A Type Scale Is a Convention, Not a Law
Where the traditional point sizes came from, what a ratio actually buys, and a demonstration that the classic scale everyone cites is an imperfect fit to its own formula.
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Between 1886 and 1984 a point was 0.013837 inches. Not approximately: exactly that, by the definition the Type Founders Association of the United States adopted for the Johnson pica, which set one pica at 0.166044 inches and divided it by twelve. Seventy-two of those points came to 0.99624 inches, so a "72 point" line was very slightly under an inch, and everybody lived with it. Then PostScript arrived in 1984 and redefined the point as exactly one seventy-second of an inch, CSS inherited that in 1996, and the discrepancy quietly disappeared.
I start there because the type scale argument usually begins with ratios and harmony, and it is worth remembering that the thing being scaled was, for four centuries, a physical object you had to buy. The sizes in the traditional scale are not the output of a formula. They are an inventory.
The sizes you could actually buy
Before the point systems, type sizes had names rather than numbers, and the names came from use. Wikipedia's survey of traditional point-size names records that "as early as 1600, the sizes of these types acquired traditional names in English, French, German, and Dutch, usually from their principal early uses", and that "these names were used relative to the others and their exact length would vary over time, from country to country, and from foundry to foundry". The etymologies are usually given as devotional books and liturgical manuals, but the reference I checked does not supply them individually, so I will not repeat the standard list as fact.
Once the American point system standardised them, the names map onto points like this.
Points | American name | Millimetres |
|---|---|---|
5 | Pearl | 1.764 |
5.5 | Agate | 1.940 |
6 | Nonpareil | 2.117 |
7 | Minion | 2.469 |
8 | Brevier | 2.822 |
9 | Bourgeois | 3.175 |
10 | Long Primer | 3.528 |
11 | Small Pica | 3.881 |
12 | Pica | 4.233 |
14 | English | 4.939 |
18 | Great Primer | 6.350 |
20 | Paragon | 7.056 |
24 | Double Pica | 8.467 |
Look at the spacing of the first column. Single point steps from 5 to 12, then a jump to 14, then a jump to 18. That is not a ratio. That is a catalogue shaped by what compositors ordered, and the fine-grained region is exactly where books were set.
The competing systems make the same point differently. Pierre Simon Fournier fixed his point in 1737 at about 0.0135 English inches by dividing a French inch into 72. François-Ambroise Didot redefined it in 1783 as one eight hundred and sixty-fourth of a French foot, roughly 0.375972 mm, which made twelve Fournier points equal to eleven Didot points. Three incompatible definitions of "a point", each a local administrative decision, none derived from perception or proportion.
American Type Founders specimen book, 1912. The sizes available are the sizes that were cast, which is where the traditional scale actually comes from. No known restrictions, via Wikimedia Commons.
The classic scale is not a clean geometric series
The scale that gets quoted in design writing runs 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 21, 24, 30, 36, 48, 60, 72. Spencer Mortensen's article "The typographic scale", published 16 November 2011 and revised 19 July 2022, attributes that list to Bringhurst and then does the obvious thing nobody else does: he checks whether it is actually geometric.
It nearly is. Take a base of 12 points, a ratio of 2 and five steps per doubling.
Mortensen's finding is that the historical values and the mathematically derived ones diverge in two specific places: there is an extra 11 point that the progression does not call for, and there is a missing 42 point that it does. Above 24 the fit degrades badly.
That is the correction I would put on the first slide of any talk about type scales. The canonical scale, the one presented as the distilled wisdom of four hundred years of European typography, is an approximate geometric series with documented exceptions, and the exceptions are where the typesetters needed a size and the maths did not offer one. Small Pica at 11 points exists because compositors wanted something between Long Primer and Pica. No ratio produced it.
What Bringhurst actually recommends
Robert Bringhurst's The Elements of Typographic Style was published by Hartley & Marks in 1992, with a second edition in 1996, a third in 2005 and a fourth in 2012. Hermann Zapf's blurb for it, "I wish to see this book become the Typographers' Bible", turned out to be a self-fulfilling prophecy, which is part of the problem: the book is quoted more often than it is read.
Richard Rutter's The Elements of Typographic Style Applied to the Web quotes rule 3.1 directly, and the quotation is not what the modular-scale literature implies:
"In the sixteenth century, a series of common sizes developed among European typographers, and the series survived with little change and few additions for 400 years. [...] Use the old familiar scale, or use new scales of your own devising, but limit yourself, at first, to a modest set of distinct and related intervals."
Three things in that sentence. He describes the old scale as something that developed, not something that was derived. He explicitly authorises inventing your own. And the actual instruction, the imperative verb, is limit yourself. The constraint is the recommendation. The ratio is not mentioned.
The other Bringhurst line that circulates comes from the chapter on shaping the page, and Tim Brown quotes it in "More Meaningful Typography", published in A List Apart on 3 May 2011: "A modular scale, like a musical scale, is a prearranged set of harmonious proportions." That is a definition, not an endorsement of any particular proportion. Brown's own framing is careful in the same way: a modular scale is "a sequence of numbers that relate to one another in a meaningful way", and he calls scales "tools, not dogma", advising designers to treat the generated numbers as educated suggestions.
The tool Brown built with Scott Kellum, modularscale.com, offers seventeen ratios, most of them named after musical intervals: minor second 1.067, major second 1.125, minor third 1.2, major third 1.25, perfect fourth 1.333, augmented fourth 1.414, perfect fifth 1.5, minor sixth 1.6, golden section 1.618, major sixth 1.667, minor seventh 1.778, major seventh 1.875, octave 2, and larger. Seventeen options is itself an argument that no one of them is right.
A word about 1.618
The golden section deserves a caveat that design writing rarely supplies. George Markowsky's paper "Misconceptions about the Golden Ratio", in The College Mathematics Journal volume 23, number 1, January 1992, pages 2 to 19, opens with this assessment: "Typically, the mathematical properties concerning the golden ratio are stated correctly, but much of what is presented with respect to the golden ratio in art, architecture, literature, and aesthetics is false or seriously misleading."
That is a mathematician writing in a mathematics journal about the claims made for the number outside mathematics. It does not mean 1.618 is a bad ratio for a type scale. It means the historical and aesthetic authority usually invoked to justify it does not exist, and you are choosing it because you like what it produces. Which is a fine reason, stated plainly.
What a ratio buys, and where it stops paying
A ratio buys you three real things. It guarantees that any two sizes in the set have a consistent relationship, so a heading two steps up from body text has the same relationship everywhere in the product. It gives you a defensible answer to "why 25 and not 26". And it makes the set extensible: you can generate another step without reopening the argument.
What it does not do is survive contact with integer pixels at small sizes. Here is the comparison at real interface sizes.
The hand-set scale is not a single ratio. It is a ratio that grows: around 1.11 to 1.17 at the small end, 1.20 to 1.25 in the middle, 1.33 at display sizes. That is the same shape as the metal-type inventory, which stepped by one point from 5 to 12 and then by four and six points above that.
The reason is that perceptual size difference and arithmetic size difference are not the same at the bottom of the range. Two pixels between 12 and 14 is a visible hierarchy step. Two pixels between 48 and 50 is a rendering artefact. A constant ratio gets the top of the range right and either crushes the bottom or blows the top out, depending on which end you anchor.
The 1.25 column above shows the second failure clearly: nothing usable between 16 and 20, a 25 that is awkward beside a 24 px icon grid, and then 31, 39, 49, 61, none of which are numbers anyone wants to type. The 1.2 column is better behaved but gives you 19 where you wanted 18, which is exactly the size you need for a slightly larger body paragraph.
When a hand-set scale is better
Three situations, in my experience.
The first is when the scale has to meet something that is not a scale. Icon grids come in 16, 20 and 24. Touch targets have minimums. Line heights want to land on a baseline unit. A generated scale that produces 25.2 px will be rounded by somebody downstream, and it is better to do the rounding yourself, once, deliberately, than to ship a token whose value is a lie.
The second is when the range is wide. If you need caption text and a hero headline in the same system, no single ratio serves both ends. Either run two ratios with a documented switch point, or set the sizes by hand and record the ratios afterwards as a check on your own consistency.
The third is when you have fewer than about six sizes. Bringhurst's instruction was to limit yourself to a modest set of distinct and related intervals. A six-value scale does not need a generator; it needs six good decisions. The generator earns its keep when the set is large enough that you cannot hold it in your head.
What I would say instead
A ratio is a starting point, not a result. Generate the scale, then look at it set in the actual typeface at the actual sizes, then move the numbers. If you end up with 12, 14, 16, 18, 20, 24, 30, 36, 48, you have arrived at something very close to the metal-type inventory by a different route, and that convergence is worth more than any derivation.
Two honest limitations on everything above. I quoted Bringhurst's rule 3.1 from Richard Rutter's site and from Ariel Salminen's 2012 essay, both of which reproduce the same passage; I did not have the book itself open in this session, and I could not verify from a primary source that the specific list of seventeen sizes Mortensen gives appears in Bringhurst in that form. And I have found no perceptual study establishing that ratio-based size relationships are read as more harmonious than hand-tuned ones. If such a study exists I have not seen it, which means that the entire case for modular scales rests on the analogy with musical intervals, an analogy that Bringhurst offers as a description and that everyone since has treated as a proof.
Sources
"Point (typography)." Wikipedia. Fournier's 1737 point at about 0.0135 inches, Didot's 1783 redefinition at roughly 0.375972 mm, the twelve-to-eleven Fournier-Didot relation, the 1886 American point system (pica 0.166044 in, point 0.013837 in, 72 points at 0.99624 in), and the 1984 PostScript and 1996 CSS point at exactly 1/72 in. en.wikipedia.org/wiki/Point_(typography)
"Traditional point-size names." Wikipedia. The table of names and point sizes, the note that names were in use as early as 1600 and derived from principal early uses, and that bodies varied from foundry to foundry. en.wikipedia.org/wiki/Traditional_point-size_names
Mortensen, Spencer. "The typographic scale." Published 16 November 2011, modified 19 July 2022. The classic scale list, the scaling property, the fit with base 12 pt, ratio 2 and five steps, and the documented extra 11 pt and missing 42 pt. spencermortensen.com/articles/typographic-scale/
Rutter, Richard. The Elements of Typographic Style Applied to the Web, rule 3.1. The quoted passage from Bringhurst on the sixteenth-century series and the instruction to limit yourself to a modest set of intervals. webtypography.net/3.1.1
Salminen, Ariel. "On Typography." 2012. Reproduces the same Bringhurst passage, used here as a second witness to the wording. arielsalminen.com/2012/on-typography/
Brown, Tim. "More Meaningful Typography." A List Apart, 3 May 2011. The definition of a modular scale, the Bringhurst quotation "A modular scale, like a musical scale, is a prearranged set of harmonious proportions", and the "tools, not dogma" framing. alistapart.com/article/more-meaningful-typography/
Kellum, Scott, and Tim Brown. Modular Scale. The seventeen ratios and their values, and the attribution to Brown's 2010 Build talk. modularscale.com
Markowsky, George. "Misconceptions about the Golden Ratio." The College Mathematics Journal 23, no. 1 (January 1992): 2–19. The quoted assessment of golden-ratio claims in art, architecture, literature and aesthetics. eric.ed.gov/?id=EJ445071
"The Elements of Typographic Style." Wikipedia. Bringhurst, Hartley & Marks, editions of 1992, 1996, 2005 and 2012, and Hermann Zapf's "Typographers' Bible" remark. en.wikipedia.org/wiki/The_Elements_of_Typographic_Style
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