Should I convert the Utah Neck to 22 frets from 21

[CheshireCat]

Okay, got a question for you guys.

Do to a mishap on the end of the Utah's neck, I need to recap it with some solid maple. The neck, as you guys may or may not know, is a Strat style neck (and may very well have been a Strat neck . . . it still remains a mystery).

Well, while looking at what it would take to do this, it occured to me that I could do what Fender did, and add an extra fret. Well, it will be getting really tight in their, and I am seriously debating it. I'm definitely recapping it. The question is, do I add the extra fret? It will be the same amount of work regardless.

So, for those Gibson players (and whoever else), do you guys find that the extra fret is worth it?

Chesh

[sumgai]

Chesh,

I'm greedy, I need that 22nd fret! ;D Sure makes playing anything by Santana a lot easier, but that's just me.

It's a matter of personal taste, AFAIC. Don't worry about any 'fit', the end of the fretboard will easily clear the pickup (unless you've positioned it in a non-standard place, closer to the neck pocket).


sumgai

[Runewalker]

The question is really, do you play up there. I prefer at least 22 but it is more convention and the reassurance that it is there if I want it. But realistically I like big sound and that is not up high.

so if you are going to use it get it, if not, don;t worry the little stuff.

[CheshireCat]

Well, I can't say that it fits my playing style one way or another, because I've never had access to it before, but now I have the possibility to do that. Ergo, the internal debate.

[CheshireCat]

sumgai said:

I'm greedy, I need that 22nd fret! ;D Sure makes playing anything by Santana a lot easier, but that's just me.

Funny thing: in EJ's "The Cliffs of Dover", the piece creshendos to a D on the 22nd fret . . . or at least it appears that way based on the transcription, even tho EJ did COD before Strat (which he plays) came out with 22 fret necks.

[dunkelfalke]

add three frets
24 fret guitars are the way to go

[CheshireCat]

dunkelfalke said:

add three frets - 24 fret guitars are the way to go

Can't do that. I can only squeeze one on their, without doing some major rework. That and the fact that that would totally screw up my neck pickup assembly.

But that does bring up an interesting issue. Do you find the extra frets really pay off?

[dunkelfalke]

yep.
just slide slowly on high e from 24 to 12. sounds great, more or less like gilmour's marooned, but dave needed a digitech whammy for that.

also, 24 fret guitars usually have a very good neck access for higher frets so they are more comfortable to play.

or the third solo on money (also pink floyd of course), 22th fret and full tone bend on it, so basically 24th fret is frequently used.



e[-----------7-10-12-14fb~~10-12-7~~19h22fb~~~~22-22-22-19~~\-----------]

[CheshireCat]

Any more insights guys?

[RandomHero]

I have a 24 fretter, and writing my own music, I don't think I'd mind losing a few frets up there for the sake of having that neck 'bucker in the right position. Harmonics on the neck sound so dead on a 24-fret...

[sumgai]

admin said:

I have a 24 fretter, and writing my own music, I don't think I'd mind losing a few frets up there for the sake of having that neck 'bucker in the right position. Harmonics on the neck sound so dead on a 24-fret...

With a humbucker, that's true. However, a single coil pup is a different story. I've seen it in several cases, but all of them were expensive custom jobbies.

I'm setting myself up to test various pup placement configurations, later this summer. I'll have more data to work with as the testing progresses, but I can't start until after the July 4th holidaze.


sumgai

[ChrisK]

This is an interesting discussion. I usually see comments that the neck humbucker sounds dead on a 22 fret neck (LP), and moving up to 24 frets helps due to the neck pickup being moved toward the bridge.

I had plotted the sine waves of harmonics up to the ?15th to see the dead spots on a neck. There certainly IS a dead spot at the 24th fret "location", often where the neck pickup IS on a 22 (or 21) fret guitar.

However, this all depends on where the string is fretted. Fretting at the 2nd fret reduces a 24 fret neck to a 22 fret neck, and the neck pickup is NOW at the new 24th fret location.

The choice between a 21, 22, or a 24 fret neck is based on WHAT you play. The neck pickup location should be based on WHERE you play (on the neck). For instance, the Fender Jerry Donahue Tele has a 21 or 22 fret neck, but the Strat neck pickup is closer to the bridge (around the 24th or 25th fret location).

I've also been thinking about constant ratio pickup placement vs the more common equal spacing.

[sumgai]

Chris,

....
I had plotted the sine waves of harmonics up to the ?15th to see the dead spots on a neck. There certainly IS a dead spot at the 24th fret "location", often where the neck pickup IS on a 22 (or 21) fret guitar.

However, this all depends on where the string is fretted. Fretting at the 2nd fret reduces a 24 fret neck to a 22 fret neck, and the neck pickup is NOW at the new 24th fret location.

The choice between a 21, 22, or a 24 fret neck is based on WHAT you play. The neck pickup location should be based on WHERE you play (on the neck). For instance, the Fender Jerry Donahue Tele has a 21 or 22 fret neck, but the Strat neck pickup is closer to the bridge (around the 24th or 25th fret location).

I've also been thinking about constant ratio pickup placement vs the more common equal spacing.

Your last comment intrigues me. But first, a quick test. If you'll hold your left hand so as to 'chime' a string at the 2nd harmonic (the 24th fret), you'll see that there is a point wherein the chime sounds beautifully full, and that the neck pickup can't sense it very well. Switching to the bridge pup will detect the sound effortlessly.

Now, where is that magic 'chime' point in relation to the pup's pole pieces? A little off, I imagine. Not as far as the 25th fret, that just opens up another can of worms.... it's more likely that the offset is between a 1/16" and 1/8", in the direction of towards the bridge. Always has been on every Fender I've ever picked up. (Exception: The Jazzmaster is 'way' forward, like about 5/8" or so.)

I was all set to launch into some deep theory about nodes, standing waves, complex harmonic theory, etc. But then I decided to give it a break (you're all welcome), and just cut to the chase. What do you have in mind when you say 'constant ratio' versus 'equal' placement?


sumgai

[ChrisK]

sumgai,

Your last comment intrigues me. But first, a quick test. If you'll hold your left hand so as to 'chime' a string at the 2nd harmonic (the 24th fret), you'll see that there is a point wherein the chime sounds beautifully full, and that the neck pickup can't sense it very well. Switching to the bridge pup will detect the sound effortlessly.

By "chiming" a string at the 24th fret, you're setting up a "mass reference node" (a "lingering point of anchor") when plucked. Since the string is an integer multiple of this length, the resulting vibration will indeed have a dead spot there. It won't remain a pure" harmonic "chime" since the string has a natural resonance tendency at all harmonics, including the fundamental.

The same effect occurs when "chiming" at the 12th fret. If we had a pickup at the 12th fret, it would detect little. QED, see what your VG-88 thinks of this since one can "place" a pickup anywhere on the neck (I don't think that the VG-88 will be that clever).

The dead spots, while being fairly exact in location, will be region oriented in that a pickup actually see string vibrations that vary as a sine (cosine) function of the amplitude of the harmonics as it moves away from the exact points of common harmonic zero cross. No pickup, except a piezo saddle (and it's not sensing the same way/thing, it's sensing pull), actually senses at that narrow of a window to fully detect only exact harmonics at an exact location. Since we have to intonate guitars, due to the real characteristics of physical devices (strings), these locations aren't exact and precise.

AND, don't forget the pickup magnet's effect on the vibration of the string itself (one cannot measure anything without affecting it).


If one looks at a Strat, the pickups (once one "adjusts" for the bridge pickup slant) are """relatively""" equally spaced. If, for example's sake, one assumed that the bridge pickup was 2" away from the bridge, the middle pickup was 2" away from the bridge pickup, and the neck pickup was 2" away from the middle pickup, one would have equal spacing.

Now, the bridge pickup is 2" away from the bridge and the neck pickup is 6" away from the bridge. This ratio is 3:1 or the neck pickup is 3 times as far away from the the bridge as the bridge pickup. One might presume that a good location for the middle pickup would be 3^1/2 [the square root of 3] times 2" or 3.464..." from the bridge.

Just as the frets are at equal GAIN (or reduction) intervals (2^1/12 [the 12th root of 2 or 1.059463.....]) in string length, one might presume that pickups might be similarly located.

I haven't analyzed just what this might mean against said string harmonics plot, but it's a thought.


Or not!

[sumgai]

Chris,

I'll take all of that as a thought! ;D

You do strike an interesting chord, crossing as you do the line I have been contemplating for several weeks now. As I've noted elsewhere, I'm gonna make some empirical experiments later this summer. I have to admit, I haven't before come across the "tempered" placement theory, did you derive that on your own?

And just for drill, how does that theory stack up when evaluating the pup placement of three humbuckers? From memory of what those pups look like as mounted on a LP or an SG, I'd say the middle pole pieces just may come close to what you've expressed here.

Analysis of the standing wave (that doesn't stand still!) is where we start in harmonic theory. But what I've not yet been able to pin down is why does a 2nd harmonic (24th fret) chime sound so weak to the neck pickup, and yet the 1st harmonic (12th fret) chime sounds so perfect. There must be a lot of cancellation going on there, eh? And why is the neck pickup susceptible to that phenomenon, but not the other two (on a Strat)?

I intend to find out, or at least get a leg up on it. Perhaps we'll be collaborating more closely on this, as time marches on. Do you have any reference websites I should be viewing?


sumgai

[ChrisK]

I haven't before come across the "tempered" placement theory, did you derive that on your own?

Yes, but many may have preceded me. It's a natural extrapolation of music theory. (1/2, 2/3, 3/4, 4/5,.....) And since 2^1/12 is the basis for equal temper, 2^1/2, 2^1/3, and 3^1/2 run amuck. Most people (those not innumerate) are algebraic, I start at ratiometric.

I suspect that one may be better off analyzing/implementing the following tome and "choosing wisely".

Analysis of the standing wave (that doesn't stand still!) is where we start in harmonic theory. But what I've not yet been able to pin down is why does a 2nd harmonic (24th fret) chime sound so weak to the neck pickup, and yet the 1st harmonic (12th fret) chime sounds so perfect. There must be a lot of cancellation going on there, eh? And why is the neck pickup susceptible to that phenomenon, but not the other two (on a Strat)?

It may come down to semantics and definition. The fundamental is easy, perchance it's half a full sine wave cycle (180 degrees). The rope is.

The second will have a null at the 12th fret. Half is. It will be at peak AT THE 24th (and 5th) FRET!

The third is 3 times the fundamental, and has nulls at the 7th and 19th frets.

The fourth has a null at the 24th fret (and the 12th and 5th frets). Which shows why a harmonic "anchored" at a realization point will have a "standing" null at said point.

I spawned a quick worksheet that lists the spacing of each fret from the bridge, starting at 25.5" (scale length doesn't matter since it's ratiometric) and reducing the string length as the bridge is approached. I plotted constant columns of divisions of said scale length thru the 15th harmonic (which gives simple harmonic location nulls from the bridge (!).

One can immediately see the null locations et. al.

Some years ago I used the same technique to develop harmonic content envelopes along the string that were sums of the sine waves at very fine granularity. One could alter the harmonic weighting to suit (as a decreasing linear/power series interpolation as one goes higher in harmonics). A fundamental premise was that a string plucked at mid length would have no harmonics, and one plucked infinitely close to the bridge would have equal harmonic amplitudes. (Which is like sort'a true.)

I'd also plotted a constant amplitude series in AutoCAD just for the visual Halibut.

[UnklMickey]

i can see where this discussion might be headed.......................and it ain't pretty.


i've seen it before.


the musician sez:

no, no, no, the 1st harmonic is twice the frequency.



the scientist/engineer/mathmagician sez:

of course not, twice the frequency is the SECOND harmonic.

the 3rd is 3 times the frequency, the 4th is four times, etc.


the musician sez:

so what is the FIRST HARMONIC?


the engineer sez:

the root, or fundamental, of course.


musician:

that's just silly, the root isn't a harmonic!




on and on and on they go!






......................who's on first?

[ChrisK]

So the the scientist/engineer/mathmagician thinks that the 1st harmonic is the root [Hn = n*F], while the musician thinks that the 0th harmonic is the root [Hn+1 = n*F]?

[UnklMickey]

assuming the role of the musician (don't ask me why i'm doing this!):


no, of course not, that would be silly!

the root isn't a harmonic of any kind!

it's just the fundamental tone of course.

[sumgai]

unk,

Ah, but the musician would have a difficult time believing that 2^0 = 1, wouldn't he though? Engineers, however, take this as a gospel fact. They need to, in order to found the rest of exponentiation theory, or there'd be hell to pay in the Mathematics Department. ;D

It is, as Chris correctly noted, a matter of one word being purloined for two slightly different definitions. I've seen both engineers and musicians that are adamant that their use of the word is the only correct usage, and I've also seen both kinds that are willing to bend for the purposes of discussion. It takes all kinds.

Fortunately, I don't foresee that Chris or I will have problems with each other. And I'm fairly certain that if someone here has questions about how we use the word, he and I are both amenable to explaining what we're saying.

But that doesn't mean that the results will be a pretty sight! ;D


sumgai

[ChrisK]

2^0 = 1

2^3=8
2^2=4
2^1 1/2=2.828.....
2^1=2
2^1/2=1.414......
2^0=1
2^-1/2=0.707.....
2^-1=1/2
2^-1 1/2=.353553.......
2^-2=1/4

Continuum is!


QED e^(-i*Pi) -1=0 (Euler, w/ liberty)

i= (-1)^1/2

[sumgai]

Chris,

You and I see it quite easily, but nearly all math-challenged folk see only "If you don't multiply it by anything, then you've done nothing to it, so you still have your original number. Don't you?" Common error on their part. ;D

Your proof is a shortcut in that it only quotes a table of values. The way I learned it was by virtue of the algebraic powers of distribution and association, like so:

Given the rule that you you add exponents to imitate multiplication in the base number system, so to do you subtract exponents to imitate division in the base number system. With that in mind:

2⁰ = 2^{(1 - 1)}

2^{(1 - 1)} = 2¹ / 2¹

2¹ = 2

2 / 2 = 1

ergo, 2⁰ = 1

Still seems true after all these years. (Or have the Dark Lords changed this one on me, too? )


sumgai

[ChrisK]

In the land of logs and exponents, we're actually raising to powers and not multiplying. But that's OK.

My experience has been that most folk tune out after the wrenching exposure to multiplication tables. I find it amazing that many can make it thru college. (People make it thru college because society needs people that have made it thru college.)

But, persistence is. No use'y, most lose'y. And, as we progress thru our careers, we're reduced to sound bytes ;D and power points. I'm astounded by the number of engineers that have become innumerate.

Every time I go into a Papa John's pizza place, I see a crew member staring at a poster that attempts to describe the "proofing" (correct rising) of the crust dough. The poster states that properly proofed dough is twice the volume of the unproofed. Twice the volume, holy crust Batman, spatial reasoning required.

One who remembers anything from high school (you know, that institution that all of these crew members recently vacated), MIGHT surmise that a means may exist to convert spatial concepts to easy measurements.

Gee, lets see, if a bowling ball was twice the diameter, how much would its mass vary.
Hmmm, 2 x 2 x 2 = 8.
Bingo, ergo 2^3 = 8!
(Which proves why we can't have 12 foot tall people, the mass is times 8, but the bone strength is only times 4.)

Hmmm'ski, I wonder what X^3 = 2 is?
log[X^3] = log 2
log 2 = 0.301...
log[X^3] = 3 log X (by definition)
[log 2]/3 = [3 log X]/3
0.301.../3 = 0.10034.......
log X = 0.10034.......

X = 10^0.10034.......
X = 1.25992....

Holy anti-brain aneurysm Batman, if the shape stays the same (scalability), properly proofed dough is exactly 26% larger or, 1.26 times the unproofed dough in diameter (a single dimensional measurement).

Wow, 25% is close enough for me. Ship it!


I had the unique pleasure of studying advanced mathematics when the scientific calculator was born. One could suddenly use brute calculation to "hammer about the framework" of the number system. One could calculate in a minute what took a day in the past. I wrote an AC circuit analysis program in 1976 that enabled me to do a final in 10 minutes as opposed to 2 hours with a slide rule. The next year everybody had one!!!

And yet, I LOVE the slide rule. An absolutely perfect visualization of the log/exponential framework! (Continuum is.) The log adder/subtracter.


And all of the interest and study that I've had in math theory has led me to suspect the very framework that we use for representation and calculation. Some chaotic functions that ALWAYS render random results at certain points, DO NOT do so depending on which alternate representations and calculation means are used.

In the end, I believe none of this and more.


Math is just a language.

Experiment, it probably won't kill you.

[dunkelfalke]

btw wish me luck, i am currently bidding for a body and neck of a hohner revelation prototype with 27 frets!

just like this one, but without the suburst

[CheshireCat]

dunkelfalke said:

btw wish me luck, i am currently bidding for a body and neck of a hohner revelation prototype with 27 frets!

27? Hmmmmmmmmmmmm . . .

[dunkelfalke]

didn't get it