Angle of the saddle or bridge.

[Jack Clark]

My odd bass instrument--a highly-modified guitarrón--has a straight-across bridge and saddle set up. I notice that on bass guitars the saddle is set at an angle so that the scale length is longer in the bass strings. Yet double basses--whose bridges define the string length--are always set up straight across.

So, I have several questions: Why is an angled saddle used in bass guitars? Why is an angled bridge not used in double basses? How does any of this affect my odd bass.

To be specific about my guitarrón: It is strung with RotoSound 88s E1-A1-D2-G2-C3-F3 and the balls of each string are against the side of the wooden bridge farthest from the nut. The string length is really defined by a brass plate that is flush against the side of the wooden bridge nearest the nut. (In double bass terms, the brass is the bridge and the wood is now just a tailpiece; in bass guitar terms, the brass is the saddle and the wood is the bridge.) But on my instrument both the brass and the wood are at 90-degrees to the strings--so there is no angle to the brass saddle-bridge.

Thanks.

 

[Beej]

The angle is necessitated by the length of string required to intonate properly when the string is depressed against a fret. Frets, by definition, are stationary. The witness point required for accurate intonation on a fretless is movable - ie you can move your finger up or down the fingerboard in order to intonate properly to compensate for a poorly located bridge.

By the way, the bridges on my stringed instruments are all angled slightly to improve the intonation locations on the fingerboards.

The bottom line is, if your saddle witness points are all perpendicular to the strings, and in line with each other, your guitarron will be a bit out in its intonation when the strings are depressed into the frets. If it were fretless, this would be moot, as you could just relocate where you put your fingers in order to acheive perfect intonation.

I hope this helps...

 

[Jack Clark]

Thanks, Beej-

That helps a bit. But I still don't understand why a 26" E1 string should have a different witness point, e.g., for its fifth tone than a 26" G2 string has? Is it simply due to the different thickness of the strings--and perhaps even a difference in the materials used--such that bending the strings to the fingerboard causes the true fifth tone to vary between the strings?

My guitarrón is fretless. When I first got it, it was oddly strung in the traditional Mariachi manner, and checking the strings with an electronic tuner I found that the imaginary fifth fret was in a different spot on the neck for each string. It didn't dawn on me until later that a Mariachi guitarrónist could not care less about that since, as you say, he just learns where the correct spot is for each string, presumably by ear. With my restringing job, though, I play the instrument in the fashion of a double bass, and I was hoping to find more straight-across imaginary frets, but apparently that is not to be. I do have a few MOP dots installed on the side of the neck, but I've already learned that they are general reference points only--like a grain mark in the wood.

 

[pilotjones]

But I still don't understand why a 26" E1 string should have a different witness point, e.g., for its fifth tone than a 26" G2 string has? Is it simply due to the different thickness of the strings--and perhaps even a difference in the materials used--such that bending the strings to the fingerboard causes the true fifth tone to vary between the strings?

There are several things that go into it, but primarily,
1. The The further the string stretches when fretting or stopping it, the more intonation compensation it needs. Bass strings as a rule have their action set higher than treble strings, and hence need more (string-lengthening) compensation.
2. The higher the tension of the string, the less compensation it needs. Bass strings tend to be at lower tension than treble strings.

 

[Son of Magni]

The need for intonation adjustment is primarily due to the stiffness of the strings.

The stiffer the vibrating component is the higher the rate of vibration. Take a wooden rod and a metal rod each 1" in diameter and three feet long. The metal rod will vibrate at a much higher frequency due to it being stiffer.

The frequency of a string on an instrument is affected by both the tension and the stiffness and in general the thicker the string is the stiffer it is (all else being equal).

Because higher stiffness causes higher rate of vibration, your thicker strings will sound sharper than the tension alone would dictate. And this effect is increased as you decrease the vibrating length (play on a higher fret). This is because the stiffness is really also a function of the ratio of thickness to length.

So what all this means is that as you play higher up the string, the notes get sharper than they should, and the thicker the string is the worse this effect is. Therefore thicker strings need a little more length at the nut to "compensate".

As to this being a moot point on a fretless, that is just not true. You still want your instrument to intonate perfectly across the neck.

And lastly regarding the violin family. The strings used on bowed stringed instruments are very flexible, ie have very little stiffness. Therefore on these instruments intonation compensation is generally not an issue.

If you want more information on all this I suggest looking up "inharmonicity" on wikipedia...

 

[pilotjones]

Sorry, Thor, but that's mostly not correct.

The model of a vibrating rod does not apply to an ideal string, and does not apply to any significant amount to a real string. What makes something a string, and not a rod, is mostly it's slenderness ratio, L : D. Once this passes a high number, say 100:1 or so, then many factors drop out, it can be treated as a one-dimensional object, all the equations simplify, and it starts to vibrate and sound like a string instead of a rod.

This is precisely why we use wound strings. They vibrate as if they have the mass of the full thickness, but have the D of the core only.


Agreed that the inharmonicity is largely due to the string being hampered by its small stiffness. But the intonation compensation is needed due to stretching the string. If you raised the fret to the string, it would mostly be unnecessary, and the only compensation needed would be due to the stiffness that you mention, but it would be miniscule by comparison.

 

[Son of Magni]

Darn, I wish I knew where to get ideal strings.

If what you say is true then we can throw 200 years of piano tuning technique out the window...

 

[Hookus]

Darn, I wish I knew where to get ideal strings.

If what you say is true then we can throw 200 years of piano tuning technique out the window...

Pianos are not guitars. The strings are all open strings that are hammered. Guitars strings must be stretched in order to fret them, and though it only stretches by a fraction of a millimeter, it raises pitch when you fret nonetheless. AFAIK, this is why every fret on the board is not perfectly intonated at the same time. Most folks use the 12th fret, but I bet if you check your frets in the lower position, they will be a little sharp.

 

[Son of Magni]

Pianos are not guitars. The strings are all open strings that are hammered. Guitars strings must be stretched in order to fret them, and though it only stretches by a fraction of a millimeter, it raises pitch when you fret nonetheless. AFAIK, this is why every fret on the board is not perfectly intonated at the same time. Most folks use the 12th fret, but I bet if you check your frets in the lower position, they will be a little sharp.

My point exactly. Pianos exhibit the same symptoms even though the strings are not stretched by being pressed down to a fret. It's not a coincidence. Octave stretching is required when tuning a piano, even though the strings are hundreds of times as long as they are thick.

Take middle C (C4), the string is say 3 feet long. That string's 2nd order harmonic (one octave up which is the same as a string half it's length) is already so sharp that C5 needs to be tuned sharp to sound in tune. This is due solely to the string's stiffness.

Looking at this from the opposite perspective. Take a 6-string bass, BEADGC with a nice low action. Now set the C string to have twice the height above the 12th fret compared to the B string. Now re-do your complete setup. You'll still find that the B string needs to be intonated much longer than the C. Unless your action is ridiculously high, bending the string down to the fingerboard has only a minute effect on the pitch.

 

[pilotjones]

Thor, maybe I'm not being that clear. Wouldn't be the first time.

I'm certainly not debating inharmonicity, which is due to the non-ideal stiffness of real strings. But there you're talking about the upper harmonics not being tuned perfectly with the lower harmonics, all on one string, unfretted, with the fundamental being exactly the frequency you want it to.

Also, I understand and "believe in" stretch tuning. I've tuned a piano using it.

But, while inharmonicity is caused by the string acting slightly like a rod, and not 100% like an ideal string, intonation compensation (moving the saddles) makes up for the string stretch. It would be necessary even if you had an ideal string.

On a real string after doing the compensation, harmonics are still just as out of tune to their fundamental, whatever frequency that is. The compensation is an imperfect, but sufficiently effective, solution to the string stretch on fretting; and does not address the inharmonicity of real strings in any way.

 

[Son of Magni]

Ok PJ, I really appreciate your patience with me while I insist that my theory is correct

So I seriously ask you to try one thing. On a correctly set-up bass, play the octave harmonics on all the strings. If they are lined up then I am correct, if they are skewed at an angle then I am wrong.

Since you are not pressing down the strings during this experiment either the compensation should significantly move the lower string's harmonics towards the bridge (your theory), or they should stay in line (my theory). Of course both the string stretching and the inharmonicity have some effect, but IMO the inharmonicity is by far the greater of the two, and not commonly understood.

 

[mikeyswood]

Wow. Pete and Karl - you have a very good debate going here and I might be more impressed by the civility that is on display. Well done guys!

 

[pilotjones]

Karl

While it's too late tonight to test it tonight, I'm pretty confident that the harmonics will follow a line that is at half the angle to the perpendicular as is the (compensated) bridge saddle line.

Think about it this way: before compensation, the 12th fret is exactly at the center of the string, as is the 2nd harmonic point. On a 34" scale bass, it is dividing the string into two 17" halves. Now, compensate the sadle out 1/2". How could the harmonic point stay in place? If it did so it would be dividing the string into a 17" section and a 17.5" section. These couldn't possibly play the same pitch, given a uniform string all at the same tension! Plus, how would the string "know" which side of the harmonic point to put the 17.0 section and which to put the 17.5 section?



Mikey

Thanks. We used to have some fairly deep but wholly civil arguments in this forum back in the "olden days," which is to say probably 2002-2005ish. And knowledge was gained by everyone, along with respect. Let's hope we see a positive trend here.

 

[Son of Magni]

Ha, apparently your brain is working better at 2:30 than mine was at 10:15.

What we really need is a mechanical engineer to model an E string with proper tension and determine what the pitch change is at a normal deflection. Then calculate the compensation required to cancel that out.

But maybe it could be measured in the real world by removing all compensation, nut at exactly 34". Then the harmonic is right over the fret, so the change in pitch between the harmonic and the fretted note is the change from stretching.

 

[pilotjones]

Ha, apparently your brain is working better at 2:30 than mine was at 10:15.

Just drove home from a gig and my brain was still engaged. Not doing as well this morning, though.

What we really need is a mechanical engineer to model an E string with proper tension and determine what the pitch change is at a normal deflection.

Already did that a few years ago. I think the spreadsheet is in the FAQs. "BigAssStringTensionAndReferenceDocument.xls". Second tab of the ss IIRC.

 

[Son of Magni]

Great spreadsheet.

Without dissecting the math behind it I can only guess that the plucking effects data might produce useful data. So I entered:

PluckingDistance = 17, 17 (fret at octave)
PluckingDeflection = 0.12, 0.16 (action at octave)

and got:

TheoreticalIncreasedPitch = 4.519, 8.018 cents

Of course that's the increase over the full 34 inches but I think that with half the stretch over half the length the pitch increase in cents would be the same.

Of course I'm making a few assumptions that you can probably correct. But those pitch increases are pretty small, probably not detectable for most people.

Thoughts?

 

[pilotjones]

One small note on the ss, unless you are assuming a string that is fully able to slip over the bridge saddle and nut as you deflect it (a condition that I think is not the case), you should enter zero as the beyond nut and beyond bridge lengths. Those factors were originally added to the sheet in order to figure out just how much difference there would be in perceived tension of the string (in the form of force required to deflect the string to pluck it) with varying lengths of nut-to-tuner.



You know, you're making me rethink this thing. Do you have any figures on the inharmonicity of a bass string? This could be gotten by, using a sensitive and accurate tuner, setting a bass string exactly to a pitch, and then seeing how sharp the second, third and fourth harmonics are.

 

[Son of Magni]

Yes, I did set the nut and bridge stubs to zero.

I suppose I could try to find my old Peterson Strobe and find out whether it has a control that offsets it by cents...

Edit:
It appears my R450 has an offset control calibrated in cents. I will attempt your suggested experiment, probably tonight. Also probably with TI Flats... But I should mention that I haven't plugged in my R450 in a couple of years, so who knows what it's condition is?

 

[Beej]

I'm not thinking clearly enough to contribute to the discussion, but I did do Karl's suggested experiment.

With my finger, the octave harmonics did appear to all be in a straight line. However, when I did the harmonics with the edge of a pick, not my finger, the accurate placement of the pick edge in order to strike the harmonic cleanly was a little closer to the bridge on the bass strings and became progressively less close to the bridge as I moved to the treble strings.

From this little experiment, it seems that Karl's prediction of proving pilot's theory is consistent with my results (investigator error notwithstanding). Don't really know what this means for your discussion though...

 

[Son of Magni]

I'm not thinking clearly enough to contribute to the discussion, but I did do Karl's suggested experiment.

With my finger, the octave harmonics did appear to all be in a straight line. However, when I did the harmonics with the edge of a pick, not my finger, the accurate placement of the pick edge in order to strike the harmonic cleanly was a little closer to the bridge on the bass strings and became progressively less close to the bridge as I moved to the treble strings.

From this little experiment, it seems that Karl's prediction of proving pilot's theory is consistent with my results (investigator error notwithstanding). Don't really know what this means for your discussion though...

Well, Pete already proved that that experiment was merely the silly ramblings of a tired mind