[{"data":1,"prerenderedAt":937},["ShallowReactive",2],{"content:\u002F2026\u002Fmath-charts-music":3,"surround:\u002F2026\u002Fmath-charts-music":926},{"id":4,"title":5,"body":6,"categories":902,"date":904,"description":905,"draft":906,"extension":907,"image":908,"meta":909,"navigation":911,"path":912,"permalink":913,"published":913,"readingTime":914,"recommend":913,"references":913,"seo":919,"series":920,"sitemap":921,"stem":922,"tags":923,"type":924,"updated":904,"__hash__":925},"content\u002Fposts\u002F2026\u002Fmath-charts-music.md","公式、图表与乐谱",{"type":7,"value":8,"toc":894},"minimark",[9,13,34,316,319,611,617,813,825,828,846,849,852,855,867,871],[10,11,12],"h2",{"id":12},"数学公式",[14,15,16,17,21,22,25,26,29,30,33],"p",{},"数学公式由 ",[18,19,20],"code",{"code":20},"remark-math"," + ",[18,23,24],{"code":24},"rehype-katex"," 驱动，行内公式写作 ",[18,27,28],{"code":28},"$...$","，块级公式写作 ",[18,31,32],{"code":32},"$$...$$","：",[14,35,36,37,156,157,315],{},"行内公式：当 ",[38,39,42,74],"span",{"className":40},[41],"katex",[38,43,46],{"className":44},[45],"katex-mathml",[47,48,50],"math",{"xmlns":49},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[51,52,53,69],"semantics",{},[54,55,56,60,65],"mrow",{},[57,58,59],"mi",{},"a",[61,62,64],"mo",{"mathvariant":63},"normal","≠",[66,67,68],"mn",{},"0",[70,71,73],"annotation",{"encoding":72},"application\u002Fx-tex","a \\ne 0",[38,75,79,146],{"className":76,"ariaHidden":78},[77],"katex-html","true",[38,80,83,88,93,98,143],{"className":81},[82],"base",[38,84],{"className":85,"style":87},[86],"strut","height:0.8889em;vertical-align:-0.1944em;",[38,89,59],{"className":90},[91,92],"mord","mathnormal",[38,94],{"className":95,"style":97},[96],"mspace","margin-right:0.2778em;",[38,99,102,135,139],{"className":100},[101],"mrel",[38,103,105],{"className":104},[101],[38,106,109],{"className":107},[91,108],"vbox",[38,110,113],{"className":111},[112],"thinbox",[38,114,117,120,131],{"className":115},[116],"rlap",[38,118],{"className":119,"style":87},[86],[38,121,124],{"className":122},[123],"inner",[38,125,127],{"className":126},[91],[38,128,130],{"className":129},[101],"",[38,132],{"className":133},[134],"fix",[38,136],{"className":137},[96,138],"nobreak",[38,140,142],{"className":141},[101],"=",[38,144],{"className":145,"style":97},[96],[38,147,149,153],{"className":148},[82],[38,150],{"className":151,"style":152},[86],"height:0.6444em;",[38,154,68],{"className":155},[91]," 时，方程 ",[38,158,160,200],{"className":159},[41],[38,161,163],{"className":162},[45],[47,164,165],{"xmlns":49},[51,166,167,197],{},[54,168,169,171,180,183,186,188,190,193,195],{},[57,170,59],{},[172,173,174,177],"msup",{},[57,175,176],{},"x",[66,178,179],{},"2",[61,181,182],{},"+",[57,184,185],{},"b",[57,187,176],{},[61,189,182],{},[57,191,192],{},"c",[61,194,142],{},[66,196,68],{},[70,198,199],{"encoding":72},"ax^2 + bx + c = 0",[38,201,203,265,287,306],{"className":202,"ariaHidden":78},[77],[38,204,206,210,213,254,258,262],{"className":205},[82],[38,207],{"className":208,"style":209},[86],"height:0.8974em;vertical-align:-0.0833em;",[38,211,59],{"className":212},[91,92],[38,214,216,219],{"className":215},[91],[38,217,176],{"className":218},[91,92],[38,220,223],{"className":221},[222],"msupsub",[38,224,227],{"className":225},[226],"vlist-t",[38,228,231],{"className":229},[230],"vlist-r",[38,232,236],{"className":233,"style":235},[234],"vlist","height:0.8141em;",[38,237,239,244],{"style":238},"top:-3.063em;margin-right:0.05em;",[38,240],{"className":241,"style":243},[242],"pstrut","height:2.7em;",[38,245,251],{"className":246},[247,248,249,250],"sizing","reset-size6","size3","mtight",[38,252,179],{"className":253},[91,250],[38,255],{"className":256,"style":257},[96],"margin-right:0.2222em;",[38,259,182],{"className":260},[261],"mbin",[38,263],{"className":264,"style":257},[96],[38,266,268,272,275,278,281,284],{"className":267},[82],[38,269],{"className":270,"style":271},[86],"height:0.7778em;vertical-align:-0.0833em;",[38,273,185],{"className":274},[91,92],[38,276,176],{"className":277},[91,92],[38,279],{"className":280,"style":257},[96],[38,282,182],{"className":283},[261],[38,285],{"className":286,"style":257},[96],[38,288,290,294,297,300,303],{"className":289},[82],[38,291],{"className":292,"style":293},[86],"height:0.4306em;",[38,295,192],{"className":296},[91,92],[38,298],{"className":299,"style":97},[96],[38,301,142],{"className":302},[101],[38,304],{"className":305,"style":97},[96],[38,307,309,312],{"className":308},[82],[38,310],{"className":311,"style":152},[86],[38,313,68],{"className":314},[91]," 有两个解。",[14,317,318],{},"块级公式：",[38,320,323],{"className":321},[322],"katex-display",[38,324,326,382],{"className":325},[41],[38,327,329],{"className":328},[45],[47,330,332],{"xmlns":49,"display":331},"block",[51,333,334,379],{},[54,335,336,338,340],{},[57,337,176],{},[61,339,142],{},[341,342,343,373],"mfrac",{},[54,344,345,348,350,353],{},[61,346,347],{},"−",[57,349,185],{},[61,351,352],{},"±",[354,355,356],"msqrt",{},[54,357,358,364,366,369,371],{},[172,359,360,362],{},[57,361,185],{},[66,363,179],{},[61,365,347],{},[66,367,368],{},"4",[57,370,59],{},[57,372,192],{},[54,374,375,377],{},[66,376,179],{},[57,378,59],{},[70,380,381],{"encoding":72},"x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}",[38,383,385,403],{"className":384,"ariaHidden":78},[77],[38,386,388,391,394,397,400],{"className":387},[82],[38,389],{"className":390,"style":293},[86],[38,392,176],{"className":393},[91,92],[38,395],{"className":396,"style":97},[96],[38,398,142],{"className":399},[101],[38,401],{"className":402,"style":97},[96],[38,404,406,410],{"className":405},[82],[38,407],{"className":408,"style":409},[86],"height:2.2764em;vertical-align:-0.686em;",[38,411,413,418,607],{"className":412},[91],[38,414],{"className":415},[416,417],"mopen","nulldelimiter",[38,419,421],{"className":420},[341],[38,422,425,598],{"className":423},[226,424],"vlist-t2",[38,426,428,595],{"className":427},[230],[38,429,432,448,459],{"className":430,"style":431},[234],"height:1.5904em;",[38,433,435,439],{"style":434},"top:-2.314em;",[38,436],{"className":437,"style":438},[242],"height:3em;",[38,440,442,445],{"className":441},[91],[38,443,179],{"className":444},[91],[38,446,59],{"className":447},[91,92],[38,449,451,454],{"style":450},"top:-3.23em;",[38,452],{"className":453,"style":438},[242],[38,455],{"className":456,"style":458},[457],"frac-line","border-bottom-width:0.04em;",[38,460,462,465],{"style":461},"top:-3.677em;",[38,463],{"className":464,"style":438},[242],[38,466,468,471,474,477,480,483],{"className":467},[91],[38,469,347],{"className":470},[91],[38,472,185],{"className":473},[91,92],[38,475],{"className":476,"style":257},[96],[38,478,352],{"className":479},[261],[38,481],{"className":482,"style":257},[96],[38,484,487],{"className":485},[91,486],"sqrt",[38,488,490,586],{"className":489},[226,424],[38,491,493,581],{"className":492},[230],[38,494,497,558],{"className":495,"style":496},[234],"height:0.9134em;",[38,498,502,505],{"className":499,"style":501},[500],"svg-align","top:-3em;",[38,503],{"className":504,"style":438},[242],[38,506,509,540,543,546,549,552,555],{"className":507,"style":508},[91],"padding-left:0.833em;",[38,510,512,515],{"className":511},[91],[38,513,185],{"className":514},[91,92],[38,516,518],{"className":517},[222],[38,519,521],{"className":520},[226],[38,522,524],{"className":523},[230],[38,525,528],{"className":526,"style":527},[234],"height:0.7401em;",[38,529,531,534],{"style":530},"top:-2.989em;margin-right:0.05em;",[38,532],{"className":533,"style":243},[242],[38,535,537],{"className":536},[247,248,249,250],[38,538,179],{"className":539},[91,250],[38,541],{"className":542,"style":257},[96],[38,544,347],{"className":545},[261],[38,547],{"className":548,"style":257},[96],[38,550,368],{"className":551},[91],[38,553,59],{"className":554},[91,92],[38,556,192],{"className":557},[91,92],[38,559,561,564],{"style":560},"top:-2.8734em;",[38,562],{"className":563,"style":438},[242],[38,565,569],{"className":566,"style":568},[567],"hide-tail","min-width:0.853em;height:1.08em;",[570,571,577],"svg",{"xmlns":572,"width":573,"height":574,"viewBox":575,"preserveAspectRatio":576},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[578,579],"path",{"d":580},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[38,582,585],{"className":583},[584],"vlist-s","​",[38,587,589],{"className":588},[230],[38,590,593],{"className":591,"style":592},[234],"height:0.1266em;",[38,594],{},[38,596,585],{"className":597},[584],[38,599,601],{"className":600},[230],[38,602,605],{"className":603,"style":604},[234],"height:0.686em;",[38,606],{},[38,608],{"className":609},[610,417],"mclose",[14,612,613,614,616],{},"也可以用 ",[18,615,47],{"code":47}," 代码块书写：",[38,618,620,667],{"className":619},[41],[38,621,623],{"className":622},[45],[47,624,625],{"xmlns":49},[51,626,627,664],{},[54,628,629,633,635],{},[630,631,632],"mtext",{},"平均绩点(GPA)",[61,634,142],{},[341,636,637,658],{},[54,638,639,642,646,649,652,655],{},[61,640,641],{},"∑",[61,643,645],{"stretchy":644},"false","(",[630,647,648],{},"课程学分",[61,650,651],{},"×",[630,653,654],{},"课程绩点",[61,656,657],{"stretchy":644},")",[54,659,660,662],{},[61,661,641],{},[630,663,648],{},[70,665,666],{"encoding":72},"\\text{平均绩点(GPA)} = \\frac{\\sum(\\text{课程学分} \\times \\text{课程绩点})}{\\sum \\text{课程学分}}\n",[38,668,670,699],{"className":669,"ariaHidden":78},[77],[38,671,673,677,690,693,696],{"className":672},[82],[38,674],{"className":675,"style":676},[86],"height:1em;vertical-align:-0.25em;",[38,678,681,686],{"className":679},[91,680],"text",[38,682,685],{"className":683},[91,684],"cjk_fallback","平均绩点",[38,687,689],{"className":688},[91],"(GPA)",[38,691],{"className":692,"style":97},[96],[38,694,142],{"className":695},[101],[38,697],{"className":698,"style":97},[96],[38,700,702,706],{"className":701},[82],[38,703],{"className":704,"style":705},[86],"height:1.53em;vertical-align:-0.52em;",[38,707,709,712,810],{"className":708},[91],[38,710],{"className":711},[416,417],[38,713,715],{"className":714},[341],[38,716,718,801],{"className":717},[226,424],[38,719,721,798],{"className":720},[230],[38,722,725,754,762],{"className":723,"style":724},[234],"height:1.01em;",[38,726,728,731],{"style":727},"top:-2.655em;",[38,729],{"className":730,"style":438},[242],[38,732,734],{"className":733},[247,248,249,250],[38,735,737,744,748],{"className":736},[91,250],[38,738,641],{"className":739,"style":743},[740,741,742,250],"mop","op-symbol","small-op","position:relative;top:0em;",[38,745],{"className":746,"style":747},[96,250],"margin-right:0.1952em;",[38,749,751],{"className":750},[91,680,250],[38,752,648],{"className":753},[91,684,250],[38,755,756,759],{"style":450},[38,757],{"className":758,"style":438},[242],[38,760],{"className":761,"style":458},[457],[38,763,765,768],{"style":764},"top:-3.485em;",[38,766],{"className":767,"style":438},[242],[38,769,771],{"className":770},[247,248,249,250],[38,772,774,777,780,786,789,795],{"className":773},[91,250],[38,775,641],{"className":776,"style":743},[740,741,742,250],[38,778,645],{"className":779},[416,250],[38,781,783],{"className":782},[91,680,250],[38,784,648],{"className":785},[91,684,250],[38,787,651],{"className":788},[261,250],[38,790,792],{"className":791},[91,680,250],[38,793,654],{"className":794},[91,684,250],[38,796,657],{"className":797},[610,250],[38,799,585],{"className":800},[584],[38,802,804],{"className":803},[230],[38,805,808],{"className":806,"style":807},[234],"height:0.52em;",[38,809],{},[38,811],{"className":812},[610,417],[814,815,818],"alert",{"title":816,"type":817},"转义","warning",[14,819,820,821,824],{},"正文中如需直接使用美元符号，请写成 ",[18,822,823],{"code":823},"\\$","，否则会被当作公式起始符。",[10,826,827],{"id":827},"图表",[14,829,830,831,834,835,838,839,845],{},"图表由 ",[18,832,833],{"code":833},"remark-code-component"," 插件实现：把 ",[18,836,837],{"code":837},"mermaid"," 代码块渲染为 ",[59,840,844],{"href":841,"rel":842},"https:\u002F\u002Fmermaid.js.org\u002F",[843],"nofollow","Mermaid"," 图表。它会跟随亮暗模式重绘，进入视口附近才加载渲染器；超宽图表可横向滚动。",[837,847],{"code":848},"graph TD\n    A[内容] --> B[分类]\n    A --> C[标签]\n    A --> D[合集]\n    B --> B1[多级分类]\n    C --> C1[关键词]\n    D --> D1[系列与顺序]",[837,850],{"code":851},"sequenceDiagram\n    participant 作者\n    participant 仓库\n    participant 站点\n    作者->>仓库: 提交 Markdown\n    仓库->>站点: 触发构建\n    站点-->>作者: 生成静态页面",[10,853,854],{"id":854},"乐谱",[14,856,857,858,861,862,33],{},"同一插件也支持把 ",[18,859,860],{"code":860},"music-abc"," 代码块渲染为可播放的乐谱，语法参见 ",[59,863,866],{"href":864,"rel":865},"https:\u002F\u002Fabcnotation.com\u002F",[843],"ABC notation",[868,869],"music-score",{"abc":870},"L:1\u002F8\nQ:1\u002F4=100\nM:2\u002F4\nK:D\n\"D\" FA A>B | AF DD\u002FE\u002F | \"G\" FF ED | \"A\" E2 z2 |]",[814,872,875],{"title":873,"type":874},"实现方式","info",[14,876,877,878,886,887,889,890,893],{},"这三个能力的共同点是：",[879,880,881,882,885],"strong",{},"在 ",[18,883,884],{"code":884},"nuxt.config.ts"," 的 remark 插件里，把特定语言的代码块映射为组件","。图表映射到 ",[18,888,844],{"code":844},"，乐谱映射到 ",[18,891,892],{"code":892},"MusicScore","，因此 Markdown 作者无需关心渲染细节。",{"title":895,"searchDepth":896,"depth":896,"links":897},"",4,[898,900,901],{"id":12,"depth":899,"text":12},2,{"id":827,"depth":899,"text":827},{"id":854,"depth":899,"text":854},[903],"功能演示","2026-10-03 10:20:00","Clarity 内置数学公式（KaTeX）、Mermaid 图表与 ABC 乐谱渲染，三者都以代码块或行内语法的形式书写。",false,"md","\u002Fcovers\u002Fmath-charts-music.jpg",{"slots":910},{},true,"\u002F2026\u002Fmath-charts-music",null,{"text":915,"minutes":916,"time":917,"words":918},"2 min read",1.15,69000,230,{"title":5,"description":905},"Clarity 功能地图",{"loc":912},"posts\u002F2026\u002Fmath-charts-music",[12,844,854],"tech","pYA63VNKnyUwC7bC6yKE1NAHZ5RZJvvtJiEsA5HLsRQ",[927,932],{"title":928,"path":929,"stem":930,"date":931,"type":924,"children":-1},"代码块与高亮","\u002F2026\u002Fcode-blocks","posts\u002F2026\u002Fcode-blocks","2026-10-03 10:10:00",{"title":933,"path":934,"stem":935,"date":936,"type":924,"children":-1},"侧栏插槽与文章内插槽","\u002F2026\u002Faside-slots","posts\u002F2026\u002Faside-slots","2026-10-03 10:30:00",1791033609858]