Why is the linespread factor as it is?

The blog post Quick note on line spacing discusses line spacing and it says

To change the line spacing for the entire document, you can use the linespread command in your preamble:

The factor is somewhat confusing. For double-spacing you have to use 1.6 and for one-and-a-half spacing 1.3. Not very intuitive, but I'm sure there is a reason for it.

This unintuitive factor triggered my curiosity. What is the reason for it being as it is?

This question is just motivated by my curiosity and I have no practical reason for asking it. Feel free to close it if it's inappropriate or see at as post in the same vein as \nothing, \varnothing and \emptyset in that it asks about history or some design decision.

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Perhaps not an exact duplicate, but surely of interest: tex.stackexchange.com/questions/13742/… –  lockstep Sep 30 '11 at 15:41
There's no official definition of "double spaced". Pick what is less displeasing ("more pleasing" would be an oxymoron). –  egreg Sep 30 '11 at 15:44
In my previous question, there may be 3 different definitions of "double-spacing". setspace package uses a different one other than MS Word, Ooo Write, etc. –  Leo Liu Sep 30 '11 at 15:51
I like curiosity questions. There should be an extra tag for it :) –  topskip Sep 30 '11 at 19:53

With the LaTeX standard classes (article, book, and report) and no class options added, \normalsize results in a font size (size of the largest glyphs in a font -- typically, braces) of 10pt and a \baselineskip (vertical skip between the base lines of two successive lines of type) of 12pt. The ratio between font size and \baselineskip is 1.2.

The linespread command (which must be issued in the document preamble) may be used to change the \baselineskip without changing the font size.

A possible definition of \onehalfspacing and \doublespacing is that the ratio between font size and \baselineskip should be 1.5 resp. 2. Because the "basic" ratio for 10pt is 1.2, a multiplier of 1.25 and (approximately) 1.667 has to be applied -- and this is basically what the setspace package does. ("Basically" because it retains the ratio of 1.2 for footnotes and the like.)

The statement "For double-spacing you have to use 1.6 and for one-and-a-half spacing 1.3" amounts to either a rounding error, or being confused, or both.

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Extending lockstep's answer to other documentclass options (like 11pt and 12pt) gives rise to the seemingly strange scaling factors used by the setspace package:

• 10pt (already discussed)

setspace defines the scaling factor to be 1.25 for \onehalfspacing and 1.667 for \doublespacing, since the "basic" ratio is 1.2 (\normalfont has a \baselineskip of 12pt; see size10.clo)

• 11pt

setspace defines the scaling factor to be 1.213 for \onehalfspacing and 1.618 for \doublespacing, since the "basic" ratio is 1.236 (\normalfont has a \baselineskip of 13.6pt; see size11.clo)

• 12pt

setspace defines the scaling factor to be 1.241 for \onehalfspacing and 1.655 for \doublespacing, since the "basic" ratio is 1.208 (\normalfont has a \baselineskip of 14.5pt; see size12.clo)

As such, in the following hypothetical situation, a scaling factor of 2.4 (that is, \setstretch{2.4}) would provide "triple spacing" in a document with normal font size of 16pt and \baselineskip of 20pt.

All scaling factors are rounded to 3 digits after the decimal.

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