Re: Font questions about absolute

[Aaron Hill]

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
> help.
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