There must be typos in your example code, thus I don't understand what you want 
to demonstrate. Could you elaborate?

Nevertheless, if you comment the lines with
\override #'(full-length . #f)
in my markup-code above, then the dashed-line starts/ends exactly. It ensures 
the line starts _and_ ends with a dash. The dash itself is _not_ scaled.
Though the off-values (specified was 8.0) is scaled to 12.5179170455133 and 
8.5914367305527
So, in one case the provided value is scaled by ~150%
I wouldn't call this slightly...
But I don't see a way to avoid such a big scaling for certain off-values (the 
dash-period), if we want to ensure dashes at start _and_ end of the line.

IIUC, the situation for TextSpanners is as follows:
'dash-period can be specified, then lily calculates how to scale the setted 
dash-period to ensure full line-extent.
And _then_ the dash-fraction is applied to the _scaled_ value.
As a consequence this results in different dash-extends (on-values).

In the markup command I tried to keep the dash-extend wherevere possible.
Only for small lines I implemented some conditions to either drop the line or 
print a dot or print a solid line.
For TextSpanners one could probably implement some settable not scaleable 
on-value (for the dash-extend), a scaleable off-value (for the white-space) and 
go for treshold-conditions like:
if no room for 1 dash, drop the line
if no room for 2 dashes, print a solid line
else scale the off-value to fit.




---

** [issues:#5539] TextSpanner: left text incorrectly influences dashes**

**Status:** New
**Created:** Sat Jul 20, 2019 08:17 AM UTC by Werner LEMBERG
**Last Updated:** Sun Jul 21, 2019 05:28 AM UTC
**Owner:** nobody
**Attachments:**

- 
[text-spanner-wrong-dash-spacing.png](https://sourceforge.net/p/testlilyissues/issues/5539/attachment/text-spanner-wrong-dash-spacing.png)
 (4.6 kB; image/png)


[git commit 49f41bf1c64ae1e2490571e73a85cbc4b2a9fb27]

~~~~
\version "2.21.0"

\header { texidoc = "
  For a text spanner, the length of the (left) text element
  must not influence the distance between and the length of
  dashes.

  Here is a counterexample.
" }

\relative c' {
  \override TextSpanner.dash-period = #8
  \override TextSpanner.dash-fraction= #0.1

  \override TextSpanner.bound-details.left.text = "im"
  e1\startTextSpan e1 e1\stopTextSpan

  \override TextSpanner.bound-details.left.text = "immer"
  e1\startTextSpan e1 e1\stopTextSpan
}
~~~~



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