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Re: Font questions about absolute

From: Aaron Hill
Subject: Re: Font questions about absolute
Date: Sat, 11 May 2019 12:16:01 -0700
User-agent: Roundcube Webmail/1.3.8

On 2019-05-11 10:52 am, Reggie wrote:
Is there any easy way to quickly see or convert absolutely font to #3 or #5 and so on? In frescobaldi like a function() or something. Thank you for any

Within \markup, you can use \abs-fontsize to get a specific size that will not scale based on the global staff size. That does not require any conversion.

If you are trying to set the relative font size of a grob that produces text and you want it to match a specific absolute font size, then you are going to need to break out your calculator and do some arithmetic. (LilyPond has some Scheme functions to assist here.)

One thing to understand is the logarithmic scale that LilyPond uses for relative font sizes. A value of 6 results in doubling the size of a font, whereas a value of -6 will halve the size of the font. Each increment of 6 in either direction is another doubling or halving. So in this system, adding an amount on the logarithmic scale results in multiplying the value on the linear scale.

The magstep and magnification->font-size procedures help with converting between linear and logarithmic. So (magstep 6) will produce 2.0 as output, and (magnification->font-size 1/2) will produce -6.0 as output. But if you need to do the math by hand, here are those functions:

  magstep(x) = 2 ^ (x / 6)
  magnification->font-size(x) = 6 * log_2(x)

(Recall that a logarithm of any one base can be used to compute the logarithm of any other base. So to compute the base-two log above using the natural log is simply: ln(x) / ln(2).)

Another thing to be aware of is how the global staff size plays into font size. The default is a 20pt staff (5pt staff spaces) and a resulting font size of 11pt. The ratio of 11/20 is important, since if you were to shrink the staff size to 16, for example, the resulting font will be 16 * 11/20 = 8.8.

Putting this together, we can calculate precisely what the resulting font size would be given our knowledge of the global staff size and the relative font size of a text element. Likewise, we can determine a relative font size that will result in an absolute font size.

For the first case--going from relative to absolute--let us assume we have a staff size of 18 and our grob's font-size is 2. The global font size is 18 x 11/20 = 9.9 and the magnification factor is 2^(2/6) ~= 1.26, so our result is approximately 12.5pt. And in Scheme, we could say:

  (* 18 11/20 (magstep 2))
  --> 12.4732183939592

For the second case--going from absolute to relative--let us assume we have a staff size of 24 and need to set the grob's font-size so that the result is exactly 18pt. The global font size is 24 * 11/20 = 13.2. To get from 13.2 to 18 requires a magnification of 18 / 13.2 ~= 1.36. This, in the logarithm scale, is 6 * log_2(1.36) ~= 2.68. In Scheme, we do:

  (magnification->font-size (/ 18 (* 24 11/20)))
  --> 2.68475386182733

Now all that said, is this "easy"? Depends on your comfortability with maths, I suppose. I usually stick to relative font sizes and do not concern myself with the absolutes, since it is my eye that determines whether something is big enough or small enough, not a ruler.

Of course, I recently did have to use the above computations when I was typesetting hymns for projection. I needed to have the flexibility of changing the staff size independent of the lyric font size as I was experimenting with what would look good. So rather than have to compute things by hand, I used something similar to the absolute-to-relative Scheme code above.

-- Aaron Hill

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