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Positioning fingering indications precisely

From LilyPond wiki

The semi-automatic positioning of fingering within a chords works usally well, but if one of the indications needs to be positioned more precisely the following tweak may be used. This is particularly useful for correcting the positioning when intervals of a second are involved.

\version "2.24"

\markup \with-true-dimensions % work around a cropping issue
\score {
  \relative c' {
    \set fingeringOrientations = #'(left)
    <c-1 d-2 a'-5>4
    <c-1 d-\tweak extra-offset #'(0 . 0.2)-2 a'-5>

    \set fingeringOrientations = #'(down)
    <c-1 d-2 a'-5>
    <c-\tweak extra-offset #'(0 . -1.1)-1
     d-\tweak extra-offset #'(-1.2 . -1.8)-2 a'-5> |

    \set fingeringOrientations = #'(down right up)
    <c-1 d-\tweak extra-offset #'(-0.3 . 0)-2 a'-5>4
    <c-1 d-\tweak extra-offset #'(-1 . 1.2)-2 a'-5>

    \set fingeringOrientations = #'(up)
    <c-1 d-\tweak extra-offset #'(0 . 1.1)-2
     a'-\tweak extra-offset #'(0 . 1)-5>
    <c-1 d-\tweak extra-offset #'(-1.2 . 1.5)-2
     a'-\tweak extra-offset #'(0 . 1.4)-5> |
  }
}