Scale Length, Physics, and 22 vs. 24 Frets -- Why Ed Roman is Full of Crap

A while back while I was looking for my Hagstrom guitar I ended up on the Ed Roman site and poked around a bit to see what he had to say. His site definitely has a high entertainment value compared to many other high traffic guitar sites on the web because unlike most other sites that simply reproduce the marketing copy of the big name guitar makers and avoid much controversy, Ed Roman (or Ed Roman's ghost writer, if he uses one) aims to attract an audience that is suspicious of these marketing claims.

The gist of Ed Roman's arguments can be summed up in two sentences: You're a sucker if you buy a big name guitar from a corporate music store. Smart guitar players buy hand built American guitars from Ed Roman. Ed puts forth this argument wherever he can, weaving it through his ad copy and linking in and out of his webpage to lead surfers from the popular brands on his site to one of the guitars -- an Abstract, Baker, Pearlcaster, or Quicksilver -- for which Ed Roman is the primary distributor.

Ed also weaves together his own rants with "tech articles" in order to further his claims that his own guitars are far superior to any of the big name guitars that he disparages on his site. I was especially intrigued by one of his "technical papers" that featured prominently on his site where he criticized Paul Reed Smith's design for his 22 fret guitars with a 25 inch scale length. This article, which Ed characterizes as "[maybe] one of the best technical articles on this website."

Go ahead. Click and read. His hit counter will love you for it. Just be sure to come back and finish reading this once you are through there.

The quick summary of his article (or of John Johnson's explanation) is simple -- 24 fret guitars are better than 22 fret guitars because the pickup on a 22 fret guitar is right were the 24th fret would be, and this is a "dead node of the third overtone." This is a fatal design flaw because you can't change the laws of physics.

Assuming for a moment that this were true, I have yet to figure out what law of physics prevents someone making a 22 fret guitar from moving the pickup back to where it would be if there were two more frets. Just leave a little more space between the fretboard and the pickup. The difference is only a little more than 0.75" on a 25.5" scale guitar. How hard is that?

But that assumes that the basic claim is both a. true and b. relevant in the first place. Is it?

I put together a table that lists the fret placement for a 25.5" scale neck (found at ProjectGuitar.com and taken from Melvyn Hiscock's well respected book Make Your Own Electric Guitar) and expanded it out for our purposes here:

Fret	Dist. from Nut	Dist. From Bridge	1st Harm.	2nd Harm.	3rd Harm.	4th Harm.
		(Speaking Length)
0	0.000	25.500	12.750	8.500	6.375	5.100
1	1.431	24.069	12.035	8.023	6.017	4.814
2	2.782	22.718	11.359	7.573	5.680	4.544
3	4.057	21.443	10.722	7.148	5.361	4.289
4	5.261	20.239	10.120	6.746	5.060	4.048
5	6.397	19.103	9.552	6.368	4.776	3.821
6	7.469	18.031	9.016	6.010	4.508	3.606
7	8.481	17.019	8.510	5.673	4.255	3.404
8	9.436	16.064	8.032	5.355	4.016	3.213
9	10.338	15.162	7.581	5.054	3.791	3.032
10	11.189	14.311	7.156	4.770	3.578	2.862
11	11.992	13.508	6.754	4.503	3.377	2.702
12	12.750	12.750	6.375	4.250	3.188	2.550
13	13.466	12.034	6.017	4.011	3.009	2.407
14	14.141	11.359	5.680	3.786	2.840	2.272
15	14.779	10.721	5.361	3.574	2.680	2.144
16	15.380	10.120	5.060	3.373	2.530	2.024
17	15.948	9.552	4.776	3.184	2.388	1.910
18	16.484	9.016	4.508	3.005	2.254	1.803
19	16.990	8.510	4.255	2.837	2.128	1.702
20	17.468	8.032	4.016	2.677	2.008	1.606
21	17.919	7.581	3.791	2.527	1.895	1.516
22	18.344	7.156	3.578	2.385	1.789	1.431
23	18.746	6.754	3.377	2.251	1.689	1.351
24	19.125	6.375	3.188	2.125	1.594	1.275

The first two columns are from Hiscock's calculations. The third just reverses these calculations to measure the distance from the bridge rather than from the nut (the scale length minus the distance from the nut) which is important because this gives us the speaking length of the string when fretted at each fret. The remaining columns calculate the location of the nodes for the first four harmonic overtones of the string (at 0.50, 0.33, 0.25, and 0.20 the length of the string, respectively). These harmonic overtones give us the values for the intervals incorporated into the Western musical scale, but that is outside of our concern here. What we are interested in here is the correspondence between column 3 and row 1. According to my calculations here the node of the third harmonic overtone does indeed coincide with the location of the 24th fret -- both are 6.375" from the bridge -- so the basic claim that Ed Roman (and John Johnson) makes is true, but that does not mean that the claim is relevant, or that the conclusions that they draw from this fact are warranted. If we understand the rest of the table and what it is saying we will understand why Ed's point is far less relevant than it pretends to be.

The scale length of the guitar is important for the feel of how it plays and the distance between the frets, but if we are making claims about where to put the neck pickup we need to understand that these relationships only tell us anything absolute about the notes we play on the open strings or at the octaves on those strings because fretting a note changes the speaking length of the string and this changes the mathematical relations between them. If we were playing a harp where the speaking length of the string is fixed, we could optimize the pickup placement the way that the tech article on Ed Roman's website implies, but playing a guitar involves changing the speaking length of the string with every different note. Just look at the way the location of the overtone nodes change as you move down the neck. As the string length shortens so does the distance of the node from the bridge (the only really fixed node on the guitar.

For example, if we are playing an open A string on a standard E tuned guitar then a pickup where the 24th fret would be is at the node for the third overtone of that A note (6.375" from the bridge), but is not at the node for the third overtone of the B note played at the second fret on the same string (5.68" from the bridge). In fact, the node for the third harmonic of the B is closer to where the pickup on a 24 fret guitar would be. So by Ed Roman's line of reasoning you should never buy one of his guitars if you ever plan to play a B note and have it sound good.

Screw E minor. Who needs it anyway.

And this is just comparing single notes on the same string. Think about trying to optimize pickup placement for a jazz chord like a Gadd9 or a Dmin7 with an open string and a three fret spread somewhere up the neck where three of the four strings being played have very different speaking lengths.

So the 'design flaw' that the Ed Roman article points out only really holds true for notes played on the open strings (or at the octaves). The moment you fret any other note the mathematical relations all change. That's the other immutable law of physics that neither Ed Roman nor his physicist engineer friend John Johnson mention in the article.

Guitars are built to be fretted, and the shifting relationship between speaking lengths is what makes chords played on different strings sound so different from each other even when they are composed of the same notes. The only reason Ed wants you to buy that this is a design flaw is so that he can sell you his own guitar rather than one you can buy almost anywhere.

Frankly, if I wanted a semi-custom, American made guitar I'd go with Carvin long before Ed Roman.