How to string an instrument with scale length 19.5 in?
How to string an instrument with scale length 19.5 in?
So about a year ago my father got for me a (completely nondescript and unmarked) "octave mandolin" on E-bay as a present. Thing is... tuned GDAE it didn't sound so good and there was a lot of string buzzing, especially with the G string.
So I figured what the heck, and for nothing I tuned all the strings up a fifth to CGDA--I never played it anyway, might as well try something new. For awhile, I kind of liked the sound, and the buzz was gone, but then of course after two days a string snapped.
Now I'm wondering, should I buy octave mandolin strings again or try to string it as a mandola? Would the tension of trying to string it as a mandola be bad for the instrument?
The places I've looked for guidelines on scale length are telling me that mandola's go up to about 19 inches in length and octave mandolins start at about 20 inches... so I'm really confused about what I should be doing.
Re: How to string an instrument with scale length 19.5 in?
The CBOM forum ( Citterns, Bouzoukis, and Octave Mandolins ) has had some discussion on this over the years.
I reckon you could try tuning up maybe a third, and capoing to give you the mandola tuning.
Or looking at the gauges and going one or two degrees heavier to stay at octave mandola pitch. Or even try contacting the string manufacturers direct to ask them. Everyone has their own solutions to this.
Incidentally, the european mandolas, the original ( pre-modern folk instruments ) mandolas, had a much shorter scale than currently used by these hot-shot luthiers, hence all the confusion.
There is also a formula, which I'm sure someone here can quote, to give you the string tension for any gauge and scale length.
Re: How to string an instrument with scale length 19.5 in?
You obviously had the wrong gauges on, but it's a minefield trying to sort them out.
I would reckon that mandola-tuning is too high for your instrument, and that what you need to do is to put a slightly heavier set on. The european mandolas had a much shorter scale then your instrument, which is probably why your stringing didn't work well.
Also the nomenclature is confusing - 'tenor' mandola, meaning the same pitches as an old style tenor banjo, ie same as mandola but with a longer scale, 'octave' mandola, meaning an octave mandolin, an octave below mandolin but not double the scale length, whereas the 'irish bouzouki' has a scale double that of a mandolin, and is an octave below it.
Re: How to string an instrument with scale length 19.5 in?
I've built instruments with odd scales on a number of occassions, altough I am not, by any means, qualified to call myself a "luthier". Having said that, I disavow responsibility for the time consuming mish mash which follows. (Happy New Year to all those who sensibly stop reading at this point.)
I would caution you to consider how the strings are connected at the bridge end of the instrument. If the instrument uses a tailpiece, the additional distance from the bridge to the tailpiece will increase the total tension on the strings. If the strings connect just behind the bridge in the context of a saddle structure, the distance from the nut to the bridge, or twice the distance from the nut to the 12th fret, the "scale", will serve as a useful input in computations of tension based on string gauge, but only for instruments that also terminate in tailpieces with approximately the same distance from the bridge to the tailpiece.
If the instrument uses a tailpiece, as many mandolas do, consider the distance from the nut to the tailpiece when seeking a measurment to use in formulas for string tension based on string length under tension. (I had to modify the tailpiece on three instruments to move the string tie-on point close enough to the bridge to reduce string tension to the point that I could tune one string up to "A" in the octave of middle C with C-G-D-A tuning using nylon strings. Prior to that the string would consistently snap due to tension issues even though the manufacturer assured me it would work with a 26.5 inch scale measured from nut to bridge.)
I would suggest that you get a copy of D'Addario's string catalog from their web site. It is a downloadable PDF. A formula for string tension is included.
The D'Addario Catalog indicates that it employs a 15 7/8 inch (15.875 inch) scale length for mandolas as the basis for its tension computations for mandola. (I don't know if this allows for a tailpiece. I will assume that whatever your setup, it is the same as that used by D'Addario, which could be a gross error.) You are applying roughly 50% more tension due to a 19.5 inch scale than would occur with a 15 7/8 inch scale. That is not a condition that should be sustained.
Loop end banjo strings designed for 26 1/4 inch scale would produce roughly 50% of the design tension of a 19 1/4 inch scale (assuming the same tail piece to bridge distance for both instruments). If you can employ loop end strings, you may wish to consider banjo strings as a substitute with C-G-D-A tuning.
The mandola is designed to be tuned a fifth lower than a mandolin, to C-G-D-A, with "A" in the octave of middle C. In terms of the D'Addario Catalog, you may wish to CONSIDER the following set for C-G-D-A tuning with the highest note, "A", in the octave of middle C. I won't force you to do anything, so please don't hold any resulting effects against me. Check with a music store or a manufacturer to confirm the selections. My logic and related selections are based on the goal of 12 to 15 pounds of tension per string as previously recommended to me by an expert for GUITARS for an decent volume. The suggested set may not conform to your sense of how much tension the strings should have, or your instrument's capacity to amplify specific frequencies. I am presuming it is small enough that its natural resonances include the "A" note in the octave of middle C, permitting a somewhat lighter gauge string to be used. This will, in my experience with plain steel strings, give the notes produced a rounder sound with fewer higher frequency overtones associated with an unpleasantly harsh tone at the high end.
THE FOLLOWING ARE MY BEST "GUESS" BASED ON D'ADDARIO LOOP END BANJO STRINGS (for C-G-D-A tuning with 19.5 inch scale):
C string, one octave below middle C:
LE032PB, PHOSPHOR BRONZE ROUND WOUND, unit weight 0.00020573, approx. tension with 19.5 inch scale is 12.8 pounds PER STRING.
G string, just below middle C:
LEO22PB, PHOSPHOR BRONZE ROUND WOUND, unit weight 0.00009571, approx. tension with 19.5 inch scale is 13.35 pounds PER STRING.
D string, octave of middle C:
LE013, PLAIN STEEL LOOP END, unit weight 0.00003744, approx. tension with a 19.5 inch scale is 11.75 pounds PER STRING.
A string, octave of middle C:
LE008, PLAIN STEEL LOOP END, unit weight 0.00001418, approx. tension with a 19.5 inch scale is 10 pounds PER STRING.
Total estimated tension with this set is approximately 95 pounds. Total tenson may vary depending on effect of distance from bridge to tailpiece of your mandola versus distance from bridge to tailpiece of a banjo. (More distance from bridge to tailpiece of your mandola relative to banjo will increase total tension.)
(As for your nut and related buzzing, you may need to have a new nut made. If you had the experience, I would suggest acquisition of a small, triangular cross section file to file slots, a set of welding pipe tip cleaners, selection of a gauge of pipe tip cleaner (small file) suitable to each string, and an hour or so of modification to a carefully marked blank nut. With fine metal strings, the nut groove can be smoothed with a single-sided razor blade. Be sure to clean any debris from the existing nut grooves using a clean, damp cloth, before inserting any strings. A music shop that sets up guitars can probably fix this for you, if you'd rather not risk doing it yourself. If cleaning doesn't work, you may be able to either lightly file a flat slot using a triangular cross section file. If the action gets too low, consider removing the nut, using cellophane tape to block both sides of the slots, and using superglue to fill the slot near the bottom. Let the glue dry thoroughly, then you can try to file a clean slot in the dry glue.)
Re: How to string an instrument with scale length 19.5 in?
"Loop end banjo strings designed for 26 1/4 inch scale would produce roughly 50% of the design tension of a 19 1/4 inch scale (assuming the same tail piece to bridge distance for both instruments)."
SHOULD READ:
Loop end banjo strings designed for a 26 1/4 inch scale would produce roughly 50% of the design tension (for a 26 1/4 inch scale) if installed on an instrument with a 19 1/4 inch scale (assuming the same tail piece to bridge distance for both instruments).
Re: How to string an instrument with scale length 19.5 in?
P.P.S.
Wikipedia states that an octave mandolin ("Irish Bazouki") has a typical scale from 20 to 22 inches in length. Your 19.5 inch scale isn't that far off. You may wish to compare your strings to the following D'Addario set.
Are the string gauges listed comparable to what you have?
The octave mandolin tuning with a set of octave mandolin strings is supposed to be G-D-A-E with the E in the octave of middle C, just a like a guitar. Tuning it up a fifth will cause the kind of tension problems you have already encountered.
You may only have dirty nut slots, or a need for a little more to correct the buzzing nuts by smoothing the base of the buzzing nut slots (assuming the buzz is due to an open string, rather than occurring when you fret at a particular fret, which may indicate a fret that is too high just below the highest fret that causes the buzzing).
If you prefer C-G-D-A tuning (up a fifth), you may find that you prefer a 009 gauge first string rather than the 008 gauge plain steel string I suggest above for a little more tension.
Re: How to string an instrument with scale length 19.5 in?
Arthur, not that I would wish to complain, but occasionally you speak a load of rubbish. You did well to wish everyone a Happy New Year. And the same to you.
1) the only relevant length in determining the string tension is the scale length, nut to bridge. The rest is irrelevant. I don't know what you are going on about. The only thing would affect the situation slightly is the 'break' angle of the strings over the bridge - some instruments have a relatively shallow angle, others, like the arched-top instruments, have a steeper 'break' angle but are designed to take the extra down pressure this produces onto the soundboard. The string tension will, however, remain exactly the same for the same scale length, for the same note..
2) I would ignore the Wikipedia advice, as whoever contributed that piece of information doesn't know the difference between the three different instruments, the 'tenor' mandola ( tuned CGDA ), the 'octave' mandola/mandolin (tuned GDAE )with a longer scale, more like 21 - 22", and the 'irish bouzouki' tuned GDAE with the 26.5" scale length that you have been quoted here, the longest scale of the three instruments.
The D'Addario catalogue obviously indicates strings for the european mandola, a much shorter-scale instrument, 15.85" as they say, not the more modern "folk" or "tenor" mandola, and these would be too heavy for a CGDA tuning on the instrument we are talking about.
Finding the correct set of strings is a problem if you are not in an area with a large enough population of similar-minded musicians encouraging the music shops to stock appropriate spares.
Re: How to string an instrument with scale length 19.5 in?
Pete is entirely correct, and took the words out of my mouth (or fingers) in point 1) above.
I tune my 17" mandola CGDG, and use D'Addario's stock mandola string set. I think the guages are something like 14, 24. 36, 49, so going with something like 11, 20, 32, 45 would be about right for 19.5". I would expect the D'Addario set to be too slack for short-scale (15.85") mandolas, which historically are the Gibson H series.
Re: How to string an instrument with scale length 19.5 in?
Actually, the gauges of the D'Addario set I mentioned, which is their lightest of three sets (J72), is 14, 23, 34, 49. In coming up with suitable gauges for a 19,5" scale, here is a handy fact to consider:
A 21" mandola (scale 1.5 that of a standard mandolin) could use strings of mandolin gauge, tuned CGDA, with the same tension as they would be on mandolin, tuned GDAE.
I recommend pondering this, as an aid to understanding the inter-relationships of gauge, length and tension.
So, Twitch, I think your instrument is best considered a mandola, and strung accordingly, with perhaps some adjustment for the particularities of Irish music. I find just tuning the top string pair down a whole tone from standard, and capoing at the second fret, or not, gives a useful set of open strings, in roughly the right pitch parameters.
Re: How to string an instrument with scale length 19.5 in?
I think that a closer reading of what I stated will establish that I sought to answer, in very specific terms, the question posed.
I computed string tension based on the C-G-D-A tension that the party posing the question indicated he had kind of liked.
I use a 19.5 inch scale to compute that tension based on the specific instrument described.
I do not assert that scale is anything other than the distance from the nut to the bridge (for uncompensated bridge placement). It is more correctly twice the distance from the nut to the 12th fret. I specifically state this.
String tension is affected by the total length of the string under tension. This is why instruments that are tuned to higher frequencies (mandolins) are shorter in scale than instruments tuned a fifth lower ("octave mandolins"). The height of the bridge slightly affects the total string length under tension.
You're a fine fellow, Guernsey Pete, and I'm pleased you're interested in keeping people honest. Would you consider correcting the Wikipedia article for "Octave Mandolin", for the benefit of us cultural outsiders?
Re: How to string an instrument with scale length 19.5 in?
"I would caution you to consider how the strings are connected at the bridge end of the instrument. If the instrument uses a tailpiece, the additional distance from the bridge to the tailpiece will increase the total tension on the strings. If the strings connect just behind the bridge in the context of a saddle structure, the distance from the nut to the bridge, or twice the distance from the nut to the 12th fret, the "scale", will serve as a useful input in computations of tension based on string gauge, but only for instruments that also terminate in tailpieces with approximately the same distance from the bridge to the tailpiece."
Arthur, the above statement is what Pete was disputing, and it is indeed rubbish. Where did you get such an idea?
Re: How to string an instrument with scale length 19.5 in?
twitchard
There's a high probability that a "nondescript and unnamed" instrument never will sound good regardless of the tuning unless some work is done on its setup and action.
The way to go here is get a set of strings for CGDA tuning according to will morgan's specs and also get a set of medium gauge GDAE octave mandolin strings, like Pete described, in the 12–46 range. There'll likely be more stress on the neck with the CGDA tuning but will morgan seems to be compensating for that in his choice of gauges. String her up and see which works and for how long.
We were all cautioned by Arthur that his post was a time-consuming stew that even he wouldn't eat , so you avoid it too and keep it simple.
Re: How to string an instrument with scale length 19.5 in?
Thank you, Will.
I'll gladly repeat that the only part of the string you need to consider is the part between nut and bridge. The extraneous parts of the string are, of course, at exactly the same tension. The distance the tailpiece is away from the bridge is irrelevant to this. The height of the bridge only affects the action and intonation if the string has to be pushed down further to reach the fretboard.
Arthur, did you consult any experienced luthier concerning your tailpiece problem ? I'm sure someone could have sorted you out, but I feel that the difficulties you were experiencing had their cause elsewhere.
I'll have a look at Wikipedia at my leisure, but, like this forum, it is open to everyone, sometimes the misguided and misinformed. Not to mention the malicious.
Anyone hear about Van Morrison's new baby ?
Re: How to string an instrument with scale length 19.5 in?
On an instrument with a tailpiece there is additional string (though not vibrating length) behind the bridge, which must be stretched in order to maintain the pitch of the string. "Tension," in this situation, means the force required to maintain that pitch - essentially, the force applied by the tuner. The question is: Is that force greater on a tailpiece instrument? Does it require additional force to stretch the string to the same tautness as on a fixed-bridge instrument?
Re: How to string an instrument with scale length 19.5 in?
Thinking about physics problems gives me a headache and it's been several decades since my last physics course, but here's my reasoning:
The tension in a stretched string is, by definition, the force applied to the string to stretch it. A certain amount of force is required in order to stretch the string up to its target pitch over its vibrating length. The length of string between the bridge and the tailpiece is not rigid; it will stretch, and that stretching requires additional force beyond the force required to stretch only the vibrating length. It's not just a matter of taking up some extra slack. It's actual extra work, which needs extra force. The force (tension) to stretch the extra bit of string has to come from somewhere.
Re: How to string an instrument with scale length 19.5 in?
When you wind the tuner to pull the string to tension you are doing work. Every little partial twist takes some effort on your part. If you have a longer string you have to wind a bit further, do a bit more work, to bring it up to tension because you have more string to stretch. The tension in the whole string is the same - you just had to work harder to get it there with a longer string.
Or look at it another way, if you brought it up to tension by running it over a pully and hanging a weight on it then you wouldn't expect adding a bit more string would change the tension. (ignoring the weight of the string)
when playing around with tunings and string gauges
(the first necessitates the second I'm afraid - you can't just tune up a fifth with the same strings without most likely coming to grief)
I'm no physics expert, so my observation on the debate above is just that there are two or three good reasons to consider tension in relation to loading:
the string tensile strength, and the total pressure on the top and neck of your instrument
If you have unusual scale lengths, then you need to experiment a bit to find tunings and string gauges that go with it, and with the music you play and musicians you play with.
Sometimes the tuning and tension and playability can be all right, but the sound is unbalanced
Re: How to string an instrument with scale length 19.5 in?
Bob himself - I hope you convinced yourself. You'll break fewer strings if, like me, you build an instrument with a tailpiece, push the smallest diameter of nylon string that you can get close to its limit with a 26.5 inch scale, and watch that string (for me tuned to 440 Hz) snap either instantly or by the following morning (repeatedly) when tuned to 440 Hz, on an instrument constructed with a tailpiece that extends the length of the string by too many inches behind the bridge. (I resorted to fising line to reduce the cost of replacement. The manufacturer could not explain the reason for the strings breaking. Hannabach insisted on all dimensions related to the string when I sought a replacement from them, including the overall length of the string under tension.)
I corrected that problem by making a new, longer tailpiece, permitting connection of strings much closer to the bridge, thus reducing the tension on the string required to bring about the 440 Hz tuning. The string remained in one piece after that on two different instruments using a first string tuned to A = 440 Hz.
Your observation that the natural frequency at which the string will vibrate is a function of tension for a fixed vibrating string length is correct and the well known basis for tuning stringed instrument. Longer strings require more tension to achieve the same open string natural resonant frequency.
I've applied the design principle to build three,short scale guitars using 4/4 length, nylon strings.
For what its worth, www.stringsbymail.com is a good source for odd, D'Addario string sizes, while www.elderly.com sells a lot of string sets at competitive prices. They also have a tech staff that can answer questions associated wtih selecting strings for a particular instrument. There's an e-mail link on their site.
Re: How to string an instrument with scale length 19.5 in?
Bob yerself - you're trying to convince yourself you need more effort to bring a longer string up to the same tension - well, you may need to make an extra couple of turns of the tuner knob to bring this longer string, which has, of course, a slight stretch inherent in it, from dead slack to up to the same tension, but I think most people will not notice this extra effort, you just wind the string till it's up to tension.
Bren has it right.
Will got my points the first time. And I heard about Van The Man's being hoaxed - he should just take it as a complement to his virility !
I think Arthur needs to go and talk his problems through with a luthier, as I certainly remain unconvinced.
Re: How to string an instrument with scale length 19.5 in?
oh, and I did look up Wikipedia on the octave mando , it's neither well written, IMNSHO, nor entirely accurate and precise.
Perhaps I should have a go at that.
Re: How to string an instrument with scale length 19.5 in?
An explanation of the basis for considering distance from the bridge to the tailpiece relative to string tension that must be achieved to produce a specific tuning with a specific string material and string diameter:
A. When one tunes a string, one does work to produce tension. This work (consisting of turning a tuning mechanism against string tension) stores potential energy in the string. The resonant frequency of the string is dependent in part on the density of the string material per unit length. For a given string material density per unit length, to produce a resonant frequency that is higher one must store more potential energy per unit length of the string to cause the mass per unit length of the string to be inclined to respond at a rate consistent with the desired natural resonant frequency when the string is excited. (A string vibrates faster at higher frequencies, so the mass must move faster at higher frequencies. This requires more stored potential energy to bias the string mass to move at a higher velocity to achieve a higher natural open string tuning frequency.)
If one increases the length of the string, the energy that must be stored per unit length of the string to produce the same resonant frequency on the segment of the string between the nut and the bridge that vibrates remains the same even if all parts of the string are not vibrating. This means that a longer string must store more energy (in total) to maintain a constant ratio of mass density per unit length to stored energy per unit length toachieve a specific natural resonant frequency. A measure of the magnitude of the stored potential energy in the string is the tension in the string. If one accepts that more energy must be stored in a long string than in a short string to maintain the same stored energy per unit length to mass per unit length ratio required to produce a specific, open string resonant frequency, one must also accept that the tension required for a longer string due to an extension behind the bridge to the tailpiece is greater than that for a shorter string connected just behind the bridge to a saddle structure to achieve a specific, open string resonant frequency even if the segment of the string in which potential energy is stored extends behind the bridge of the instrument to the tailpiece. Energy still must be stored in that non-vibrating segment of string between the bridge and the tailpiece. That additional potential energy corresponds to additional tension.
The placement of the bridge controls the lowest whole wavelength that can occur, at 2L, with L the distance from the nut to the bridge of the instrument. The placement of the bridge does not control the energy that must be stored per unit length of the string, as reflected in tension, to produce a specific open string resonant frequency.
(Comments on the string sets I have suggested.)
B. I would note that what Elderly Instruments is calling a set of "octave mandolin" strings from its perspective in America based on the D'Addario octave mandolin string set to which I have provided a link includes string gauges for the D-A-E open tuned strings (of G-D-A-E tuning) that are very close to those I chose for the C-G-D open tuned strings of (C-G-D-A) tuning for strings tuned within one full tone of each other. Given that the string gauges associated with strings from either set tuned C or D, G or A, and D or E (respectively) are within a tone of each other in each, individual instrument tuning, the similarities in string gauges for strings tuned within a tone of each other from each set suggests a correlation in instrument scale assuming that 12 to 15 pounds per string is a common standard for adequate string tension. (This does not mean that either set, the custom set I suggest or the ready-made D'Addario set from Elderly can be used to produce either tuning by simply tuning the strings up or down.) I would feel comfortable selecting a desired tuning and applying the appropriately designated set with a 19.5 inch scale for an instrument with robust construction given the preceding observation. Instruments that are subject to stated limits in terms of the tension that they can withstand may require a lighter weight set of strings. I presume robust construction and a "typical" distance from the bridge to the tailpiece relative to the type of instrument. The specialty set I suggest for C-G-D-A tuning may have a little less tension associated with the A string than one may desire, and a shift from a 008 to a 009 gauge string might be preferred over the long run.
Re: How to string an instrument with scale length 19.5 in?
Most of what you read about vibrating stretched strings is based on idealized and simplified models. The case of a string breaking over a bridge, with significant afterlength, adds another level of complexity and it's not intuitively obvious how compare it to the fixed-bridge case.
Re: How to string an instrument with scale length 19.5 in?
Its secondary school physics.The pitch is dependant on the sounding length of the string and the tension in it (at constant temperatures etc). Unless its sticking at the bridge or nut the tension is the same all the way along and at at the points where the ends are fixed.
But, at a particular tension, the localised sideways pressure on the string wherever it touches something (tailpiece, bridge, nut, machine head) depends on the angle that it is bent through at that point and how localised the contact is (knife blades don't work too well as bridges).
One of the things that luthiers do is design things so that vibrations are transmitted well through those points of contact but the string doesn't break at them.
Re: How to string an instrument with scale length 19.5 in?
Right, but the particular question was whether the tension is greater on a tailpiece instrument compared with a fixed bridge instrument with the same vibrating length and tuned to the same pitch.
Re: How to string an instrument with scale length 19.5 in?
The tension in the string is the same. A variable length of string beyond the bridge includes no length. But is the angle at the saddle steeper ? However, could it be that with a lot of string between the tailpiece and the bridge the string moves over the bridge as it is tuned up whearas with a fixed bridge the same part of the string is always bent over the saddle and so it takes all the damage ? There won't be much movement during day-to-day tuning what there is will be in proportion to the amunt of string beyond the tailpeice.
Re: How to string an instrument with scale length 19.5 in?
There's an awful lot of spurious physics going on here, and I blame the education system for producing people who don't know their farce from their elbow.
To repeat - it's only the length of string between bridge and nut that defines the tension needed to produce the pitch required. This is not to say that the string length beyond the bridge, and beyond the nut, are not involved in the process. They will be at the same tension as the rest of the string, and will resonate with harmonics, depending on their length, from the energy applied to the string when it is plucked. These harmonics, in some instruments, will produce "wolf" notes, unwanted resonances that adversely affect the tone of the instrument. In violin family instruments these are sometimes damped down by adding a weight that is attached to the string between bridge and tailpiece to absorb these extraneous energies. Other people like myself, on plucked instruments, use both a heavy brass tailpiece, so that energy is more likely transferred through the light bridge rather than the heavier tailpiece, plus adding a piece of soft cloth between tailpiece and strings to dampen and absorb these vibrations. The initial energy that was required to apply to the string when it was tightened up to pitch remains in the tension but cannot be harvested in any way - it is balanced by the tension within the body and neck, including truss-rod, and the instrument depends on this tension as the basic point from which to create musical tones.
NB; There's a woman who appeared on television a lot here in the UK recently; she used to give some quite reasonable advice on diets, but gave reasons such as "Eat green leaves, because they contain chlorophyl which gives you oxygen." Only if you shine a UV light up your rectum, dear lady. It turned out she claimed to have a Phd, but a doctor in the media proved her as bogus, by buying a similar qualification for his dead cat from her 'college'. What I'm trying to say is that false science, or science misapplied, proves nothing. There's been a bit of that in this correspondence already.
Let's leave it there.
Re: How to string an instrument with scale length 19.5 in?
But spurious physics is fun, Pete.
Hmmm, that mythbusting link starts off with a confused statement of what tension means.
"The tension of the string of a stringed musical instrument is defined completely by the pitch the string is tuned to, its vibrating length, and its mass (weight) per unit of length."
This is backward. The tension in a stretched string is, by definition in physics, equal to the longitudinal force applied to stretch the string. Vibrating length and tension are independent (ignoring friction over the bridge saddle and nut).
And then there's this:
"[Note for those intending to read the original American Lutherie article: In the paper Bob uses the term “tension” in the vernacular sense, referring to perceived tension and compliance as tension. Whereas this sin probably would have got a submission of a paper to a physics journal rejected, I encourage you to not get too hung up on the terminology there. Bob is not a physicist. But he designed and performed a very clever and useful experiment and obtained good results.]
I think we have a similar confusion of terminology in this discussion. The link doesn't really address the question of whether extra tension (static longitudinal force) is required to stretch the afterlength on a tailpiece instrument.
Re: How to string an instrument with scale length 19.5 in?
A minor correction to my last post. (I excluded a word.)
The placement of the bridge controls the lowest FREQUENCY whole wavelength that can occur, at 2L, with L the distance from the nut to the bridge of the instrument.
.
Re: How to string an instrument with scale length 19.5 in?
Bob, think of it this way: the longer the string, regardless of how much of it is on either side of the bridge, the more work required to bring it up to any given tension. If the string was ten feet long, you would be cranking that tuning peg a long time before you got it up to 18 pounds, say. But after all that work, the tension of the string would still be only 18 pounds, on either side of the bridge or nut, and in no greater danger of breaking than a four inch string that required a quarter turn of the peg to bring it up to 18 pounds.
Arthur, I hardly know where to begin with you. Please define "resonant frequency of the string" for me.
Re: How to string an instrument with scale length 19.5 in?
"The tension of the string of a stringed musical instrument is defined completely by the pitch the string is tuned to, its vibrating length, and its mass (weight) per unit of length."
One may quibble with the word "defined" as used above - I would have used "determined", and the statement would clearly, and correctly, mean that if the values of any three of the variables "pitch (frequency)", "tension", "length", and "mass" are known, the remaining value is calculable.
Re: How to string an instrument with scale length 19.5 in?
Yes, what will morgan said. Which is what I meant if not what I said clearly.
I have just been in the bin for a set of classical guitar strings that had been on for far, far too long a time (New Year resolution - if I'm going to keep it make sure its not embarrasing next time a visitor plays it). The nylon ones have a flat spot where they rest on the saddle, the wound ones have slightly damaged turns. I reckon that on insrument with a tailpiece that damage would be distributed over slightly more string making it less likely to break.
Re: How to string an instrument with scale length 19.5 in?
“Bob, think of it this way: the longer the string, …”
That’s how I thought of it originally, before I thought to account for the static force required to maintain the stretch in the afterlength. Maybe we’d be better off dropping the word “tension,” since, as the link above indicates, it has different interpretations.
Here’s an analogy:
Suspend a spring vertically from a fixed point and attach a 10 pound weight to the bottom of it. Suppose the spring stretches to a length of 25 inches. Now remove the weight and attach an identical second spring to the end of the first. Attach the 10 pound weight to the end of the second spring and measure how far the first spring is stretched. Will it still stretch 25 inches or will additional weight (force) be required to achieve the 25 inch stretch? Think of the 25 inch stretch as the vibrating length of the string.
Re: How to string an instrument with scale length 19.5 in?
That's all quite amusing.
But going back to the original poster, are you sure that the instrument should have a 19.5" scale lenght? Most of the 'nondescript, unlabelled' instruments on Ebay come from the Ozark/Trinity College factory in China, and have a scale length of just under 20.5". I wonder if yours is one of these with the bridge in the wrong place, which would account for why it never sounded so good.
Re: How to string an instrument with scale length 19.5 in?
Are you serious? I've been giggling at this thread since I came home - I thought everyone was winding each other up.
If you are serious, then to use your 'weight on a string' analogy, but adapting it so that it actually represents a musical instrument, replace the spring with a length of knicker elastic. Hang your 10lb weight on the end of it, then hold the elastic 25cm from the top (to represent the saddle) and twang it above where you are holding it. Note the pitch produced. Now add the extra length of elastic, hold it again at 25cm from the top, and twang it again. You will get exactly the same pitch, because the tension (10lb) and the length (25cm) are the same. The after length and nut to tuning peg distance have absolutely nothing to do with the pitch. The ONLY things that affect the pitch of a string are the vibrating length, weight per unit length, and tension. The afterlength, break angle, and other spurious factors that have been mentioned in this thread can have a marked affectg on the timbre or tone of the note, but not the pitch.
Re: How to string an instrument with scale length 19.5 in?
Bob, Having just re-read your early posts, I think I can see what is confusing you - I think you think that a longer string needs more 'pull' to produce the same tension, is that right?
If so the answer is no, it doesn't. If you think of your 10lb weight hanging on a piece of string, you could cut the string anywhere and insert a spring balance, and it will always read 10lb. So if you have a 20cm long string terminated at the bridge and you tighten the peg to give a pull of 10lbs, the string tension will be 10lbs. If you have another string that is 25cm long, but passes over a bridge at 20cm, and you tighten the peg to give 10lbs pull, the vibrating length is still 20cm, and it still has 10lbs tension, so the pitch will be exactly the same as for the bridge terminated string - the afterlength has absolutely no affect on the relationship between tension and pitch.
Re: How to string an instrument with scale length 19.5 in?
"The afterlength ... can have a marked effect on the timbre ..."
Yes, and particularly so in the case of instruments of the violin family in which the bridge is not a rigid member but vibrates in a wave form. The bridge vibration is affected not only by the vibrations of the nut-to-bridge length of string but also by the vibrations of the afterlength.
There is an optimum ratio of the afterlength to the string length which is 1:6. This ratio ensures that, if the strings are tuned in perfect 5ths, the frequency of an after-length will be equal to the 2nd octave harmonic of the next string up; e.g the frequency of the after-length of the violin G should be d' (using standard ABC notation) - which is the 2nd D up the D string in the dusty region, or the first D on the E-string. Needless to say, this ratio is very difficult to achieve in practice. For instance, add-on micrometer adjusters will immediately mess it up, and even integral adjusters, because you're dealing in fractions of millimeters. Imperfections in strings and slight misalignment or warping of the bridge will also nullify attempts at perfection. If you really want to get close to (unobtainable) perfection in this area, then don't use micrometer adjusters on the lower three strings.
In practice, of course, it is mostly only those virtuosos who play Strads and record unaccompanied Bach in the world's top studios who will be actively concerned with this policy of perfection, and even then their instruments will usually be set up with great care by the best luthiers. For the rest of us, it doesn't really make much difference.
Re: How to string an instrument with scale length 19.5 in?
Lazyhound - what you say about violin afterlength is all true (except that your comments on fine tuners doesn't apply to integral ones - with integral tuners the afterlength still ends at the tailpiece fret, so is no different to a standard tailpiece).
But the effect on timbre is much more profound on mandloin family instruments, where afterlength ringing can make an otherwise good instrument sound really tinny - Find a mandolin or OM with no afterlength damping and play it with you hand clear of the strings, then rest the side of your hands on the strings behind the bridge and play again - the difference is profound. The sliding cover on a 'standard' mandolin tailpiece should have a felt pad under it to damp the afterlength (that is what the cover is for) but for some reason the pad isn't fitted on a lot of modern instruments. As GP will tell you, a heavy tailpiece helps a lot, and bowl-back players (where the strings terminate on simple pins on the end of the instrument) often either use a damper that clamps onto the strings, or weave a £1 note between the strings to damp the afterlength.
Re: How to string an instrument with scale length 19.5 in?
So apparently my spring analogy wasn't convincing.
I'm still going to try to avoid using the term "tension," since I think it's being used in at least two different defintions here. The most common seems to be refering to the "tautness" or the degree of stretch in the string. This is what must remain constant over a given vibrating length in order to maintain the same pitch.
Can we agree that, in order to maintain the same pitch as a fixed bridge instrument, the string length between the bridge and tailpiece must be stretched to the same degree as the vibrating length?
Does this afterlength stretching come for free? Of course not. Stretching four inches of afterlength requires just as much force as stretching four inches of vibrating length. Right?
If it takes 10 pounds to stretch the vibrating length to pitch (as on the fixed-bridge instrument), then it takes 10 pounds plus a little extra to stretch the vibrating length plus the afterlength. If not, then what stretches the afterlength? The force has to come from somewhere.
"I think you think that a longer string needs more 'pull' to produce the same tension, is that right?"
Avoiding the word "tension," I would say that a longer string needs more pulling force to stretch a segment of the string the same amount.
I just read the Lutherie Myth/Science link more closey. The word "tension," as used in the article, properly applies only to a string with no afterlength (or beforelength). From the article:
"Conventional wisdom has it that a number of other factors affect string tension. Some of these are (in no particular order):
The length of the string between the string anchor and the saddle of the bridge;
The length of the string between the tuning machine post or peg and the nut;
The breakover angle of the string at the bridge and/or the nut;
Once again, looking at the formula it is clear that none of these have any affect whatsoever on string tension."
The confused usage of "tension" makes it a circular argument.
Re: How to string an instrument with scale length 19.5 in?
Wow... this discussion has been most educational for me. Thank you all for being so interesting and helpful.
First thing: after learning how to actually measure scale length (distance to 12th fret x 2, not distance nut to bridge) thanks to exploring some of your guys' links, I have discovered that the _real_ scale length of my instrument is actually only 19 inches.
So, Skreech, it could have been that the bridge was in the wrong place, (I've taken all the strings out now so the bridge has moved), but I don't think so since it was in tune up for the most part, and the harmonic at the 12th fret was the same pitch as the fret.
I think what I'm going to do is just order the lightest gauge mandola strings I can find, maybe tune them a whole step low and capo up to get CGDG or farther for GAEA. That'll be nice considering I'm used to Mandolin and unused to stretching my fingers. Don't think there should be any problems with that, with what you guys have been telling me.
Thank you Arthur for the string ordering links, especially, and
And thank you all for helping to educate me on how string tension works... I wish I had known about all this a couple years ago... maybe I would have had a more interesting High School science project.
Re: How to string an instrument with scale length 19.5 in?
Bob. *Hypothetically* ('cos it may do damage) lay an instrument with a slotted head flat on a table with the head sticking over the end, run the string over the bit you would normally wind it round and hang weights on it until it is in tune. The weight you need will be the same no matter how much string is between the bridge and the tailpice and the nut and the weight.
If you were to increase the length of string between the bridge and the tailpiece (e.g. shorter tailpiece) that extra length would need to be stretched (say for example by 1mm) . The weight would drop by 1mm. The string would still be in tune.
Here comes the physics - the energy to stretch the string came from the difference in potential energy between the weight were it was and the weight 1mm lower. The energy is in the stretched string (same as in a kids catapult pulled to throw a stone). It is the energy you would neet to lift the weight by 1mm. It is energy that would become kynetic energy when the string breaks at the bridge and the end flies back and hits you.
Re: How to string an instrument with scale length 19.5 in?
#Posted on January 5th 2010 by Bob himself:
"So apparently my spring analogy wasn't convincing."
"The confused usage of "tension" makes it a circular argument"
It isn't that your analogy wasn't convincing, it was simply wrong. Tension isn't just a vague term meaning 'tightness', it is a scientific term, defined as 'force per unit cross sectional area' . So if your springs have a cross sectional area of 1 square mmm, and you apply a force of 10 Newtons, the tension will be 10N per mm sq. And that will be the same however long the spring is. Certainly a longer spring will extend more, but that doesn't mean it is under more tension, or more force is being applied.
Re: How to string an instrument with scale length 19.5 in?
screech - you embarrased me into turning round and opening a textbook, which I had been to lazy to do. What I read under little drawings of with ropes, spring balances, weights and pullys is that 'tension' has the same units as 'force' . So if you replace the machine head with a hanging 10lb weight the 'tension' in the string, and the 'force' acting on the tailpiece, is 10lb.
And this has nothing to do with stretching, different chapter in the book for that, which says that the thing that has units of lb per square inch is 'stress'. The stretching it causes is 'strain'.
For an instrument string, at the level of this discussion, (meaning I am not going to read yet another chapter in the book) stress and strain are simply related so it does not matter which of them influence the pitch of a length of string. But its them that do it.
And I'm steering clear of Newtons because its a North American textbook and all the examples are in what I know as 'Imperial' units but it refers to as 'the British system'
But the upshot of what is illustrated in the little drawings is what you and will morgan are saying.
Re: How to string an instrument with scale length 19.5 in?
"Tension isn't just a vague term meaning 'tightness', it is a scientific term, defined as 'force per unit cross sectional area'."
More specifically, tension in a string is the force pulling the string. That's exactly one of the points I tried to get across earlier. However, the "tightness" of the string over its vibrating length has also been referred to as tension, which is why I've been trying to avoid using the term "tension." Further confusion comes from referring to textbook models of strings under tension where it's not always clear that the textbook string is presumed to be inextensible. But extensibility/stretching is the essence of this discussion. That's why I tried to use a spring analogy.
If my analysis is incorrect, will someone please tell me exactly where and why? Specifically, to repeat...
>Can we agree that, in order to maintain the same pitch as a fixed bridge instrument, the string length between the bridge and tailpiece must be stretched to the same degree as the >vibrating length?
>Does this afterlength stretching come for free? Of course not. Stretching four inches of afterlength requires just as much force as stretching four inches of vibrating length. Right?
>If it takes 10 pounds to stretch the vibrating length to pitch (as on the fixed-bridge instrument), then it takes 10 pounds plus a little extra to stretch the vibrating length plus the >afterlength. If not, then what stretches the afterlength? The force has to come from somewhere.
Now for a bow and arrow analogy. Without the arrow. Suppose you have a bow - the old fashion kind without the pulleys - with a fifty pound draw. It takes fifty pounds of force to pull the string back to your ear. In the center of the hand grip, on the outside, you have an eyelet. Pass the string of another identical bow through the eyelet so that the two bows are now in series, so to speak. Now, assuming your arms are extra long, pull the outer bowstring. Do you really think you can pull both bows to full cock with the same fifty pound force?
Re: How to string an instrument with scale length 19.5 in?
Suppose you have two spring balances, that will weigh up to 50lb (more likely 56 lb, 1/2 cwt - they exist). Hook one up to a beam. Pull on it until it reaches 50lb. Stop pulling and hook the second balance onto the bottom. Pull on that (and so the other one) until they both read 50 lb. Are you pulling any harder ?
Stop pulling and hook a 50lb weight on the bottom. What does the top one read ? What does the bottom one read ?
How is that different to the bows ?
ALL strings are extensible, the example in my textbook was an iron rod.
Experiment is better than intuition.
Intuition says that when you let go of an apple it falls because nothing is holding it up. It took thousands of years before a very clever guy to work out something was pulling it down. He also, wrote out, in latin, all the rules about force and tension etc. Before wikipeidia even !
Re: How to string an instrument with scale length 19.5 in?
Hi David,
If experiment is better than intuition, how come nobody realised before Newton that something was pulling apples down? The experiment had been carried out countless billions of times.
Re: How to string an instrument with scale length 19.5 in?
Ha, Bernie 29
Response 1: The was two seperate paragraphs, the second one was just airing concern about intution. Will that do ?
Response 2: I think (but I'm not going to check) that it was experiments (and observations of the planets etc) not intuition that resulted in newton's laws of motion which led him to point out that something was pulling the apple.
But most of us, informally at least, still think of it falling because nothing is holding it up - and that's the sort of thought that needs questioning when the strings start breaking (unless, as I guess skreech can tell us, we instead rely on the experience of luthiers and their experiments over the centuries)
Re: How to string an instrument with scale length 19.5 in?
In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.
Re: How to string an instrument with scale length 19.5 in?
First definition Google offers for intuition is "instinctive knowing (without the use of rational processes) " The pensive meandering of a scientist and mathematician who said he stood on the shoulders of giants is hardly likely to be without the use of rational processes. Inspiration maybe. Even if he was also an alchemist (though I had better get in first with that).
Re: How to string an instrument with scale length 19.5 in?
#Posted on January 5th 2010 by david_h:
"screech - you embarrased me into turning round and opening a textbook, which I had been to lazy to do. What I read under little drawings of with ropes, spring balances, weights and pullys is that 'tension' has the same units as 'force' . So if you replace the machine head with a hanging 10lb weight the 'tension' in the string, and the 'force' acting on the tailpiece, is 10lb"
I stand corrected on the definition of tension, I was confusing it with stress, but in this situation it makes no difference, because we are considering a string with a constant cross sectional area.
#Posted on January 5th 2010 by Bob himself
"Now for a bow and arrow analogy. Without the arrow. Suppose you have a bow - the old fashion kind without the pulleys - with a fifty pound draw. It takes fifty pounds of force to pull the string back to your ear. In the center of the hand grip, on the outside, you have an eyelet. Pass the string of another identical bow through the eyelet so that the two bows are now in series, so to speak. Now, assuming your arms are extra long, pull the outer bowstring. Do you really think you can pull both bows to full cock with the same fifty pound force?"
Yes. If you pull the two bows in series with 50lbs, they will both fully extend. You are doing twice as much work as you would pulling a single bow, but the extra work is in the form of doubling the distance, not doubling the force. (work = force x distance). If you put the two bows in parallel, then you would need double the force, but the distance would be the same, and the work done would be the same, and exactly double what it would be for a single bow.
To translate that back to our musical instrument, if you have an instrument with a long afterlength behind the bridge, yes, you will have to do more WORK to tension the string to a given pitch, but the extra work is in the form of extra distance, not extra force - you will have to turn the machine head through a greater angle, but you will not need to apply any more force.
Re: How to string an instrument with scale length 19.5 in?
Yes. And if my spring balance analogy was any use (maybe a less surprising result ) then they would both read 50 lb but hanging the weight on the two in parallel would have them both reading 25lb.
Re: How to string an instrument with scale length 19.5 in?
Yes. I was just trying to quickly connect my analogy to skreech's good description of what the bows would do in the hope that it would help explain the 'counterintuitive' result to Bob when he gets back.
Re: How to string an instrument with scale length 19.5 in?
I’ve been on a road trip, which gave me some uninterrupted quiet time. I turned off the radio and, somewhere between Atlanta and Spartanburg, I had a Doh! moment:
I’ve been thinking about this as a system in static equilibrium, but I wasn’t considering that, in order to stretch the system into that static equilibrium, somebody has to do some *work,* as screech says above. So, thanks for the discussion and apologies to twitchard for rat-holing the topic.
Guernsey Pete blames the educational system. I blame creeping senility.
No excuses.
Re: How to string an instrument with scale length 19.5 in?
I'm now searching for two spring balances to try to perform the experiment described.
Hmmmmmm.
I'll believe it when I see it, but, logically, both balances will record the same weight, give or take the weight of the second balance, but I must see it to be convinced.
King Charles II, him of the spaniels, was one of the earliest of the British monarchs to be interested in science; he once asked his courtiers how was it that, if you have a goldfish bowl full of water, and you then put a goldfish in, it doesn't displace any water ? They argued about this for days till one of them tried it - of course, it DOES displace water ! The object of the question was to show that only experiment will verify a theory.
So I want my two spring balances......
How to string an instrument with scale length 19.5 in?
How to string an instrument with scale length 19.5 in?
So about a year ago my father got for me a (completely nondescript and unmarked) "octave mandolin" on E-bay as a present. Thing is... tuned GDAE it didn't sound so good and there was a lot of string buzzing, especially with the G string.
So I figured what the heck, and for nothing I tuned all the strings up a fifth to CGDA--I never played it anyway, might as well try something new. For awhile, I kind of liked the sound, and the buzz was gone, but then of course after two days a string snapped.
Now I'm wondering, should I buy octave mandolin strings again or try to string it as a mandola? Would the tension of trying to string it as a mandola be bad for the instrument?
The places I've looked for guidelines on scale length are telling me that mandola's go up to about 19 inches in length and octave mandolins start at about 20 inches... so I'm really confused about what I should be doing.
# Posted on January 1st 2010 by twitchard
Re: How to string an instrument with scale length 19.5 in?
The CBOM forum ( Citterns, Bouzoukis, and Octave Mandolins ) has had some discussion on this over the years.
I reckon you could try tuning up maybe a third, and capoing to give you the mandola tuning.
Or looking at the gauges and going one or two degrees heavier to stay at octave mandola pitch. Or even try contacting the string manufacturers direct to ask them. Everyone has their own solutions to this.
Incidentally, the european mandolas, the original ( pre-modern folk instruments ) mandolas, had a much shorter scale than currently used by these hot-shot luthiers, hence all the confusion.
There is also a formula, which I'm sure someone here can quote, to give you the string tension for any gauge and scale length.
# Posted on January 1st 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
You obviously had the wrong gauges on, but it's a minefield trying to sort them out.
I would reckon that mandola-tuning is too high for your instrument, and that what you need to do is to put a slightly heavier set on. The european mandolas had a much shorter scale then your instrument, which is probably why your stringing didn't work well.
Also the nomenclature is confusing - 'tenor' mandola, meaning the same pitches as an old style tenor banjo, ie same as mandola but with a longer scale, 'octave' mandola, meaning an octave mandolin, an octave below mandolin but not double the scale length, whereas the 'irish bouzouki' has a scale double that of a mandolin, and is an octave below it.
# Posted on January 1st 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
And now my lost first reply re-appears !
GRRRRRR !!
# Posted on January 1st 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
12, 24w, 36, 48 is the usual set for a 21" mandola at GDAE so try something like 13, 26w, 38, 50 for the shorter scale
the scale length is really just too short to work well in with either tuning
# Posted on January 1st 2010 by millionyears_bc
Re: How to string an instrument with scale length 19.5 in?
I've built instruments with odd scales on a number of occassions, altough I am not, by any means, qualified to call myself a "luthier". Having said that, I disavow responsibility for the time consuming mish mash which follows. (Happy New Year to all those who sensibly stop reading at this point.)
I would caution you to consider how the strings are connected at the bridge end of the instrument. If the instrument uses a tailpiece, the additional distance from the bridge to the tailpiece will increase the total tension on the strings. If the strings connect just behind the bridge in the context of a saddle structure, the distance from the nut to the bridge, or twice the distance from the nut to the 12th fret, the "scale", will serve as a useful input in computations of tension based on string gauge, but only for instruments that also terminate in tailpieces with approximately the same distance from the bridge to the tailpiece.
If the instrument uses a tailpiece, as many mandolas do, consider the distance from the nut to the tailpiece when seeking a measurment to use in formulas for string tension based on string length under tension. (I had to modify the tailpiece on three instruments to move the string tie-on point close enough to the bridge to reduce string tension to the point that I could tune one string up to "A" in the octave of middle C with C-G-D-A tuning using nylon strings. Prior to that the string would consistently snap due to tension issues even though the manufacturer assured me it would work with a 26.5 inch scale measured from nut to bridge.)
I would suggest that you get a copy of D'Addario's string catalog from their web site. It is a downloadable PDF. A formula for string tension is included.
The D'Addario Catalog indicates that it employs a 15 7/8 inch (15.875 inch) scale length for mandolas as the basis for its tension computations for mandola. (I don't know if this allows for a tailpiece. I will assume that whatever your setup, it is the same as that used by D'Addario, which could be a gross error.) You are applying roughly 50% more tension due to a 19.5 inch scale than would occur with a 15 7/8 inch scale. That is not a condition that should be sustained.
Loop end banjo strings designed for 26 1/4 inch scale would produce roughly 50% of the design tension of a 19 1/4 inch scale (assuming the same tail piece to bridge distance for both instruments). If you can employ loop end strings, you may wish to consider banjo strings as a substitute with C-G-D-A tuning.
The mandola is designed to be tuned a fifth lower than a mandolin, to C-G-D-A, with "A" in the octave of middle C. In terms of the D'Addario Catalog, you may wish to CONSIDER the following set for C-G-D-A tuning with the highest note, "A", in the octave of middle C. I won't force you to do anything, so please don't hold any resulting effects against me. Check with a music store or a manufacturer to confirm the selections. My logic and related selections are based on the goal of 12 to 15 pounds of tension per string as previously recommended to me by an expert for GUITARS for an decent volume. The suggested set may not conform to your sense of how much tension the strings should have, or your instrument's capacity to amplify specific frequencies. I am presuming it is small enough that its natural resonances include the "A" note in the octave of middle C, permitting a somewhat lighter gauge string to be used. This will, in my experience with plain steel strings, give the notes produced a rounder sound with fewer higher frequency overtones associated with an unpleasantly harsh tone at the high end.
THE FOLLOWING ARE MY BEST "GUESS" BASED ON D'ADDARIO LOOP END BANJO STRINGS (for C-G-D-A tuning with 19.5 inch scale):
C string, one octave below middle C:
LE032PB, PHOSPHOR BRONZE ROUND WOUND, unit weight 0.00020573, approx. tension with 19.5 inch scale is 12.8 pounds PER STRING.
G string, just below middle C:
LEO22PB, PHOSPHOR BRONZE ROUND WOUND, unit weight 0.00009571, approx. tension with 19.5 inch scale is 13.35 pounds PER STRING.
D string, octave of middle C:
LE013, PLAIN STEEL LOOP END, unit weight 0.00003744, approx. tension with a 19.5 inch scale is 11.75 pounds PER STRING.
A string, octave of middle C:
LE008, PLAIN STEEL LOOP END, unit weight 0.00001418, approx. tension with a 19.5 inch scale is 10 pounds PER STRING.
Total estimated tension with this set is approximately 95 pounds. Total tenson may vary depending on effect of distance from bridge to tailpiece of your mandola versus distance from bridge to tailpiece of a banjo. (More distance from bridge to tailpiece of your mandola relative to banjo will increase total tension.)
(As for your nut and related buzzing, you may need to have a new nut made. If you had the experience, I would suggest acquisition of a small, triangular cross section file to file slots, a set of welding pipe tip cleaners, selection of a gauge of pipe tip cleaner (small file) suitable to each string, and an hour or so of modification to a carefully marked blank nut. With fine metal strings, the nut groove can be smoothed with a single-sided razor blade. Be sure to clean any debris from the existing nut grooves using a clean, damp cloth, before inserting any strings. A music shop that sets up guitars can probably fix this for you, if you'd rather not risk doing it yourself. If cleaning doesn't work, you may be able to either lightly file a flat slot using a triangular cross section file. If the action gets too low, consider removing the nut, using cellophane tape to block both sides of the slots, and using superglue to fill the slot near the bottom. Let the glue dry thoroughly, then you can try to file a clean slot in the dry glue.)
Happy New Year!
Happy Hogmonay!
Don't blame me if this doesn't work!
# Posted on January 2nd 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
"Loop end banjo strings designed for 26 1/4 inch scale would produce roughly 50% of the design tension of a 19 1/4 inch scale (assuming the same tail piece to bridge distance for both instruments)."
SHOULD READ:
Loop end banjo strings designed for a 26 1/4 inch scale would produce roughly 50% of the design tension (for a 26 1/4 inch scale) if installed on an instrument with a 19 1/4 inch scale (assuming the same tail piece to bridge distance for both instruments).
# Posted on January 2nd 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
P.P.S.
Wikipedia states that an octave mandolin ("Irish Bazouki") has a typical scale from 20 to 22 inches in length. Your 19.5 inch scale isn't that far off. You may wish to compare your strings to the following D'Addario set.
http://elderly.com/accessories/items/J80.htm .
Are the string gauges listed comparable to what you have?
The octave mandolin tuning with a set of octave mandolin strings is supposed to be G-D-A-E with the E in the octave of middle C, just a like a guitar. Tuning it up a fifth will cause the kind of tension problems you have already encountered.
You may only have dirty nut slots, or a need for a little more to correct the buzzing nuts by smoothing the base of the buzzing nut slots (assuming the buzz is due to an open string, rather than occurring when you fret at a particular fret, which may indicate a fret that is too high just below the highest fret that causes the buzzing).
If you prefer C-G-D-A tuning (up a fifth), you may find that you prefer a 009 gauge first string rather than the 008 gauge plain steel string I suggest above for a little more tension.
Hope this helps.
# Posted on January 2nd 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
Arthur, not that I would wish to complain, but occasionally you speak a load of rubbish. You did well to wish everyone a Happy New Year. And the same to you.
1) the only relevant length in determining the string tension is the scale length, nut to bridge. The rest is irrelevant. I don't know what you are going on about. The only thing would affect the situation slightly is the 'break' angle of the strings over the bridge - some instruments have a relatively shallow angle, others, like the arched-top instruments, have a steeper 'break' angle but are designed to take the extra down pressure this produces onto the soundboard. The string tension will, however, remain exactly the same for the same scale length, for the same note..
2) I would ignore the Wikipedia advice, as whoever contributed that piece of information doesn't know the difference between the three different instruments, the 'tenor' mandola ( tuned CGDA ), the 'octave' mandola/mandolin (tuned GDAE )with a longer scale, more like 21 - 22", and the 'irish bouzouki' tuned GDAE with the 26.5" scale length that you have been quoted here, the longest scale of the three instruments.
The D'Addario catalogue obviously indicates strings for the european mandola, a much shorter-scale instrument, 15.85" as they say, not the more modern "folk" or "tenor" mandola, and these would be too heavy for a CGDA tuning on the instrument we are talking about.
Finding the correct set of strings is a problem if you are not in an area with a large enough population of similar-minded musicians encouraging the music shops to stock appropriate spares.
# Posted on January 2nd 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
Pete is entirely correct, and took the words out of my mouth (or fingers) in point 1) above.
I tune my 17" mandola CGDG, and use D'Addario's stock mandola string set. I think the guages are something like 14, 24. 36, 49, so going with something like 11, 20, 32, 45 would be about right for 19.5". I would expect the D'Addario set to be too slack for short-scale (15.85") mandolas, which historically are the Gibson H series.
# Posted on January 2nd 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
Actually, the gauges of the D'Addario set I mentioned, which is their lightest of three sets (J72), is 14, 23, 34, 49. In coming up with suitable gauges for a 19,5" scale, here is a handy fact to consider:
A 21" mandola (scale 1.5 that of a standard mandolin) could use strings of mandolin gauge, tuned CGDA, with the same tension as they would be on mandolin, tuned GDAE.
I recommend pondering this, as an aid to understanding the inter-relationships of gauge, length and tension.
So, Twitch, I think your instrument is best considered a mandola, and strung accordingly, with perhaps some adjustment for the particularities of Irish music. I find just tuning the top string pair down a whole tone from standard, and capoing at the second fret, or not, gives a useful set of open strings, in roughly the right pitch parameters.
# Posted on January 2nd 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
I think that a closer reading of what I stated will establish that I sought to answer, in very specific terms, the question posed.
I computed string tension based on the C-G-D-A tension that the party posing the question indicated he had kind of liked.
I use a 19.5 inch scale to compute that tension based on the specific instrument described.
I do not assert that scale is anything other than the distance from the nut to the bridge (for uncompensated bridge placement). It is more correctly twice the distance from the nut to the 12th fret. I specifically state this.
String tension is affected by the total length of the string under tension. This is why instruments that are tuned to higher frequencies (mandolins) are shorter in scale than instruments tuned a fifth lower ("octave mandolins"). The height of the bridge slightly affects the total string length under tension.
You're a fine fellow, Guernsey Pete, and I'm pleased you're interested in keeping people honest. Would you consider correcting the Wikipedia article for "Octave Mandolin", for the benefit of us cultural outsiders?
Again, Happy New Year!
(How do you say that in Gaelic?)
# Posted on January 2nd 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
"I would caution you to consider how the strings are connected at the bridge end of the instrument. If the instrument uses a tailpiece, the additional distance from the bridge to the tailpiece will increase the total tension on the strings. If the strings connect just behind the bridge in the context of a saddle structure, the distance from the nut to the bridge, or twice the distance from the nut to the 12th fret, the "scale", will serve as a useful input in computations of tension based on string gauge, but only for instruments that also terminate in tailpieces with approximately the same distance from the bridge to the tailpiece."
Arthur, the above statement is what Pete was disputing, and it is indeed rubbish. Where did you get such an idea?
# Posted on January 2nd 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
twitchard
, so you avoid it too and keep it simple.
There's a high probability that a "nondescript and unnamed" instrument never will sound good regardless of the tuning unless some work is done on its setup and action.
The way to go here is get a set of strings for CGDA tuning according to will morgan's specs and also get a set of medium gauge GDAE octave mandolin strings, like Pete described, in the 12–46 range. There'll likely be more stress on the neck with the CGDA tuning but will morgan seems to be compensating for that in his choice of gauges. String her up and see which works and for how long.
We were all cautioned by Arthur that his post was a time-consuming stew that even he wouldn't eat
# Posted on January 2nd 2010 by ∅
Re: How to string an instrument with scale length 19.5 in?
Thank you, Will.
I'll gladly repeat that the only part of the string you need to consider is the part between nut and bridge. The extraneous parts of the string are, of course, at exactly the same tension. The distance the tailpiece is away from the bridge is irrelevant to this. The height of the bridge only affects the action and intonation if the string has to be pushed down further to reach the fretboard.
Arthur, did you consult any experienced luthier concerning your tailpiece problem ? I'm sure someone could have sorted you out, but I feel that the difficulties you were experiencing had their cause elsewhere.
I'll have a look at Wikipedia at my leisure, but, like this forum, it is open to everyone, sometimes the misguided and misinformed. Not to mention the malicious.
Anyone hear about Van Morrison's new baby ?
# Posted on January 2nd 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
On an instrument with a tailpiece there is additional string (though not vibrating length) behind the bridge, which must be stretched in order to maintain the pitch of the string. "Tension," in this situation, means the force required to maintain that pitch - essentially, the force applied by the tuner. The question is: Is that force greater on a tailpiece instrument? Does it require additional force to stretch the string to the same tautness as on a fixed-bridge instrument?
# Posted on January 2nd 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Bob: No, and no.
Pete: it was a hoax.
# Posted on January 2nd 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
Thinking about physics problems gives me a headache and it's been several decades since my last physics course, but here's my reasoning:
The tension in a stretched string is, by definition, the force applied to the string to stretch it. A certain amount of force is required in order to stretch the string up to its target pitch over its vibrating length. The length of string between the bridge and the tailpiece is not rigid; it will stretch, and that stretching requires additional force beyond the force required to stretch only the vibrating length. It's not just a matter of taking up some extra slack. It's actual extra work, which needs extra force. The force (tension) to stretch the extra bit of string has to come from somewhere.
I think I've almost convinced myself.
# Posted on January 2nd 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
When you wind the tuner to pull the string to tension you are doing work. Every little partial twist takes some effort on your part. If you have a longer string you have to wind a bit further, do a bit more work, to bring it up to tension because you have more string to stretch. The tension in the whole string is the same - you just had to work harder to get it there with a longer string.
Or look at it another way, if you brought it up to tension by running it over a pully and hanging a weight on it then you wouldn't expect adding a bit more string would change the tension. (ignoring the weight of the string)
# Posted on January 2nd 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
I use the Graham McDonal String tension calculator:
http://www.mcdonaldstrings.com/stringxxiii.html
when playing around with tunings and string gauges
(the first necessitates the second I'm afraid - you can't just tune up a fifth with the same strings without most likely coming to grief)
I'm no physics expert, so my observation on the debate above is just that there are two or three good reasons to consider tension in relation to loading:
the string tensile strength, and the total pressure on the top and neck of your instrument
If you have unusual scale lengths, then you need to experiment a bit to find tunings and string gauges that go with it, and with the music you play and musicians you play with.
Sometimes the tuning and tension and playability can be all right, but the sound is unbalanced
# Posted on January 2nd 2010 by Bren
Re: How to string an instrument with scale length 19.5 in?
Bob himself - I hope you convinced yourself. You'll break fewer strings if, like me, you build an instrument with a tailpiece, push the smallest diameter of nylon string that you can get close to its limit with a 26.5 inch scale, and watch that string (for me tuned to 440 Hz) snap either instantly or by the following morning (repeatedly) when tuned to 440 Hz, on an instrument constructed with a tailpiece that extends the length of the string by too many inches behind the bridge. (I resorted to fising line to reduce the cost of replacement. The manufacturer could not explain the reason for the strings breaking. Hannabach insisted on all dimensions related to the string when I sought a replacement from them, including the overall length of the string under tension.)
I corrected that problem by making a new, longer tailpiece, permitting connection of strings much closer to the bridge, thus reducing the tension on the string required to bring about the 440 Hz tuning. The string remained in one piece after that on two different instruments using a first string tuned to A = 440 Hz.
Your observation that the natural frequency at which the string will vibrate is a function of tension for a fixed vibrating string length is correct and the well known basis for tuning stringed instrument. Longer strings require more tension to achieve the same open string natural resonant frequency.
I've applied the design principle to build three,short scale guitars using 4/4 length, nylon strings.
For what its worth, www.stringsbymail.com is a good source for odd, D'Addario string sizes, while www.elderly.com sells a lot of string sets at competitive prices. They also have a tech staff that can answer questions associated wtih selecting strings for a particular instrument. There's an e-mail link on their site.
# Posted on January 3rd 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
Bob yerself - you're trying to convince yourself you need more effort to bring a longer string up to the same tension - well, you may need to make an extra couple of turns of the tuner knob to bring this longer string, which has, of course, a slight stretch inherent in it, from dead slack to up to the same tension, but I think most people will not notice this extra effort, you just wind the string till it's up to tension.
Bren has it right.
Will got my points the first time. And I heard about Van The Man's being hoaxed - he should just take it as a complement to his virility !
I think Arthur needs to go and talk his problems through with a luthier, as I certainly remain unconvinced.
# Posted on January 3rd 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
oh, and I did look up Wikipedia on the octave mando , it's neither well written, IMNSHO, nor entirely accurate and precise.
Perhaps I should have a go at that.
# Posted on January 3rd 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
An explanation of the basis for considering distance from the bridge to the tailpiece relative to string tension that must be achieved to produce a specific tuning with a specific string material and string diameter:
A. When one tunes a string, one does work to produce tension. This work (consisting of turning a tuning mechanism against string tension) stores potential energy in the string. The resonant frequency of the string is dependent in part on the density of the string material per unit length. For a given string material density per unit length, to produce a resonant frequency that is higher one must store more potential energy per unit length of the string to cause the mass per unit length of the string to be inclined to respond at a rate consistent with the desired natural resonant frequency when the string is excited. (A string vibrates faster at higher frequencies, so the mass must move faster at higher frequencies. This requires more stored potential energy to bias the string mass to move at a higher velocity to achieve a higher natural open string tuning frequency.)
If one increases the length of the string, the energy that must be stored per unit length of the string to produce the same resonant frequency on the segment of the string between the nut and the bridge that vibrates remains the same even if all parts of the string are not vibrating. This means that a longer string must store more energy (in total) to maintain a constant ratio of mass density per unit length to stored energy per unit length toachieve a specific natural resonant frequency. A measure of the magnitude of the stored potential energy in the string is the tension in the string. If one accepts that more energy must be stored in a long string than in a short string to maintain the same stored energy per unit length to mass per unit length ratio required to produce a specific, open string resonant frequency, one must also accept that the tension required for a longer string due to an extension behind the bridge to the tailpiece is greater than that for a shorter string connected just behind the bridge to a saddle structure to achieve a specific, open string resonant frequency even if the segment of the string in which potential energy is stored extends behind the bridge of the instrument to the tailpiece. Energy still must be stored in that non-vibrating segment of string between the bridge and the tailpiece. That additional potential energy corresponds to additional tension.
The placement of the bridge controls the lowest whole wavelength that can occur, at 2L, with L the distance from the nut to the bridge of the instrument. The placement of the bridge does not control the energy that must be stored per unit length of the string, as reflected in tension, to produce a specific open string resonant frequency.
(Comments on the string sets I have suggested.)
B. I would note that what Elderly Instruments is calling a set of "octave mandolin" strings from its perspective in America based on the D'Addario octave mandolin string set to which I have provided a link includes string gauges for the D-A-E open tuned strings (of G-D-A-E tuning) that are very close to those I chose for the C-G-D open tuned strings of (C-G-D-A) tuning for strings tuned within one full tone of each other. Given that the string gauges associated with strings from either set tuned C or D, G or A, and D or E (respectively) are within a tone of each other in each, individual instrument tuning, the similarities in string gauges for strings tuned within a tone of each other from each set suggests a correlation in instrument scale assuming that 12 to 15 pounds per string is a common standard for adequate string tension. (This does not mean that either set, the custom set I suggest or the ready-made D'Addario set from Elderly can be used to produce either tuning by simply tuning the strings up or down.) I would feel comfortable selecting a desired tuning and applying the appropriately designated set with a 19.5 inch scale for an instrument with robust construction given the preceding observation. Instruments that are subject to stated limits in terms of the tension that they can withstand may require a lighter weight set of strings. I presume robust construction and a "typical" distance from the bridge to the tailpiece relative to the type of instrument. The specialty set I suggest for C-G-D-A tuning may have a little less tension associated with the A string than one may desire, and a shift from a 008 to a 009 gauge string might be preferred over the long run.
Best wishes.
# Posted on January 3rd 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
Most of what you read about vibrating stretched strings is based on idealized and simplified models. The case of a string breaking over a bridge, with significant afterlength, adds another level of complexity and it's not intuitively obvious how compare it to the fixed-bridge case.
# Posted on January 3rd 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Give it a go, Pete.
# Posted on January 3rd 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Its secondary school physics.The pitch is dependant on the sounding length of the string and the tension in it (at constant temperatures etc). Unless its sticking at the bridge or nut the tension is the same all the way along and at at the points where the ends are fixed.
But, at a particular tension, the localised sideways pressure on the string wherever it touches something (tailpiece, bridge, nut, machine head) depends on the angle that it is bent through at that point and how localised the contact is (knife blades don't work too well as bridges).
One of the things that luthiers do is design things so that vibrations are transmitted well through those points of contact but the string doesn't break at them.
# Posted on January 3rd 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
Right, but the particular question was whether the tension is greater on a tailpiece instrument compared with a fixed bridge instrument with the same vibrating length and tuned to the same pitch.
# Posted on January 3rd 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
The tension in the string is the same. A variable length of string beyond the bridge includes no length. But is the angle at the saddle steeper ? However, could it be that with a lot of string between the tailpiece and the bridge the string moves over the bridge as it is tuned up whearas with a fixed bridge the same part of the string is always bent over the saddle and so it takes all the damage ? There won't be much movement during day-to-day tuning what there is will be in proportion to the amunt of string beyond the tailpeice.
# Posted on January 4th 2010 by David50
. . .
"Lutherie Myth/Science:
Human Perception of String Tension and Compliance in Stringed Musical Instruments"
http://liutaiomottola.com/myth/perception.htm
# Posted on January 4th 2010 by Ben Steen
Re: How to string an instrument with scale length 19.5 in?
There's an awful lot of spurious physics going on here, and I blame the education system for producing people who don't know their farce from their elbow.
To repeat - it's only the length of string between bridge and nut that defines the tension needed to produce the pitch required. This is not to say that the string length beyond the bridge, and beyond the nut, are not involved in the process. They will be at the same tension as the rest of the string, and will resonate with harmonics, depending on their length, from the energy applied to the string when it is plucked. These harmonics, in some instruments, will produce "wolf" notes, unwanted resonances that adversely affect the tone of the instrument. In violin family instruments these are sometimes damped down by adding a weight that is attached to the string between bridge and tailpiece to absorb these extraneous energies. Other people like myself, on plucked instruments, use both a heavy brass tailpiece, so that energy is more likely transferred through the light bridge rather than the heavier tailpiece, plus adding a piece of soft cloth between tailpiece and strings to dampen and absorb these vibrations. The initial energy that was required to apply to the string when it was tightened up to pitch remains in the tension but cannot be harvested in any way - it is balanced by the tension within the body and neck, including truss-rod, and the instrument depends on this tension as the basic point from which to create musical tones.
NB; There's a woman who appeared on television a lot here in the UK recently; she used to give some quite reasonable advice on diets, but gave reasons such as "Eat green leaves, because they contain chlorophyl which gives you oxygen." Only if you shine a UV light up your rectum, dear lady. It turned out she claimed to have a Phd, but a doctor in the media proved her as bogus, by buying a similar qualification for his dead cat from her 'college'. What I'm trying to say is that false science, or science misapplied, proves nothing. There's been a bit of that in this correspondence already.
Let's leave it there.
# Posted on January 4th 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
PS Random notes link above puts forward the point exactly.
# Posted on January 4th 2010 by Guernsey Pete
Re: How to string an instrument with scale length 19.5 in?
But spurious physics is fun, Pete.
Hmmm, that mythbusting link starts off with a confused statement of what tension means.
"The tension of the string of a stringed musical instrument is defined completely by the pitch the string is tuned to, its vibrating length, and its mass (weight) per unit of length."
This is backward. The tension in a stretched string is, by definition in physics, equal to the longitudinal force applied to stretch the string. Vibrating length and tension are independent (ignoring friction over the bridge saddle and nut).
And then there's this:
"[Note for those intending to read the original American Lutherie article: In the paper Bob uses the term “tension” in the vernacular sense, referring to perceived tension and compliance as tension. Whereas this sin probably would have got a submission of a paper to a physics journal rejected, I encourage you to not get too hung up on the terminology there. Bob is not a physicist. But he designed and performed a very clever and useful experiment and obtained good results.]
I think we have a similar confusion of terminology in this discussion. The link doesn't really address the question of whether extra tension (static longitudinal force) is required to stretch the afterlength on a tailpiece instrument.
# Posted on January 4th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
A minor correction to my last post. (I excluded a word.)
The placement of the bridge controls the lowest FREQUENCY whole wavelength that can occur, at 2L, with L the distance from the nut to the bridge of the instrument.
.
# Posted on January 4th 2010 by Arthur Nordstrom
Re: How to string an instrument with scale length 19.5 in?
Bob, think of it this way: the longer the string, regardless of how much of it is on either side of the bridge, the more work required to bring it up to any given tension. If the string was ten feet long, you would be cranking that tuning peg a long time before you got it up to 18 pounds, say. But after all that work, the tension of the string would still be only 18 pounds, on either side of the bridge or nut, and in no greater danger of breaking than a four inch string that required a quarter turn of the peg to bring it up to 18 pounds.
Arthur, I hardly know where to begin with you. Please define "resonant frequency of the string" for me.
# Posted on January 4th 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
"The tension of the string of a stringed musical instrument is defined completely by the pitch the string is tuned to, its vibrating length, and its mass (weight) per unit of length."
One may quibble with the word "defined" as used above - I would have used "determined", and the statement would clearly, and correctly, mean that if the values of any three of the variables "pitch (frequency)", "tension", "length", and "mass" are known, the remaining value is calculable.
# Posted on January 4th 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
Yes, what will morgan said. Which is what I meant if not what I said clearly.
I have just been in the bin for a set of classical guitar strings that had been on for far, far too long a time (New Year resolution - if I'm going to keep it make sure its not embarrasing next time a visitor plays it). The nylon ones have a flat spot where they rest on the saddle, the wound ones have slightly damaged turns. I reckon that on insrument with a tailpiece that damage would be distributed over slightly more string making it less likely to break.
# Posted on January 4th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
“Bob, think of it this way: the longer the string, …”
That’s how I thought of it originally, before I thought to account for the static force required to maintain the stretch in the afterlength. Maybe we’d be better off dropping the word “tension,” since, as the link above indicates, it has different interpretations.
Here’s an analogy:
Suspend a spring vertically from a fixed point and attach a 10 pound weight to the bottom of it. Suppose the spring stretches to a length of 25 inches. Now remove the weight and attach an identical second spring to the end of the first. Attach the 10 pound weight to the end of the second spring and measure how far the first spring is stretched. Will it still stretch 25 inches or will additional weight (force) be required to achieve the 25 inch stretch? Think of the 25 inch stretch as the vibrating length of the string.
# Posted on January 4th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
That's all quite amusing.
But going back to the original poster, are you sure that the instrument should have a 19.5" scale lenght? Most of the 'nondescript, unlabelled' instruments on Ebay come from the Ozark/Trinity College factory in China, and have a scale length of just under 20.5". I wonder if yours is one of these with the bridge in the wrong place, which would account for why it never sounded so good.
# Posted on January 4th 2010 by skreech
Re: How to string an instrument with scale length 19.5 in?
So Arthur was right.
# Posted on January 4th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Are you serious? I've been giggling at this thread since I came home - I thought everyone was winding each other up.
If you are serious, then to use your 'weight on a string' analogy, but adapting it so that it actually represents a musical instrument, replace the spring with a length of knicker elastic. Hang your 10lb weight on the end of it, then hold the elastic 25cm from the top (to represent the saddle) and twang it above where you are holding it. Note the pitch produced. Now add the extra length of elastic, hold it again at 25cm from the top, and twang it again. You will get exactly the same pitch, because the tension (10lb) and the length (25cm) are the same. The after length and nut to tuning peg distance have absolutely nothing to do with the pitch. The ONLY things that affect the pitch of a string are the vibrating length, weight per unit length, and tension. The afterlength, break angle, and other spurious factors that have been mentioned in this thread can have a marked affectg on the timbre or tone of the note, but not the pitch.
# Posted on January 5th 2010 by skreech
Re: How to string an instrument with scale length 19.5 in?
Bob, Having just re-read your early posts, I think I can see what is confusing you - I think you think that a longer string needs more 'pull' to produce the same tension, is that right?
If so the answer is no, it doesn't. If you think of your 10lb weight hanging on a piece of string, you could cut the string anywhere and insert a spring balance, and it will always read 10lb. So if you have a 20cm long string terminated at the bridge and you tighten the peg to give a pull of 10lbs, the string tension will be 10lbs. If you have another string that is 25cm long, but passes over a bridge at 20cm, and you tighten the peg to give 10lbs pull, the vibrating length is still 20cm, and it still has 10lbs tension, so the pitch will be exactly the same as for the bridge terminated string - the afterlength has absolutely no affect on the relationship between tension and pitch.
# Posted on January 5th 2010 by skreech
Re: How to string an instrument with scale length 19.5 in?
"The afterlength ... can have a marked effect on the timbre ..."
Yes, and particularly so in the case of instruments of the violin family in which the bridge is not a rigid member but vibrates in a wave form. The bridge vibration is affected not only by the vibrations of the nut-to-bridge length of string but also by the vibrations of the afterlength.
There is an optimum ratio of the afterlength to the string length which is 1:6. This ratio ensures that, if the strings are tuned in perfect 5ths, the frequency of an after-length will be equal to the 2nd octave harmonic of the next string up; e.g the frequency of the after-length of the violin G should be d' (using standard ABC notation) - which is the 2nd D up the D string in the dusty region, or the first D on the E-string. Needless to say, this ratio is very difficult to achieve in practice. For instance, add-on micrometer adjusters will immediately mess it up, and even integral adjusters, because you're dealing in fractions of millimeters. Imperfections in strings and slight misalignment or warping of the bridge will also nullify attempts at perfection. If you really want to get close to (unobtainable) perfection in this area, then don't use micrometer adjusters on the lower three strings.
In practice, of course, it is mostly only those virtuosos who play Strads and record unaccompanied Bach in the world's top studios who will be actively concerned with this policy of perfection, and even then their instruments will usually be set up with great care by the best luthiers. For the rest of us, it doesn't really make much difference.
# Posted on January 5th 2010 by Trevor Jennings
Re: How to string an instrument with scale length 19.5 in?
Skreech gets it. No further comment needed at this time.
# Posted on January 5th 2010 by will morgan
Re: How to string an instrument with scale length 19.5 in?
"string length" - between the nut and bridge, to be precise.
# Posted on January 5th 2010 by Trevor Jennings
Re: How to string an instrument with scale length 19.5 in?
Lazyhound - what you say about violin afterlength is all true (except that your comments on fine tuners doesn't apply to integral ones - with integral tuners the afterlength still ends at the tailpiece fret, so is no different to a standard tailpiece).
But the effect on timbre is much more profound on mandloin family instruments, where afterlength ringing can make an otherwise good instrument sound really tinny - Find a mandolin or OM with no afterlength damping and play it with you hand clear of the strings, then rest the side of your hands on the strings behind the bridge and play again - the difference is profound. The sliding cover on a 'standard' mandolin tailpiece should have a felt pad under it to damp the afterlength (that is what the cover is for) but for some reason the pad isn't fitted on a lot of modern instruments. As GP will tell you, a heavy tailpiece helps a lot, and bowl-back players (where the strings terminate on simple pins on the end of the instrument) often either use a damper that clamps onto the strings, or weave a £1 note between the strings to damp the afterlength.
# Posted on January 5th 2010 by skreech
Re: How to string an instrument with scale length 19.5 in?
So apparently my spring analogy wasn't convincing.
I'm still going to try to avoid using the term "tension," since I think it's being used in at least two different defintions here. The most common seems to be refering to the "tautness" or the degree of stretch in the string. This is what must remain constant over a given vibrating length in order to maintain the same pitch.
Can we agree that, in order to maintain the same pitch as a fixed bridge instrument, the string length between the bridge and tailpiece must be stretched to the same degree as the vibrating length?
Does this afterlength stretching come for free? Of course not. Stretching four inches of afterlength requires just as much force as stretching four inches of vibrating length. Right?
If it takes 10 pounds to stretch the vibrating length to pitch (as on the fixed-bridge instrument), then it takes 10 pounds plus a little extra to stretch the vibrating length plus the afterlength. If not, then what stretches the afterlength? The force has to come from somewhere.
"I think you think that a longer string needs more 'pull' to produce the same tension, is that right?"
Avoiding the word "tension," I would say that a longer string needs more pulling force to stretch a segment of the string the same amount.
I just read the Lutherie Myth/Science link more closey. The word "tension," as used in the article, properly applies only to a string with no afterlength (or beforelength). From the article:
"Conventional wisdom has it that a number of other factors affect string tension. Some of these are (in no particular order):
The length of the string between the string anchor and the saddle of the bridge;
The length of the string between the tuning machine post or peg and the nut;
The breakover angle of the string at the bridge and/or the nut;
Once again, looking at the formula it is clear that none of these have any affect whatsoever on string tension."
The confused usage of "tension" makes it a circular argument.
# Posted on January 5th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Wow... this discussion has been most educational for me. Thank you all for being so interesting and helpful.
First thing: after learning how to actually measure scale length (distance to 12th fret x 2, not distance nut to bridge) thanks to exploring some of your guys' links, I have discovered that the _real_ scale length of my instrument is actually only 19 inches.
So, Skreech, it could have been that the bridge was in the wrong place, (I've taken all the strings out now so the bridge has moved), but I don't think so since it was in tune up for the most part, and the harmonic at the 12th fret was the same pitch as the fret.
I think what I'm going to do is just order the lightest gauge mandola strings I can find, maybe tune them a whole step low and capo up to get CGDG or farther for GAEA. That'll be nice considering I'm used to Mandolin and unused to stretching my fingers. Don't think there should be any problems with that, with what you guys have been telling me.
Thank you Arthur for the string ordering links, especially, and
And thank you all for helping to educate me on how string tension works... I wish I had known about all this a couple years ago... maybe I would have had a more interesting High School science project.
# Posted on January 5th 2010 by twitchard
Re: How to string an instrument with scale length 19.5 in?
Bob. *Hypothetically* ('cos it may do damage) lay an instrument with a slotted head flat on a table with the head sticking over the end, run the string over the bit you would normally wind it round and hang weights on it until it is in tune. The weight you need will be the same no matter how much string is between the bridge and the tailpice and the nut and the weight.
If you were to increase the length of string between the bridge and the tailpiece (e.g. shorter tailpiece) that extra length would need to be stretched (say for example by 1mm) . The weight would drop by 1mm. The string would still be in tune.
Here comes the physics - the energy to stretch the string came from the difference in potential energy between the weight were it was and the weight 1mm lower. The energy is in the stretched string (same as in a kids catapult pulled to throw a stone). It is the energy you would neet to lift the weight by 1mm. It is energy that would become kynetic energy when the string breaks at the bridge and the end flies back and hits you.
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
Sorry, it is 1mm's worth of the energy that would become kynetic energy.
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
#Posted on January 5th 2010 by Bob himself:
"So apparently my spring analogy wasn't convincing."
"The confused usage of "tension" makes it a circular argument"
It isn't that your analogy wasn't convincing, it was simply wrong. Tension isn't just a vague term meaning 'tightness', it is a scientific term, defined as 'force per unit cross sectional area' . So if your springs have a cross sectional area of 1 square mmm, and you apply a force of 10 Newtons, the tension will be 10N per mm sq. And that will be the same however long the spring is. Certainly a longer spring will extend more, but that doesn't mean it is under more tension, or more force is being applied.
# Posted on January 5th 2010 by skreech
Re: How to string an instrument with scale length 19.5 in?
screech - you embarrased me into turning round and opening a textbook, which I had been to lazy to do. What I read under little drawings of with ropes, spring balances, weights and pullys is that 'tension' has the same units as 'force' . So if you replace the machine head with a hanging 10lb weight the 'tension' in the string, and the 'force' acting on the tailpiece, is 10lb.
And this has nothing to do with stretching, different chapter in the book for that, which says that the thing that has units of lb per square inch is 'stress'. The stretching it causes is 'strain'.
For an instrument string, at the level of this discussion, (meaning I am not going to read yet another chapter in the book) stress and strain are simply related so it does not matter which of them influence the pitch of a length of string. But its them that do it.
And I'm steering clear of Newtons because its a North American textbook and all the examples are in what I know as 'Imperial' units but it refers to as 'the British system'
But the upshot of what is illustrated in the little drawings is what you and will morgan are saying.
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
Sorry. skreech , not screech. '... little drawing with ropes ...'
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
"Tension isn't just a vague term meaning 'tightness', it is a scientific term, defined as 'force per unit cross sectional area'."
More specifically, tension in a string is the force pulling the string. That's exactly one of the points I tried to get across earlier. However, the "tightness" of the string over its vibrating length has also been referred to as tension, which is why I've been trying to avoid using the term "tension." Further confusion comes from referring to textbook models of strings under tension where it's not always clear that the textbook string is presumed to be inextensible. But extensibility/stretching is the essence of this discussion. That's why I tried to use a spring analogy.
If my analysis is incorrect, will someone please tell me exactly where and why? Specifically, to repeat...
>Can we agree that, in order to maintain the same pitch as a fixed bridge instrument, the string length between the bridge and tailpiece must be stretched to the same degree as the >vibrating length?
>Does this afterlength stretching come for free? Of course not. Stretching four inches of afterlength requires just as much force as stretching four inches of vibrating length. Right?
>If it takes 10 pounds to stretch the vibrating length to pitch (as on the fixed-bridge instrument), then it takes 10 pounds plus a little extra to stretch the vibrating length plus the >afterlength. If not, then what stretches the afterlength? The force has to come from somewhere.
Now for a bow and arrow analogy. Without the arrow. Suppose you have a bow - the old fashion kind without the pulleys - with a fifty pound draw. It takes fifty pounds of force to pull the string back to your ear. In the center of the hand grip, on the outside, you have an eyelet. Pass the string of another identical bow through the eyelet so that the two bows are now in series, so to speak. Now, assuming your arms are extra long, pull the outer bowstring. Do you really think you can pull both bows to full cock with the same fifty pound force?
# Posted on January 5th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Bad idea with the ">" thingies. Sorry.
This is fun, but I have to be away for a couple of days.
# Posted on January 5th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
Suppose you have two spring balances, that will weigh up to 50lb (more likely 56 lb, 1/2 cwt - they exist). Hook one up to a beam. Pull on it until it reaches 50lb. Stop pulling and hook the second balance onto the bottom. Pull on that (and so the other one) until they both read 50 lb. Are you pulling any harder ?
Stop pulling and hook a 50lb weight on the bottom. What does the top one read ? What does the bottom one read ?
How is that different to the bows ?
ALL strings are extensible, the example in my textbook was an iron rod.
Experiment is better than intuition.
Intuition says that when you let go of an apple it falls because nothing is holding it up. It took thousands of years before a very clever guy to work out something was pulling it down. He also, wrote out, in latin, all the rules about force and tension etc. Before wikipeidia even !
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
Hi David,
If experiment is better than intuition, how come nobody realised before Newton that something was pulling apples down? The experiment had been carried out countless billions of times.
# Posted on January 5th 2010 by Bernie 29
Re: How to string an instrument with scale length 19.5 in?
Ha, Bernie 29
Response 1: The was two seperate paragraphs, the second one was just airing concern about intution. Will that do ?
Response 2: I think (but I'm not going to check) that it was experiments (and observations of the planets etc) not intuition that resulted in newton's laws of motion which led him to point out that something was pulling the apple.
But most of us, informally at least, still think of it falling because nothing is holding it up - and that's the sort of thought that needs questioning when the strings start breaking (unless, as I guess skreech can tell us, we instead rely on the experience of luthiers and their experiments over the centuries)
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.
..........................................................................................
That makes it sound like intuition played a major role at the beginning.
# Posted on January 5th 2010 by Bernie 29
Re: How to string an instrument with scale length 19.5 in?
First definition Google offers for intuition is "instinctive knowing (without the use of rational processes) " The pensive meandering of a scientist and mathematician who said he stood on the shoulders of giants is hardly likely to be without the use of rational processes. Inspiration maybe. Even if he was also an alchemist (though I had better get in first with that).
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
#Posted on January 5th 2010 by david_h:
"screech - you embarrased me into turning round and opening a textbook, which I had been to lazy to do. What I read under little drawings of with ropes, spring balances, weights and pullys is that 'tension' has the same units as 'force' . So if you replace the machine head with a hanging 10lb weight the 'tension' in the string, and the 'force' acting on the tailpiece, is 10lb"
I stand corrected on the definition of tension, I was confusing it with stress, but in this situation it makes no difference, because we are considering a string with a constant cross sectional area.
#Posted on January 5th 2010 by Bob himself
"Now for a bow and arrow analogy. Without the arrow. Suppose you have a bow - the old fashion kind without the pulleys - with a fifty pound draw. It takes fifty pounds of force to pull the string back to your ear. In the center of the hand grip, on the outside, you have an eyelet. Pass the string of another identical bow through the eyelet so that the two bows are now in series, so to speak. Now, assuming your arms are extra long, pull the outer bowstring. Do you really think you can pull both bows to full cock with the same fifty pound force?"
Yes. If you pull the two bows in series with 50lbs, they will both fully extend. You are doing twice as much work as you would pulling a single bow, but the extra work is in the form of doubling the distance, not doubling the force. (work = force x distance). If you put the two bows in parallel, then you would need double the force, but the distance would be the same, and the work done would be the same, and exactly double what it would be for a single bow.
To translate that back to our musical instrument, if you have an instrument with a long afterlength behind the bridge, yes, you will have to do more WORK to tension the string to a given pitch, but the extra work is in the form of extra distance, not extra force - you will have to turn the machine head through a greater angle, but you will not need to apply any more force.
# Posted on January 5th 2010 by skreech
Re: How to string an instrument with scale length 19.5 in?
Yes. And if my spring balance analogy was any use (maybe a less surprising result ) then they would both read 50 lb but hanging the weight on the two in parallel would have them both reading 25lb.
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
You could attach the balances in line with the bows. Using meathooks or something.
# Posted on January 5th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
Hi David_h,
If you hang a 50 lb weight on two spring balances in series, wouldn't the top one read 50 lb + the weight of the bottom one?
# Posted on January 6th 2010 by Bernie 29
Re: How to string an instrument with scale length 19.5 in?
Yes. I was just trying to quickly connect my analogy to skreech's good description of what the bows would do in the hope that it would help explain the 'counterintuitive' result to Bob when he gets back.
There have been other approximations throguhout.
# Posted on January 6th 2010 by David50
Re: How to string an instrument with scale length 19.5 in?
I’ve been on a road trip, which gave me some uninterrupted quiet time. I turned off the radio and, somewhere between Atlanta and Spartanburg, I had a Doh! moment:
I’ve been thinking about this as a system in static equilibrium, but I wasn’t considering that, in order to stretch the system into that static equilibrium, somebody has to do some *work,* as screech says above. So, thanks for the discussion and apologies to twitchard for rat-holing the topic.
Guernsey Pete blames the educational system. I blame creeping senility.
No excuses.
# Posted on January 7th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
I meant "skreech."
# Posted on January 7th 2010 by Bob himself
Re: How to string an instrument with scale length 19.5 in?
I'm now searching for two spring balances to try to perform the experiment described.
Hmmmmmm.
I'll believe it when I see it, but, logically, both balances will record the same weight, give or take the weight of the second balance, but I must see it to be convinced.
King Charles II, him of the spaniels, was one of the earliest of the British monarchs to be interested in science; he once asked his courtiers how was it that, if you have a goldfish bowl full of water, and you then put a goldfish in, it doesn't displace any water ? They argued about this for days till one of them tried it - of course, it DOES displace water ! The object of the question was to show that only experiment will verify a theory.
So I want my two spring balances......
# Posted on January 8th 2010 by Guernsey Pete