String height reduction

Dunno if I've already asked this question before (I can't find it in my posting history) so please humour me.   Purely hypothetical situation so please feel free to offer geometric theorems. If a string is lowered at the saddle by, say, 2mm.........how much lower would the string be at the twelfth and first fret?
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Comments

  • ICBMICBM Frets: 71960
    12th fret  - 1mm.

    1st fret - barely detectable.

    That is, assuming it isn't an acoustic, in which case lowering the saddle will most likely mean the top is being pulled up less hard, so you may get slightly more than a 1mm reduction at the 12th.

    "Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski

    "Just because I don't care, doesn't mean I don't understand." - Homer Simpson

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  • Thanks.......so the lowering at fret one wouldn't be by 0.5mm ?!
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  • ICBMICBM Frets: 71960
    No. It would be 0.5mm at the 5th fret.

    The actual reduction at the 1st fret would be 0.11mm, if you do the maths. The distance from the nut to the first fret is 5.6% of the scale length, so the height reduction at the 1st fret is 5.6% of the height reduction at the bridge.

    "Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski

    "Just because I don't care, doesn't mean I don't understand." - Homer Simpson

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  • FunkfingersFunkfingers Frets: 14323
    edited November 2017
    In Imperial measurements, the height reduction achieved at the first fret by lowering a bridge saddle would be described as "a gnat's". 

    If you desire substantial reduction of the gap between the first fret and a tensioned string, the nut slots need attention.
    Be seeing you.
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