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Equal spaces on fanned fret.

Discussion in 'Luthier's Corner' started by Arx, Feb 27, 2008.


  1. Arx

    Arx

    Jan 22, 2008
    Has anyone set up a fanned fret with equal spaces (at the nut).

    If so, how did you go about calculating the spacing at the bridge, from the edge of the board, etc.

    I've sketched mine out, but could use a blind double check to see if I've missed anything. ;)

    -Nick
     
  2. eleonn

    eleonn

    Aug 24, 2006
    Lima - PerĂº
  3. Arx

    Arx

    Jan 22, 2008
  4. SDB Guitars

    SDB Guitars Commercial User

    Jul 2, 2007
    Coeur d'Alene, ID
    Shawn Ball - Owner, SDB Guitars
    In all honesty, it is not that different. I've done both equal spacing and equal centers, and I've never had an intonation problem with my multi-scale instruments. It will work.
     
  5. Arx

    Arx

    Jan 22, 2008
    Really? That doesn't make much sense to me, because up at the ~20th fret or so, where the frets are at a steep angle any horizontal error will effectively move the fret almost as far.

    Besides, I'm sure I'm not the only one here obsessive enough to want it "perfect"

    For this description "horizontal" is in the higher/lower string direction, and vertical is along the length of the fretboard.

    I calcultated my string positions by measuring the amount of horizontal shift per unit (I used mm) of string length. I then calculated how much horizontal shift should be on each of the other strings, so that its position at the bridge would be proportional to its position at the nut.

    Of course, since the string doesn't get proportionally thicker, this means that at the bridge, the spacing will be wider on the bass strings than on the treble stings.

    on my 3d model, it appears to work that way.

    Can anyone see a problem with my methods? Ignore the fact that the neck is still rectangular.

    Also interresting is the slight curve which gets worse as it goes down the neck. I think this can be ignored, since the only effect is the slightly shortened scale on the middle strings.

    Comments, suggestions?
     

    Attached Files:

  6. The problem i see is that frets are essentially straight so you have to settle for an approximation and base your string spacing on what feels more comfortable. If you go for equal centres or equal width between string thicknesses, the frets can only go in straight. To me, string spacing at bridge is always equal-centres, whereas at the nut, they are often cut at equal-gaps. I don't think the approximation neceesary will be significant when it comes to intonation or fret accuracy achievable by hand.
     
  7. SDB Guitars

    SDB Guitars Commercial User

    Jul 2, 2007
    Coeur d'Alene, ID
    Shawn Ball - Owner, SDB Guitars
    Fanned-fret basses, along with every other 12-tone fretted instrument, are still "equally tempered", meaning that you cannot have purely intonated notes at every fret. Tempering build in minor "dissonances" at certain intervals (mostly 3rds and 6ths) because these notes have been sacrificed for the more common notes (4ths and 5ths).

    I have made several fanned fret basses, and I've never had intonation issues. I generally space my strings with equal spacing (gaps) at the nut and equal centers at the bridge.

    As an aside, I would probably set the perpendicular fret at the 7th or so, rather than the 4th or 5th, as your diagram seems to indicate.
     
  8. Arx

    Arx

    Jan 22, 2008
    No, of course you can't have all of your intervals perfect, but you should still have everything match your chosen temperment accurately.

    Thanks for pointing out the parallel fret. it looks more like the 5th/6th to me, but I was intending the 7th. obviously There's something wrong.

    It's strange though. I divided the spread to 33.33mm at the nut, and 66.66mm at the bridge, which I thought would give me a parallel 7th fret. I wonder what I did wrong.

    -Nick
     
  9. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    US-NY-NYC
    Are the five white circles in a row below the base supposed to represent the string horizontal position at their bridge terminations? Or at some section line maybe? They look very odd, and not in line with your description of the bridge spacing.
     
  10. SDB Guitars

    SDB Guitars Commercial User

    Jul 2, 2007
    Coeur d'Alene, ID
    Shawn Ball - Owner, SDB Guitars
    If you're really concerned that it's not going to intonate, you should e-mail or call Novax guitars... for their licensing fee, they can give you the technical information that you are looking for... beyond that, all I can give you is my experience. I don't think that you will be able to tell a difference between the intonation or equal spacing vs. equal centers with the fanned fret design. All of the information I can find about it on the internet indicates that you only "set" the scales of the outside two strings, and that each of the inside strings "finds it's own scale".

    In all honesty, I think you're over-engineering this problem... you won't have any more difficulty with the string spacing on fanned fret than you would on a standard perpendicular fretboard. After all, on a standard guitar or bass, the strings don't travel perpendicular to the frets, do they? If they did, your nut width would be the same as your bridge spacing. On a normal instrument, only a center string would really be perpendicular to the frets, all other strings travel at a slight angle off from perpendicular, as the string spacing spreads out from the nut to the bridge.
     
  11. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    US-NY-NYC
    Shawn

    Incorrect argument. On a parallel fret instruments, a string crossing the frets at any angle continues to be divided up proportionally. The angled strings are ever-so-slightly longer in scale length, as well in every fret distance, in proportion. When both the strings and the frets are nonparallel, this no longer holds.

    Novax' information is not likely to be useful. His patent is incorrect, and one luthier I know who licensed the patent and received the info said that there is nothing there that you can't find elsewhere. He actually tells you to lay out the board the "standard" way, by using two scales for the outer strings, which is in direct contradiction to his patent claims.
     
  12. Arx

    Arx

    Jan 22, 2008
    Shawn: I appreciate that It'll work well enough anyways, and I'm glad to hear it, but I'm pretty picky about such things. If I know that I built in the small degree of error which I could have avoided by doing the math properly, it will always bother me whether it's really audible or not.

    pilotjones: Yes. This is what I'm asking about. While I'm sure the standard pick 2 scale lengths and draw lines between them is "close enough" for most people, I'd really like to get mine more accurate than that. Is my assumption that a proportional movement of the string at the nut and fret will keep proper intonation correct?

    As far as the Novax patent goes, I'm not interested in giving him any money. And besides that, I like to learn things. I'd rather come up with my own solutions and have the great folks on here as a double check, than to pay someone else to send me a "here's how you do it" sheet, which may or may not be correct. (In a precision sense, not an it'll work well enough sense)

    So has anyone here actually done the math to get a very accurate string/fret positioning? If so, how did you go about it, and do you think the method I described is working correctly?

    -Nick
     
  13. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    US-NY-NYC
    You're not the only one to feel that way. Beyond that, even if a person is not bothered simply by it being "not right," it may still bother him if he considers that if 12TET temperament is not perfect, and intonation compensation is not perfect, then he might not want to add an avoidable built-in fret position inaccuracy to those two conventionally unavoidable issues.
    Use of two proper scales for the outer strings, "connecting the dots," and placing the strings at equal centers between these two scales results in perfect fret placement (not just "close enough"). In addition to this, any string placed an equal percentage of the distance from side to side at the bridge and at the nut will also result in string crossings at proper distances.

    I recently discovered a new wrinkle in this (new to me, at least). The equal centers, or proportional centers, have to be (e.g. in the case of equal centers) equal along the nut or bridge line, as opposed to along a perpendicular-to-centerline line drawn at those locations.

    This is actually a "saving grace" for those who prefer equal gaps, because it actually widens the gaps a bit at the bass side of the nut.
    See the other current related thread for info on this.
    Novax' sheet was a simple description of the two outer scales method, which was not the method protected by his patent.
     
  14. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    US-NY-NYC
    Also, about the equal spacing along nut line thing, I still need to do it in CAD to verify.
     
  15. Arx

    Arx

    Jan 22, 2008
    Yeah, that would be really good to know. I'm modeling mine in blender (a 3d modeling app for linux) It's not really intended for actual drafting, but seems to be doing a passable job for the most part. Also, it gives me a nice rotatable view of what the whole bass will look like, so I can mess with the body shape, etc.

    but, back to the subject at hand, I did my calculations from a horizontal nut, which sits slightly behind the actual nut. You can see it in the picture, and I'm actually going to build it that way. It'll look unusual, but I figure it's the cleanest way to do it on a pre-built neck which already has a flat cut for a nut, and a square end on the fretboard, and there's nothing usual about a fanned fret bass anyhow.

    I made the assumption that thet amount of offset between my diagonal nut, and the horizontal one would be pretty much nothing, but upon checking, it's not as negligible as I had expected.

    What is actually pretty hard to see in the picture is that there is a definite curve to the frets as you move farther toward the bridge. I can see it clearly when I rotate the image so I'm looking along a fret. It's not a lot, and it does affect the frets towards the nut progressively less, so straightening them out would probably mostly be just shortening the scales of those strings very slightly, but it does still bug me, since it appears to me to be more curve than the arc of the string ends should normally cause. (only eyeballed this though)

    I'd really like to see your cad drawings. I'm getting a little anxious to get the actual physical part of the build underway, but I'm holding off until I'm satisfied that my plans are an order of magnitude more accurate than my measurement and construction abilities.

    having someone else on the same page, with some independant work agreeing with my own would give me a lot more confidence that I'm getting it right, and not merely "close enough"

    -Nick
     
  16. That's the first thing that struck me when I saw your pic, hence my comments about practicalities of fitting straight frets onto a fanned neck being the only workable compromise. It's a very interesting thread and quite thought-provoking. Be interested to see what you come up with.
     
  17. Arx

    Arx

    Jan 22, 2008
    It's not necessarily a compromise though. As long as the error is linear (every fret gets longer by the same percentage), then it's still 100% correct intonation-wise, the scale will just be slightly shorter.

    Whether that's the case here, I don't really know.
     
  18. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    US-NY-NYC
    I've started the verification of the ideas put forth previously.

    I know arx may be just looking for results, but I'm including a full description so that the methodology can be criticized and any mistakes, or just differences from other peoples' methods, can be found. If anyone is interested.

    Here's what I've got so far.

    1. basic setup for all tests
    background:
    this is building a neck that is symmetrical about a centerline, assuming there will be an equal margin added beyond the outer strings to the edge of the actual neck. It is a 5-string, with the 1/3 point perpendicular, which is close to identical to the 7th fret position. Scales of the outer strings are 34" and 37".
    method:
    1.1 Start with fixed datum point. This will represent the intersection of the neck centerline and the "7th fret" position.
    1.2 Draw vertical line through the datum, 1/3 above and 2/3 below the datum point. This line lies on the centerline of the neck, but it does not necessarily terminate at the eventual bridge and nut lines.
    draw a horizontal line through the datum. This is the "1/3 line," or the "perpendicular fret line," but I'll call it the "7th fret line" henceforth.
    1.3 Draw two horizontal lines, 1.5 and 3.0" wide, attach their center points to the endpoints of the previous line. The endpoints of these establish two lines, symmetric about the centerline, along which the outer strings will lie.
    1.4 Draw two outer strings of appropriate lengths, make them lie on the two outer string lines, and attach their 1/3 points to the 7th fret line. These represent the actual outer strings in all cases, regardless of which method is used later to place the inner strings.
    1.5 Draw lines connecting the endpoints of the outer strings. These are the bridge and nut lines.
    1.6 The bridge and nut lines, the two outer strings, and the centerline form the "box" that is used for all following tests.
    1.7 divide the outer strings into 1/4 sections, and connect the points across. These lines establish the (approximate) 5th fret line, the 12th fret line, and the 24th fret line. They land at "perfect" positions on the outer strings. We'll see what happens with the inner strings.
    1.8 These inner fret lines will be the reference to see any errors in the following inner string placement tests.
    observations:
    - the bridge and nut lines do not end up being coincident with the endpoints from 1.2. Surprise!

    2. test: strings at equal centers along nut and bridge
    method:
    2.1 divide nut and bridge lines at 1/4, 1/2, 3/4 points.
    2.2 create two strings as to be the 2nd and 4th strings. divide them into quarters.
    2.3 attach the strings at the bridge and nut points created in 2.1
    2.4 compare where the 1/4 points on the strings fall with respect to the fret lines.
    observations-results:
    - the points from 2.4 lie exactly on the 5th, 12th, and 24th fret lines. So, the method produces proper intonation on all strings, that is, the frets will divide the inner strings properly.
    - the strings are not "equal centers" in the conventional sense. The inner strings are biased a bit towards the treble at the nut (similar to "equal gaps) and towards the bass at the bridge. The 3rd (middle) string does not run down the centerline exacly; it is rotated clockwise, and crosses the centerline at the 7th fret.

    3. test: strings with "even fan", i.e. at equal centers on the lines from 1.3, even centers on any line drawn perpendicular to the centerline, and converging to a single point above the nut
    method:
    to be described later-gotta get back to work
    observations-results:
    - quickly: there are errors. frets would indeed have to curve for perfect placement on all strings.
     
  19. Arx

    Arx

    Jan 22, 2008
    No, not just results! This is exactly what I'm looking for. I want to understand how to do it, not just know where to put my strings. :)
     
  20. pilotjones

    pilotjones Supporting Member

    Nov 8, 2001
    US-NY-NYC
    :cool:
     

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