Using a non-standard scale on a 25.5" scale designed body

[SSS-tonelover]

This is just the issue I had earlier this week. A non-Fender eBay neck had arrived and was built and used on an S-type body. It looked the part and fitted fine until.... intonation time.
Turned out the nut to 12th fret distance was 322mm (12.688") which gives a scale length of 644mm (25.354") instead of the usual 25.5" (647.7mm).
I did solve the problem (changed to a saddle with a break point far forward of the Fender stamped type) but it made me consider how to anticipate and correct for non-standard necks on a standard body and keep in the normal intonation adjustment ranges without drama.

If we say the body is a given (no change needed), and if we want to use a different scale (and it could a broader range then the one I had) then the obvious answer is to change the nut to heel length (routing, etc) so that new scale is intonatable. This can work on a neck with overhang just as well as a 21 fret neck without overhang, the nut-heel length is just slightly more complicated to measure, that's all. It's all about the math and measurements, so luthier design execution info we should have in an easy to use form

If this is interesting just let me know where to park the Excel file and you can use it for your own purposes.
Note: - blue shading indicates "body constants" and don't change.
           - green shading is the new calculated nut-heel length

P.S. Using the basic idea, the same math concepts can easily be used on any body and any neck just be plugging in the new default values and let the formula derive the nut-heel number for you,

 

[Bizman62]

1 hour ago, SSS-tonelover said:

how to anticipate and correct for non-standard necks on a standard body and keep in the normal intonation adjustment ranges without drama.

That's a good question and any effort trying to explain and offer potential fixes is welcome!

Now knowing your issue and the exact measurements it seems that the neck pocket on your body is too short for the neck. Carving the pocket 1.85 mm longer towards the bridge should take you spot on. The thin wall between the neck pocket and the neck pickup cavity is of minor structural importance.

[curtisa]

Are you sure the nut is positioned correctly? Nut-to-12th measurement x2 as a measure of scale length only holds true if the nut is positioned exactly at the 'zero'. If the nut is cut closer to the first fret it will throw the nut-to-12th reference short.

Note that some manufacturers purposely move the nut closer to the first fret by a small amount to apply a degree of intonation compensation for the lower frets without changing the nominal scale length (PRS for example is notable for doing this).

The blue cells in your spreadsheet are largely irrelevant to scale length and only matter assuming the body is made to match a particular neck and bridge. The correct way to marry *any* bridge to a body (whether it be a Floyd Rose, Tele bridge, Tune-o-Matic or anything in between) is to position the screws/routes/distance to heel cutout based on where *the saddles* satisfy the scale length and work backwards from there.

[SSS-tonelover]

9 hours ago, Bizman62 said:

Carving the pocket 1.85 mm longer towards the bridge should take you spot on. The thin wall between the neck pocket and the neck pickup cavity is of minor structural importance.

You took the 3.7 scale difference (647.7-644) and divided by 2 to get 1.85. Out of curiously why not carve 3.7? Just wondering if I'm using some wrong assumptions.

Certainly material has to be removed either from the neck heel side, or the body pocket side. The  good point of removing it exclusively from the neck heel is that later another neck (a standard length one) can be used as the body has been undisturbed. Also the shortened neck can go on any standard body now and someone (unaware it is a different scale) will never notice an issue, they can intonate blithfully and think all is well in the world

[SSS-tonelover]

7 hours ago, curtisa said:

1. Are you sure the nut is positioned correctly? Nut-to-12th measurement x2 as a measure of scale length only holds true if the nut is positioned exactly at the 'zero'. If the nut is cut closer to the first fret it will throw the nut-to-12th reference short.

2. Note that some manufacturers purposely move the nut closer to the first fret by a small amount to apply a degree of intonation compensation for the lower frets without changing the nominal scale length (PRS for example is notable for doing this).

3. The blue cells in your spreadsheet are largely irrelevant to scale length and only matter assuming the body is made to match a particular neck and bridge. The correct way to marry *any* bridge to a body (whether it be a Floyd Rose, Tele bridge, Tune-o-Matic or anything in between) is to position the screws/routes/distance to heel cutout based on where *the saddles* satisfy the scale length and work backwards from there.

1. I did not check that but have noticed that on other necks and even done nut shifting on one occasion (in that case moving the nut toward the body, so the other way [see image]). What would be the normal range for the nut offset? A correction factor could be built in. I suppose measuring from the 1st to the 13th fret is the foolproof way to know scale length (referring to a table for that distance of course)
2. Noted
3. Agreed to all points.

Typically I do exactly as you mention: I mount the neck and then 'drift' the saddle into position so the strings are centered over fretboard edges working backward [see second image]. It works well, of course assuming the scale length was verified....(my major error on this build, which is all on me!) 

This 'formula' limits itself to assume a standard S-type body with a non-standard neck. It also assumes the body is already made and tremolo screw holes are drilled, and body painted. More typically one can plug the holes (should they exist) and move the bridge to compensate for neck variation. The only downside would be a new neck later on (a very rare case) that could recreate the issue. The formula is meant to 'future-proof' later work such as neck substitution (as well as allow a finished body to be used as is).

 

[Bizman62]

3 hours ago, SSS-tonelover said:

You took the 3.7 scale difference (647.7-644) and divided by 2 to get 1.85. Out of curiously why not carve 3.7? Just wondering if I'm using some wrong assumptions.

That's what I did. And now re-thinking about it you may be right. Or maybe not?

The logic behind my thinking is that the 322 from the nut to the 12th fret is a set value. From the 12th to the bridge it's ~323,8. There's a flaw in my math: If the frets are truly made for a 644 mm scale length and the neck pocket is carved to a 647.7 mm scale length, the distance from the 12th to the 21th fret is shorter than it would be with a fretboard of a 647.7 mm scale.

Thus the accurate method would be to put the neck in place and measure how much the distance from the bridge to the 12th differs from 322 mm and act accordingly.

[curtisa]

4 hours ago, SSS-tonelover said:

What would be the normal range for the nut offset?

1 - 1.5mm is typical. It doesn't take much, but because it's a global compensation applied uniformly to all strings it has more benefit to some strings than others. The most notable improvement tends to be switching between an open-E major chord and an open-G major chord, where the change between the G# major 3rd of the E chord (3rd string 1st fret) and the tonic of the G chord (3rd string open) is more harmonically pure. Without compensation the typical error is that the G# tends to be mildly sharper than expected. But because it's a global compensation, if taken too far it will have a negative impact to the overall intonation as some strings get progressively worse while others get closer to 'perfect'.

Ideally you'd apply nut compensation per string (look up Earvana nuts for example), but it is fiddly to do right, and many players don't feel the excess work is warranted.

Of course, we could be overthinking what's happened here and the neck is just made...well, wrong. 1.5mm error at the nut could be half the thickness of the nut itself, which might happen if the nut was positioned centrally over the initial 'zero' cut when the fretboard was slotted, instead of butted up against the edge of the cut like it probably should have been. In an age of 'CNC everything' these kinds of errors are hard to imagine slipping by, but without knowing the true history of a no-name neck I guess anything's possible?

 

4 hours ago, SSS-tonelover said:

This 'formula' limits itself to assume a standard S-type body with a non-standard neck. It also assumes the body is already made and tremolo screw holes are drilled,

Yep. Given the sheer volume of Partscasters suppliers out there it's probably a miracle that so many guitars (apparently?) get put together without any issues. I guess it'd be pretty foolproof buying both the body and neck from a single reputable supplier known for that kind of thing (eg Warmoth, Mighty Mite etc). But I'd personally be a bit squeamish about trying to marry any old Strat body with any old neck without worrying about fit and intonation.

[SSS-tonelover]

1 hour ago, Bizman62 said:

Thus the accurate method would be to put the neck in place and measure how much the distance from the bridge to the 12th differs from 322 mm and act accordingly.

Well, the interesting thing is that if you use the high E string (such as 0.10) you really have no real measurable compensation you have to make on the saddle. What I mean by that is by direct tape measurement (actual guitar) I get 644mm nut to saddle break point, and 322mm 12th to saddle break point, Since saddle have an adjustment range, it's kind of a losing battle to use them as the bridge measurement as it's too amorphous in terms of overall calculation (more just for final intonation touchup). That's way Stew-Mac used the tremolo screw holes (fixed measureable location) for the Strat, Floyd, etc., as that is tangible and can be measured.

[SSS-tonelover]

13 minutes ago, curtisa said:

1 - 1.5mm is typical.

Yep. Given the sheer volume of Partscasters suppliers out there it's probably a miracle that so many guitars (apparently?) get put together without any issues. I guess it'd be pretty foolproof buying both the body and neck from a single reputable supplier known for that kind of thing (eg Warmoth, Mighty Mite etc). But I'd personally be a bit squeamish about trying to marry any old Strat body with any old neck without worrying about fit and intonation.

Thanks!  I have always been intrigued by compensated nuts, such as Earvana, and the various tunings to compensate. I guess the ultimate expression would be the True Temperament guitar neck in which every fret is adjusted, not just a crude nut correction LOL!  For the moment I try to get the string slots way down (without buzzing) so the sharping is reduced on the first frets. 

I've done quite a number of partscaster.... and body and necks range from crap dimensional accuracy to darn good. This whole experience is pushing me to make neck (not just bodies) to have total control.... We'll see,
Frankly it's impossible to compete with eBay neck prices, so something has to take a hit (time, money, accuracy, etc). I've always been able to work my way out of trouble but then I have time issues on the 'fix it ' side or have to engineer clever ways out o the situations.

[curtisa]

The problem with the Stewmac calculator quoting those positions based on some feature of the bridge is that it doesn't help you if the bridge you want to use isn't listed there, or if the manufacturer of the bridge decides to change the design of the bridge slightly (unlikely, but could happen in the name of 'continual product improvement').

The easiest way is to simply move the saddles as far forward as possible and use the breakpoint of the saddles themselves as the scale length point when positioning your bridge on the body. Intonation compensation will only ever result in the saddle moving backwards, so the saddles being forward gives you maximum leeway for setting intonation as you need to.

[curtisa]

23 minutes ago, SSS-tonelover said:

I guess the ultimate expression would be the True Temperament guitar neck in which every fret is adjusted, not just a crude nut correction LOL! 

True Temperament (TT) necks are actually a bit of a red herring. The frets are compensated to give better harmonic purity to certain intervals and chords. But because of the way our western-ised 12-tone equal temperament (12-TET) system works, the compensation applied by TT makes some intervals better at the expense of making others worse. Equal temperament means that any interval is exactly the same frequency ratio no matter what the base key is. The result of this is that some intervals are already 'pure-ish' (eg, 4ths and 5ths are pretty close) and others are slightly out (major 3rds and major 6ths are some of the worst). TT attempts to even some of these discrepancies out, but because it's impossible to re-calibrate all ratios in any fret position the intervals in some keys get notably over- or under-corrected.

Short story is that if you only ever play your guitar in 'friendly' keys like E, A, B, G, D etc TT can have a useful impact on the purity of intervals played. But if you start including 'off' keys like Bb, F#, G#, or chords with extended and complex intervals TT can actually make the situation worse. Steve Vai was an early exponent of the TT system and had one of his Jems fitted with a TT fretboard, but you never see him with it anymore. Considering he's a player not afraid of exploring melodically awkward things, I suspect this 'incompatibility' with equal temperament is possibly one reason why he dropped it.

There's actually no reason why any old guitar can't be set up to intonate perfectly within 12-TET and sound as pure as our western ears need it to in any key; all it takes is decent construction and adjustment. TT by and large just puts a bandaid on a problem that doesn't really exist in the first place.

[Bizman62]

I realized another flaw in my calculations regarding the length of the neck pocket:

If we assume that the neck is properly fretted for a 644 mm scale length, from the nut to the 12th fret it should be 322 mm, right? Similarly it should be 161 mm to the 5th fret and 483 mm to the 24th fret if there's one as approximately 3/4 of the scale length is on the fretboard. That's why I divided the scale length difference in two, trying to make both halves to 322 mm. But as three quarters already are correct, I should have divided by four, meaning that shaving only about 0.9 mm should suffice. But my logic may fail here as well...

Anyhow, it's almost impossible to tell the scale length of a body without having the neck and bridge attached.

 

 

[SSS-tonelover]

7 hours ago, curtisa said:

The problem with the Stewmac calculator quoting those positions based on some feature of the bridge is that it doesn't help you if the bridge you want to use isn't listed there, or if the manufacturer of the bridge decides to change the design of the bridge slightly (unlikely, but could happen in the name of 'continual product improvement').

The easiest way is to simply move the saddles as far forward as possible and use the breakpoint of the saddles themselves as the scale length point when positioning your bridge on the body. Intonation compensation will only ever result in the saddle moving backwards, so the saddles being forward gives you maximum leeway for setting intonation as you need to.

I agree with both your paragraphs, especially the second, the CAVEAT being I typically do the "all the way forward based on the break point" with the traditional Strat saddles, as the GraphTech have a different break point. If you used the Graphtech 'all the way forward', then switch to the stamped Strat type down the road you can run out of adjustment room on the low E, etc.... 
For other bridges (Floyd, Chinese, etc) I do as you say 99% of the time and it works great (assuming scale length is correct to the actual neck).

In terms of the 1st paragraph, I recently bought a Vega Trem and after querying their team, they could only tell me to follow Fender placements, and not give any adjustment range info at all, which was disappointing news. Their design is a bit odd (two saddle sizes on their tremolo which complicates 'moving it as far forward as possible' (for max rearward leeway). ...I reverse engineered their drawing and put it 1:1 on a Fender blueprint to see 'adjustment range' etc. The crazy thing is my reverse engineering drawings (middle and bottom) are better than theirs (top of illustration) and with far more detail. I'm actually trying to get the saddles and adjustment range quantified.
Alternatively, maybe I should just do a test on junk body and neck before drilling out a good one (LOL).
I really did want to quantify this in design before building (and in case you have not guessed), I love design/engineering though seat of the pants 'just trying it', is valid too, and is fine for some work.

 

[SSS-tonelover]

7 hours ago, curtisa said:

True Temperament (TT) necks are actually a bit of a red herring.

There's actually no reason why any old guitar can't be set up to intonate perfectly within 12-TET and sound as pure as our western ears need it to in any key; all it takes is decent construction and adjustment. TT by and large just puts a bandaid on a problem that doesn't really exist in the first place.

Could be and I knew Steve Vai gave it a shot, but have not seen him playing it since, but musicians can be fickle. I tend to concur that a traditional layout is fine in dealing with temperament evening through all keys.

Hard to pull off but the Micro-fret company I believe was on to something. I know I've always been fascinated by an true intonatable nut since I heard about their innovation years ago. No one has resurrected that idea really to my knowledge.

[curtisa]

15 hours ago, SSS-tonelover said:

the CAVEAT being I typically do the "all the way forward based on the break point" with the traditional Strat saddles, as the GraphTech have a different break point. If you used the Graphtech 'all the way forward', then switch to the stamped Strat type down the road you can run out of adjustment room on the low E, etc.... 

I guess ideally you'd plan your build for the hardware you wanted to use. Even then I'd still consider retrofitting new hardware to an existing design on its merits and problem-solving the second install as the issues arose. In the original installation I'd still site the bridge based on 'saddles all the way forward'. If the retrofitted saddles mean I had an issue with them no longer allowing correct intonation adjustment based on my first install, I'd have to find a way to make it work after the fact (maybe use longer/shorter intonation screws, removing the intonation screw spring to squeeze a little more range out on the lowest strings, plug/redrill the trem pivot screws or simply use different saddles that were a better fit).

If you were trying to retrofit a 351 into a Honda Civic, you wouldn't design the Civic to take the 351 in the first place. You'd be looking at ways to modify the Civic take the engine

 

16 hours ago, SSS-tonelover said:

I recently bought a Vega Trem and after querying their team, they could only tell me to follow Fender placements, and not give any adjustment range info at all, which was disappointing news. Their design is a bit odd (two saddle sizes on their tremolo which complicates 'moving it as far forward as possible' (for max rearward leeway)

The saddles-all-forward guideline would still hold true on a cold install, though - you'd just pick the longest saddle(s) to do it with. The shorter ones I assume are reserved for the G and low-E, where you need more room at the rear to pull the compensation back in line.

As a retrofit I assume the Vega is primarily designed to just drop in place of an existing Strat-style bridge (that's certainly the way they word it on their product page). If it were me I'd still check everything was going to line up, but I'd have more confidence that Vega have offered a product that by its very nature is designed to fit straight in without any extra math or sawdust creation.

[SSS-tonelover]

51 minutes ago, curtisa said:

 I'd have to find a way to make it work after the fact (maybe use longer/shorter intonation screws, removing the intonation screw spring to squeeze a little more range out on the lowest strings, plug/redrill the trem pivot screws or simply use different saddles that were a better fit).

-On Strat type objects I design for compatibility of aftermarket parts to avoid future upgrading nightmares, though it will be a rare day when I select a swimming pool rout as a default (though I have nothing against them personally).
-On custom builds like a 30" scale baritone using a Schaller roller bridge I maximize the potential of that bridge as it won't get changed, meaning I use the approach you advocate.
in other words two approaches are used, and the selection is made on likelihood of future changes balanced versus optimizing a design to one or another parts choice.

51 minutes ago, curtisa said:

[Vega] The saddles-all-forward guideline would still hold true on a cold install, though - you'd just pick the longest saddle(s) to do it with. The shorter ones I assume are reserved for the G and low-E, where you need more room at the rear to pull the compensation back in line.

As a retrofit I assume the Vega is primarily designed to just drop in place of an existing Strat-style bridge (that's certainly the way they word it on their product page). If it were me I'd still check everything was going to line up, but I'd have more confidence that Vega have offered a product that by its very nature is designed to fit straight in without any extra math or sawdust creation.

3 long (high e,b,d) and 3 short (low e,a,g) saddles.
I'd prefer they'd let me maximize the potential of the unit, instead of dumbing down all the info.... In other words their approach  is all great for a technician, but lousy for a designer willing to do the math and make the sawdust if you catch my meaning.

Edited April 15, 2023 by SSS-tonelover