Don't Understand "scale length"

[FrDNicholas]

I get that different instruments have different scale lengths. What confuses me is where the measurement comes from? My Trinity College mandola has a scale length of 17 (inches, centimeters?) and I know there are stretches that I don't remember from the H1 Gibson I had. But doesn't each fret have to be the same width to keep the instrument in tune? In other words, isn't the distance from one fret to the next a constant to get an in-tune scale? How does this work?

[Gail Hester]

Simply put, the scale length is the distance from the leading edge of the nut to the leading edge of the bridge, the active string length.

Fret positions are typically calculated using equal temperament, successively dividing the scale length minus the offset to the previous fret by 17.817. This series of calculations puts the 12th fret (octave) at exactly half the scale length.

[Jim Garber]

Yes there are mathematical ratios to determine the fret distance. As far as scale goes the easiest way to determine that for us math-challenged is to measure from the nut to the 12th fret and double it. the 12th fret is the middle of the scale length.

Your mandola is probably 17 inches not centimeters. Std Gibson mandolin scale length is 13 7/8 inches and classical (bowlback) scale is 13 inches.

[mandroid]

Length of the vibrating string .. I have an H 5 style mandola it's a 40cm scale 0.4M.
.. on one string course, the intonation offsets in the bridge are variants from that ..

[FrDNicholas]

If someone just explained this and I missed it, I apologize. So where on the instrument do the differences in scale length come from? Where on the instrument is the "extra" length on a 17in vs a 16in?

[JEStanek]

There is no extra length. The scale length is a function of lenght, string gauge and tension. If a mandola comes in two scale lengths 16 or 17 inches and it is tuned the same (CGDA) there will be greater string tension on the 17 inch one than the 16 inch one (I hope I have that right and not backwards- I'm a microbiologist!). You'll sometimes hear about people saying shorter scale length octave mandolins sounding rubbery on the G courses (like a losse rubber band). This is a string tension function. You can get around that by using different string gauges. That's why the standard mandolin scale makes it easier to compare instrument to instrument more than when comparing mandolas, OMs, Zouks, or mandocellos.

Jamie

[man dough nollij]

I got confused about this when somebody converted a guitar to a mandocello. Since it will now use different gauge strings, have different tensions, and way different string tunings, it seemed that the guitar frets would be in the wrong places for a 'cello.

I got to thinking about it, and figured out that the fret spacing will be the same, no matter the tuning. It is a math thing. If I put a C string on, the middle of the string will be at the 12th fret, and that'll be a C, an octave higher. The rest of the frets will be B,A,G,F, etc on up (towards the nut) the neck (with the appropriate extra frets for half steps).

It was pointed out recently in another thread that the 12th fret isn't exactly 1/2 way-- it is tweaked a tiny bit to account for the deflection of the string and the string stretching.

Pretty cool stuff!

[mandroid]

A vibrating string's length , think of the nut as birth, the bridge as death,
the length between those is when you make music,

[Woody Turner]

"The scale length is a function of lenght, string gauge and tension."
I respectfully disagree with this statement. The scale length is strictly a measure of distance between the nut and bridge; it is totally independent of string tension. Different string gauges affect tone, feel, and playability, but they don't affect scale length. I think the OP is asking about where the difference is added when a builder chooses to make an instrument with a 17" scale rather than a 16" one. Well, she could simply enlongate the neck only and make the diminishing spaces between the frets slightly wider on the longer instrument. Or she could also lengthen the body a tad, but with a longer fingerboard. Or both.

[allenhopkins]

Originally Posted by JEStanek

The scale length is a function of length, string gauge and tension.

I think what Jamie meant is that the pitch of the string -- the note that results when plucked -- is a function of length, string gauge and tension.

The scale length is the scale length, period. You can measure it with a ruler. On mandolins and other "floating" bridge instruments, it's (slightly) variable, depending on where the bridge is placed. However, once the neck is fretted, there's only one place the bridge can be, and still have correct intonation up the scale.

To raise a longer string to the same pitch as a shorter string of the same gauge (thickness), the tension must be greater. Therefore, instruments with longer scale lengths require either thinner or tenser strings to reach the same pitch as instruments with shorter scale lengths.

The "floppiness" of lower strings on short-scale instruments, can be cured by using thicker strings, which have to be given more tension to reach the same pitch. However, since the stress on the top of the instrument is also a function of string length, thickness (gauge), and tension, one needs to consult a chart that indicates how much total force is exerted by strings of a particular length, thickness and tension. Too much, and the top can collapse, the neck bow upward, the tailpiece pull off, or other disasters.

By the way, did I mention that the composition of the string -- what it's made from -- also affects the pitch, as well as length, thickness and tension? Many many factors come into play.

[Bill Snyder]

Originally Posted by FrDNicholas

... But doesn't each fret have to be the same width to keep the instrument in tune? In other words, isn't the distance from one fret to the next a constant to get an in-tune scale? How does this work?

No. On an instrument with a longer scale length the space between frets is longer than on a shorter scale length instrument.
Example:
On a 17" scale length (no matter the tuning) the distance from the nut to fret 1 is 61/64 of an inch.
On a 16" scale length it is 57/64.
On a 13 7/8" scale length it is 25/32 (or 50/64) of an inch.

FWIW I used a handy little program by Jon Whitney named WFRET to come up with my numbers.

[JEStanek]

Thanks, Allan. I wasn't clear and defined my term with it (length). No offense taken, David. I'm happy to have vague things I say get clarified! I hope the discussion is proving useful to the OP. I'm learning new stuff too.

Jamie

[Tobin]

Since we're on the subject, and forgive me if this has been answered before, why is it that the bridge has a "zigzag" shape to it? The G and A strings are offset lengthwise from the D and E strings. Is this necessary for proper intonation, and if so, why? It seems that the offsets would change the scale length of these strings as opposed to the others. And no matter where or how you place the bridge, they will always be slightly different. A guitar bridge is pretty much straight across, although sometimes it has a notch for one string (the B string, as I recall). And most other instruments I've casually looked at have a straight bridge too. Why is the mandolin's offset like this?

And is there such thing as a floating bridge with individual adjustments for each pair of strings? Kind of like the way electric guitars usually have individual adjustments for length?

[Bill Snyder]

The"zigzag" pattern is the compensation. Due to the different gauges of the strings they all require differing compensation. As far as guitars most of the steel string guitars have the saddle set at a slight angle such as in this photo.

[Chris Keth]

Most stringed instruments have some sort of compensated bridge saddle to be able to intonate. Some guitars just have the saddle slanted and it's pretty good but not exact. Electric guitars have bridges with separate saddles for each string that can be individually adjusted.

The very simplified jist of it is that you're trying to make each effective string length the same as the scale length of the instrument. The problem with just making each string that length is that the lower, fatter strings have a stiffness to them and they can't vibrate right up to the saddle like a thin string can. To conquer that, we make the fatter strings a bit longer. If we could make each string the same diameter somehow (like if we had a ductile metal dense enough to make a .10 high E for a guitar weight the same as a .056 string), the saddle could be straight across and good intonation would still be possible.


Eric Clapton's old 12-string martin (or guild, I forget) came up on ebay not long ago and it has a very elaborate compensated saddle. I saw a better photo than this one and each string in each course has it's own compensation via different filed bevels of the bone.

[Tobin]

The"zigzag" pattern is the compensation. Due to the different gauges of the strings they all require differing compensation. As far as guitars most of the steel string guitars have the saddle set at a slight angle such as in this photo.

Yes, I understand why guitar bridges are set at an angle. That's not unlike how mandolin bridges can be set at an angle. But that doesn't explain the zig-zag of the bridge. What's the logic behind the compensation being alternated like that?

The problem with just making each string that length is that the lower, fatter strings have a stiffness to them and they can't vibrate right up to the saddle like a thin string can. To conquer that, we make the fatter strings a bit longer.

That would make sense to me if the mandolin bridge design were compensated so that the fatter G and D strings were longer than the thinner A and E strings. But the way the bridge is compensated, the G and A strings are longer than the D and E strings. It still doesn't make any sense to me why this is so.

It would seem to me that since mandolin strings are tuned at 7ths from each other (a linear progression across the strings), the bridge should also have a linear progression in scale length for proper intonation. If one sets the bridge so that the G and E strings are properly intonated, without a linear bridge between them, shouldn't the D and A strings be off a bit?

I know, I'm probably overthinking this. The design obviously works as is. But I'm an engineer; I can't help it. It has to not only work, but make sense to me.

[Capt. E]

I just realized that many string sets vary in gauge and that may have an affect on intonation. Example: the gauges of D'Addario J-74's are from E to G are 11,15,26,40. The gauges of Gibson Sam Bush strings are 11, 14, 25, 41. Do these differences have a "significant" affect on intonation?

[Tobin]

They will require adjustments to the intonation, yes, mostly as a result of different tensions required for different gauge strings. The height of the action will play a large part too.

[allenhopkins]

OK, I'm starting to get a bit confused. Is there a consensus that bridge placement would need to be changed, if one used a different gauge or composition of strings? That hasn't been my experience, except in one fairly extreme case, when I went from steel to nylon strings on a banjo-ukulele.

It is true that the action of pressing a string down on the neck, stretches it slightly, which would "sharp" it. Strings of different gauges show this effect to different degrees, so a "straight across" bridge generally doesn't work; the thinner strings and the thicker strings "sharp" at different rates, and a bridge needs to be slanted, or compensated, to allow for the difference.

But I've never heard that changing from light to medium strings requires a different scale length. If that's true, I've been missing something all these years. Hope to be enlightened...

[Tobin]

But I've never heard that changing from light to medium strings requires a different scale length. If that's true, I've been missing something all these years. Hope to be enlightened...

Considering that intonation is initially set on any given pair of strings by checking the open tone with a fretted tone (at the 12th fret), then it is obvious that the change in tension when fretted comes into play. And it's true that different gauge strings which require different tensions for open tone will have different changes in tension when pushed down the same distance to the fret. So that minor differential in tension between the two sets of strings will require minor adjustment to scale length. Only because of the change in tension when fretted. And like I said above, the height of the action will come into play here as well. The lower the action, the less additional tension that is added when fretted, and thus the less differential in scale length between two different gauge strings.

I hope that explanation of my logic made sense.

[Chris Keth]

Tobin, the reason for the zigzag is that wound and unwound strings need to be compensated for differently. I can't explain the exact reason but I suspect it's a combination of sting mass, tension, and stiffness of the metal. So you'll have the stairstep pattern for the unwound strings and a similar but slightly further from the nut stairstep for the wound strings. It's easier to see on an electric guitar bridge:




As for having to set intonation if you change string gauge, I think that depends on what you play and how sensitive your ears are. For electric guitar, I set my intonation with a strobe tuner because I want it to be as "on" as possible everywhere on the neck because I play a lot of music with long sustained notes as well as play with other instruments. For the mandolin, I really doubt it's quite as sensitive because of the sustain issue. If your note is a tiny, tiny bit off, nobody will notice because it's never sustained long enough for your head to think about it. It's sort of like suggesting a higher note by bending only partway up to it. If you held the note you bend to for any amount of time it would sour but it sounds fine because you don't hold it and go to a solid fretted note next in the phrase and your mind fills in the gap.

[Tobin]

So you'll have the stairstep pattern for the unwound strings and a similar but slightly further from the nut stairstep for the wound strings.

Now THAT makes sense to me. Thank you very much. I hadn't thought of it like that.

[Chris Keth]

Glad I could help. I'm very new to mandolin (don't even have a playable one, yet) but not to some other stringed instruments.

I should mention one other thing that makes me think that tension is a big part of intonation. If the G string (on the guitar whose bridge I posted) were wound, the saddle would be up closer to the nut than the D string's. Something about the thinner core wire being lower tension but, with windings, being a similar mass to the unwound string.

[EdHanrahan]

FWIW, I've seen at least one "mandolin" bridge on e-Bay that was actually a mandola bridge. Mandolas lose the mando's high E strings but add a low C course (I think?), so three courses are wound and only one is unwound. This moves the bridge's "zig" from the middle to in between the 1st and 2nd sets of strings.

Thus, the mandola's different offset is STILL between the wound Ds and plain As, just as on mandolin. (Insert "Twilight Zone" music here!)

[Graham McDonald]

The reason you get a 'zig-zag' bridge saddle on a mandolin is that the amount of 'compensation' - the little extra on the scale length to make it play in tune - is dependent on the gauge of the plain string or in the case of the wound strings the gauge of the core wire. The core of a D string is much the same as the a plain E, so about the same compensation.

Of course getting the harmonic and the fretted note at the 12th fret the same by moving the bridge back and forwards is only part of playing in tune. Frets are placed in an average "well-tempered" positioning based on the 17.817 formula, and that means that some notes in some keys are always going to be a little out of tune. Some players of fretted instruments get very upset when they realize they can never play in tune. Other just deal with it and play music instead

cheers