:root{color-scheme:light;--ink:#24364b;--muted:#536478;--line:#dce3ec;--blue:#13759c;--red:#b83f35;--paper:#fff;--wash:#f3f6fa}*{box-sizing:border-box}html{scroll-behavior:smooth;scroll-padding-top:30px}body{margin:0;background:var(--paper);color:var(--ink);font-family:"Yu Gothic","Meiryo",sans-serif;font-size:18px;line-height:1.95}button,input,select{font:inherit}button{border:1px solid #aebdce;background:white;color:var(--ink);padding:9px 15px;border-radius:5px;cursor:pointer;font-size:15px;line-height:1.5}button:hover{background:#e9f0f7;border-color:var(--blue)}button:active{transform:translateY(1px)}:focus-visible{outline:3px solid #167da8;outline-offset:4px}a{color:inherit}label{display:block;font-size:15px;margin:12px 0}select{max-width:100%;padding:6px 10px;background:white;border:1px solid #aebdce;border-radius:4px;font-size:16px}input[type=range]{accent-color:var(--blue);max-width:100%}input[type=checkbox]{accent-color:var(--red);width:18px;height:18px;vertical-align:middle}.site-header{display:flex;justify-content:space-between;align-items:center;padding:24px 5%;border-bottom:1px solid var(--line)}.brand{font-size:28px;font-weight:800;text-decoration:none;letter-spacing:.1em}.brand span{display:block;font-size:12px;letter-spacing:.08em;font-weight:400}.edition{font-size:13px;color:var(--muted)}.layout{display:grid;grid-template-columns:230px minmax(0,850px);gap:65px;max-width:1220px;margin:0 auto;padding:0 30px}.toc{position:sticky;top:30px;align-self:start;margin-top:76px;font-size:13px}.toc summary{font-size:14px;font-weight:bold;margin-bottom:20px;cursor:pointer}.toc a{display:flex;gap:12px;line-height:1.6;text-decoration:none;margin:0 0 15px;color:var(--muted)}.toc a:hover{color:var(--red)}.toc a span{font-variant-numeric:tabular-nums;color:var(--red)}main{min-width:0}.article-title{padding:64px 0 65px;border-bottom:1px solid var(--ink)}.eyebrow{font-size:12px;font-weight:bold;letter-spacing:.13em;color:var(--blue);margin:0 0 12px}h1{font-family:"Yu Mincho","MS PMincho",serif;font-size:clamp(36px,4vw,54px);line-height:1.55;letter-spacing:.045em;margin:10px 0 22px;font-weight:600}h1 span{font-size:.65em;margin-left:12px}.intro{font-size:17px;color:var(--muted)}.byline{font-size:14px;margin-top:30px}.byline span{margin-left:25px;font-size:12px;color:var(--muted)}.chapter{padding:48px 0 20px}.chapter-heading{display:flex;gap:20px;align-items:baseline;margin-bottom:32px}.chapter-heading>span{font-family:Georgia,serif;font-size:35px;color:var(--red)}h2{font-size:25px;line-height:1.6;margin:0}h3{font-size:21px;line-height:1.6;margin:0 0 20px}h4{font-size:15px}.prose{margin:0 0 1.5em;overflow-wrap:anywhere}.equation{font-family:"Cambria Math","Yu Mincho",serif;background:var(--wash);padding:18px 22px;overflow-x:auto;font-size:19px;line-height:1.9}.principle{border-left:3px solid var(--red);padding:10px 20px;font-weight:700}.experiment{background:var(--wash);padding:28px;margin:35px 0 45px;border-top:2px solid var(--ink);border-radius:0 0 7px 7px}.experiment p{margin:12px 0}.ui-copy{font-size:16px}.small,small{font-size:14px;line-height:1.8;color:var(--muted)}.actions{display:flex;gap:10px;flex-wrap:wrap;margin:20px 0}.reference{margin-top:25px;padding-top:20px;border-top:1px solid var(--line)}.circle-layout{display:grid;grid-template-columns:1.2fr 1fr;align-items:center;gap:20px}svg{width:100%;height:auto;display:block}svg text{font-family:"Yu Gothic","Meiryo",sans-serif}.math-output{font-size:21px;line-height:1.85;padding:24px 0;overflow-wrap:anywhere}.math-output span{display:block;font-size:16px}.table-wrap{overflow-x:auto}table{border-collapse:collapse;width:100%;font-size:14px;white-space:nowrap}th,td{padding:9px 10px;border-bottom:1px solid #cfd8e3;text-align:left}th{font-weight:bold}tr.changed{background:#fff0ea}caption{text-align:left;font-size:14px;margin-bottom:10px}.coordinate-table{overflow:auto;margin:25px 0}.coordinate-table h4{margin:0}.legend{display:flex;gap:20px;flex-wrap:wrap;font-size:14px}.c-color{color:var(--red)}.g-color{color:var(--blue)}.series-notes{display:flex;justify-content:space-between;gap:5px;margin:30px 0;padding:14px 2px}.note-chip{position:relative;text-align:center;flex:1;min-width:0;padding:16px 0;font-size:24px;font-weight:600;line-height:1.4}.note-chip::before,.note-chip::after{content:"";position:absolute;inset:0;border:2px solid transparent;border-radius:50%;pointer-events:none}.note-chip.c::before{border-color:var(--red);transform:rotate(-12deg)}.note-chip.g::after{border-color:var(--blue);transform:rotate(12deg);inset:-5px 5px}.note-chip small{display:block;font-size:12px;margin-top:6px;font-weight:400}.voicing{display:grid;grid-template-columns:1fr 1fr;gap:20px}.voicing>div{border-left:2px solid var(--line);padding-left:15px}.voicing p{font-size:16px}.proof-steps{padding-left:28px}.proof-steps li{padding:12px 6px;opacity:.35;font-size:16px}.proof-steps li.active{opacity:1}.proof-steps span{color:var(--blue);font-family:serif;font-size:18px}.minor-flow{display:flex;gap:12px;align-items:center;justify-content:space-between;flex-wrap:wrap}.minor-flow b{font-size:14px}.minor-flow p{font-family:serif;font-size:21px}.inline-audio{margin:20px 0}footer{border-top:1px solid var(--line);padding:45px 0 140px;font-size:16px}.audio-bar{position:fixed;bottom:0;left:0;right:0;z-index:5;background:#24364bf5;color:white;display:flex;gap:18px;align-items:center;padding:12px 5%;font-size:14px;box-shadow:0 -4px 20px #24364b18}.audio-bar button{background:transparent;color:white;border-color:#9cabbc}.audio-bar label{margin:0 0 0 auto;display:flex;gap:10px;align-items:center}.audio-bar input{width:100px}.skip{position:absolute;left:10px;top:-80px;background:white;z-index:10}.skip:focus{top:10px}sup,sub{font-size:.7em}#audio-status{line-height:1.4}#harmonic-n{width:100%}@media(max-width:1050px){.layout{grid-template-columns:175px minmax(0,1fr);gap:30px;padding:0 24px}.circle-layout{grid-template-columns:1fr}.circle-layout svg{max-width:400px;margin:auto}.circle-layout>div{display:flex;flex-wrap:wrap;gap:10px;align-items:center}.circle-layout p{flex-basis:100%}.circle-layout label{margin:0}.experiment{padding:22px}}@media(max-width:720px){body{font-size:17px}.site-header{padding:16px 20px}.edition{font-size:12px}.brand span{display:none}.layout{display:block;padding:0 20px}.toc{position:static;margin-top:20px;padding-bottom:5px;border-bottom:1px solid var(--line)}.toc details:not([open]) summary{margin:0}.toc a{font-size:14px}.article-title{padding:30px 0}.chapter{padding-top:35px}.chapter-heading{gap:12px}h2{font-size:22px}.experiment{padding:18px;margin:25px -5px 35px}h3{font-size:19px}.audio-bar{gap:10px;padding:10px 14px;flex-wrap:wrap}.audio-bar label{font-size:12px}.audio-bar input{width:65px}#audio-status{max-width:45%;font-size:12px}.note-chip{font-size:18px;padding:12px 0}.note-chip small{font-size:12px}.series-notes{gap:4px}.note-chip.g::after{inset:-5px 1px}.voicing{grid-template-columns:1fr}.equation{padding:14px;font-size:17px}.byline span{margin-left:12px}.minor-flow{justify-content:flex-start}}@media(prefers-reduced-motion:reduce){html{scroll-behavior:auto}button:active{transform:none}}@media print{.toc,.audio-bar,button,.skip{display:none}.layout{display:block}.experiment{break-inside:avoid}footer{padding-bottom:0}}
/* Revision 2: article-first listening and colorful mathematical notation. */
:root{--ink:#21172f;--muted:#43354f;--red:#ba235f;--blue:#006e8a;--wash:#f7f1ff;--line:#d9cee7}
body{background:#eef3ff;color:var(--ink);font-weight:500;line-height:2.05}
.music-background{position:fixed;inset:0;z-index:-1;overflow:hidden;pointer-events:none;background:radial-gradient(ellipse at 0 20%,#f5c9e6aa,transparent 55%),radial-gradient(ellipse at 100% 70%,#b9ecf8bb,transparent 55%)}
.music-background svg{position:absolute;width:100%;height:100%;opacity:.28}.music-background path{fill:none;stroke-width:2.5;vector-effect:non-scaling-stroke}
.music-background span{position:absolute;color:#ba2582;opacity:.28;font-family:'Segoe UI Symbol',serif;font-size:70px;animation:float-note 12s ease-in-out infinite alternate}
.music-background span:nth-of-type(1){left:3%;top:12%}.music-background span:nth-of-type(2){right:4%;top:25%;color:#006e8a;animation-delay:-3s}.music-background span:nth-of-type(3){left:8%;top:72%;color:#6334b8;animation-delay:-5s}.music-background span:nth-of-type(4){right:2%;top:82%;color:#b87500;animation-delay:-8s}.music-background span:nth-of-type(5){left:1%;top:43%;color:#1472a1;animation-delay:-2s}
@keyframes float-note{to{transform:translate(12px,-35px) rotate(12deg)}}
.site-header{background:#ffffffed;border-bottom:2px solid #d2b6f1}.brand{color:#602591}.layout{grid-template-columns:130px minmax(0,900px);gap:28px;max-width:1190px;padding:0 25px}
main{background:#fffffff5;padding:0 38px;box-shadow:0 0 45px #7866960d}.toc{font-size:12px}.toc a{gap:7px;color:#362741;line-height:1.65;margin-bottom:13px}.toc a span{color:#922c70}.toc summary{color:#21172f}.article-title{border-bottom:2px solid #ad63d8}h1{color:#302042}.chapter-heading>span{color:#b82874}.chapter-heading{margin-bottom:22px}.prose{color:#21172f}.intro,.small,small{color:#43354f}.principle{border-color:#ab42b1;background:linear-gradient(90deg,#f3e4fb,transparent);padding:10px 16px;font-size:20px;margin:28px 0 16px}
math{font-family:'Cambria Math','STIX Two Math','Latin Modern Math',math;font-weight:normal;color:#241635;font-size:1.12em}math[display=block]{font-size:1.22em;margin:0;text-align:left;white-space:nowrap;flex:1;min-width:0}mtext{font-family:'Yu Gothic','Meiryo',sans-serif;font-size:.8em}.display-equation{display:flex;align-items:center;flex-wrap:wrap;gap:16px;margin:22px 0 26px;padding:12px 4px;overflow-x:auto}.display-equation math{flex:0 0 auto}.display-equation button{margin-left:8px}.math-label{font-size:14px;margin-bottom:0;color:#493057}.prose math{font-size:1.05em}
.listen-row{display:flex;flex-wrap:wrap;gap:9px;margin:12px 0 22px;align-items:center}button{background:#faf4ff;border-color:#c28bdd;color:#45215d;font-weight:600;border-radius:25px;padding:9px 16px}button:hover{background:#eee0fb;border-color:#9b4ac0}button.playing,button[aria-pressed=true]{background:#6e268f;border-color:#6e268f;color:white}button:focus-visible{outline-color:#ca3385}
.audio-note{font-size:14px;color:#403147;line-height:1.75;margin:-10px 0 26px}.audio-label{font-size:16px;font-weight:700;margin:8px 0}.scale-listening{margin:25px 0 30px;padding:12px 0;border-top:1px solid #dec8ed;border-bottom:1px solid #dec8ed}.scale-listening table{font-size:15px}.scale-listening th,.scale-listening td{padding:10px 8px}.scale-listening td button{font-size:14px}.scale-listening th{white-space:normal}
.inline-figure{margin:25px 0 32px;padding:12px 0;background:transparent}.inline-figure figcaption{font-size:15px;color:#30223f;font-weight:600;margin-bottom:12px}.circle-figure{display:grid;grid-template-columns:minmax(200px,360px) 1fr;gap:22px;align-items:center}.circle-figure figcaption{font-weight:400}.circle-figure .listen-row{margin-bottom:12px}#rise-readout{font-size:14px}.graph-scroll{overflow-x:auto}.graph-scroll svg{min-width:580px}.plot-figure{border-top:1px solid #d4bfeb;padding-top:15px}.legend{color:#21172f}.note-chip{color:#21172f}.series-notes{margin:24px 0}.audio-bar{background:#302040f7}.audio-bar button{background:#ffffff12;color:white}.audio-bar label{color:white}#audio-status{color:white}
@media(max-width:1050px){.layout{grid-template-columns:110px minmax(0,1fr);gap:18px;padding:0 14px}main{padding:0 25px}.circle-figure{grid-template-columns:1fr}.circle-figure svg{max-width:330px;margin:auto}.circle-figure figcaption{text-align:center}.circle-figure .listen-row{justify-content:center}}
@media(max-width:720px){.layout{display:block;padding:0 12px}main{padding:0 16px}.toc{margin:12px 4px;padding:8px 12px;background:#ffffffec;border-radius:8px}.toc a{font-size:14px}.site-header{padding:12px 20px}.article-title{padding-top:25px}.display-equation{padding:8px 0;gap:8px}.display-equation math{font-size:1.12em}.display-equation button{font-size:14px}.scale-listening th,.scale-listening td{padding:8px 3px}.scale-listening td button{font-size:13px;padding:8px 10px}.music-background span{font-size:45px}.inline-figure{margin:20px 0}.audio-bar{font-size:13px}.chapter-heading>span{font-size:28px}.chapter-heading h2{font-size:21px}}
@media(prefers-reduced-motion:reduce){.music-background span{animation:none}}
@media print{.music-background{display:none}main{padding:0;background:white}.layout{display:block}math{color:black}}

/* v3: statements and synchronized listening figures */
.statement{border:1px solid #cdbbdc;border-radius:8px;padding:18px 22px;margin:28px 0;background:#fcfaff}.statement .principle{background:none;border:0;padding:0;margin:0 0 10px}.statement .prose{margin:0}.live-spectrum{margin:12px 0 24px;max-width:680px}.live-spectrum figcaption,.odd-circle-figure figcaption{font-size:14px;color:#403147}.odd-circle-figure{max-width:350px;margin:18px auto 30px}.odd-circle-figure figcaption{text-align:center}.live-spectrum svg{min-height:130px}
@media(max-width:720px){.statement{padding:15px}.live-spectrum{margin:12px 0 24px}.live-spectrum svg{min-height:115px}}

.note-ratio-table{margin:22px 0 28px}.note-ratio-table table{font-size:17px;min-width:420px}.note-ratio-table th,.note-ratio-table td{text-align:center;padding:13px 10px}.note-ratio-table thead{background:#f4eafc}.note-ratio-table math{font-size:1.2em}.note-ratio-table th:first-child{font-size:14px}

/* Real sampled audio output, shared by nearby play controls. */
.waveform{margin:8px 0 24px;padding:6px 10px 8px;border:1px solid #d6c8e5;border-radius:7px;background:linear-gradient(110deg,#faf7ff,#f2fbfd);max-width:100%;min-width:0}.waveform svg{height:100px;width:100%}.wave-grid{fill:none;stroke:#ded6e8;stroke-width:1}.wave-trace{fill:none;stroke:#087a94;stroke-width:1.6;vector-effect:non-scaling-stroke}.waveform.is-playing{border-color:#ba74ca}.waveform.is-playing .wave-trace{stroke:#af2785}.waveform figcaption{display:flex;justify-content:space-between;gap:12px;font-size:12px;line-height:1.6;color:#453450;font-weight:400}.wave-state{font-variant-numeric:tabular-nums}.waveform+ .audio-note{margin-top:0}button[aria-busy=true]{opacity:.75;cursor:progress}
@media(max-width:720px){.waveform svg{height:85px}.waveform figcaption{flex-wrap:wrap;font-size:12px}}

/* v5: centered mathematics and vertically related octave tables */
.display-equation{display:block;text-align:center;padding:15px 0}.display-equation math[display=block]{display:block;text-align:center;margin:0 auto;min-width:max-content}.display-equation button{display:block;margin:14px auto 0}.equation-condition{text-align:center;font-size:15px;color:#403147;margin:-12px 0 26px;line-height:1.8}.equation-condition i{font-family:'Cambria Math',math}.vertical-equivalence{display:flex;justify-content:center;align-items:center;height:44px;margin:-10px 0;color:#372246}.vertical-equivalence span{font-family:'Cambria Math',math;font-size:32px;display:block;transform:rotate(90deg);line-height:1}.odd-circle-figure{max-width:440px}.odd-circle-figure>svg{max-width:350px;margin:auto}.odd-listen{justify-content:center}.odd-circle-figure .waveform{margin-bottom:12px}.brand{font-size:25px;letter-spacing:.04em}.brand sup{font-size:.6em}