I would like to include a translation of a brief passage from Euler's music text Tentamen novae theoriae musicae (1739) in an article I am writing, but find the original somewhat tricky to work with. The constructions and seemingly inconsistent cases make it a bit confusing to me, so maybe some of you have some insight into this. The original:
Totus autem hic temperationis processus ex adiecta hic figura distinctius percipietur. Cum ergo soni E,H, Gs, Fs, Ds et B duplici modo tum per quintas tum per tertias determinentur, ex hoc non contemnendum obtinebitur subsidium in temperandis instrumenti, cum error qui forte sit commissus, statim percipi et corrigi queat.
Here is my attempt at trying to understand it:
However, all this process of tempering will be more clearly observed from this additional figure. Using two methods, the notes E, B, G#, F#, D# and Bb are determined not only by fifths but also by thirds, ...(something about temperament of instruments, undespised help obtained??), with the error (?? errore?) that perhaps be committed, may be immediately perceived and corrected.
The clause starting ex hoc non contemnendum is particularly unclear to me. Any ideas to help me through my amateur understanding? Many thanks.