Guitar Nut conundrum: equal spaces and equal centers question

Replies to This Discussion

Permalink Reply by discopimp on June 17, 2017 at 12:32pm

ok, so i integrated your new patch but i need to clean everything up and sort out my errors.

Maybe i should explain a bit more the context of this quest. i have recently become fascinated by multiscale guitar. the last one i built was really promising but i now want to experiment a bit more with the different parameters. i'm already using your solution from here: http://www.grasshopper3d.com/forum/topics/fretboard-calculator?xg_s... and am trying to cobble it together with the equations for fretboard radius calculation from here http://www.stewmac.com/How-To/Online_Resources/Neck_Building_and_Re...

i was previously using the fret positon calculator from here: http://www.ekips.org/tools/guitar/fretfind2d/ or here http://www.liutaiomottola.com/formulae/fret.htm for the multiscale calculation. The fretfind2d can export a DXF but i only realised during my first build that the DXF is buggy, the line ends don't meet so i need to redraw everything in rhino.

i'm attaching my current monster so you see what i'm up to. i'm having quite a bit of fun with this trying to simplify things, it teaches me a lot about rhino, grasshoper and guitars as well :-)

as you might have guessed i'm not very good with maths or patching logic and try to build something chaotically that sort of works and then try to sort out the errors, probably not the most elegant way to goabout it

eventually the whole thing can be controlled with the input parameters on the left and spit out a model of strings (extended a bit beyond the nut and bridge to design the bridge, headstock and string attachements), the compound radius fretboard, the fretlines for slotting, a dummy model of the fretwires ... and the string pipes should be offset in te perfect radius at bridge and nut calculated by the fretwire height and 'action' desired.

Attachments:

• fretboardBuilder_parametric_b01_jun17.gh, 53 KB

Permalink Reply by Joseph Oster on June 17, 2017 at 1:13pm

Fascinating.  Give yourself more credit, it looks like you are doing pretty well with GH.  I know nothing about guitars so don't want to say anything that steers you wrong...  I might be able to help if you narrow the problem scope a bit.  Two questions:

1. Do you want the nut and bridge curves to match the curvature (radius) of your "Fretboard Radius" curves?
2. I've never seen frets that are angled like that; tricky business!

Keep up the good work and have fun.

Permalink Reply by Joseph Oster on June 17, 2017 at 2:10pm

Meant to include this image from one of the pages you mentioned:

Here's another one (news to me, probably not to you):

Ralph Novak, luthier of Fanned-Fret, Multi-Scale Guitars
http://www.novaxguitars.com/

The concept arose from the observation that although instruments with different body styles and pickups would display obvious differences in tone, there was a consistency in the string response of the various instruments.

Shorter-scale instruments (many Gibson solid body guitars and short-scale Fenders) had a “warm” tone with a “muddy” bass response. Longer-scale instruments (like many Fender guitars and the longer-scale Gibson arch tops) had a brighter tone and the basses were more “piano-like”. In addition, when compared to the older Kay guitars with an even longer 26.25" scale length, the difference in the tone of the strings resulting from the string length was striking.

Novak sought a way to combine the warm, sweet trebles of shorter-scale instruments with the rich, piano-like basses of the long-scale instruments. This was the genesis of Fanned-Frets.

P.S.  This is interesting too: Compound Radius: Explained

Permalink Reply by discopimp on June 17, 2017 at 2:11pm

hey thx for the encouragements.my theory is that multiscale guitars are the way guitars should be built, it's not for nothing that piano bass strings are longer than the treble strings, or that bass and baritone guitars have longer scale lengths. when you precisely match the string spacing, string gauge and scale lengths and match the fretboard radius and 'action' you end up with a supremely balanced instrument, both in terms of playablitly (very even string tension) and sound, fuller bass, more precise mids and highs. the string spacing is crucial here because it determines how parallel the strings run along the compound radiused frets.

(action is what we guitarists call how high the stings are over the frets, the more precise your fretboard and fretjob is the lower you can set the action without the strings buzzing and the easier and faster you can play.)

99,9% of all guitars manufactured in the last 60 years are single scale, mostly for historic practical and economic reasons. with the two main scale lengths (Fender Strat/Tele and Gibson Les Paul) that wrote rock n roll history most manufactured guitars follow loose standards so that components with little variations can be used. once you change the scale length to a multiscale and maybe even experiment with different string spacings at bridge and nut the design of pickups for example needs to be matched so that the magnet pole spacing also works out. where the pickups are positioned also influences this. and then there is the problem of the bridge which is now slanted whcih makes it much more complicated to fit to the body of a guitar with a sculpted top like a Les Paul (Fender Guitars are flat on top mostly).

of course single scale guitars also work and can sound great, but the more i play my multiscale the more i'm convinced that the sound balance and intonation is better. and surprisingly it doesn't feel weird at all compared to straight frets, everyone who trys it is surprised how quickly you adapt to the slanted frets and how unprblematic it is to switch back to a straight frt guitar. very cool ...

normally when you change string gauge, you should change your nut ..no body does that of course but hey why not if you can do it with the help of a parametric solver :-)

i recently designed/built my first 'really different' guitar and as a result had to develop my own bridge and pickups because no standard pickups or bridges would work. calculating all the positions was a nightmare starting with the broken DXF from fretfind2d. for that build i just used a Stratocaster scale length for the bass string and a Les Paul scale length for the treble. But if i had fully parametric system of bridge, nut, strings, fretboard, frets then it would be so easy to empirically try out completely different combinations and see where it goes.

here are a couple of picof the Strat/LesPaul hybrid neck: 

the bridge construction: https://postimg.org/gallery/fhcm6i52/

the pickups: https://postimg.org/gallery/1n04by1ee/

and the finished baby:

it did the nut calculation for that in Fusion where i do the CAM but made a mess when cutting the nut in the end, cutting a nut by hand precisely for equal spacing is still a matter of experience when it comes to translating the parametric calculation into the physical world :-)

Permalink Reply by discopimp on June 17, 2017 at 2:24pm

as to your question 1.: not necessarily, the nut slots are cut by hand anyways and then the top of the nut levelled with a file by hand also. the bridge is a whole different ball game altogether, the strings on the bridge rest on saddles which can be height adjusted, so for a 'low action' you just go as low until it starts to buz when you strike an open string, and then go higher until it doesn't buzz anymore when you play your usual style. it's all up to manual fine tuning in the end, it's wood and metal so of course the whole thing moves and adjusts with environmental conditions .. but the goal is to be as precise as possible.

so all i need for nut and bridge are reference lines.

Permalink Reply by Joseph Oster on June 17, 2017 at 12:31pm

Added blue group to give you the dimensions to the center of the strings:

Attachments:

• stringSet_2017Jun17c.gh, 25 KB

Permalink Reply by discopimp on June 17, 2017 at 12:34pm

weird our replies crossed it seems, you replied to something before i even posted it, the magic of the internet :-)

Permalink Reply by David Rutten on June 17, 2017 at 2:36pm

Probably just different time zones. Or maybe moon light reflected in some swamp gas.

Permalink Reply by Joseph Oster on June 17, 2017 at 3:20pm

B. [...] the spacing of the top and bottom strings to the fretboard/neck edge.

Small changes to implement a feature you asked for in your original post but that we glossed over by using half the computed "gap" between strings.  I'll let you handle the unit conversions (mixing millimeters and inches?  oh my!), but this adds a pair of sliders to set the 'Edge_Nut' and 'Edge_Bridge' distances directly.  They are multiplied by two and added to the sum of 'String Gauges' before subtracting from the 'Nut' and 'Bridge' lengths.  Then 'gap' is computed by dividing that result by 5 instead of 6 ("x-1" expression applied to the output of 'Lng (List Length)' of 'String Gauges').

Attachments:

• stringSet_2017Jun17d.gh, 30 KB

Permalink Reply by discopimp on June 17, 2017 at 3:52pm

hey thx, half the string space is actually a cool idea and seems quite pleasant but precise control will be much better .. and yeah mixing imperial and metric :-) matter of habitin the guitar world ... for some reason fretboard radius in inches (i know what a 9", 12" inch or 16" feels like fom standard guitars). but of course i want to work in metric when it comes to building :-) i know it's weird but feels natural to me, just like string gauges, they are always expressed in inches, even here in europe everyone would refer to a 10 gauge for the high e string (meaning 0.010"), no one would say a 0.254 mm. a legacy of the american electric guitar heritagei guess.

Permalink Reply by Joseph Oster on June 18, 2017 at 12:33pm

Love this thread/project for several reasons:

1. It's a real-world application, not just an academic exercise.
2. I've learned a lot about guitars in the process, thank you.

I looked at your "current monster" code and decided I could do better on the fanned frets.  Had to chuckle at my use of Anemone in that "Fretboard Calculator" from last March; it's obviously not necessary.  Here's what I added to the code I posted yesterday; the results match your version:

Attachments:

• stringSet_2017Jun18a.gh, 21 KB

Permalink Reply by discopimp on June 18, 2017 at 2:45pm

really cool of you to help me out, glad you're enjoying it :-) this has been on my bucket list for such a long time, i tried many times to do it but i'm in over my head when it comes to stringing together math and logic. i can usually conceptualise what i want to do and cobble some semi working thing together but don't know which components to use and how to patch it. so i'm super happy to have someone who knows what he's doing to find this interesting.

and i'm glad you mention the fanned frets again, there is one input parameter that's still missing for the multiscale frets to be fully parametric, it's the angle of the nut or which fret should be straight. it depends a bit on personal preferences and playing posture what is more comfortable. so being able to adjust this easily would be cool. again i have no idea how the maths for that work or if you can just rotate each fret the same amount around it's middle point. The input either as fret number (for the straight fret) or as a simple slider from bridge to nut should do as input setting.

Here are the two extremes and the middle ground:

i've been thinkin today while analysing your patches and cleaning up my mess what exactly the monster should do.

Here are the input parameters needed, i think it's the complete list

1. scale length low E string
2. scale length high e string
3. fret angle/straight fret
4. string width at nut
5. string width at bridge
6. number of frets
7. fretboard overhang at nut (distance from string to fretboard bounds) 
8. fretboard overhang at last fret
9. string gauges
10. string tensions
11. fretboard radius at nut (for compound radius fretboard radius at bridge is calculated with the stewmac formula)
12. fretwire crown width
13. fretwire crown height
14. action height at nut (distance between bottom of string and fretwire crown top)
15. action height at last fret
16. pickup 1 neck position
17. pickup 2 middle position
18. pickup 3 bridge position
19. nut width

the pickup positions should be used to draw circles for the magnet poles on each string so they are perfectly aligned and can be used for the pickup flatwork construction. ideally they would need a rotation control aligning the center line of the pickup so it's somewher between the last fret angle and bridge angle. personally i do this visually depending on the design i'm looking for, some people have huge theories on pickup positioning but personally i don't believe in it.

that should result in everything needed to quickly generate all the necessary construction curves or geometry for nut/fingerboard/frets/pickups. this is the core of what makes a guitar work, the more precise this dynamic system is the better the guitar plays and sounds. 

i posted another thread trying to understand how i could use datasets form spreadsheets,databse, csv to organize the input parameters. What would make sense for the strings for example is hook into a spreadsheet with the different string sets, i attached one for the d'Addario NYXL string line which basically covers all combos that make sense.

The string tension is an interesting one, and implmenting it would sure be overkill albeit super interesting to try. it should be possible to extrapolate from the scale length of each string what the tension for a given string gauge of that string would be so that you could say 'i want a fully balanced set' or 'heavy top light bottom) and it would calculate which SKU from d'addario would best match the required tension. All the strings listed in the spreadsheet are available as single strings to buy.

i'm trying to reorganize everything which helps me understand it. i just discovered the 'hidden wires' feature which is great since once i understood what a certain block does or have finished one of my own, i can get the wires out of the way to carry on undistracted. a bit risky to hide so many wires but it makes it so much easier not to get completely lost :-)

btw, the 'fanned fret' term is trademarked, some guy tried to patent it in the 80's which is a bit silly since it has been done for centuries. there is a level of sophistication above this as well, check out http://www.truetemperament.com/ and that really is something else. it really is astounding how superior the tuning is on those wigglefrets, the problem is that it's rather awkward for string bending and also you can't easily recrown or level the frets when they are used. 

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