"Slide-rule" for estimate of in-line dual-valve tuning.

[Sesquitone]

Here's a (rough) "slide-rule" for making a quick estimate of the double-valve tuning, given the two individual in-line valve tunings. For (i) thumb-operated valve tuned to F; and (ii) thumb-operated valve tuned to G.

As can be immediately seen, with the thumb-operated valve tuned to F, a second valve tuned to G gives a double-valve tuning almost 30¢ flatter than Eb. A second-valve tuned to Gb gives a double-valve tuning about 8¢ flatter than D. A well-in-tune D can be obtained by tuning the F and Gb valves each a few cents sharp. The "Bollinger" tuning of the second valve (half-way between G and Gb) results in a double-valve tuning about 30¢ sharper than D.

With the thumb-operated valve tuned to G, a second valve tuning 19¢ sharper than E results in a perfectly in-tune D for the double. [This, Bb/G-E-D, happens to be my preferred tuning for a continuously chromatic dual in-line valve tenor or bass. (Compatible with minor-third single-valve instruments such as Eb/C alto, and C/A and Bb/G tenors.)] With the a finger-operated valve tuned to Eb, this results in a slightly flat Db for the double—this Bb/G-Eb-Db is a transposition up by a P4 of the Thein F/D-Bb-Ab contrabass.
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[psybersonic]

Took me a while to grasp this . So we are looking at wavelength increases in mm descending from Bb2 ?
Equal temperament pianos are 10c flat at Eb2 . My Yamaha 613h is somewhere near in tune at Eb2 if I push the G crook full in and engage it and the F trigger . Proves your calculation.