Harmonics in tablature

[Lukas-Fabian Moser]

Folks,

Stacy's question ("Three problems with harmonics") prompted me to try 
LilyPond's tablature facilities for the first time.

I beg forgiveness for using it not for guitar/bass but for the cello - 
for me it's the most convenient way since I know the 
fingerings/imaginary "frets" and harmonics positions by heart on that 
instrument, and luckily, the physics is the same :-).

My question is:

\version "2.21.0"

music =
{
  c4 d e f g a b c'
  \bar "||"
  \harmonicByFret #12 g,
  \harmonicByFret #7 g,
  \harmonicByFret #5 g,
}

<<
  \new TabStaff {
    \set TabStaff.stringTunings = \stringTuning <c, g, d a>
    \music
  }

  \new Staff {
    \clef bass
    \music
  }
>>

The first two bars are fine and standard 1st position cello fingering.

But the harmonics that follow confuse me. I read the input as "use the 
12th/7th/5th fret over the open g, string". If you play this, you 
definitely get the sounding pitches the lower staff indicates.

But why are the harmonics in tablature are printed for the d and a strings?

Either I fundamentally misunderstand the way harmonics should be read in 
tablature, or there is a serious flaw in LilyPond's logic that 
determines the string number in tablature. (Yes, I know that I can fix 
the output by adding \3 manually, but...)

Lukas

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