2c:null 2d:["$","title",null,{"children":"Seven Week Starts: Calendar Sensitivity Atlas | Mateo Pedersen | Observable"}] 32:T6be,# Seven Week Starts: Calendar Sensitivity Atlas Week origins are conventions, not properties of a month. Moving the origin shifts day 1 to a new column and can add or remove a natural grid row. This atlas compares Monday through Sunday for each 2027 month. ## How sensitivity is measured The layout sensitivity score is the number of distinct natural row counts observed across the seven week starts. It is a descriptive metric defined for this notebook, not an industry standard. The matrix can encode row count, leading offset, or trailing capacity; numbers accompany color so the pattern remains readable without it. [Project context: Beta Calendars](https://www.betacalendars.com/) ## Month reference table The grids are computed locally; these links are printable human-readable examples. | Month | Reference | |---|---| | January | [January](https://www.betacalendars.com/january-calendar.html) | | February | [February](https://www.betacalendars.com/february-calendar.html) | | March | [March](https://www.betacalendars.com/march-calendar.html) | | April | [April](https://www.betacalendars.com/april-calendar.html) | | May | [May](https://www.betacalendars.com/may-calendar.html) | | June | [June](https://www.betacalendars.com/june-calendar.html) | | July | [July](https://www.betacalendars.com/july-calendar.html) | | August | [August](https://www.betacalendars.com/august-calendar.html) | | September | [September](https://www.betacalendars.com/september-calendar.html) | | October | [October](https://www.betacalendars.com/october-calendar.html) | | November | [November](https://www.betacalendars.com/november-calendar.html) | | December | [December](https://www.betacalendars.com/december-calendar.html) |33:T17ef,const app3 = (() => { const M=["January","February","March","April","May","June","July","August","September","October","November","December"],W=["Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"],root=document.createElement("section");root.style.cssText="font:14px/1.5 system-ui,sans-serif;color:#17233b;background:#fbfaf6;padding:22px;border:1px solid #dfe6e8;border-radius:14px;max-width:1100px;margin:auto";const css=document.createElement("style");css.textContent=".a3bar{display:flex;gap:12px;flex-wrap:wrap}.a3bar label{display:grid;font-size:12px}.a3bar select{padding:7px;border-radius:7px;border:1px solid #bac7cf}.a3grids{display:grid;grid-template-columns:repeat(auto-fit,minmax(190px,1fr));gap:10px}.a3card{border:1px solid #dce3e7;border-radius:10px;padding:10px;background:white}.a3grid{display:grid;grid-template-columns:repeat(7,1fr);gap:2px;text-align:center}.a3grid span{background:#edf3f3;padding:3px;font-size:10px}.a3grid .lead{background:#dce9ed;color:#486171}.a3small{font-size:13px;color:#536174}.a3table{border-collapse:collapse;width:100%}.a3table td,.a3table th{border:1px solid #e3e8ea;padding:5px;text-align:center;font-size:12px}@media(max-width:520px){.a3card{padding:7px}.a3grid span{padding:2px;font-size:9px}}";root.append(css);const h=document.createElement("h2");h.textContent="Week-origin transformations";root.append(h);const bar=document.createElement("div");bar.className="a3bar";function select(label,vals){const l=document.createElement("label");l.textContent=label;const s=document.createElement("select");vals.forEach(v=>{const o=document.createElement("option");o.textContent=v;s.append(o)});l.append(s);bar.append(l);return s}const ms=select("Month",M),metric=select("Matrix metric",["Rows","Leading offset","Trailing capacity"]);root.append(bar);const summary=document.createElement("p");summary.className="a3small";root.append(summary);const grids=document.createElement("div");grids.className="a3grids";root.append(grids);const rad=document.createElement("div");rad.className="a3card";root.append(rad);const mat=document.createElement("div");mat.className="a3card";root.append(mat); function leap(y){return y%4===0&&(y%100!==0||y%400===0)}function days(y,m){return[31,leap(y)?29:28,31,30,31,30,31,31,30,31,30,31][m-1]}function wd(y,m,d){return(new Date(Date.UTC(y,m-1,d)).getUTCDay()+6)%7}function off(y,m,w){return(wd(y,m,1)-w+7)%7}function rows(y,m,w){return Math.ceil((off(y,m,w)+days(y,m))/7)}function trail(y,m,w){return rows(y,m,w)*7-off(y,m,w)-days(y,m)} function draw(){const m=M.indexOf(ms.value)+1,d=days(2027,m),first=wd(2027,m,1),rs=W.map((_,i)=>rows(2027,m,i)),score=new Set(rs).size;summary.textContent="Sensitivity score: "+score+" distinct natural row counts across seven origins · day 1 falls on "+W[first]+" in the Monday-first reference frame.";grids.replaceChildren();W.forEach((name,w)=>{const c=document.createElement("div");c.className="a3card";const title=document.createElement("strong");title.textContent=name+" first · "+rows(2027,m,w)+" rows";c.append(title);const g=document.createElement("div");g.className="a3grid";for(let i=0;i<7;i++){const x=document.createElement("span");x.textContent=W[(w+i)%7].slice(0,2);x.style.background="#d8e8e6";g.append(x)}const n=rows(2027,m,w)*7;for(let i=0;i0&&day<=d?day:"·";x.className=day===1?"lead":"";if(day===1)x.title="First day shifts to column "+(w+off(2027,m,w)+1);g.append(x)}c.append(g);const p=document.createElement("p");p.className="a3small";p.textContent="Leading "+off(2027,m,w)+" · trailing "+trail(2027,m,w);c.append(p);grids.append(c)}); rad.replaceChildren();const rh=document.createElement("h3");rh.textContent="Weekday origin and day-one offset";rad.append(rh);const svg=document.createElementNS("http://www.w3.org/2000/svg","svg");svg.setAttribute("viewBox","0 0 360 260");svg.setAttribute("role","img");svg.setAttribute("aria-label","Circular view of seven week origins and required day-one offset");const ns="http://www.w3.org/2000/svg";W.forEach((name,i)=>{const a=2*Math.PI*i/7-Math.PI/2,x=180+90*Math.cos(a),y=125+90*Math.sin(a),c=document.createElementNS(ns,"circle");c.setAttribute("cx",x);c.setAttribute("cy",y);c.setAttribute("r",18);c.setAttribute("fill",i===first?"#176f76":"#d7e7e8");svg.append(c);const t=document.createElementNS(ns,"text");t.setAttribute("x",x);t.setAttribute("y",y+4);t.setAttribute("text-anchor","middle");t.setAttribute("font-size","11");t.textContent=String(off(2027,m,i));svg.append(t);const lab=document.createElementNS(ns,"text");lab.setAttribute("x",180+126*Math.cos(a));lab.setAttribute("y",125+126*Math.sin(a)+4);lab.setAttribute("text-anchor","middle");lab.setAttribute("font-size","10");lab.textContent=name.slice(0,3);svg.append(lab)});rad.append(svg);const rp=document.createElement("p");rp.className="a3small";rp.textContent="At each origin, the number inside the node is the leading offset needed to place day 1. The highlighted node marks the weekday on which the month begins.";rad.append(rp); mat.replaceChildren();const mh=document.createElement("h3");mh.textContent="Month × week-start transition matrix";mat.append(mh);const table=document.createElement("table");table.className="a3table";const head=document.createElement("tr");head.innerHTML="Month"+W.map(x=>""+x.slice(0,3)+"").join("");table.append(head);M.forEach((name,j)=>{const tr=document.createElement("tr");tr.innerHTML=""+name.slice(0,3)+""+W.map((_,w)=>{const v=metric.value==="Rows"?rows(2027,j+1,w):metric.value==="Leading offset"?off(2027,j+1,w):trail(2027,j+1,w);return ""+v+""}).join("");table.append(tr)});mat.append(table);const p=document.createElement("p");p.className="a3small";p.textContent="Every cell reports the selected metric; switching the selector rebuilds the table. The score counts distinct row counts, while the matrix reveals offset and trailing-space transitions.";mat.append(p)}[ms,metric].forEach(x=>x.addEventListener("change",draw));draw();return root})(); app334:[] 30:{"id":"62cd4b2b36125688","slug":"seven-week-starts-sensitivity-atlas","title":"Seven Week Starts: Calendar Sensitivity Atlas","thumbnail":"343e9f60169c1b70a512fa984a2a1d00265b46c40d56b451a18a23a15904b540","access_level":"public","create_time":"$D2026-10-07T11:21:51.122Z","update_time":"$D2026-10-07T11:29:11.521Z","view_time":null,"first_public_time":"$D2026-10-07T11:38:40.992Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"0608cb6e6fdd19ad","login":"mateopedersen","name":"Mateo Pedersen","avatar_url":"https://avatars-next.observableusercontent.com/1656f6350cbcad592ca7fe8675140cd56effd725832498d28117b54dc11cfe4b","tier":"free_2026","bio":"Independent product builder exploring calendar computation, printable-layout geometry and temporal data visualization. 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