Strings, gauges, mechanics

ed packard · Post by **ed packard** » 24 Feb 2004 2:18 pm

It looks like I am talking myself into getting a new instrument (PSG) soon. It will incorporate some things new and different. One of these is the combination changer and tuner in one mechanism. Another is placing this mechanism at the left end of the instrument (as you sit at it). These, and other changes, motivated looking at the present instruments via physics 101.

This "look" means throwing some basic measurements and calculations at the vibrating string from a strength of materials and tolerances standpoint.

A single finger of changer/tuner combo was fabricated and subjected to functional test on the instrument. No noticeable problems encountered. Sent photos to several knowledgeable folk and PSG makers for comments. One maker says that he will make the combo, so on to the next issues.

The issues of Scale Length, string separation, string gauges, string tensions, string termination structures, and body/mechanism structural strength and stability.

The unit will have 14 strings. I have no problem with having the strings 11/32 apart at both ends of the instrument, ..in fact, I want that. That makes it easier to move the changer to the left end and not having to shrink it down.

One issue with having 14 strings is body/mechanism stability. The total pull (tension) from the 14 strings will approach 400 pounds. To get a feel for how stable your instrument is, bring all the strings up to pitch, then release the slack on all but a center string and measure how much that string changes tuning; return the strings to pitch without touching the string under test and remeasure the string under test. Repeat this with a high outside string as the string under test (G#!) as it is the most sensitive. The smaller the change the better the stability.

The 400 pounds tension is such as to pull the top of the changer toward the nut/tuner. Both of these elements stick up above the body/neck to which they are anchored. This has the effect of magnifying/amplifying the effect of the string tension on the body/mechanisms.

Ever try to get technical info on strings from the string maker? Most makers may have a person hidden away in a back room that has the data, but there are several layers of folk insulating you from him. Easier to go to the music wire makers to get the data; Use Google or equiv' and type in the buzz words.

Items such as Modulus of Elasticity, Tensile and Shear strength, Yield strength, Thermal coefficient of expansion, Gauge tolerance (diameter variation allowed per string, per batch, per ??), magnetic permeability, etc. all enter into the design, and that is just for strings. The properties of the strings determine the limits re tensions, which in turn determine scale length limits, terminating methods, required tuner excursions, finger radii, and other more or less important things.

Over the years I have put together a rather extensive spreadsheet based program that combines the machanical with the musical to get solutions for stringed instruments. What will follow in this thread will use much of that. If you don't like numbers and measurements applied to the PSG, it will not be your cup of tea, ..if you do please enter in and comment, critique, question, and generally try to set me straight (where is Bob Farlow when I need him?).

The next post will cover the values re gauges, tensions, and elongations.

David L. Donald · Post by **David L. Donald** » 24 Feb 2004 3:14 pm

The Doctor is in!
This should be very interesting.

Charlie Moore · Post by **Charlie Moore** » 24 Feb 2004 3:29 pm

Roy THomas Pedalmaster guitar's has built a guitar with the string width the same at nut and changer,Pee Wee Whitewing had the guitar built by Mr.Roy,i think all these thing's have been addressed by Roy,i think his webb site is www.pedalmasterguitars@aol.com
Charlie...........

ed packard · Post by **ed packard** » 24 Feb 2004 4:21 pm

Donald, ..where are you located re Nice/Antibe?

Charlie, ..you LA. folk sure stick together! I am familiar with Pee Wee's Pedalmaster guitar, and with Pee Wee. Should see the "old boy" in Dallas.

Edp

ed packard · Post by **ed packard** » 24 Feb 2004 4:45 pm

I presently use a 25" scale (played string length), and a variation on the E9/B6 tuning/setup structure, so we will start with the most problematic string in the setup, ..G#. It seems to be most common to use an 0.11 gauge for this string. I have a keyless tuner on the 25 " scale instrument. differentiating between the "played" string length, and the "stretched" string length gives the following conditions and values.
<pre>
FOR AN 0.011" G# AT PITCH

STRETCHED STRING = 26.38 INCHES
PLAYED STRING = 25.00 INCHES
BALL TO FINGER TANGENT = 1.00 INCHES
BALL END STRING WINDING = 0.50 INCHES
BRIDGE TO NUT = PLAYED STR L = 25.00 INCHES
NUT TO CLAMP SCREW = 0.88 INCHES
G# DOWN TO G# = 0.25 INCHES
G# UP TO A = + 1 HALFTONE = + 0.0330 INCHES AT TOP OF FINGER, 0 AT CLAMP SCREW;
IN PER IN INCREASE = 0.00125 INCHES 0.00125 INCH MOTION AT THE ROLLER.
STRETCHED STRING L + 1 HALFTONE = 26.41 INCHES
INCR' IN STR L FOR G# TO A = 0.12512 PERCENT
SAME MOTION @ LO G# = + 4.00 HALFTONES
</pre>
When we tension the string up to pitch, we stretch it. If we stretch it, the diameter of the string decreases. Should we be concerned?, depends upon a few other items TBD, hence we will run the numbers.

What are the tolerances on strings? You probably get as good as you pay for. I tend to use +/- 10% for worse case design purposes.

The amount that the string stretches becomes an issue in deciding the "throw" of the keyless tuning mechanism. The 0.011 gauge is the smallest dia string, and requires the most throw to bring it up to pitch. One would like NOT to need pliers, or other extra tools to bring a new string to pitch.

The numbers for getting a common 0.011 gauge (tolerance unknown) on a 25" scale, from G# an octave below pitch to G# at pitch is a stretch of about 0.250" (measured). If the G# to A pedal/change is activated, it takes another 0.033" of stretch to get to A. G# is 415.3 Hz, A is 440.0 Hz (so called straight up). An octave (G# to G#) is 1200 cents. The halftone change from G# to A is 100 cents, the first cent of which is nearly 4.153 Hz, and the last cent of which is nearly 4.400 Hz.

The amount of string motion over the nut/roller for a G# to A change is something on the order of 1/27 of the 0.033 inches, or about 1.25 milliinches (thousandths of an inch) per inch of string length. The string capture screw is about 1.0 inches behind the tangent point on the nut roller, hence the string moves about 1.25 milliinches across the nut/roller for a change of the 0.011 gauge string raised from G# to A. Supose that the roller sticks and the string cannot loose the 0.00125" amount when the pedal/change is released? How far out of tune would it be? If my calcs are correct, about 3 cents worse case for a complete siezure of the roller at one extreme of the G# to A movement. Is a complete siezure likely to happen in such a way as to capture the string at either extreme? NO. Why?, because if the roller freezes, the string will slip over the surface to return to its nominal length/tension because the angle of the string to the roller tangent point is shallow enough that the frictional force of the string against the roller is far less than the string tension. If the distance from the roller tangent point to the string capture screw were half the distance (0.5") the cents off for a total non return would be only 1.5; The roller mechanism is a lot of mechanics and cost for the function if that is the only function that it serves.

That was the analysis for a one half tone change on the 0.011 gauge string. We do commonly use changes of up to 3 halftones in some tuning/setups, but on much larger strings, none of which have the throw per halftone required for the 0.011 gauge. The quick conclusion is that a solid bar would perform the described nut function on a keyless tuner equipted PSG. We will explore another nut/roller scenario later and address string top planarity.

It should be kept in mind that when the same amount of travel (activated pedal) to tension the G# to A was applied when the string was tuned an octave low it provided about 4 halftones of pitch change as opposed to the 1 halftone when used at pitch.

Next, questions and charts re string tension.
[This message was edited by ed packard on 25 February 2004 at 10:46 AM.]

Ray Minich · Post by **Ray Minich** » 24 Feb 2004 5:25 pm

Ed, please keep these cards and letters coming. I'm one of the unfortunate nerds that enjoys this stuff. Never gave thought much before to string composition being important to the pickup, but I can see why...

Anyone ever given any thought to building a PSG on a section of I-beam? It works for log splitters. Talk about stiff...

David Parker · Post by **David Parker** » 24 Feb 2004 6:25 pm

Concrete Block!

ed packard · Post by **ed packard** » 25 Feb 2004 10:42 am

Now lets have a look at what string tension does for/to us besides stretch strings and change pitch.

Here is the 14 string tuning/nominal gauges, and calculated tensions that I will use as the basis for discussion. It is a 25" scale with a keyless changer and "gauged" rollers.

<pre>
CHART #1 MY TUNING, GAUGES, TENSIONS
A B C D E
TUNED FREQUE' POUNDS STR DIA STR
STR # NOTE IN Hz TENSION INCHES TYPE
"GAUGE"
1 C# 277.18 28.40 0.0160 P
2 G# 415.30 30.00 0.0110 P
3 F# 369.99 33.00 0.0130 P
4 E 329.63 30.50 0.0140 P
5 B 246.94 28.50 0.0180 P
6 G# 207.65 30.00 0.0220 P
7 F# 185.00 33.30 0.0260 W
8 E 164.81 35.00 0.0300 W
9 B 123.47 31.60 0.0380 W
10 G# 103.83 32.70 0.0460 W
11 E 82.41 30.60 0.0560 W
12 C# 69.30 24.80 0.0600 W
13 B 61.74 25.30 0.0680 W
14 E 41.20 15.60 0.0800 W
TOTAL NECK TENSION = 409.3 LBS
</pre>
Assumptions are made re the wound strings in all these calcs because I have no idea what the core diameter/shape/material is, or what the winding material diameter/material/turns per inch or other pertinent data might be, so they are treated as if they were plain strings for the purpose of the calculation. Some folk would prefer to use a factor of 0.90 to 0.95 for the dia to compensate for the effect of winding on the mass, density, and/or other parameters; The numbers are there if they wish to do so.

There is a lot of terminology floating around to describe the cause of pitch change as a function of activated changes (pedals and levers). If there is a change in oitch, it will be because something has been tensioned into the plasticity region of the stress/strain curve, The tuner and/or changer mechanism is tilting or bending, or the body is changing the degree of "banana shape" that it takes on as a function of string tension.

Notice that the tension on the body/mechanisms on my instrument is about 400 pounds. Can you bench press that much? Here is a little experiment that I ran again this AM, ..it has been a few years since I did it last.

Using a tuning meter, bring all strings up to pitch. Then while monitoring the pitch of a center string (I used F#), relax all the other strings to 0 tension. how much did the F# change? In my case +50 cents. Did it stay there, or creep? This instrument stayed there,. ..as checked 1/2 hour later. Removing 370 or so pounds of tension was worth a raise of 50 cents for the F# string. The raise was steady re the tension loosening, as opposed to going in jumps, ..jumps would worry me a bit.

I did the same thing on a 1970 or so Sho-Bud Professional. This F# also went smoothly to +50 cents, ..but did a creep to + 60 cents over the next 1/2 hour.

The temperature was a constant 70 deg, as it had been for weeks where the instruments are.

The difference between the two instruments is that the first is a single 14 that has a 25" scale, Aluminum extrusion body, hardwood block for a neck, U bottomed nut rollers (single point contact with the strings)on an axle that is supported between each string, a keyless tuner the pressure plate of which is NOT supported/anchored between each string, and a changer that IS supported between each string. The strings are about 1.5" above the body top.

The second is a D10 24 inch scale, wood body, wood neck, two point contact with the strings nut rollers (small diameter re the other instrument and on a smaller axle supported between each string, a keyed tuner with up to 6" of extra string length, and a changer that appears to be supported between each string and on about the same size shaft. The E9 neck was used for the experiment. The strings are about 1.25 inches above the body top. Then the C6 neck was slacked with not noticeable effect.

The above test can be performed any time you decide to change your strings, and is an index to the stability of your instruments body/changer/tuner structure. It would be nice if there were no change, but smaller per pound of tension would seem to be better.

Next time you change your strings why not take the same data and send/publish the results? The test can also be run in reverse as the new strings are put on, and other sophistications are possible also.

Next we will provide three more charts that are extended versions of chart #1 above, but using a "constant tension" tuning principle and let the gauges fall where they may. Do you think that that will make a difference?, good or bad?

[This message was edited by ed packard on 25 February 2004 at 10:45 AM.]

ed packard · Post by **ed packard** » 26 Feb 2004 8:24 am

So far, we have shown a way to measure string motion, for a change in pitch, for the purpose of calculating string motion (or lack thereof) at any point in the stretched string for that change in pitch (we used the nut area but it is the same approach for any part of the string); Introduced Stiction/Friction as a major component in the "return to pitch" issue(whether rollers, bar, or ??; And measure the relative stability of your instrument's body/neck/mechanisms re change in tension. We have pointed out the "banana effect", which is the tendency of the total string tensions to bend the structure into a banana shape, thus having an effect upon pitch. We have pointed to the two towers named changer and tuner that protrude above the body/neck to which the total string tensions are applied. The further up they extend from the mounting popint(s), the greater the banana (tendency to bow) forces applied to the body/neck by the string tension. We have shown that the string gauge before stretching is greater than the string gauge after tensioning, and insinuated a way to calculate it. We have warned that the string gauge on the package is likely NOT the actual string gauge because of manufacturing tolerances (picky, picky).

Now lets look at some more issues re string tensions. We will present three charts with a variety of string parameters as a function of tension. Each chart has the string gauges calculated for a different CONSTANT applied tension. Again, the wound strings are treated as plain strings for these calculations.

Three charts are given because "three points determine/define the curve". For those that wish, the chart parameters may be plotted in graph form to determine any "in between" tensions, gauges, string top planarity compensations, etc..
<pre>
CHART #2 EQUAL TENSION = 28 LBS PER STRING
A B C D E F G H I J K
TUNED FREQUE' POUNDS STR DIA MAKE IN SMALL TO ADJACENT GROOVE STR CS LBS/STR
STR # NOTE IN Hz TENSION INCHES ORDER LARGE STR DIFF DEPTH AREA CS AREA
"GAUGE" DIA
1 C# 277.18 28.00 0.01593 2 0.0106 0.0000 0.0053 0.0001 315424
2 G# 415.30 28.00 0.01063 3 0.0119 0.0013 0.0066 0.0001 250353
3 F# 369.99 28.00 0.01193 4 0.0134 0.0015 0.0081 0.0001 198705
4 E 329.63 28.00 0.01339 1 0.0159 0.0025 0.0106 0.0002 140506
5 B 246.94 28.00 0.01788 5 0.0179 0.0020 0.0126 0.0003 111519
6 G# 207.65 28.00 0.02126 6 0.0213 0.0034 0.0159 0.0004 78856
7 F# 185.00 28.00 0.02387 7 0.0239 0.0026 0.0186 0.0004 62588
8 E 164.81 28.00 0.02679 8 0.0268 0.0029 0.0215 0.0006 49676
9 B 123.47 28.00 0.03576 9 0.0358 0.0090 0.0304 0.0010 27880
10 G# 103.83 28.00 0.04253 10 0.0425 0.0068 0.0372 0.0014 19714
11 E 82.41 28.00 0.05358 11 0.0536 0.0111 0.0483 0.0023 12419
12 C# 69.30 28.00 0.06372 12 0.0637 0.0101 0.0584 0.0032 8782
13 B 61.74 28.00 0.07152 13 0.0715 0.0078 0.0662 0.0040 6970
14 E 41.20 28.00 0.10716 14 0.1072 0.0356 0.1018 0.0090 3105
TOTAL NECK TENSION = 392.00 LBS

CHART #3 EQUAL TENSION = 30 LBS PER STRING
A B C D E F G H I J K
TUNED FREQUE' POUNDS STR DIA MAKE IN SMALL TO ADJACENT GROOVE STR CS LBS/STR
STR # NOTE IN Hz TENSION INCHES ORDER LARGE STR DIFF DEPTH AREA CS AREA
"GAUGE" DIA
1 C# 277.18 30.00 0.01649 2 0.0110 0.0000 0.0055 0.0001 294396
2 G# 415.30 30.00 0.01100 3 0.0124 0.0013 0.0068 0.0001 233662
3 F# 369.99 30.00 0.01235 4 0.0139 0.0015 0.0084 0.0002 185458
4 E 329.63 30.00 0.01386 1 0.0165 0.0026 0.0110 0.0002 131139
5 B 246.94 30.00 0.01851 5 0.0185 0.0020 0.0130 0.0003 104085
6 G# 207.65 30.00 0.02201 6 0.0220 0.0035 0.0165 0.0004 73599
7 F# 185.00 30.00 0.02470 7 0.0247 0.0027 0.0192 0.0005 58416
8 E 164.81 30.00 0.02773 8 0.0277 0.0030 0.0222 0.0006 46364
9 B 123.47 30.00 0.03701 9 0.0370 0.0093 0.0315 0.0011 26021
10 G# 103.83 30.00 0.04402 10 0.0440 0.0070 0.0385 0.0015 18400
11 E 82.41 30.00 0.05546 11 0.0555 0.0114 0.0500 0.0024 11591
12 C# 69.30 30.00 0.06595 12 0.0660 0.0105 0.0604 0.0034 8196
13 B 61.74 30.00 0.07403 13 0.0740 0.0081 0.0685 0.0043 6505
14 E 41.20 30.00 0.11092 14 0.1109 0.0369 0.1054 0.0097 2898
TOTAL NECK TENSION = 420.00 LBS

CHART #4 EQUAL TENSION = 33 LBS PER STRING
A B C D E F G H I J K
TUNED FREQUE' POUNDS STR DIA MAKE IN SMALL TO ADJACENT GROOVE STR CS LBS/STR
STR # NOTE IN Hz TENSION INCHES ORDER LARGE STR DIFF DEPTH AREA CS AREA
"GAUGE" DIA
1 C# 277.18 33.00 0.01729 2 0.0115 0.0000 0.0058 0.0001 267633
2 G# 415.30 33.00 0.01154 3 0.0130 0.0014 0.0072 0.0001 212420
3 F# 369.99 33.00 0.01295 4 0.0145 0.0016 0.0088 0.0002 168598
4 E 329.63 33.00 0.01454 1 0.0173 0.0028 0.0115 0.0002 119217
5 B 246.94 33.00 0.01941 5 0.0194 0.0021 0.0136 0.0003 94622
6 G# 207.65 33.00 0.02308 6 0.0231 0.0037 0.0173 0.0004 66908
7 F# 185.00 33.00 0.02591 7 0.0259 0.0028 0.0201 0.0005 53105
8 E 164.81 33.00 0.02908 8 0.0291 0.0032 0.0233 0.0007 42150
9 B 123.47 33.00 0.03882 9 0.0388 0.0097 0.0331 0.0012 23656
10 G# 103.83 33.00 0.04617 10 0.0462 0.0073 0.0404 0.0017 16727
11 E 82.41 33.00 0.05817 11 0.0582 0.0120 0.0524 0.0027 10537
12 C# 69.30 33.00 0.06917 12 0.0692 0.0110 0.0634 0.0038 7451
13 B 61.74 33.00 0.07764 13 0.0776 0.0085 0.0719 0.0047 5914
14 E 41.20 33.00 0.11633 14 0.1163 0.0387 0.1106 0.0106 2634
TOTAL NECK TENSION = 462.00 LBS

</pre>
Now, ain't that a MESS!!!

The units are inches and pounds.

The first column = A in each chart gives the string # in the order that I use them for my tuning; This is the tuning that I use.

The second Column = B gives the note to which the string is tuned.

The third column = C gives the frequency in Hz to which I tune the string = straight up value.

The fourth column = D gives the pounds tension assigned to the string for the purpose of these calculations.

The fifth column = E gives the diameter of the string (gauge) required to get the Hz and note in the prededing columns. The Gauge value is the "under tension" value per the calculations.

The sixth column = F gives the string number as in column A, but rearranged to place the string diameter in ascending order (reading down the column).

The seventh column = G gives the string diameter when placed in the acsending order.

The eighth column = H gives the difference between the reference string top (smallest dia string) and the top of the next largest string, values from column G.

The ninth column = I gives the required depth of a U shaped groove into which the string would be placed to make it in plane with the top of the smaller dia strings. The smallest dia string has been placed in a groove that is 1/2 the dia of the string.

The tenth column = J gives the cross sectional area (CS) of the string. This is the same as the area of a circle whose dia = the string dia.

The eleventh column = K gives the pounds tension divided by the strings cross sectional area. This is an indication of where the string is on the stress/strain curve, ..larger numbers mean that the string is closer to the plasticity, and breaking point.

Column twelve was the string dia in the untensioned state. It did not fit without making the forum column too wide for convenient reading; Not to worry, it was much smaller than the tolerance of the purchased strings.

Here are a few questions to be considered re string gauges, tensions, and mechanisms; no single grain of sand determines the shape of the beach!

The first thing to notice is the effect of the tension increases on the total body/mechanism tension; 392 to 462 pounds. Is bigger better, or worse? A 10 string instrument would of course be 10/14ths or 5/7ths those values. Remember the "instrument stability test" from the earlier post.

Consider the tension per unit of string cross section values; Is more tension better of worse for any given string dia?

What are the pros and cons of an "equal tension" approach to selecting string gauges?

If grooves are used to get "string top planarity", should they be U shaped for single point contact, or V shaped for added friction with the string?

How important is it to adjust for the tolerances of the purchased strings?

How important is the "string top planarity" issue? Is it worth all the added mechanism and cost of rollers? Would a rod do as well? How about a grooved rod/nut as in the old lap top instruments.

What would combining the changer and tuner into a single unit do re tension, gauge, string top planarity, pretensioning, roller/rod/nuts, materials, stability, etc.?

Ponder these for a while, then we will continue.

Feel free to correct, add, comment, ask, throw stones, or whatever.

Would the [This message was edited by ed packard on 26 February 2004 at 12:03 PM.]

Paul Brainard · Post by **Paul Brainard** » 26 Feb 2004 7:09 pm

Hey there was a steel built up around Portland I think a while back that had changers on both ends (maybe one was raise & one was lower?) I think the name was Wheeler - only saw one once in an antique store. . .

ed packard · Post by **ed packard** » 28 Feb 2004 9:05 am

Paul; It seems that there was a time when the steel guitar passed from the carpenter/cabinet maker to the machinist that a lot of things were tried re mechanisms. This is no small problem as anyone that has tried to make a changer that raises, lowers, and returns would know. There were two or more double ended approaches tried. I think the motivation was to have more available changes and simple mechanisms by dedicated raise, and lower units. These days one can get 5 raises and 5 lowers per string in a single changer. These will handle +/- 3 halftones, so there is less motivation for double ended changers. The move now would seem to be toward simplification of the PSG. One possible move is to combine the changer and tuning mechanisms into one, ..we shall see.

To those that have e-mailed me, thanks for the thoughts. I will get back to you soon.

Back to the thread subject(s):
What are the effects of string tension on the PSG? We can break this down into several categories:

The catastrophic effects, the long term change effects, and the annoying pesky type troubles. Lets deal with the catastrophic first.

String breakage: The myth is, that too much tension breaks the string. This is true only if nothing else changes but the tension. The real culprit is pounds per square inch of string. Look at the values in columns J & K in each of the three charts (#2,3,4) above. Look at the effect of the string's cross sectional area on the value in colm(s) K. If this value raises above a certain limit the string will break from tensile failure, or if it is bent around a sharp curve the outside of the curve of the string is stretched and the inside of the curve is compressed. This make a differential tension across the string and it may fail from shear forces. The values in the chart are for NO curves involved. Rule one, ..do not increase the values of differential tension across the string (small gauge in particular) by wrapping them around sharp curves, as in small diameter fingers and/or small roller/nut devices.=; Shallow angles are better. The limits on how shallow are to some degree a matter of what makes you feel good, ..after all, the angle of the string leaving the bar is mighty shallow.

If you have a roller nut, the roller will lose pressure against the axle as the angle becomes increasingle shallow and may tend to buzz/rattle against the axle. If the sound does not come out the pickup when playing with open strings, it is an annoyance only.

If you get shallow enough, the string will slide back and forth across the roller/nut surface (assuming no grooves). How bad is that ? It does the same beneath your bar. If it does not show up as a bad thing in the output sound, do you really care? There is, of course, a compromise position re angle, but keep it as shallow as taste(asthetic and tonal) permits.

Another advantage to a shallow angle is that it tends not to make grooves in fingers and roller/nuts made of soft materials (Brinnelling) because the downward forces are smaller with increasing shallowness. All these things are valid whether we are talking keyed or keyless. The materials chosen, and the radii on the changer finger, and the roller nut are part of the characteristic sound of a given instrument, ..different designs = different sound, all else being kept the same. Large radii and soft materials make for a more mellow tone, and less string breakage. Too large and/or soft may give a bit of sizzle sound on the smallest strings.

Look at the effect of the diameter (gauge) of the smallest string on the cross sectional forces (colms G & K). Notice that a small increase in string gauge makes for a large reduction in the colm K values. Notice also that the greater tension on the string is less important than the gauge re these forces. That 0.0115 (as opposed to 0.011) dia string really does some good for any string material. Basic string material(music wire, it is NOT all alike) and the process used to manufacture the particular gauge from the basic material (it is not all the same) determine a lot re string breakage, tone, and output from the pickup for a given excitation (string vibration). Material and process have a large effect upon the values in colm K, which in the case of the small G#
is at the edge of disaster anyway (even without sharp bends).

You older farm boys will remember "hay bales and (bale)ing wire". Remember how we used to break it by bending it sharply and rapidly, ..remember the heat that we felt near the bend? Now think about the small strings and the changer motion.

OK, fatter strings, more tension, shallower angles seems like a good thing, if it does not kill the tone that you like. try this little experiment, ..pluck you E (4th string), now loosen it to the E an octave below, ..pluck it again. Now pluck the E an octave lower as provided by string #8(?). Which sounds best to you. Now think tension vs tone; would you agree that greater tension is good as long as it does not break or deform things. Now try fatteneing up the dia of your big strings, increase the tension and see if you like the sound better. By plotting the data from the 3 charts(#2,3,4) you can see gauge vs tension to decide on a reasonable gauge size for this experiment.

Lets have string makers publish the tensile strength ratings on their finished product, preferrably on the package!!!

But what about the "Banana Effect" re increased total tension? OK, back to the experiment of loosening all of the strings but one, and seeing how much pitch change occurred in the one. It was about 50 cents for a 300 pound (about)or more total tension change. You can repeat the experiment and note the change in pitch of the control string as each string is tightened or loosened. You now have a curve of pitch change versus increased tension. What is the shape of this curve? What will a given increase in pitch because of fatter strings do to the pitch of the control string? Therein lies the answer, .."the excercise is left to the student" was the famous school line.

While we are tweaking string tension, loosen the E(str 4?) to an octave lower. Place the bar flat on the strings and push down a little compare the pitch of the E4 against the E8, or against a tuner. Tune it back up to pitch and do it again. This is an extreme illustration of the effect of tension on pitch difference between strings. If all strings are in plane on top, and all the same tension, the pitch change for a given deflection (equal increase in downward force)will be proportional. If the tensions between strings are different, their pitch shift for a given deflection will be different by some amount, ..how fussy are you re this effect? If the string tops are not in plane, then a given deflection will produce a greater pitch change for each string. Repeat this near the nut, ..in the middle of the string, etc and see if the differences are enough to bother you. You should find that a greater string tension gives a reduced pitch change for a given deflection, ..another possible reason for as much tension as you can stand without the catastrophic physical effect(s) or unacceptable tone biting you.

[This message was edited by ed packard on 02 March 2004 at 09:52 AM.]

ed packard · Post by **ed packard** » 24 Mar 2004 12:15 pm

Texas show is out of the way, got thoroughly Bush-ed (Johnny Bush-ed that is, vocals, drums, bass, etc.), taxes are prep'ed and off, new PSG design done up and off for quote, ..if translation does not get in the way should know reaction soon. If you are interested in a copy of the RFQ I will send you one; S/B good for a laugh. Had a little sparring session re string breakage (is/will be covered in this thread in some detail). So now back to the mechanics of the PSG.

In the preceding posts, we have dealt with played and unplayed string lengths and some of their possible effects/annoyances in the finished instrument. We have touched upon the "properties of the materials" of the strings, and of the properties of materials and the geometries of the changer fingers and nut/rollers and their effect upon the tone of the instrument. For those that wish to read more on the string clamping/body structure vs. tone issue, do a search re vibrating string and look for some work done at McGill University. Now we will address the material issues in greater detail.

The science of immediatly contiguous or touching surfaces is called TRIBOLOGY. The TRIB part is from the GR for rubbing. A bit of humor here, ..TRIB is also found as the root for TRIBE, ..tribes are caused by a reasonable degree of "rubbing"; so this is a very sexy subject!

We have surfaces in contact on the PSG. The strings contact the changer fingers, and the nut/rollers, plus the screws and pins/catchers that hold the strings in place. These materials come in a variety of properties and shapes.

Strings come in an assortment of materials. The labels on the packages may be anything from Bronze, to Stainless steel, to Nickle, to ???. Some materials are specified for acoustic instruments, as the string "permeability" is not compatible with magnetic pickups. I have yet to see a permeability value for anyones strings on the package, or on their website. I do seriously doubt that they are all the same.

If the materials listed on the string package are the "real" materials of the string, then we can get the properties of these materials from a materials handbook.
Lets pick on Stainless Steel first.Therein we will find that there are three basic (at least) categories of Stainless Steel, and many types within each category. Many of the Stainless types are "non magnetic", ..I don't think that we want those kinds for the PSG. Bronze would not be good for electric instruments with mag pickups, ..piezo or optical pickups OK.

Most strings start out as "music wire", ..for more info do a search on Google or? The strings are brought to gauge by "drawing" the material thru a "die". This involves heat, friction, and stressing. Variations in these, and other process steps affect the properties and tolerances of the finished string.

What are some of the properties of concern re strings and the materials with which they will be in contact? Modulus of Elasticity, Hardness, Thermal Coefficient of Expansion, Corrosion Resistance, Elongation factors, Tensile strength, Shear strength, Plasticity point, Coefficient of Friction, Abrasion resistance factor, and a lot more.

If the string is in contact with a changer finger, and pressed against it with a force, the finger will deform (a hardness related function) as a function of the force with which the parts are pressed together. The finger will also tend to deform the string in the same manner; Rule of thumb = reducing the force will reduce the tendency toward deformation. Reduce the deformation and the string will be less likely to break. We need the tension of approximately 30 pounds on the string for the PSG so we are stuck with that. We do however have the way that the materials are "pushed" together as a variable. If instead of wrapping 90 deg around the changer finger, the string crossed at a shallow angle the force against the finger would be less, hence less tendency for either to deform at the point of contact from a "Brinnelling" mode. The finger material could also be chosen with a higher hardness factor in mind (stainless steel, bronze/brass, certain ceramics,), or perhaps a harder grade of aluminum, and/or applying a surface hardening process to the finger material.

The above comments can essentially be repeated for the nut/rollers.

Remember that changes in material/structure may affect the tone of the instrument in either a "good" or "bad" way.

The next item of concern is Coefficient of Friction for the materials in contact. It will also be higher for a higher contact force, ..reduce the contact force and reduce the amount of friction. Again, this can be done by reducing the wrap angle while keeping the tension constant. Harder finger, Nut/roller materials, or those having a surface hardening process applied may be used to reduce the friction factor for these components.

Next issue is the Abrasion resistance. When two materials are rubbed together, they tend to scratch each other, in general, harder is more scratch resistant, in particular, that is not always the case.

OK, now lets apply the above to the string/finger/nut/rollers structure and see what falls out. The string has friction with and force into the finger. Because the string stretches and has a tension change as the changer is activated, it will be "dragged" across the finger material, and "rolled" into it (for most changer designs), thus tending to deform both finger and string. When the change is released, the string will attempt to return to its origonal location/tension. To the extent that the friction is high, it will have to overcome said friction to do this. If it cannot overcome the friction, it will NOT return to pitch! The same is true on the nut/rollers end. It seems that the thing to do might be to reduce the friction at these points of concern. How can this be done?, ..reduce the angle.

But if I reduce the wrap angle across the rollers I will have no guarantee that the rollers will turn to allow the string stretch motion! You are right, ..but the reason for the rollers is to allow for string travel when the changer is activated, ..to the extent that the string travel is short, we don't need rollers (for that purpose), and to the extent that the friction is lowered we don't need rollers for that purpose either.

Given a design where the string forces the roller against the roller axle, we have both the friction of the string against the roller, and the roller against the axle to overcome, and any string/roller deformation at the point of quiescent contact to deal with also. Conclusion = get as much friction and unplayed string travel out of the equation as possible.

Look at your changer finger, at the top and around the radius, ..you may find that the wound strings dig into the finger material, ..a harder surface, and/or less friction via a shallow wrap angle would help. You ma also see that the ball winding is digging into the back side of the finger, ..another source of friction giving non return to pitch problems.

A shallow wrap angle also tends to reduce the different length of the outside of the string and the inside of the string when it is bent/wrapped. This is most meaningful with respect to the 0.011 gauge (small diameter) strings. This is because they are already tensioned close to their elastic limit (see the "pounds tension per unit of cross sectional area" col'ms in charts 2,3,&4) without being bent/wrapped, or heated from having the changer activated.

This AIN'T rocket science, but it ain't the everyday language of cabinet makers either. This is a somewhat complex instrument!

Jerry Overstreet · Post by **Jerry Overstreet** » 24 Mar 2004 1:39 pm

Ed, you're making my brain hurt!

ed packard · Post by **ed packard** » 24 Mar 2004 2:11 pm

Jerry; I may be a sadist to you, but I'm a masochist to me.

Did you hear about the sadist and the masochist that had a fight? the masochist said "beat me", the sadist said "no I won't"!

ed packard · Post by **ed packard** » 26 Mar 2004 9:28 am

Lets take a particular issue (I think of it more as an annoyance) that keeps showing up on the forum, ..string top planarity, or lack thereof at the tuner/nut/roller end. Some playing techniques are more sensitive to this than others. Those that play with the bar flat and tend to approach the nut/rollers, or even slide over it/them, will find it at least annoying if the tops are not in plane. Those that do hammer ons, pull offs, and tip down noodling will not be as bothered by lack of planarity.

If you like a nut instead of rollers, then notch the nut rod/? as per the nominal gauges that you use so as to put the string tops in plane. This approach has the problem that any deforming of the string bottoms or the notch/groove via pressure will put the string tops out of plane, as will any variation in string gauge via manufacturing tolerances. If you use an under the string capo, you will have to notch/groove it also, and live with the same problem (plus others).

So now for the rollers. I have described this fix in the past, but not in detail, so I think that the point was missed; Here we will give one of several possible manufacturing approaches that will solve the problem.

Take a rod of material of the type and outer diameter of which the rollers will be made. Make a scribe line along the length of the bar (witness line). Cut your preferred shape of groove/notch into the rod for each string gauge for which you wish to compensate. It might be nice to leave about half of the string Dia above the top of the notch/groove so you can finger block or slide over the finished roller.

Slice the bar into the roller width pieces.

We will now drill the axle hole in these pieces, but we will drill it off center! Suppose that you wanted to have an adjustment range of +/- 0.006" for an 0.011 gauge string; drill the axle hole 0.006" off center re the outside diameter of the roller, and at 90 degrees from the witness line/scribe line. When the striong is in the notch/groove you may now adjust the string top up and/or down by 0.006". This will allow compensation for any string gauge variation, for any axle flex, and for any local deforming of the string.

You might want to knurl the lip tops of the rollers for easy adjustment. Now repeat the process for the rest of the rollers with the appropriate axle hole center offset.

The actual string length will also move back and forth a bit because of the off center holes, ..I don't think that you will notice the change in pitch that this might cause.

Karlis Abolins · Post by **Karlis Abolins** » 26 Mar 2004 1:04 pm

Ed, That is an innovative approach to gauged rollers. Off-center and knurled for infinite adjustability.

Karlis

David L. Donald · Post by **David L. Donald** » 26 Mar 2004 3:50 pm

Hi Ed, looking good so far.

But I just finished a 5 hour gig and don't at the moment have the time, nor brain cells working, to through this with comprehension.

I am near Nimes about 4 hours from Antibes.
Pretty much dead center of the south of france. right above the Gulf de Lyon.

Sleep sleep is calling me!

Jeff Peterson · Post by **Jeff Peterson** » 26 Mar 2004 5:33 pm

Ed, I'd recommend purchasing a JCH.....but your tolerances are way too big.

ed packard · Post by **ed packard** » 26 Mar 2004 6:14 pm

JP; I work at being tolerant, ..or is it intolerable, ..I forget. Seriously, to which tolerances do you refer?

KA; Put that in the same basket as the tuner/changer combo. Thanks for the nice words.

DD; Sweet dreams of non breaking G#s. I have a good friend with a home in Antibe, which is why I asked. I used to be in France/Europe twice a year. Did a good bit of design work with a great company called SAGEM.

Edp

David L. Donald · Post by **David L. Donald** » 27 Mar 2004 1:59 am

Hi Ed, I know SAGEM well, I am logging on with an old SAGEM ISDN adaptor.
They build everything from netowrks to traffic lights.

You must have been working at Sophia Antipolas.
I had been looking for a home around there, but found some more west instead.

I don't break too many G#'s, but those ARE the strings I break if they do.

I think I like the Excell changer design in principal. A straight extention, not a bend of the strings. I have also heard the new MSA's don't break strings much either.

ed packard · Post by **ed packard** » 28 Mar 2004 9:59 am

Previous posts in this thread have dealt with string gauges, tensions, tolerances, materials; Body/mechanism stability vs tension; Materials at the string/mechanism interface; And getting string top or string bottom planarity. Every so often someone raises the question of string length adjustment, as found on standard guitars. Without commenting on whether this is a usefull approach on the PSG, we will look at how it might be accomplished.

Making the assumption that we want to accomplish this on the right hand end of the instrument, one would like to not have to deal with the changer mechanism as it is commonly made these days (rotary or semi rotary); Lets imagine the changer mechanism moved to the left hand end of the instrument. If this is done, then something as flexible and simple as the threaded bridge with up/down, back and forth screw adjustment as used on the fender standard guitars (Mustang etc.) could be employed. This could be combined with the tuner, placing the changer on the left end and the tuner on the right end.

for myself, I have chosen an approach that further simplifies the string length compensation issue, by combining the Changer and Tuner into a single unit and having them both on the left end of the instrument. This provides several advantages (as I see it): Allowing the largest ratio of "played" to "unplayed" string length; Allowing shallow angles of string bending at both ends thus tending to minimize the string breakage that is caused by the changer continually flexing the string at the changer finger area; Moving the largest amount of string motion away from the bridge/pickup area, thus allowing the use of alternative string vibration sensing devices; and some other things to be covered later.

This Changer/Tuner combo has been addressed in an earlier thread. Again, if anyone wants to see one, e-mail me and I will e-mail you back photos of it.

For those that are convinced that the instrument's tone is major related to the body and how the strings vibration is coupled to it, moving the changer to the left end opens up a whole new range of experimental possibilities; For those that think that it is the material/clamping/ bridge material that is the major tone determinent, again moving the changer to the left end on the instrument allows your preferred experiments to be run/applied.

For those that prefer traditional cosmetics to function, ..take your place in a long line that starts with I see no reason for more than 6 strings; I don't like pedals; I can't see keyless; 10 strings is enough; If it was any good XXXXXXX would have done it/used it; And any number of other "traditionalist" views. You may be/have been right, but some of us see other roads yet to be travelled, ..and the wagon trains moved west. Admitted, you could tell the pioneers, they were the ones with the arrows in their backs!

Soon, back to material choices available for mechanisms, and some really radical mods to the instrument.

"Don't just bitch about it, see if you can fix it!"

Edp

ed packard · Post by **ed packard** » 29 Mar 2004 12:37 pm

<pre>MATER' TYPE HARDN' MOD E DENSITY CTE,L TENSILE

ALUM 6061-0 30
ALUM 6061-T6 95 10.6 169 13.5
ALUM 6151-T6 100
ALUM 7075-0 60 174
ALUM 7075-T6 150
ZINC 12 253 9.4/2
T STEEL 481
STEEL+ 30 489 8/10
BRONZE 509
BRASS 534
NICKEL+ 90/320 26/31 537 6/8 83/320
MONEL 555
COPPER 17 556 9.2
LEAD 2 710 29.3
GOLD 10 1200
TUNG' 50 1200 2.5
PLATI' 21 1330
WOOD+ 22/69
S STEEL 150/610 75/350
TITAN'+ 35/180
</pre>
Above is a table showing the properties of a number of materials, some of which might be used in the construction/playing of a PSG. Contractions have been used to allow the table to fit the forum. When the material (MATER') is followed by a + it means that the material values represent a class, and not a specific type within the class. 80/120 would read as "from 80 to 120".

The fancy units are left out to make it less frightening, and easier to determine "relative goodness" for any given application just by mentally taking ratios.

One of the most used materials in the PSG is Aluminum/Aluminium. All aluminum's are not created equal; to show the range of differences in the Aluminum types, several types and tempers are given.

Note that all the Aluminums are soft as compared to the Nickel alloys, and the various types of Stainless (S Steel). Note also that the difference in Aluminum hardness varies over a 3:1 range just because of the Temper (0 or T6) chosen. Where other metals are pressed or rubbed against the Aluminum it will/would deform more quickly than the harder materials. Changer finger radii are an area of concern. A steep string wrap over the finger will be worse than a shallow one re deforming the fingers critical area. At least use a harder Aluminum for this purpose, or use a surface treatment that will harden the surface.

From a sonic standpoint, the softer the metal where the string meets it, the sooner the high frequencies die out (less sustain). Try an Aluminum bar and see the result.

Notice that the CTE,L column shows the Aluminum as expanding about twice as much as the Steels or Nickels for a given amount of temperature change. Steel strings tensioned on an Aluminum structure will change pitch more radically than if the structure had the same linear coefficient of thermal expansion. This statement is complicated by another thermal effect; The thermal conductivity of the structure material and the volume difference between the strings and the structure.

While the Density column provided a reasonable way to guestimate relative weight, it is not a good way to guestimate "goodness" of Tone/Sustain related choices. If it were, Lead would be high on the list; for these functions Mod E and Hardness are the better index shown here.

For strings, the Tensile strength column shows that there might be some good choices in the Nickel alloys, and the Stainless Steel alloys, ..but the range to be found in these categories indicates that just saying the the strings are Stainless Steel, or Nickel is not enough!

The Coefficient of Friction is important re the fingers, Nut/Rollers, and other parts of the mechanism where metal might rub on metal. Corrosion resistance and Abrasion resistance are other important considerations. Friction is to a great degree a function of surface finish at the point(s) of contact.

A word about the terms MASS, WEIGHT, and SIZE, ..they are NOT the same thing when dealing with Physics problems as found re the PSG. If you are concerned, look up the definitions in a search engine like GOOGLE, or ASK JEEVES.

The possibilities re plastics and/or ceramics might be next, ..not sure yet.

[This message was edited by ed packard on 29 March 2004 at 02:11 PM.]