chord spatial mirror symmetry: {-7, -4, 0} ↔ {0, 4, 7} mod 12 (mutual inversion chords, inversion keys), mathematically transformable; space has locality, time has non-locality, jointly manifesting as spatiotemporal duality, similar to wave-particle duality. 和弦几何：和弦编码（量子化频谱）包含几何语义：开弦，闭弦，膜弦，可生成所有空间状态，也 是绘画空间的生成基础。 Chord geometry: Chord encoding (quantized spectrum) contains geometric semantics: open strings, closed strings, membrane strings, which can generate all spatial states and are also the basis for the generation of painting space. 和弦是先验的量子化时空结构，音乐，绘画是其常见现象。 Chords are a priori quantized spacetime structures, and music and painting are common examples of them. 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 关键词 ； Keywords：和弦时空、量子化、和弦场、音乐、绘画、电磁场、弦理论 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Chord spacetime, quantization, chord field, music, painting, electromagnetic field, string theory *Chord Painting*: A Visual Mapping and Experimental Foundation of Chord Space; 《和弦绘画》：和弦空间的视觉映射与实验基础 《和弦绘画》是和弦语言体系在空间几何中的视觉映射与实验基础。它揭示出一个事实：绘画中的 离散色彩分布与形态组织，本质上揭示了和弦几何（Chord Geometry）的先验空间秩序，这种结构同样 存在于欧几里得几何与膜-弦理论的深层架构中。 *Chord Painting* is a visual mapping and experimental foundation of the chord language system within spatial geometry. It reveals that the discrete color distribution and morphological organization in painting essentially reveal the a priori spatial order of chord geometry, a structure that also exists within the deep framework of Euclidean geometry and membrane-string theory. 核心机制：时空镜像对称 和弦编码（量子化频谱）是时空生成的统一基底：它在时间域展开为音乐，在空间域凝结为绘画。 两者展现出内在的镜像对称关系：-7,-4,0 ↔0,4,7 (mod 12)。这种对称性使得音乐与绘画成为同一和弦系 统的两种展开方式。 Core Mechanism: Spacetime Mirror Symmetry Chord encoding (quantized spectrum) is the unified basis for spacetime generation: it unfolds as music in the time domain and condenses into painting in the spatial domain. The two exhibit an inherent mirror symmetry: -7, -4, 0 ↔ 0, 4, 7 (mod 12). This symmetry makes music and painting two ways of unfolding the same chord system. 和弦编码的几何语义 和弦编码不仅描述频率比例，也携带几何语义（弦），从而决定空间结构： 开弦（Open String）：对应小三和弦 (−7,−3,0) mod 12，为分面线结构； 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）：对应对称和弦（Symmetrical Chords），如减七 (0,3,6,9)、全音阶 (0,2,4,6,8,10)、增三 (0,4,8)，半音阶和弦（0,1,2,3,4,5,6,7,8,9,10,11）mod12 代表非线性空间的连续面。 The Geometric Semantics of Chord Encoding Chord encoding not only describes frequency ratios but also carries geometric semantics (strings), 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 thus determining the spatial structure: Open String: Corresponds to a minor triad (−7,−3,0) mod 12, representing a faceted structure; Closed String: Corresponds to a major triad (−7,−4,0) mod 12, representing a contour structure; Membrane String: Corresponds to symmetrical chords, such as diminished seventh (0,3,6,9), whole tone (0,2,4,6,8,10), augmented third (0,4,8), and chromatic chords (0,1,2,3,4,5,6,7,8,9,10,11) mod 12, representing continuous surfaces in nonlinear space. 和弦几何框架 三和弦（开弦与闭弦）定义了对称和弦（膜弦）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。 Chord Geometry Framework: Triads (open and closed chords) define the boundaries of symmetrical chords (membrane strings), i.e., the generating lines of space. Thus, the chord geometry framework is established: the geometric semantics of a chord (the string) determines the spatial structure, while the spectral semantics of a chord (the chord itself) defines its tonal relationships. Together, they constitute the Chord Space—a unified structural field connecting music and painting. 实验验证 这些结果并非理论假设，而源自于绘画中的独立观察与实验。在色彩的离散分布、形态的空间排列 中，可以反复验证上述和弦几何特征。因此，《和弦绘画》不仅是一部艺术专著，更是一份关于和弦空 间的实验报告。 它展示了如何从视觉中测得音乐的几何结构，如何以绘画为观测仪器，揭示生命与宇宙的调性秩 序。绘画在此被重新定义：它不再是主观的感知再现，而是和弦结构的可见生成。 每一幅作品，都是一次频谱的空间展开；每一条线、每一个色面，都是和弦在时空中的几何显现。 《和弦绘画》由此成为和弦语言体系的支柱之一——它提供了观测、验证与应用的可视基础，让和弦从 音乐的时间流中，转化为绘画的空间形。 Experimental Verification These results are not theoretical assumptions, but rather stem from independent observation and experimentation in painting. The discrete distribution of color and the spatial arrangement of forms 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 repeatedly verify the aforementioned chordal geometric characteristics. Therefore, *Chord Painting* is not only an art monograph, but also an experimental report on chordal space. It demonstrates how to measure the geometric structure of music visually, and how to use painting as an observational instrument to reveal the tonal order of life and the universe. Painting is redefined here: it is no longer a subjective representation of perception, but a visible generation of chordal structures. Each work is a spatial unfolding of the spectrum; every line, every color plane, is a geometric manifestation of a chord in space and time. *Chord Painting* thus becomes one of the pillars of the chordal language system—it provides a visual foundation for observation, verification, and application, allowing chords to transform from the temporal flow of music into the spatial form of painting. Li, X. H. (2020). Chord Painting. ResearchGate. https://www.researchgate.net/publication/340492620_Chord_Painting Li, X. H. (2024). Chord Language. Zenodo. https://zenodo.org/records/11817631 14-2.Chord Packet；和弦包 和弦空间由和弦表达，基本单元是：和弦空间包（调），在前面章节已有介绍，本节主要讨论和弦 空间包的物理含义。 The chord space is expressed by chords, and its basic unit is the chord space package (key), which has been introduced in the previous chapter. This section mainly discusses the physical meaning of the chord space package. 本章的讨论默认采用爵士音阶，下面分析一个典型的和弦空间包。 The discussion in this chapter uses the jazz Scale by default, and a typical chord space package is analyzed below. 三和弦（开弦，闭弦）定义全音阶和弦（膜和弦）的边界（轮廓线，分面线等），生成爵士音阶的 和弦空间包，下面以 C大调，F#小调为例： Triads (open chords, closed chords) define the boundaries (contours, Facet line, etc.) of diatonic chords (membrane chords), and generate the chord space packet of the jazz Scale. The following takes C 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 major and F# minor as examples: 图14-2.1、爵士音阶和弦包：1、C大三和弦（闭弦），2、F#小三和弦（开弦），3、全音阶和弦 （膜弦）（◆=正音符，●=负音符，色彩=色荷） Figure 14-2.1, jazz Scale chord package: 1,C major triad (closed string), 2,F# minor triad (open string), 3,diatonic chord (membrane string) (◆=positive note, ●=negative note, color=color charge) 图14-2.2、爵士音阶，C大调，f#小调空间包 Figure 14-2.2, jazz Scale C major ,f# minor space packet 实验 1：C 大三和弦（闭弦），构成了图形的闭合轮廓线，全音阶和弦（膜弦）填充所有非线空间， 包括图形与背景。 Experiment 1: The C major triad (closed string) forms the closed contour of the figure, and the diatonic chord (membrane string) fills all non-linear Spaces, including the figure and background. 空间包的轮廓线由大三和弦（闭弦）构成，用于束缚空间包，轮廓线（闭弦）的内部由全音阶和弦 （膜弦）充实，线和弦与膜和弦分别构成和弦空间包的外层与内核。 The contour of the space packet is composed of major triads (closed strings), which are used to bind 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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 space packet. The interior of the contour line (closed strings) is enriched by diatonic chords (membrane strings), and the line chord and membrane chord form the outer and inner core of the chord space packet respectively. 和弦包是和弦时空的基本单位；那么原子，星体是和弦包吗？合理的回答是：如果原子，星体是和 弦时空中的空间单位，其形式就只能是和弦包。 The chord packet is the basic unit of chord space-time ; So are atoms, stars a chord packet? The reasonable answer is that if atoms and stars are spatial units in chord space-time, their form can only be chord packets. 图15-3.2 与下面的照片比较。 Figure 15-3.2 is compared with the following photos. 图14-2.3、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.3. Iron atoms taken by aperture grating microscope (picture from Internet) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-2.4、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.4. Iron atoms taken by aperture grating microscope (picture from Internet) 14-2.1.Electric Charge And Magnetic Charge；电荷与磁荷 音符具有正负属性，由此产生和弦的正负属性，正和弦的根音符为正音符，负和弦的根音符为负音 符，通常：正和弦为大三和弦（闭弦），负和弦为小三和弦（开弦）。见图：14-2.1 The notes have positive and negative properties, resulting in the positive and negative properties of the chord, the root note of the positive chord is a positive note, the root note of the negative chord is a negative note, generally: the positive chord is a major triad (closed string), and the negative chord is a minor triad (open string). See Figure 14-2.1 【电荷】下图和弦包中包括正和弦（大三和弦，闭弦）与 负和弦（小三和弦，开弦），闭弦构成轮 廓线，开弦构成分面线，膜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. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 和弦包成分及作用： 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 对称和弦 Symmetrical 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 14-2.3. Chord Packet Interaction；和弦包相互作用 在和弦时空中，所有空间作用都是和弦的作用，下面讨论闭合和弦包之间的相互作用。 In chord spacetime, all spatial actions are actions of chords. The interactions between closed chord packet are discussed below. 在和弦时空中，闭合和弦包之间的相互作用包含两类：结合（引力）与分离（斥力），二者皆源于 大三和弦（闭弦）的结构张力。闭弦向内表现为结合作用，向外表现为分离作用。其频谱为离散集 {0, 4, 7} mod12，其结构具有正曲率（K>0），若屏蔽和弦，可视作纯粹几何效应。 In chord spacetime, the interactions between closed chord packages include two types: binding force (gravity) and separation force (repulsion), both of which originate from the structural tension of the major triad (closed string). The closed string behaves as a binding effect inward and as a separation effect outward. Its spectrum is a discrete set {0, 4, 7} mod12, and its structure has positive curvature (K>0). If the chord is shielded, it can be regarded as a pure geometric effect. 闭弦通常成对出现在图-底关系的背景侧与图形侧，结合（引力）与分离（斥力）由闭弦的空间路径 控制，使和弦包既保持完整，又相互联系。 Closed strings usually appear in pairs on the background and figure sides of the figure-ground relationship, and the combination (attraction) and separation (repulsion) are controlled by the spatial path of the closed strings, so that the chord packages remain complete and interconnected. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-5.1、闭弦，开弦，膜弦的空间作用 Figure 14-5.1. The space effect of closed strings, open strings, and membrane strings 空间相互作用有两种方式：电磁作用与非电磁作用：和弦（调性）空间的相互作用是闭弦（正电 子），开弦（负电子），膜弦（磁场）的作用，是电磁作用；非和弦（无调性）空间不含闭弦（正电 子）、开弦（负电子），磁极，是非电磁作用。 There are two ways of space interaction: electromagnetic and non-electromagnetic interaction: Chord (tonality) Space interaction is closed string (positron), open string (negative electron), membrane string (magnetic field), is electromagnetic action; Non-chord (atonal) space does not contain closed strings (positrons), open strings (negative electrons), magnetic poles, and non-electromagnetic interactions. 图14-5.2、屏蔽和弦后的无调性空间作用 Figure 14-5.2: Atonal spatial effect after shielding chords 空间相互作用包括七声音阶与爵士音阶两种方式，七声音阶和弦包用于生命、天体表达，是时空的 宏观形式。 Spatial interaction includes two modes: the heptachord and the jazz scale. The heptachord and chord package are used to express life and celestial bodies and are the macroscopic form of space-time. 在七声音阶中，和弦空间包的结合力与闭合梯度相关，并由此产生空间的主-次秩序，解决倾向，引 力中心。参见：8.Close;闭合性，13.Multi-Layer Key Group;多层调群。 In the heptachord, the cohesion of the chord space package is related to the Close gradient, which 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 produces the major-minor order of space, the tendency of resolution, and the center of gravity. See: 8. Close, 13. Multi-Layer Key Group. 和弦包相互作用（引力，斥力等），涉及调内，调群，三和弦，重叠和弦，以及不同音阶系统等， 具有多样性，复杂性，涉及对不同和弦结构的具体分析。 The chords package interactions (attraction, repulsion, etc.), involving intra-key, key groups, triads, overlapping chords, and different scale systems, etc., are diverse and complex, and involve specific analysis of different chord structures. 14-2.4.Integrity；整体性 整体性：和弦系统具有整体性，其中的所有元素（音符，和弦，和弦包）在全局系统的控制下保持 相互关联状态，与空间距离、尺度无关。 Holism: A chord system possesses a holistic nature, where all elements (notes, chords, and chord packages) remain interconnected under the control of the global system, independent of spatial distance or scale. Poplar forest, Jazz Scale A major；白杨林、爵士音阶，A大调 上面图例由爵士音阶 A大调发挥整体控制作用，将该图放大，缩小到任何尺度，其中的音符，和弦 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 的关联保持不变。 The jazz scale A major plays an overall controlling role in the above diagram. Whether the diagram is enlarged or reduced to any scale, the relationship between the notes and chords remains unchanged. 14-3. Space-Time Duality；时-空二相性 和弦语言包含时间表达与空间表达，前面部分介绍了和弦的空间表达，本节将讨论时-空关系。 Chord language includes time expression and space expression. The previous section introduced the spatial expression of chords. This section will discuss the time-space relationship. 和弦语言包含时间语义（始-末，进行）与空间语义（线，膜），分别表达时间与空间。 和弦时间与和弦空间镜像对称： {-7,-4,0} ↔ {0,4,7} mod 12 The chord language contains time semantics (beginning-end, progression) and space semantics (line, membrane), which express time and space respectively. Chord time and chord space are mirror-symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 两者互为反结构：反和弦，反调，可以数学转换。 空间具有定域性，时间具有非定域性，整体表现为时空二相性，类似波粒二相性。 The two are inverse structures of each other: anti-chords, anti-keys, and can be converted mathematically. Space is localized, time is non-localized, and the overall performance is space-time duality, similar to wave-particle duality. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-3.1、大三和弦-小三和弦的升序，降序，镜像对称形式。Y=平均律数列的指数 Figure 1-3, Major triad - minor triad ascending, descending, mirror-symmetric form. Y= exponents of the equal temperament series. 大三和弦，升序：{0，4，7}，大三和弦，降序：{-7，-4，0}（mod 12） Major triad, ascending: {0,4,7}, Major triad, descending: {-7，-4，0}（mod 12） 小三和弦，升序：{0，3，7}，大三和弦，降序：{-7，-3，0}（mod 12） Minor triad, ascending: {0,3,7}, Major triad, descending: {-7，-3，0}（mod 12） 图14-3.2、和弦镜像：和弦时间（上），和弦空间（下）互为反和弦。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Figure 14-3.2, Chord mirror image: Chord time (top) and chord space (bottom) are each other's antichords. 图1-3.2、大三和弦-小三和弦的升序，降序，镜像对称形式。七声音阶（Heptachord）， C大调，关 系小调。 Figure 1-3.2. Ascending, descending, mirror-symmetric forms of Major - minor triads. Heptachord, C major, relation minor. Formula；公式： C大三和弦（升序）=H^0,4,7.C C major chord, (ascending)= H ^ 0,4,7.C a小三和弦（升序）=H^0,3,7.a a minor triad (ascending)=H^0,3,7.a C大三和弦（降序）=H^0,-4,-7.C C major chord(descending)= H ^ 0, -4, -7.C Eb 小三和弦（降序）=H^0,-3,-7.Eb Eb minor triad (descending)=H^0,-3,-7.Eb 和弦时间与和弦空间具有相反的数学结构，甚至还有相反的物理属性：定域性与非定域性。 和弦时间不含几何语义，没有空间状态；和弦空间不含时间语义，没有时间状态。两者整体表现为 时空二相性，类似于量子力学中的波粒二象性。 Chord time and chord space have opposite mathematical structures and even opposite physical properties: locality and non-locality. Chord time does not contain geometric semantics and has no spatial state; chord space does not contain temporal semantics and has no temporal state. The two as a whole show the duality of space and time, which is similar to the wave-particle duality in quantum mechanics. 纯时间 vs. 纯空间：巴赫与莫奈的对比 在巴赫的音乐中，我们只能观察到和弦与旋律的时间变化，无法感知任何几何形状或位置。 纯时间状态下，空间属性无法被观察，空间位置处于叠加态（Superposition State）。 如果要在巴赫的音乐中观察到空间属性，唯一的方式是将和弦时间转换为其镜像对称形式——和弦 空间。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Pure time vs. pure space: Bach and Monet’s comparison In Bach’s music, we can only observe the time changes of chords and melodies, and cannot perceive any geometric shapes or positions. In the pure time state, spatial properties cannot be observed, and spatial positions are in a superposition state. If you want to observe spatial properties in Bach’s music, the only way is to convert chord time into its mirror-symmetric form - chord space. 结论：巴赫的音乐是和弦时间，莫奈的绘画是和弦空间。在纯时间状态下，空间位置的概念是无意 义的，相当于所有位置的叠加。 Conclusion: Bach’s music is chord time, and Monet’s paintings are chord space. In the pure time state, the concept of spatial position is meaningless, which is equivalent to the superposition of all positions. 图14-3.3、巴赫手稿 Figure 14-4.2. Bach manuscript 3. 莲花的时空二相性：莫奈 vs. 莫扎特 莫奈的莲花（绘画）是空间表达，具有定域性，即它不能同时出现在卢浮宫和奥赛博物馆。 莫扎特的莲花（音乐）是时间表达，具有非定域性，可以处于任意空间位置的叠加态，包括卢浮宫 和奥赛。 3. The space-time duality of the lotus: Monet vs. Mozart 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Monet's lotus (painting) is a spatial expression with locality, that is, it cannot appear in the Louvre and the Musee d'Orsay at the same time. Mozart's lotus (music) is a temporal expression with non-locality, and can be in a superposition state of any spatial position, including the Louvre and the Musee d'Orsay. 这意味着，莲花同时具有莫奈（空间）-莫扎特（时间）二相性，类似于波粒二象性： 作为绘画（莫奈）时，它是粒子，位置固定。 作为音乐（莫扎特）时，它是波动，位置可叠加。 结论： 莲花在“莫奈-莫扎特”二相性中展现了时空结构的波粒二象性。 从和弦时间到和弦空间的转换，与量子测量导致波函数坍缩的过程类似。 This means that the lotus has both the Monet (space) and Mozart (time) duality, similar to the waveparticle duality: As a painting (Monet), it is a particle with a fixed position. As music (Mozart), it is a wave with superimposable positions. Conclusion: The lotus shows the wave-particle duality of the space-time structure in the "Monet-Mozart" duality. The conversion from chord time to chord space is similar to the process of wave function collapse caused by quantum measurement. 图14-3.4：莫奈-莫扎特二相性。 Figure 14-3.4: Monet-Mozart duality. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 References；参考文献 1、Core works (original works by the authors);核心著作（作者原著） 1. Xiaohong Li ;李晓虹. (2016). Chord Language. [预印本]. Zenodo. https://doi.org/10.5281/zenodo.10699309 2. Xiaohong Li; 李晓虹. (2018). 和弦绘画： Chord Painting. [预印本]. Zenodo. https://doi.org/10.5281/zenodo.17431483 2、音乐与和弦理论（Music & Harmony Theory） 2. Pythagoras. On the Harmony of the Spheres. (Fragments). 3. Helmholtz, H. (1877). On the Sensations of Tone as a Physiological Basis for the Theory of Music. Longmans. 4. Hindemith, P. (1940). The Craft of Musical Composition. Schott Music. 5. Schoenberg, A. (1969). Theory of Harmony. University of California Press. 6. Lydian Chromatic Concept of Tonal Organization. Wikipedia. 7. Kocur, J. (n.d.). Chord–Scale Theory. Open Music Theory. 8. Brunner, G., Wang, Y., Wattenhofer, R., & Wiesendanger, J. (2017). JamBot: Music Theory Aware Chord-Based Generation of Polyphonic Music with LSTMs. arXiv:1711.07682. 9. Zhao, Y. et al. (2020). Vertical–Horizontal Structured Attention for Generating Music with Chords. arXiv:2011.09078. 10. Lazzari, N., Poltronieri, A., & Presutti, V. (2023). Pitchclass2vec: Symbolic Music Structure Segmentation with Chord Embeddings. arXiv:2303.15306. 11. Cook, N. (1994). A Guide to Musical Analysis. Oxford University Press. 12. Meyer, L. B. (1956). Emotion and Meaning in Music. University of Chicago Press. 13. Wilson, G. (2022). The Geometry of Harmony: Mathematical Foundations of Music. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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、物理、宇宙与时间（Physics, Cosmology, and Time） 14. Einstein, A. (1916). Relativity: The Special and the General Theory. 15. Bohm, D. (1980). Wholeness and the Implicate Order. Routledge. 16. Penrose, R. (1989). The Emperor’s New Mind. Oxford University Press. 17. Smolin, L. (2013). Time Reborn: From the Crisis in Physics to the Future of the Universe. Houghton Mifflin Harcourt. 18. Greene, B. (1999). The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. 19. Rovelli, C. (2018). The Order of Time. Riverhead Books. 20. Schrödinger, E. (1944). What Is Life? Cambridge University Press. 21. Prigogine, I. (1984). Order Out of Chaos: Man’s New Dialogue with Nature. Bantam Books. 4、语言与认知科学（Language, Cognition & Structure） 22. Saussure, F. de. (1916). Course in General Linguistics. 23. Chomsky, N. (1957). Syntactic Structures. MIT Press. 24. Lakoff, G., & Johnson, M. (1980). Metaphors We Live By. University of Chicago Press. 25. Hofstadter, D. R. (1979). Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books. 26. Dehaene, S. (2020). How We Learn: Why Brains Learn Better Than Any Machine... Penguin Books. 27. Damasio, A. (1999). The Feeling of What Happens: Body and Emotion in the Making of Consciousness. Harcourt. 28. Tononi, G. (2012). Phi: A Voyage from the Brain to the Soul. Pantheon. 5、哲学与精神学说（Philosophy, Spirituality & Consciousness） 29. Plato. Timaeus. 30. Laozi. 道德经 . 31. Zhuangzi. 庄子 · 齐物论 . 32. Spinoza, B. (1677). Ethics. 33. Whitehead, A. N. (1929). Process and Reality. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 34. Teilhard de Chardin, P. (1955). The Phenomenon of Man. 35. Wilber, K. (2000). A Theory of Everything: An Integral Vision for Business, Politics, Science, and Spirituality. 36. Capra, F. (1975). The Tao of Physics. Shambhala Publications. 37. Chopra, D. (1993). Ageless Body, Timeless Mind. Harmony Books. 38. Suzuki, D. T. (1956). Zen Buddhism and Its Influence on Japanese Culture. 6、综合与前沿交叉（Interdisciplinary & Future Studies） 39. “Musical Science: Pythagoras, Einstein and Divine Principle.” (2018). Applied Unificationism. 40. Wang, Q., & Liu, J. (2022). Quantum Music: Exploring the Physics of Sound and Harmony. Frontiers in Physics, 10. 41. Kurzweil, R. (2005). The Singularity Is Near. Penguin Books. 42. Harari, Y. N. (2016). Homo Deus: A Brief History of Tomorrow. Harper. 43. Tegmark, M. (2014). Our Mathematical Universe. Knopf. 44. Hinton, G. E. (2023). The Promise and Peril of Thinking Machines. Lecture Notes, University of Toronto. 时空——看似一个抽象的概念框架，不是物质，但是诡异的是：没有时空，一切物质都无法存 在，无法感知，或者，我们不能观察到任何不具时空属性的物质。物质是时空的形式之一？或者说： 宇宙是时空事件集合？ 时空看似抽象，却是所有物质得以呈现的根本条件。如果完全剔除时空结构，位置、变化、因果 与可观测性将不复存在，物质也失去可被区分与呈现的可能。由此可见，所谓“物质”并非独立于时空 的实体，而是时空自身在某一尺度上的谐振与稳定模式，是时空事件网络的局部结构化表现。从这一 视角出发，宇宙不再是容纳物质的框架，而是由事件构成的整体：物质、能量、生命与意识皆为时空 和弦化后的形式。换言之，宇宙可以被理解为一个由时空事件所构成的和弦体系，而物质正是该体系 的局域和弦结构。