However, when I draw the position chart, I notice that the slide position of Bollinger tuning is quite similar to G/Eb tuning, so much so that the G/Eb tuning can also play the arpeggios and scales that Bollinger tuning excels with similarly minimal slide movements. The G/Eb tuning even leads in playing scales using just a distance no more than 1 position difference (16 scales VS 15 scales of Bollinger tuning). My chart might have some deviation, but it checks out with my past experience on G/Eb horns.
Bollinger tuning still has slightly less slide movements (<0.5 position distance) between notes in some arpeggios.
Translation of the four rows description:
Open horn, F partial
Open horn, low Bb partial
Thumb Valve, F partial
Thumb Valve, low Bb partial
Finger Valve, F partial
Finger and Thumb Valve, F Partial
Finger Valve, Low Bb partial
Finger and Thumb Valve, Low Bb partial


That leads to my question: what exactly is the advantage of Bollinger tuning over G/Eb tuning?
Thank you very much for your answer.