Re: Usage of ly:stencil-fonts ??

[Torsten Hämmerle]

Hi Harm,

All these numbers are quite confusing at first glance. And at second and
third glance, too.
But they are nothing but conversion factors to switch units.
And, unfortunately, LilyPond basically uses three concurrent units in
parallel:

- LilyPond units in staff-spaces
- Pango units in mm
- Typographic units in pt


This said, I'll try to derive all the values you have found using the
example of a standard 20-pt-staff with the corresponding standard text font
size of 11pt.
I will use a ridiculous number of decimal places to make it easier to
compare the results to your scheme output. 

As LilyPond is a European program, there are no inches to be seen and we'll
only use mm (millimetres).
Both mm and pt are always absolute units (as printed on the final sheet),
whereas a staff-space (let's call it 1sp) is always relative (depending on
the current staff-size).



pt value: conversion between pt and sp

The 'pt values are the conversion factor from pt to staff-spaces:
A 5-line 20-pt staff is 4sp high ==> 20pt = 4sp, in other words: 

1pt = 0.2sp (resp: 'pt = 0.2)

See? Multiply any value in pt by 'pt and you'll get staff-spaces.

With a 10-pt staff, we get 'pt = 0.4 so that you have to multiply any
pt-value by 0.4 to get the corresponding value in staff-spaces. The factor
has to be twice as big because a 10pt staff is half the size of a 20pt
staff.

 
ancestor-pt value: conversion between pt and mm

In markup (i.e. font environment), Pango fonts (metrics and size in mm!)
come into play.

This factor does not change when varying global-staff-size or anything,
because both pt and mm are absolute units and the conversion factor always
stays the same. Knowing how many mm or pt are in an inch, it's easy to
derive the factor:
1in = 25.4mm
1in = 72.27pt

1pt = 0.3514598035145980351459803514598 mm
This is your ancestor-pt value. :)

Our standard 11pt-font therefore will be 3.8660578386605783... mm in size
*Caveat:* the Pango font size from stencil-expr is not quite that, because
there is some rounding applied to avoid buffering too many fonts with with
microscopic size differences.


text-font-size: Just the actual font size in pt

The text-font-size displayed for a 20pt staff is 11pt (as suspected).
When setting global-staff-size to 10pt, text-font-size will consequently
only be half as big: 5.5pt.


font and size form stencil-expr

This is, as usual, the font size in (absolute) mm, but slightly quantized to
avoid the buffering of too many differently-sized fonts with only
microscopic font size differences.

3.865234375 is about what we'd expect for a standard 11pt font, applying
\fontsize #2 will change this by a factor of 2^(2/6) = 1.2599210498 so that
we get a
4.870927651... as reported (slight quanting/rounding effects).


output-scale: converting staff-spaces into mm

Finally, the output-scale factor is needed to transform LilyPond metrics (or
\translate #'(a . b) operations) from staff spaces to Pango mm.


In a 20pt standard stave, four staff-spaces will make up the 20pt, i.e. 1sp
= 5pt.
Using the pt-to-mm conversion factor (we want mm for Pango!), one
staff-space is
1sp = 5pt = 1.7572990175... mm (that's your output-scale).

If we change the staff-size to 16pt, we get
1pt = 4pt = 1,4058392... as output-scale.


That's about all, I think…

HTH,
Torsten



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