Designing 12-string guitars and baritones

[dshaker]

I'm trying to think about how the design principles of The Book(s) can be applied 12-string guitars
and baritones.

The 12-string, obviously needs to be stronger to take the greater string tension. The string tension will be approximately doubled, so if the braces were 26% higher (cube root of 2 = approx. 1.26) that would take care of most of the strength issues. But three or four of the doubled strings are tuned an octave higher than their conventional strings, and two or three of the doubles are tuned an octave higher. This means that the average frequency that the guitar will be generating will be a little higher than a regular guitar.

On the other hand, a baritone is tuned a third to a fifth steps lower than a conventional guitar. And, usually the scale length is longer. The scale lengths I know about are between 27" and 30".

I feel like I have some fumbling handle on the strength issues of the 12-string. I don't think I have any handle at all on how the change in frequency should change the design.

Does anyone have any coherent thoughts? Incoherent ones? Blind ignorant prejudices?

-Doug Shaker

[dshaker]

Well, I see I haven't exactly set off a storm of discussion.

Here are my thoughts, so far.

12-strings: Actually, you don't really want the frequency profiles to change much, so just engineer for
greater strength. Don't change the body shape. Don't change the bracing pattern. Just make the
bridge and braces a little stronger. Make the braces 25% taller. Add another ply to the
bridge patch sandwich that is inside the body.

Baritones: Since you are, basically, trying to lower the frequency of the entire instrument, make the body larger
so as to lower all the tap tones. If you are going from an E-E tuned instrument to a B-B tuned instrument,
all the tap tones should be 0.75 of what they were on a standard instrument.
0.75 because High E (E4) =329.628 hertz and B3 = 246.942. 246.942/329.628 = 0.749 or 75% for all practical purposes.

I am not sure what this implies about the size of the top. Should the length be 33% larger? Or the area?

[Woodsy23]

The string tension will be approximately doubled, so if the braces were 26% higher (cube root of 2 = approx. 1.26) that would take care of most of the strength issues.

I think stiffness of the braces is proportional to cube of depth but strength (stresses in wood) is proportional to the square of the depth. Increasing the depth of braces by 1.26 should take care of the top rotation at the bridge (keeping it to 2 degrees) but not necessarily the stress levels. Having said that, slightly higher stresses may be acceptable.

I am also doing a 12 string (my first), using the principles in the book so I have been tacking these issues too. One of the decisions to make is which braces to increase as they do not all affect stiffness of the top and some would have only low stress levels in a 6 string guitar. I only increased the X braces and the sound hole braces. I could not find much guidance about bracing 12 string guitars and have very limited expedience in building acoustic guitars so it was a bit of guesswork in my case. Hopefully, more experienced builders may be able to offer you more guidance.

[Trevor Gore]

Looks like this one might have raised more interest if it were in the main forum, Doug!

For the 12 string, you still want the resonances to be in the same places as you would want for a 6 string, so that it still sounds like a guitar. 12s are pretty jangly anyway, so you don't need to emphasise that any more by catering specifically for the octave strings. So the issue is about raising the stiffness to stay with the 2 degree bridge rotation guideline for the string set you plan on using (see Section 4.4) and then reducing the resonant frequency from where the extra stiffness leaves you by adding a bit more mass. The addition of mass tends to happen fairly naturally because of the larger bridge and bridge plate required to take the 12 strings.

For the baritone guitar, I would stick with the 2 degree bridge rotation guideline as before. As for pitching the resonances, it may be worthwhile researching Graham Caldersmith's papers on building a guitar family of instruments in which (I think) he gives guidance on how to scale things. One rule of thumb that comes to mind is to place the main air resonance around the pitch of the lowest string but one (that would be the 5th string or 110Hz on a standard guitar). But we normally break that rule on guitars by putting the resonance somewhere between the 5th and 6th string pitches. I've heard really good bass guitars based on a J200 chassis, so you should be able to get a good baritone out of something that size or a little smaller. Put the bridge more-or-less in the centre of the lower bout and let the neck joint fret fall wherever it falls for the scale length you chose.

[dshaker]

For others interested in the baritone question, a copy of Cladersmith's paper can be found at:
http://www.csc.kth.se/utbildning/kth/ku ... rsmith.pdf

Caldersmith defines a baritone as a fifth below a standard guitar (C-C tuning). He aims for a main air resonance of about 72 hertz.

He also makes the statement that

...to halve the frequency of the natural modes for an instrument tuned an octave lower than the standard, the plate dimensions should increase by a factor of about 1.4 if plate thickness and brace sections remain the same.

If I assume that the 1.4 represents an approximation of the square root of two and that the two came from lowering the frequency by an octave (a factor of two).
If I extend that to a B-B tuning, then I get:
Reduce the frequency to 75% of standard
Inverse of 75% = 1.333
Square root of 1.333 = 1.155
So I should be increasing the main soundboard dimensions (width and length) by about 15%.

Or that would be the case if I weren't strengthening the bracing. The article goes on to say, if I understand correctly (which is not a sure thing),
since you have to make the braces a little bigger, the soundboard needs to be a little bigger, too.

So I think I aim for a soundboard about 18% bigger and see how that goes.

Caldersmith uses a scale length of 710 mm for his baritones (a shade under 28 inches).

Comments? Suggestions?

[Trevor Gore]

Makes sense!

There's nothing like getting your hands on one and seeing how it plays, then go from there. Shouldn't be too hard in your area, Doug. If you can tap one out, and do a monopole mobility test it would certainly help you identify specific strengths and weaknesses. Caldersmith provides resonant frequencies in his paper, so that's a start. Regarding size, I'd be inclined to stick with one of the standard guitar sizes (e.g. J200 etc.) if you ever want to put it in a case.

[dshaker]

Good point about the case. I expect that bit of wisdom was learned through experience.

[weslewis]

I am retopping a 12 string I built a couple of years ago, there were several things I didn't like about it , neck profile , string spacing , and the sound....which I attributed to being over braced and too stiff..
so the new top is falcate braced, leaving the braces .200 thick and .350 tall, or at tad over 5mm and a tad under 9mm for all you SI types...I have decided that at 58 I will stay with my inch's roots and use SI units only when necessary, like using the formulas in Trevors book...LOL anyway I left the bridge plate about the same thickness, with carbon fiber of course, and will be using a 6 pin bridge..drawing in a cad program I have adjusted all the string spacing to what I hope will be more confortable string spacing to play,the sound hole is doubled and the UTB will probably be just a little larger...other than that we will see what happens, from my limited experience with falcate bracing..4 so far...I think it will be fine....or it will implode on itself!!! when I get It finished I will post some VA charts to see how in comes out...which may be a little while hopefully by mid summer.....

[weslewis]

Here is the result, great sounding 12 string, very, very loud, completely compensated nut and saddle cut on my small cnc, set up is as follows.
string height at 12 fret low e .080 high e .070 relief < .010 but > .005, string height at 1st fret .013, .015, for e and b .019 for the rest of the strings, makes for a great playing guitar.
measuring on my tuner cents different at 1st, 5th, 7th, and 12th as best as possible
low E +2 +5 0 -12
a +3 -6 -4 -3
d +1 -3 -4 -3
g +1 -3 -4 -3
b -1 -2 -3 -8
e 0 -2 -3 -6

[weslewis]

12 string final freq.pdf

(134.14 KiB) Downloaded 1043 times

here is the final freq chart main air 108 first coupled 186

[dshaker]

Sweet!

[GregL]

Hi Wes,

That looks mighty fine!
I'm really intrigued by your fine intonation. How did you work out the nut compensations - I have "the books" - do I need to look at them more closely for intonation details? From your figures, there was a total of 17 cents variation (E 5th fret = +5, E 12th fret = -12), is that right?

Thanks,
GregL.

[weslewis]

no it would be 12 the first cents error listed is at the 1st fret all based as close as i could get to zero in open strings, comp numbers were derived using a jig with a movable nut and bridge for each string including the octaves then drawen on cad the saddle used the numbers I came up with plus just a little more after adding in the exact postiion of the saddle from the 12th fret.

[Trevor Gore]

Nice work Wes. How do you find the playability with the almost uniform string spacing at the nut?

[kiwigeo]

Nice work Wes. How do you find the playability with the almost uniform string spacing at the nut?

Wow..yeah I just noticed that.

[weslewis]

nut forum.pdf

(7.19 KiB) Downloaded 708 times

here is the offsets I used, the spacing between the sets is uniform, the distance between the strings is adjusted for string width, still some room for experimentation , the playability is really good, I can't stress enough how loud this thing is especially with the soundport, at least to the player, you almost need some ear plugs !
the bottom drawing is the depth I cut into the nut for string height for each string, using a .019 bit for the e and b and octave strings and a .023 for the rest, on the setup I just reduced the bottom till I was close then final adjustments with nut files

[GregL]

Hi Wes,

Would you please post a pic of your intonation jig? I'm really interested, I have posted some pics of my jig in the "Jigs & Fixtures" section (viewtopic.php?f=24&t=6406).

Thanks,
GregL.

[weslewis]

Pretty simple jig, consists of a recycled fretboard, a movable nut and saddle, which are tapered so I could slide in and out to adjust string height, the feeler guage stuck in the middle sets relief and a old chinese tuner with a bridge pin stuck in the rear, the app is ap tuner for android, it cost 3 bucks and works great. nut slot is cut in about .200 which is more than is need but leaves plenty of room, there are lines draw for zero fret and front of saddle slot. then I use my handy dandy stew mac string gauge to measure offset, I did this for each string including octaves and then actually used these strings with the exception of the octave g, which of course broke but not till after I measured it, I had gotten 2 sets of string before starting.

[GregL]

Hi Wes,

Looks good. Thanks for the pics!

Thanks,
GregL.