Strings String Theory

[Wiggy]

...I haven't bought sets of strings for years. Instead I buy single strings based on my research and my taste in tone and preferred tension. Perhaps very few have any interest in this level of research. But I would love to compare notes with others who have not settled for buying prepackaged string sets.

Part 1:

I do buy sets that have mostly what I am seeking but always exchange 1, 2, or even 3 strings in a set to get my preferred "taste in tone and preferred tension." I would add to that, string-to-volume balance (getting rid of "howlers" or dull notes) is essential. I've likely spent several hundred on sets and singles due to my obsession. Once I get it right though, I play that instrument much more freely.

Each ukulele is unique, and strings that I find work on a specific scale do not always work on another uke with the same scale. Body resonances and such are not predictable but must be accommodated. If I can't get it strung to my liking, the instrument goes away.

 

[Wiggy]

Part 2:

String, caliper, nut slot, and file.

When changing a string you must know what diameter you are changing from and changing to. Use a caliper to measure this. They are about $20-30 and worth a million. Most notably, when you change to a larger diameter string you will likely have to widen the nut slot with an appropriate file. Otherwise, the string will be pinched in the slot and will not slide smoothly when tuning. This will damage the string and be very frustrating to tune. Going to a thinner string has not caused me problems at the nut.

To widen and deepen the slot are two very different things. To widen and deepen is precision work. To widen without deepening (which is generally what you need to do) is even more so. Also, if you have a slotted bridge that too may need to be widened. For the bridge slot, a "seed bead" may be required when going to a significantly thinner string.

When using the same type of string (nylon, 'nylgut', fluorocarbon, or 'other'), a string with a larger diameter will increase tension when tuned to the same pitch and vice versa. When going to a different type of string this may or may not be true. That is where you will need to learn the differences, either by understanding the string tension formula (and reading the charts) or by extensive experimentation. I chose the latter.

<edit> Sorry about going all-techie on this, but I felt we needed to start defining what "string theory" is all about.

 

[70sSanO]

I’m doing essentially the same thing except with Seaguar fluorocarbon.

For years I followed the generic formula, but more recently found it to be lacking. 10+ years ago Worth was about the only game in town, and that is what the generic formula was based on. These days there are a lot more fluorocarbon string choices.

Right now I just need to find other mfg’s that are comparable to Seaguar.

Diameter, which includes stretched diameter, and string chemical composition drive the bus.

John

 

[Wiggy]

Although its focus is classical guitar, this is a good introduction to terminology, Note that classical E, A, and D strings are typically wound and that is not shown in the chart examples.

How to Choose the Best Classical Guitar Strings (Expert Advice)

Choosing the best strings for your classical guitar can have a huge impact on your guitar's tone, playability, and even durability.

sixstringacoustic.com

Here is a chart for ukulele, courtesy of Lanikai. The D'addario EJ88 sets are "Nyltech" which may be similar to another brand's "Nylgut."
The * indicates a wound string. The EJ88S set (not shown) contains: g .025" C .036" E .030" A .023" diameters.

 

[Wiggy]

Here I go again: What if the string length is equal to the wavelength?

Wavelength Calculator

Learn the relationship between wavelength and frequency with this wavelength calculator.

www.omnicalculator.com

The frequency of vibration determines the pitch, not the length of the string.

Ex:
Ukuleles are tuned gCEA, where the #1 string is A440.
The wavelength of A440 is approx. 32 inches.
The standard soprano scale is 13" so it cannot physically wobble the whole wave at A440. (Same for concert and tenor scales.)

-Random thoughts (mine) on this:

It is the frequency of vibration, not the length, that determines the note you hear. However, the longer the string, combined with a larger body size, will create the fundamental (the note's frequency) sound. Harmonics above the fundamental can and will add to the fundamental to increase perceived volume. Body resonances excited by string vibrations will also affect the loudness.

Playing test tones from a sound generator (or simply singing) into the sound hole are ways to detect resonances. Some use the tap" test.

Food for thought:

Body Resonance/Tuning

I was wondering if anyone worried much about the resonant frequency of their Ukulele? There's a lot of data supporting head tension and resonant cavity affecting overall tone in Banjos, but I haven't seen much in the Ukulele world. Just for fun, I checked and my Luna Concert resonates at a near...

forum.ukuleleunderground.com

And this, from Ukuleles.com

ukulele resonances

The Ukuleles by Kawika website is a place for anyone who loves the ukulele. You'll find ukulele and guitar color photos of the instruments we make; sound files of all sizes of our ukuleles; free listing of old ukulele song books; free lutherie calculation spreadsheets; a discussion of...

www.ukuleles.com

 

[mimmo]

Al, right BUT remember one thing: when one install them upon the instrument they drop in size of a certain percentage due the tension. And this percentage is at its maximum level in the 1st, the minimum in the 3rd. hence things are very different that what it is written on the envelopes. Then this percentage is different: maximum for nylgut, minimum for nylon. Hence the theoretical tension of the nylgut strings can be apparently higher while in the reality become lover thanks to a greater stretching.
Mimmo

 

[mimmo]

Al, right... but I would like to remember one thing: when one install strings upon the instrument they drop in size of a certain percentage due to the tension that make strings thinner. And this percentage is at its maximum level in the 1st string while the minimum is in the 3rd. Hence things are very different that what it is written on the envelopes. This percentage is not of the same amount with all the plastics: it is at its maximum for nylgut, minimum for nylon. Hence the theoretical tension of the nylgut strings calculated with strings not in tension can be apparently higher while in the reality it become lover thanks to the greater stretching ratio over nylon and fluorocarbon strings.
Mimmo

 

[Nickie]

Mimmo, I have a question. I don't mean to put you on the spot, but, is it possible that you could make Aquila strings thinner? i find the 'fatness' of them pretty uncomfortable to play.

 

[Wiggy]

Overtone & Harmonics
(Not talking about touching/plinking a string to produce a harmonic, but rather about how string vibrations excite the body of the instrument.)

Mahogany, spruce, and cedar sound very different from each other. I wanted to understand a bit more about why, but from a descriptive POV rather than the physics of it. Do not fear the math, as there is very little used in these descriptions, it's OK to just skip over those parts:

Overtone & Harmonics (Physics): Definition, Differences & Frequencies

Overtones and harmonics are two concepts often confused with each other and sometimes used interchangeably. An overtone is the name given to any resonant frequency above the fundamental frequency or fundamental tone. Harmonic frequencies are whole number multiples of the fundamental frequency.

sciencing.com

 

[70sSanO]

John

 

[ailevin]

I love the title of this thread. I am a bit of a physics nerd, but in this case I think that doing the physics of a musical instrument is at best a cartoon or schematic that may help you understand the underlying phenomena in what is a very complicated real life situation. That is why we talk about the art of the luthier. Here is my amateur physicist, non-luthier take.

At the 50,000 foot level, how any object will vibrate can be quite complicated, and it depends on it's size, shape, its composition and how the energy creating the vibration is input. Resonances are just pitches where the object vibrates more readily or is easier to stimulate into vibrating. Damping is the opposite of resonance and at those pitches it is harder to make the object vibrate.

When you pluck or bow or hammer on/off a string, you are basically pumping energy into the string and based on the composition of the string (material, density, and tension), the shape of the string (mostly length but also width or cross section of the string), that energy gets transferred to the most resonant pitches of the string. I think it is fair to think that most of the energy is in the pitch that we tune to, and the rest of the energy is sprinkled around in a variety of pitches that give a particular string its characteristic sound or tone. Some significant portion of that enery at each pitch is transferred through the bridge and saddle to the top and from there to the rest of the body of the instrument. Led by the top, the body both resonates and dampens the vibrations from the strings/saddle/bridge further changing how the energy is distributed among different pitches. Again let's assume that most of the energy stays in the vibration of the body that corresponds to primary pitch of the tuned string.

You hear sound to the extent that parts of the instrument cause the air to vibrate (we hear pressure variations in air as sounds). The strings don't have very much surface area, so they don't move very much air by themselves. Most of what you hear is the body of the ukulele moving air, especially the top. It makes sense that how the top vibrates has a large influence on the sound of a ukulele. Assuming the bridge and saddle are mostly just transferring energy at each pitch, the sound of the string is shaped by the resonance/dampening of the top as it is being transferred to the rest of the body. So if the body of the ukulele, particularly the top is thicker/thinner or made of more/less dense material, or larger/smaller (shape of the body and placement of bridge matter too), it will sound different. Spruce, mahogany, koa, mango, cedar, rosewood, ebony, and on and on will tend to have somewhat different resonance/damping characteristics. I think of the different woods almost like the luthiers version of the artist's pallet. There are lots of material possibilities, but it's how that are put together that creates the sound of the instrument.

 

[kkimura]

Interesting concept Ailevin. My take is that of the two major components of the sound from a ukulele, different sound quality can be had by changing one or the other. Hence the existence of UAS as we try different ukuleles to get that perfect sound and SAS (String Acquisition Syndrome) as we try different strings to get that perfect sound. Not many try changing nuts and or saddles to get different sounds although some do. Most of us lack the luthier skills required to change woods, sound board thickness and bracing so I'll leave that for now.
Which brings us back to string theory and a question in my mind. Is there for any given ukulele a perfect string set? Are there more than one?

 

[SeemingMusic]

Scientists will tell you to have controls and eliminate variables. Has anyone tried different sets of strings between two fixed points and measured the energy transferred onto ends after being pulled to the same amplitude? I assume this would be the biggest variable for strings alone.

 

[Wiggy]

Another question:

Why do heavier strings require a longer scale length adjustment either by individual saddles for each string (common on electric guitar and bass) or a compensated saddle? Is it because of the greater vibrating height (peak-peak amplitude/motion) of heavier strings?

<edit, 30 Apr> To clarify: will a heavier string's deflection tend to make it go sharp, especially within the first three frets but then normalize (be more in tune) further up the neck?

For ukuleles, why aren't there compensated saddles specific for use with a low G string?

 

[Poul Hansen]

I believe it's because the heavier strings are stiffer around the bend of the saddle and the nut, so they don't vibrate so freely just there and thus making them virtually a bit shorter.

 

[ailevin]

@kkimura: I expect that though there may be certain strings that cause problems that would bother many or even most people, what sounds best is always going to be a rather subjective call. I doubt there is going to be a one and only best set of strings because so many brands of strings are quite similar. This video compares many sets of strings on the same model with comments by several excellent players. My sense from the video was that there were many good choices.

@Wiggy: This Wikipedia article has a very simplified model of the physics of string vibration. This is the formula for the pitch of the fundamental note for a string:

,​

where a smaller number is a lower pitch. L is the length of the string, T is the tension on the string, and μ is the weight per unit length. If you change these parameters one at a time, a longer string is lower, a tighter string is higher, a heavier string is lower. Comparing strings made of the same material, a larger diameter or thicker string will be heavier and thus have a lower pitch at the same length and tension.

In simple terms, the factor

is how fast a pressure wave travels along the length of string. A tighter string has the string material pulled back ito where it was quicker so the waves move faster. A denser string has to move more mass to get a string back to where it was so the waves move more slowly.

When you fret you are changing L, when you tune you are changing T, and when you change strings you are chaning μ. Again, this is a very over simplified explanation of something much more complex, but it is the way physicist explain things.

 

[Wiggy]

@kkimura: I expect that though there may be certain strings that cause problems that would bother many or even most people, what sounds best is always going to be a rather subjective call. I doubt there is going to be a one and only best set of strings because so many brands of strings are quite similar. This video compares many sets of strings on the same model with comments by several excellent players. My sense from the video was that there were many good choices.

@Wiggy: This Wikipedia article has a very simplified model of the physics of string vibration. This is the formula for the pitch of the fundamental note for a string:

,​

where a smaller number is a lower pitch. L is the length of the string, T is the tension on the string, and μ is the weight per unit length. If you change these parameters one at a time, a longer string is lower, a tighter string is higher, a heavier string is lower. Comparing strings made of the same material, a larger diameter or thicker string will be heavier and thus have a lower pitch at the same length and tension.

In simple terms, the factor

is how fast a pressure wave travels along the length of string. A tighter string has the string material pulled back ito where it was quicker so the waves move faster. A denser string has to move more mass to get a string back to where it was so the waves move more slowly.

When you fret you are changing L, when you tune you are changing T, and when you change strings you are chaning μ. Again, this is a very over simplified explanation of something much more complex, but it is the way physicist explain things.

The stiffness, as mentioned by Poul, is not part of the equation, so once they have settled, I do press on the heavier strings where they go over the saddle in hopes to alleviate some of that. For the least deflection, I also measure and lower the clearance over the 1st fret by holding each string at the 3rd when measuring/adjusting the nut slot depth. I'm also careful to not press the strings too hard between frets.

I sometimes find that tuning at the 3rd fret finds a happy medium.

 

[70sSanO]

Which brings us back to string theory and a question in my mind. Is there for any given ukulele a perfect string set? Are there more than one?

I’m inclined to say there is no “perfect” string set that is offered as a set.

With enough time, money, and access to all the possible strings, or fishing line available, it is possible to construct, on a string-by-string basis, a set that comes as close to perfect as each ukulele’s limitations will allow.

I have 15 varieties of Seaguar fluorocarbon leader. On different ukuleles with the same scale length tuned the same I use a different mix on each one.

I can’t tell you why a .031” Premier works best on ukulele A, but a .029” Pink Label works best and a .029” Blue Label thuds on ukulele B.

But I believe that every ukulele sound board requires a slightly different mix of overall tension between the strings to maximize the ring and minimize the dull.

This doesn’t mean that there are not great packaged ukulele string sets, it just addresses the word “perfect”.

John

 

[EDW]

Mimmo, I have a question. I don't mean to put you on the spot, but, is it possible that you could make Aquila strings thinner? i find the 'fatness' of them pretty uncomfortable to play.

We all have different tastes, but I actually like the feel of the fatter strings. Perhaps one of their strings that have an additive (Martin Premium, Aquila Red) would work better for you. I believe it creates a greater density allowing for a thinner string.