From what I understand, different companies quote their scale lengths in different ways, and some simply quote it wrong (Gibson being one). Some quote the actual string length to the bridge, some quote the 12th fret distance times two. I personally use 12th fret times two, since that makes calculating fret positions easier. The string length to bridge idea makes less sense to me, because until I string the guitar to pitch with the strings and action height I am going to use I don't know where the bridge will end up.
arxiv.org/pdf/0906.0127
is a link to a PDF file of a thesis that establishes a mathematical model for string compensation, and then tests it with three different string gauges at all fret positions. Once I figured out what I was reading, I found the charts of relative pitch accuracy at each fret illuminating and frightening... They measured the pitch of a well compensated string to be 7.9 cents flat at the first fret and 5.8 cents sharp at the second fret, and almost perfect at the 12th fret. The deviation across all frets was about equal as to sharp or flat... So the effect of equal tempered fretboard suddenly was extremely clear to me. Different string gauges (tuned to an appropriate pitch) gave different degrees of error, based on different string mass and stiffness, apparently.
Brian
Scale Calculation Questions
Please put your pickup/wiring discussions in the Electronics section; and put discussions about repair issues, including fixing errors in new instruments, in the Repairs section.
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