Calculating fret positions

Discussion in 'Hardware, Setup & Repair [BG]' started by Joris, Jun 24, 2001.

  1. I'm about to put line markers on my fretless bass with a black permanent marker. I have been practising with car pinstripe tape, but I took it off. It sounds terrible. And the positions weren't precise enough. I had to correct a bit sometimes by bending the string.

    The bass has a rosewood fingerboard with an epoxy or polyurethane finish, so eventually the markers will wear off, which is exactly what I want. I don't want to rely on fretlines forever.

    So my question is: how do I calculate or otherwise obtain a list of fret marker postions for a 34" fretless bass? Does anyone have a link? Or a ready made table?

  2. Turock

    Turock Supporting Member

    Apr 30, 2000
  3. NightVampZ


    Jun 22, 2001
    That sounds complicated. I don't know how anyone could play a fretless bass. lol. It sounds really neat but I would have to play ALOT more before being able to play a fretless.

  4. pkr2


    Apr 28, 2000
    coastal N.C.
    Joris, it might be easier to just use an electronic tuner. Calculating or even measuring fret spacing is pretty cumbersome mathemattically.

    You may need to get a little imaginitive with finding some of the notes if you use an el cheapo guitar
    tuner like I do.

    By the way , nothing wrong with marking the fretboard on a frettless. If you are recording and need to nail the tone on the first note, you will realize the value of a reference.

    You may want to consider not even marking every fret. I inlaid position markers on my URB years ago only marking A,B,C and the octave on the G string. I find that I can interpolate(sp) well enough between these markers.

  5. MikeyD


    Sep 9, 2000
    Joris, I took a cursory look at the dougsparling site, and it seemed okay. The relations for the 12-tone tempered scale are based on the 12th root of 2. If you apply 12 consecutive ratios (i.e., take the constant to the 12th power), you get 2, which is the ratio of frequencies for one octave, which you traverse in 12 steps.

    _ Let C = 2^(1/12) = 1.0594631 (the frequency ratio constant)
    _ Let L = the scale length
    _ Let n = the fret number, starting with the first fret from the nut.

    The distance from the bridge suspension point to the fret centerline would be X = L/(C^n). The distance between the nut and the fret would be D = L - X.

    Your first fret would be at n = 1, and for a 34" scale, X = 32.0917", and D = 1.90827".

    Likewise, your second fret would be at n = 2, so applying the equation gives X = 30.2906", and D = 3.70944".

    I just checked these against my fretless Jazz Bass, and they are like just dandy cool like.
    - Mike (the math-physics nerd)
  6. Thanks for the replies. It's much appreciated.

    Another question? Do the calculated numbers divert from the actual note positions or are they just, well, right on the spot? Because I used a pre-calculated table (thanks for the clear maths, Mike) for the pin stripe tape (see first post), and found some notes to be slightly off. Or did I just not put them exactly right?

    The tape acted as very low frets, it sounded that way too (intonation was impossible). Maybe that was my problem.

    Mike, you say the math numbers match up on your fretless. I guess there's my answer, right?

    I'll use the tuner trick to verify everything. I have a good tuner, it detects .5 cents off.

  7. Suburban


    Jan 15, 2001
    lower mid Sweden
    The calculated numbers are at the spot, of tempered tuning.
    When you have placed the lines on your board, I will congratulate any line that is within .2 mm. This discrepancy is the reason why all fretted instruments always sound like crap. And the unfretted is better, because you can adjust to perfection. If the note is long enough :D
  8. MikeyD


    Sep 9, 2000
    The numbers are the *ideal* free length of the string between nodes (fixed points). Real-world things that affect intonation are the string gauge, the way in which the string is "fretted" or stopped on the fingerboard, the homogeneity of the string (density per unit length), actual scale length (which can vary based on truss rod adjustment, temperature, humidity, etc.), and others. This is why most bridges are adjustable. If you are marking the fingerboard with lines, I would think that using the numbers given as the distance from the nut opening to the centerline of the fret line would be ideal. Then you can adjust your finger positioning uniformly.
    If the tape rises above the fingerboard (which it would do unless it's of zero thickness!), you have to treat it like frets, and adjust its position. Not only that, but the tape will wear down and then the effect will be unpredictable. I wouldn't think tape is the way to go. In order for it to grip well and not move, it would have to be rather wide, which would really mess up the positioning. The easiest thing is to make up a "scale" (fret positions) on the side of the neck to help you locate the notes. If you really want lines on the fingerboard, you have to mark them somehow or cut them in and fill so that the fingerboard remains smooth. I'm not a luthier, but that's my educated guess.
    They seemed to work, according to a quick check with a ruler. If you stick to the numbers, you should be able to get consistent intonation when you find out how your fingers actually create the stop relative to the lines. However, if a luthier has advice on this, I recommend heeding it, since it would likely be better than mine.
    - Mike
  9. MikeyD


    Sep 9, 2000
    BTW, my fretless was a fretted bass converted by the previous owner by pulling the frets out and filling in the grooves with something (epoxy-type substance?). It appears then, that fretted instruments also base the fret centerlines on this same formula.
    - Mike
  10. Well, here it is (oh the shear joy of a digital camera): see attachment.

    I made an aluminium ruler with the fret positions marked and a guide line exactly parallel with the A string, which is in the middle on a 5 string. Played on it for half an hour now, and I really dig it.

    I made the ruler in order to put them back on once they start to wear off, without having to measure all over again.

    Thanks for the help!