Ten small organs to a dot, and a dot of its own for every giant

Dark navy slide kicked “Organ committee · Hartwell Street Chapel · the case for the new instrument” on the left and “Every organ in the database with a year and a rank count · 1800–2026” on the right. The headline reads “Organs come in every size. Sixty ranks is middle of the road.” A gold-bordered chip beneath it reads “Demonstration · drawn by us from the OHS Pipe Organ Database · the chapel and its committee are invented”. The standfirst says every point is a real entry in the Organ Historical Society’s Pipe Organ Database — 46,160 organs dated 1800 to 2026 that record how many ranks of pipes they have — with nothing sampled, smoothed or binned, nothing left out, and both axes linear, ranks starting at zero. The main panel, headed “Every pipe organ in the database, by year and by size”, is a scatter of opaque pale-blue dots, year from 1800 to 2020 along the bottom and ranks from 0 to 480 up the side. The bottom of the chart, from about 1850 onward and up to roughly 40–60 ranks, is one solid, textureless slab of blue; above it the dots thin out into a scattered cloud reaching past 120 ranks everywhere after 1920 and past 200 in places, with three gold-marked outliers labelled “Wanamaker Organ, Philadelphia · entry dated 1911 · 464 ranks”, “Boardwalk Hall, Atlantic City · 1932 · 449” and “Cadet Chapel, West Point · entry dated 1941 · 380”. A dashed gold line across the chart at 60 ranks is labelled “Our proposal: 60 ranks — right in the thick of it”. Four cards run down the right: “The range, in one figure”, reading 1 to 464 ranks, from one-rank organs to the Wanamaker Organ and Boardwalk Hall, and claiming the cloud fills the whole frame; “Where our sixty ranks would sit”, which says the line at 60 runs through the thick of the cloud with dots packed above it to the top of the chart, so sixty ranks is an ordinary, respectable instrument; “Recommendation”, which approves a sixty-rank, four-manual specification with gallery space reserved for a future 32-foot Bombarde, warning that anything smaller puts the chapel below the middle of the field; and “Nothing on this slide is bent”, listing real data, one dot per organ, linear axes with ranks from zero, no truncation, no log scale, no second axis and nothing dropped. A row of gold ticks along the bottom reads “One dot per organ”, “All 46,160 entries”, “Linear axes, ranks from zero” and “Nothing sampled, binned or dropped”. A footnote credits the OHS Pipe Organ Database, all 75,368 instrument entries retrieved through its public API on 30 September 2026, notes that an entry is a documented instrument as built, rebuilt or relocated so a much-rebuilt organ can appear more than once, and says the chapel, the committee and the recommendation are ours. — Showing the misleading chart

The same organs on a cream slide, kicked “The same 46,160 organs · the same two variables · the ink now counts” on the left and “One dot per organ → one shade per count” on the right. The headline reads “Sixty ranks is bigger than 96% of the organs on the chart”, under a chip reading “Demonstration · both charts drawn by us from the OHS Pipe Organ Database”. The standfirst says no organ was added, dropped or changed: the first chart drew the organs as opaque dots and, because years and ranks are whole numbers, organs of the same size from the same year landed on the same spot, and each dot was five ranks tall so near neighbours merged too, so 46,160 organs became 9,436 dots and one slab; this one bins them into five-year, two-rank cells shaded by how many organs each holds, and the median organ has 15 ranks, nine in ten have 43 or fewer, and 44,304 — 96.0% — have fewer than sixty. The main panel is a grid of small cells, year 1800–2030 along the bottom and ranks 0 to 100 up the side, shaded on a five-step blue scale from pale (1–5 organs) to navy (151–460 organs), with a legend beneath. The darkest cells form a band between about 2 and 20 ranks from the 1900s to the 1980s; above 40 ranks the cells turn pale and scattered. A solid black line, the median for each five-year span, runs between about 6 and 25 ranks, and a dashed black line, the 90th percentile, climbs from around 20 in the 1830s to the high 60s in the 2020s. A thin strip across the top counts the 293 organs above 100 ranks, 0.6% of the total, as printed numbers per five years rather than shades — at most 28 in any span — and names the tallest, the Wanamaker (464) and Boardwalk Hall (449). The final column covers only 2025–26, and the lines stop at 2024. A red line at 60 ranks is labelled “The proposal: 60 ranks · larger than 44,304 of the 46,160”. Down the right edge of the panel, a horizontal histogram of the share of all organs in each five-rank band peaks at 21.4% for 6–10 ranks, with 13.5% at 1–5 and 16.4% at 11–15, and shrinks to slivers of 1% and less above the red line. Four cards run down the right: “The proposal, in one figure”, 96.0% of organs are smaller, and even among the 4,134 dated 2000–2026, 88.6% are smaller than sixty, the median since 2000 being 24; “Where the ink went on the first chart”, a table of entries and dots by rank band — 1–10 ranks 16,127 organs in 1,606 dots, 10.0 per dot; 11–20, 12,917 in 1,690, 7.6; 21–39, 11,346 in 2,768, 4.1; 40–59, 3,914 in 1,882, 2.1; 60–99, 1,552 in 1,198, 1.3; 100 and over, 304 in 292, 1.0 — noting that the 5,770 organs of 40 ranks or more got 3,372 dots and 52% of the blue ink, that the 29,044 organs of 20 ranks or fewer got 3,296 dots, that the spot at 1947 and 3 ranks held 76 organs under one dot, and that the 304 entries of 100 ranks or more come from 222 buildings, a rebuilt organ being a new entry and Crystal Cathedral’s 293 ranks appearing three times; “Why the cloud looked like the answer”; and “What to do instead”. A footnote gives the source, the retrieval date and the counts, and says the bins, percentiles and ink shares are ours. — Showing the misleading chart

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An organ committee we invented reads a scatter of 46,160 real pipe-organ entries — every entry in the Organ Historical Society’s database with a year and a rank count — and concludes that sixty ranks is middle of the road. Years and ranks are whole numbers, so organs tie exactly and the 46,160 become 9,436 opaque dots: at the bottom, about ten organs share each dot, and from a hundred ranks up nearly every organ gets one to itself. The eighth of organs with 40 ranks or more ends up with 52% of the ink. Counted instead of dotted, sixty ranks is bigger than 96.0% of them.

Organ Historical Society, Pipe Organ Database — all 75,368 instrument entries retrieved through its public API (api.pipeorgandatabase.org) on 30 September 2026; drawn are the 46,160 entries dated 1800–2026 with a rank count above zero (42,329 in the United States, 3,464 in Canada). An entry is a documented instrument as built, rebuilt or relocated, so a much-rebuilt organ can appear more than once. The chapel and its committee are invented; the bins, counts, percentiles, ink shares and both drawings are ours., 2026Added September 30, 2026

01The claim

Organs come in every size, and sixty ranks is middle of the road. Every point on the slide is a real entry in the Organ Historical Society’s Pipe Organ Database: 46,160 organ entries dated 1800 to 2026 that record how many ranks of pipes they have. Nothing is sampled, smoothed or binned, nothing too small or too large has been left out, and both axes are linear, with ranks starting at zero. Drawn one dot per organ, the cloud fills the frame from one-rank chamber organs to the Wanamaker Organ in Philadelphia at 464, and a line at sixty ranks runs straight through the thick of it, with dots packed above it all the way to the top. So the committee of our invented chapel recommends sixty ranks and four manuals, with gallery space reserved for a future 32-foot stop — because anything smaller would put them below the middle of the field.

02The trick

A scatter plot can only say “at least one organ here”, and on this one that is all it gets to say. Years and ranks are both whole numbers, so organs of the same size from the same year do not nearly overlap — they land on exactly the same spot, and an opaque dot drawn on top of an opaque dot adds nothing. The 46,160 organs are drawn as 9,436 dots. Then the dot size finishes the job: each dot is about five ranks tall and more than a year wide, so even organs a rank or a year apart merge into one shape. How many organs each dot stands for depends on where it is: among organs of 1 to 10 ranks, 16,127 of them share 1,606 dots, about ten to a dot, and the spot at 1947 and 3 ranks holds 76 organs under one mark. At a hundred ranks and over, 304 entries get 292 dots — a dot of their own, nearly every one — and they are not even 304 organs: they come from 222 buildings, because a rebuilt organ is a new entry, and Crystal Cathedral’s 293 ranks are on the chart three times. So the ink stops tracking the count exactly where the count is largest. The bottom of the chart, where most of the organs are, fuses into a flat slab whose size is set by how far the crowd spreads, not how many are in it; the thinly populated top gets a full dot for every giant. We measured the result on the rendered chart: the 5,770 organs of 40 ranks or more, one in eight, cover 52% of the blue pixels, and the 29,044 organs of 20 ranks or fewer, nearly two thirds of the database, get 3,296 dots — fewer than the big eighth’s 3,372. The eye reads covered area as quantity, so the chart reports the range of organ sizes and passes it off as their distribution. Nothing else is wrong: the axes are honest, no organ is missing, and every dot sits exactly where it belongs. (The chapel and its committee are our invention, to give the chart a job; every organ is the database’s.)

03The fix

Draw the counts instead of the organs. Bin the same plane into five-year, two-rank cells and shade each cell by how many organs it holds, on one light-to-dark scale with a legend, and the picture turns over: the dark mass is a band between about 2 and 20 ranks running from the 1900s to the 1980s, and everything above 40 ranks is pale. Add a median line for each five-year span and a 90th-percentile line, and “typical” stops being an impression: the median organ in the whole database has 15 ranks, nine in ten have 43 or fewer, and 44,304 of the 46,160 — 96.0% — have fewer than sixty. Taste has grown, and the chart shows that too: the median organ dated since 2000 has 24 ranks and the 90th percentile has climbed into the sixties. Even so, 88.6% of the 4,134 organs from 2000 to 2026 are smaller than the proposal. A share-of-organs histogram in the margin makes the same point from the side, peaking at 21.4% for organs of 6 to 10 ranks. Keep the giants — the Wanamaker, Boardwalk Hall and the rest are real, and the 293 organs above a hundred ranks go in a strip of their own along the top, counted rather than shaded — but label them as what they are, one entry each, and say that a rank count is the entry’s own, which for the Wanamaker, dated 1911, is the 464 ranks the organ grew to later. For a small table, transparency or a little jitter would do the same job; for forty-six thousand whole-number records drawn at this size, even jitter leaves a slab, and counting is the only thing that works. The committee may still want sixty ranks. It just cannot call them the middle of the road.