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 人类含两种时空观察者：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 kinds of space-time observers: chord (tonal) observers and non-chord (atonal) observers, who observe two kinds of space-time respectively: 和弦（调性）时空：和弦生成的时空场，以量子化频谱为编码结构，映射到时空语义集合，音乐 （时间域）、绘画（空间域）是其常见形式。 Chord (tonality) space-time: The space-time field generated by chords uses the quantized spectrum as the encoding structure and is mapped to a space-time semantic set. Music (time domain) and painting (space domain) are its common forms. 非和弦（无调性）时空：屏蔽了时空的和弦结构，只保留几何（图-底）与运动的纯粹关系性描 述，从外部参考系统（如时钟、尺子、参照物）获得定量，常用于经典物理学框架中，也是日常的时空 经验。 Non-chordal (atonal) spacetime : It blocks the chordal structure of spacetime, retains only the purely relational description of geometry (figure-ground) and motion, obtains quantification from external reference systems (such as clocks, rulers, reference objects), is often used in the framework of classical physics, and is also the daily experience of spacetime. 和弦频谱：和弦频谱与能量量子本质相通，均以一个基准频率 f 为单位，在整数 n 的调控下生成一 组离散的频率/能量结构。 泛音频谱公式：n*f ，N∈Z，f=频率 量子化假设：n*f*h（h=6.626×10^−34）N∈Z 两个公式结构一致，当：n=1-6=大三和弦，n=1-7=大7和弦，n=1-9=大9和弦，n=1-11=大十 一和弦——量子来自和弦。 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 泛音是一维震荡模式，大于一维的震荡模式涉及到平均律：(1.059463)^n · f₀，两种模式可以切 换。 将 n 切换为 (1.059463)^n，引入指数型量子化能级：Eₙ=h·1.059463^{n}·f₀，通过模 12 群 ℤ₁₂ 的 结构，实现和弦的系统生成。 Overtone spectrum formula: n*f, N∈Z, f=frequency Quantization assumption: n*f*h (h=6.626×10^−34)N∈Z The two formulas have the same structure when: n=1-6 = major triad, n=1-7 = major 7th chord, n=1-9 = major 9th chord, n=1-11 = major 11th chord—quantum comes from chords. Overtones are one-dimensional oscillation patterns. Oscillation patterns larger than one dimension involve equal temperament: 1.059463)^n·f₀. these two modes can be switched. Switching n to (1.059463)^n introduces exponential quantized energy levels: Eₙ=h·1.059463^{n}·f₀. Through the structure of the module 12 group ℤ₁₂, systematic generation of chords is achieved. 时空二相性：和弦时间与和弦空间镜像对称：{-7,-4,0} ↔ {0,4,7} mod 12（互为反和弦，反调），可 数学转换；空间具有定域性，时间具有非定域性，共同表现为时空二相性；波粒二象性只能在和弦（调 性）时空中成立。 Space-time duality : Chord time and chord space are mirror-symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 (they are anti-chords and anti-tones), which can be mathematically converted; Space is local and time is non-local, which together manifest as the space-time duality. The wave-particle duality can only hold true in chord (tonal) space-time. 和弦几何：和弦编码（量子化频谱）包含几何语义：开弦，闭弦，膜弦，可生成所有空间状态，也 是绘画空间的生成基础。 Chord geometry: Chord encoding (quantized spectrum) contains geometric semantics: open strings, closed strings, membrane strings, which can generate all spatial states and are also the basis for the generation of painting space. ±音符：音符具有±属性，这是频率的物理属性，应涉及所有波动、频率，也可以解释物理学中普 遍存在的±属性。 ±Notes: notes have ± properties, which are physical properties of frequency and should involve 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 all waves and frequencies. They can also explain the ubiquitous ± properties in physics. 和弦语言是时空语言，音乐（时间域）与绘画（空间域）是常见和弦时空现象，也是方便的观察途 径。 Chord language is a space-time language. Music (time domain) and painting (space domain) are common chord space-time phenomena and are also convenient ways of observation. 基本和弦表：1-1、大三和弦（闭弦），1-2、小三和弦（开弦）、2、减七和弦（膜弦）、3、全音阶 和弦（膜弦），4、增三和弦（膜弦） *和弦频谱公式：n*f，H^n*f,（H=1.059463，n∈Z） *符号：◆=+音符，●=-音符，音符色=色荷 *本文使用 mod12 记谱法 Basic chord table: 1-1, major triad (closed string), 1-2, minor triad (open string), 2, diminished 7th (membrane string), 3, diatonic chord (membrane string), 4, augmented Triads (membrane strings) * Chord spectrum formula: n*f, H^n*f (H=1.059463，n∊Z) * Symbol: ◆=+ note, ●=- note, note color = color charge ** This article uses mod12 notation 关键词 ； Keywords：和弦时空、量子化、和弦场、音乐、绘画、电磁场、弦理论 Chord spacetime, quantization, chord field, music, painting, electromagnetic field, string theory 14-1.Chord Space；和弦空间 和弦编码（量子化频谱）分别生成音乐（时间域）与绘画（空间域），两者镜像对称：{-7,-4,0} ↔ {0,4,7} mod 12，可数学转换。 Chord encoding (quantized spectrum) generates music (time domain) and painting (space domain) respectively, which are mirror-symmetric: {-7,-4,0} ↔ {0,4,7} mod 12 and can be mathematically converted. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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（量子化频谱）包含和弦几何语义 {开弦|闭弦|膜弦} 并构成和弦几何框架，以此定义和弦 空间结构。 The chord encoding (quantized spectrum) contains the chord geometry semantics {open string|closed string|membrane string} and constitutes a chord geometry framework to define the chord space structure. “弦”是“和弦”的几何语义，“和弦”是“弦”的特征频谱。不同和弦映射到不同的几何语 义： "String" is the geometric semantics of "chord", and "chord" is the characteristic spectrum of "strings". Different chords map different geometric semantics: 大三和弦 (−7,−4,0)mod 12 ↔ 闭弦（轮廓线） 小三和弦 (−7,−3,0)mod 12 ↔ 开弦（分面线） 等比和弦：减七和弦 (0,3,6,9) mod 12，全音阶和弦 (0,2,4,6,8,10)mod 12，增三和弦 (0,4,8) mod 12 ↔ 膜弦（非线性空间） 三和弦（开弦，闭弦）定义等比和弦（膜弦）的边界（轮廓线，分面线），生成所有空间状态及 相互作用。 Major triad (−7,−4,0)mod 12 ↔ closed string (contour line) Minor triad (−7,−3,0)mod 12 ↔ open string (Facet line) Geometric chords: diminished seventh chord (0,3,6,9) mod 12, diatonic chord (0,2,4,6,8,10)mod 12, augmented triad (0,4,8) mod 12 ↔ membrane chord (nonlinear space) The triads (open strings,closed stirngs) define the boundaries (contours, facets) of the geometric chords (membrane strings), generating all spatial states and interactions. 以上结果来自和弦绘画中的独立观察，在绘画中可重复，并有视觉实验支持。 The above results come from independent observations in chord painting, are repeatable in painting, and are supported by visual experiments. 和弦空间是和弦语言的重要支柱与核心部分，绘画是其主要观察基础与应用领域。 Chord space is an important pillar and core part of chord language, and painting is its main observation basis and application field. 观察、实验案例：Observation and experimental cases: 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Li, X. H. (2020). Chord Painting. ResearchGate. https://www.researchgate.net/publication/340492620_Chord_Painting Li, X. H. (2024). Chord Language. Zenodo. https://zenodo.org/records/11817631 Griffiths, D. J. (2005). Introduction to Quantum Mechanics. Pearson. 14-2.Chord Packet；和弦包 和弦空间由和弦表达，基本单元是：和弦空间包（调），在前面章节已有介绍，本节主要讨论和 弦空间包的物理含义。 The chord space is expressed by chords, and its basic unit is the chord space package (key), which has been introduced in the previous chapter. This section mainly discusses the physical meaning of the chord space package. 本章的讨论默认采用爵士音阶，下面分析一个典型的和弦空间包。 The discussion in this chapter uses the jazz Scale by default, and a typical chord space package is analyzed below. 三和弦（开弦，闭弦）定义全音阶和弦（膜和弦）的边界（轮廓线，分面线等），生成爵士音阶 的和弦空间包，下面以 C大调，F#小调为例： Triads (open chords, closed chords) define the boundaries (contours, Facet line, etc.) of diatonic chords (membrane chords), and generate the chord space packet of the jazz Scale. The following takes C major and F# minor as examples: 图14-2.1、爵士音阶和弦包：1、C大三和弦（闭弦），2、F#小三和弦（开弦），3、全音阶和弦 （膜弦）（◆=正音符，●=负音符，色彩=色荷） Figure 14-2.1, jazz Scale chord package: 1,C major triad (closed string), 2,F# minor triad (open string), 3,diatonic chord (membrane string) (◆=positive note, ●=negative note, color=color charge) 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 图14-2.2、爵士音阶，C大调，f#小调空间包 Figure 14-2.2, jazz Scale C major ,f# minor space packet 实验 1：C 大三和弦（闭弦），构成了图形的闭合轮廓线，全音阶和弦（膜弦）填充所有非线空 间，包括图形与背景。 Experiment 1: The C major triad (closed string) forms the closed contour of the figure, and the diatonic chord (membrane string) fills all non-linear Spaces, including the figure and background. 空间包的轮廓线由大三和弦（闭弦）构成，用于束缚空间包，轮廓线（闭弦）的内部由全音阶和 弦（膜弦）充实，线和弦与膜和弦分别构成和弦空间包的外层与内核。 The contour of the space packet is composed of major triads (closed strings), which are used to bind the space packet. The interior of the contour line (closed strings) is enriched by diatonic chords (membrane strings), and the line chord and membrane chord form the outer and inner core of the chord space packet respectively. 和弦包是和弦时空的基本单位；那么原子，星体是和弦包吗？合理的回答是：如果原子，星体是 和弦时空中的空间单位，其形式就只能是和弦包。 The chord packet is the basic unit of chord space-time ; So are atoms, stars a chord packet? The reasonable answer is that if atoms and stars are spatial units in chord space-time, their form can only be chord packets. 图15-3.2 与下面的照片比较。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 Figure 15-3.2 is compared with the following photos. 图14-2.3、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.3. Iron atoms taken by aperture grating microscope (picture from Internet) 图14-2.4、孔径光栅显微镜拍摄的铁原子（图片来自互联网） Figure 14-2.4. Iron atoms taken by aperture grating microscope (picture from Internet) 14-2.1.Electric Charge And Magnetic Charge；电荷与磁荷 音符具有正负属性，由此产生和弦的正负属性，正和弦的根音符为正音符，负和弦的根音符为负 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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 nonelectromagnetic 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 spacetime. 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， 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 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 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. 14-3. 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。 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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. The space-time duality of the lotus: Monet vs. Mozart Monet's lotus (painting) is a spatial expression with locality, that is, it cannot appear in the Louvre and the Musee d'Orsay at the same time. Mozart's lotus (music) is a temporal expression with non-locality, and can be in a superposition state of any spatial position, including the Louvre and the Musee d'Orsay. 这意味着，莲花同时具有莫奈（空间）-莫扎特（时间）二相性，类似于波粒二象性： 作为绘画（莫奈）时，它是粒子，位置固定。 作为音乐（莫扎特）时，它是波动，位置可叠加。 结论： 莲花在“莫奈-莫扎特”二相性中展现了时空结构的波粒二象性。 从和弦时间到和弦空间的转换，与量子测量导致波函数坍缩的过程类似。 This means that the lotus has both the Monet (space) and Mozart (time) duality, similar to the wave-particle duality: As a painting (Monet), it is a particle with a fixed position. As music (Mozart), it is a wave with superimposable positions. Conclusion: The lotus shows the wave-particle duality of the space-time structure in the "Monet-Mozart" duality. The conversion from chord time to chord space is similar to the process of wave function collapse caused by quantum measurement. 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, 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14-3.4：莫奈-莫扎特二相性。 Figure 14-3.4: Monet-Mozart duality. 14-4.Chord Spacetime Concept Framework；和弦时空概念框架 和弦时空由和弦（量子化频谱）构成，时间与空间是能量的不同形式，由此有： E=t+s 和弦时空中存在 纯时间（s=0）与纯空间（t=0），这需要与其适应的时空框架。 时间能量（T）：非定域性，类似量子态，不依赖外部时钟。 空间能量（S）：定域性，具有几何属性，如形状、位置等，质量依赖定域性。 Chord spacetime is composed of chords (quantized spectrum). Time and space are different forms of energy, so: 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： 和弦语言；李晓虹；DOI: 10.13140/RG.2.2.25415.65440/3；ISBN:9781370273348；ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 CHORD LANGUSGE, Li Xiaohong, DOI: 10.13140/RG.2.2.25415.65440/3,ISBN:9781370273348, ASIN: B0919JJ3R7 Email: [email protected]om; https://orcid.org/0000-0001-6461-1239 S+T=1 其中： S 代表和弦空间的能量占比。 T 代表和弦时间的能量占比。 当 S=0（纯时间）时，无空间信息，时间完全非定域。 当 T=0（纯空间）时，无时间信息，空间完全定域。 结论：时间和空间是互补变量，它们的分布决定了和弦时空的性质。 1.The complementary relationship between time and space: Assume that the total energy of chord space-time is normalized to 1, then: S+T=1 Where: S represents the energy proportion of chord space. T represents the energy proportion of chord time. When S=0 (pure time), there is no spatial information and time is completely non-local. When T=0 (pure space), there is no time information and space is completely local. Conclusion: Time and space are complementary variables, and their distribution determines the properties of chord space-time. 2. 速度的定义：由于速度是时间（非定域性）与空间（定域性）的叠加，时间能与空间能的比值 v=T/S+T=T 由于 S+T=1，我们有： 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。