Guitar Physics 101: Scale Length

[jackthehack]

There are a number of posts on the board in relation to 25.5 vs. 24.75 scale lengths, and terms like
"less defined sound", "punch", "deep", etc. are being bandied about; rather than using subjective
"definitions" it is easy to grasp/define what the actual differentiation(s) are, but we have to turn to
- gasp  :icon_scratch: - PHYSICS!!!

To spare some people's heads from exploding, I'll try to keep illustrations/formulae to a minimum.
Additionally, let's make the unnatural assumption that string gauge, neck/body woods, electronics and
all other factors other than scale length are identical to isolate the effect.

Regardless of scale length, all open strings are tuned to a given pitch (note that this correlates to
frequency). A major function of scale length is the amount of tension required to tune the strings to
that pitch/frequency. A longer scale length will require more tension to be placed upon it to achieve
the same pitch/frequency.

String tension/length correlates to frequency as fundamental frequency is equal to the square root of
string tension divided by string mass divided string length divided by 2 times string length, formula below:

I know you're probably thinking "WTF", but bear with me a minute.... How does this effect the actual sound
of the guitar? The timbre, a more scientific term than normally used, meaning The combination of qualities
of a sound that distinguishes it from other sounds of the same pitch and volume, of a guitar is most
directly affected by the HARMONICS of the fundamental pitch/frequency defined above. Natural harmonics
of the fundamental frequency can be expressed as in the diagram below:

Without going into more boring algebraic explantion, the longer scale length with higher tension will
ALWAYS produce harmonics of slightly higher frequency than a shorter scale length.

What does this all really mean? Something you probably already figured out from playing guitars with
different scale lengths, for example Fenders vs. Gibsons; all other things being equal, the timbre of
a Gibson with a shorter scale length will emphasize harmonics in a manner that produces a "warmer" tone,
the longer scale length of the Fender will be "twangier" to lapse into more common semantics.

Practical implications? This started out as an answer to NoNonsense Tele, who wanted to finish building
his guitar to try to get Jonny Lang's Telecaster sound, and was wondering about using a 24.75" scale neck.
The answer, for the reasons above, is that if that is the particular sound you want, you're going to get
a lot closer with a 25.5" scale neck.

Also note that string mass - which directly correlates to string gauge - is as important to determining fundamental
frequency and resulting natural harmonics and ergo timbre/tonality as scale length. If you're trying to recreate a
particular guitarist's "sound", Google his name/gear setup and try using the same brand/gauge of strings.

Jeez, I guess you can tell I've prositituted myself as an engineer for a day job for 20+ years and get REALLY
bored during pointless meetings/conference calls..... :toothy12:

 

[Nando Vallart]

Very nice your explanation! :icon_biggrin:
It help a lot! (the only problem is: I decide what I want for my life  :laughing7

 

[jackthehack]

Well you could go bullshit like some of the rest of us here and just break down and buy one of each neck to solve your dilemma!!!

Gregg - Make sure you add that to my commission check? :toothy10:

 

[Alfang]

Very Impressive Jack, Thanks

One more question for you while we got you here,  All things being equal.  What are the diferences between lighter and heavier guage strings. What diferent sounds would you expect and how is the tension on the strings diferent  i.e. would a .009 string require more or less tension than say a .010 for the same pitch?

Thanks again and dont go anywhere      John

PS can you describe Eddie VanHalens Pickup for me so I can make one? :glasses9:

 

[jackthehack]

The more mass a string has, i.e, the heavier gauge, the higher the tension needed to tune to same pitch/frequency, although per the formula, the direct relationship is less a factor than scale length overall.

Let me go research EVH's pickups......

 

[Alfang]

Thanks again Jack... So, with all this Information you have provided, It really illustrates the importance of Picking a guage ( and probably brand) of string and stickinging with it. Once you set your action, intonation etc.. for a certain string guage, changing guage means you outta at least recheck your setup?

John

 

[jackthehack]

Yes, you should recheck your setup/tonality if changing gauges, especially if making a major change.

As to replicating EVH's pickup, I'm assuming you're looking for that Frankenstrat sound from the first couple of albums?

Per multiple sources, that original red with tape Kramer had a bridge pickup from a '61 Gibson ES-335 that he obviously unsoldered/pulled the chrome pickup cover off and dipped in paraffin.

The '61 ES-335 would have still been equipped with the original '59 "P.A.F." design, you'd probably wind up paying close to a grand a piece if you could find such pickups, occasionally you'll see some on eBay.

Trust me, unless you're a REAL masochist, the level of effort to try to build your own probably isn't worth the effort; try a Seymour Duncan bridge position SH-1 '59 model, which is engineered to exactly duplicate the resistance/resonance/induction of the original '59 P.A.F. design and dip in paraffin, you can order those from the Warmoth site about as cheaply as anywhere else.

 

[Superbeast520]

Thanks Jack, that explains why Im liking my guitar more and more as time goes on. Im finiding the sweet spots that probably correlate to all you just mentioned, being Im tuned and setup to "D" and use 11,14,18,28,38,56 and with woods and stainless steel frets that are New too me as well as a pickup brand I've never used, well it explains the initial uncertainty I had about using these strings even though I have used this brand and gauge for some time, apparently all that stuff up there had its affect on the tone and it took me a bit to ( maybe know the Guitar itself ) ???????
May explain some of Stevie Ray Vaughans magic, besides the obvious stuff, he used pretty much the same guitar forever so maybe knowing a particular instrument inside and out tonally, wether perceptibly or not, ( one might venture to guess in relation to the things you stated ) that it may have a beneficial Impact on a guy's playing?????
Awesome info .........appreciate the 101 ........ :icon_smile:

 

[Alfang]

Hey Jack, Heres something I've wondered from time to time.  When a string is tuned to whatever pitch, it has a specific amount of tension on it. throughout the age of the string , the string tends to stretch a bit, and requires retuning, when retuned , will it exert the same tension.  My thought being can we create an automatic string tensioner that maintains a preset tension on the string, thus strings which stay in tune, forever.

My guess is dirt on the strings (wound strings) will affect the mass of the string , making all of the above useless.

But in theory, it should work?

Thanks allmighty master of math and science

John

 

[Jay Davidson]

Cool thread, but where is the part on the rule of 18's?  :icon_biggrin:

To the above poster, isn't your idea something like the speed loader?

 

[Alfang]

To the above poster, whats a speed loader?  You mean like for bullets? if thats correct then , No. 

Otherwise I dont havea clue what your talking about :icon_scratch:

John

 

[jackthehack]

Jay - "Rule of 18" was not incorporated as the gist of the thread was the effect of scale length on tonality, the Rule of 18 being peripheral. Fot those unfamiliar, the Rule of 18 refers to a 16th century formula for fret placement based on scale length, here's a link to a one page explantion with formula:

http://www.cybozone.com/luthier/instruments/fretscale.html

Alfgang - By speedloader, Jay is referring to a version of the Floyd Rose bridge that takes special strings that incorporates your idea of locking the strings at a given tension at either end, you can check their website for more info.

As to an "automatic" string tensioning system that would sense the tension on the string and readjust, it's not practical, as there are other outside factors that minutely affect the strings, most notably tempurature, so that there is never a completely constant value for the amount of tension on a given string to achieve proper pitch. Theoretically you could design something that could compensate for every factor, but it would have to sense current tension vs. current pitch to adjust and in terms of cost, design and possibly weight and, ergo, it's much simpler just to make minor tuning adjustments as necessary.

I didn't mean to get into a discussion of metallurgy in this thread, but further, you've probably noticed that when you put on a new set of strings, you have to stretch them out before they will retain pitch/tuning. During this intial "stretching" you pull most of the natural elasticity out of the string and subsequent changes due to further stretching is very minute. Dirt, oils, etc. from your fingers and exposure to other environmental factors don't effect mass, etc. so much as they start oxidation processes that along with microscopic "cracking" render the strings "dead"; someone else with a better grasp of metallurgy could start another whole thread just on strings/string composition and coatings, etc.