When a 1.25 type scale from base 16 yields 12.8, 31.25 and 39.06, how do you round them, and when should you hand-tune steps?

## Computed values are a starting point A **modular type scale** multiplies a **base size** by a constant **ratio** for each step. With a base of 16 and a ratio of 1.25 the computed series is 10.24, 12.8, 16, 20, 25, 31.25, 39.06, 48.83. Almost nobody ships those exact numbers. Fractional sizes are awkward to specify, to discuss in a review and to pair with line heights, and different renderers may treat fractions differently. So the computed series is rounded, and occasionally adjusted by hand. The question is how to do that without losing what the scale was for: a short list of sizes with even, visible steps. ## Rounding strategies | Strategy | Result for base 16, ratio 1.25 | Trade-off | |---|---|---| | Exact values | 10.24, 12.8, 16, 20, 25, 31.25, 39.06, 48.83 | Faithful to the ratio; awkward to use and communicate | | Whole numbers | 10, 13, 16, 20, 25, 31, 39, 49 | Small drift; easy to use | | Multiples of 4 everywhere | 12, 12, 16, 20, 24, 32, 40, 48 | Tidy large steps; the two bottom steps collide | | Whole numbers below the base, multiples of 4 above | 10, 13, 16, 20, 24, 32, 40, 48 | Common hybrid; drift of a few percent per step | The drift is real but small. In the hybrid row, neighbouring ratios wander between about 1.2 and 1.33 instead of a constant 1.25. Readers do not measure ratios; they see steps that look evenly spaced and clearly different, and that is preserved. ## Why coarse rounding breaks the small end A 4-unit grid is a reasonable granularity for large sizes, where 4 is a small fraction of the value. At the bottom of the scale, 4 is a large fraction: 12.8 and 10.24 both round to 12, and two steps become one. The fix is to round small steps more finely, to whole numbers, and to keep grid alignment mostly for **line heights**, since line height is what actually occupies vertical space and lands on a baseline grid. ## When to hand-tune a step - **A step is too small to read.** 10.24 rounds to 10, which is below the size most teams accept for readable text such as the posting date on a job card. Drop the step, or raise it — but not to 12, where it would sit a single unit from 13 and look like the same size. - **Neighbours are too close after rounding.** If two adjacent steps end up only one unit apart at small sizes, one of them is not earning its place. - **A top step is impractical.** A display step that overflows a phone-width headline for a marketplace's landing page may be compressed or dropped; how sizes change across screen widths is a separate responsive decision. - **The typeface disagrees.** A face with a large x-height can make a step look bigger than its number, so optical tuning of one step is legitimate. What does **not** justify a new or changed step is a single design that wants 17 because it fits one card. That is the drift a scale exists to prevent. ## Keep the tuned scale honest 1. **Record both columns.** Document the computed value and the shipped value for every step, and why they differ. 2. **Keep it strictly increasing.** No step may equal or undercut the one below it after rounding. 3. **Keep neighbours visibly different.** Check them side by side in real layouts, not only in a specimen sheet. 4. **Re-derive deliberately.** If the base or ratio changes, recompute the whole list and review each tuned step again, rather than editing one value in isolation. 5. **Test on real content.** Set a dense screen, such as a freelancer's proposal list, with the tuned scale and confirm the steps still read as distinct at the sizes people actually see. ## Why this still counts as a modular scale A hand-tuned, rounded scale keeps the properties that matter: a small fixed list, proportional steps that look even, and a documented origin that explains every value. Treating the exact computed series as untouchable gives none of those extra benefits and makes the scale harder to use on every platform that has to express it.