robocorpse Posted January 17, 2011 Share Posted January 17, 2011 Nerd thread alert, and some idle speculation Faced with some physics and maths I haven't got the time to work out, but I thought it would make an interesting thread. We all know longer scale lengths make for more tension on the strings. What I would like to know is the effect of the actual free string length on tension. I'll take 2 extreme examples. Headless bass: 34" scale length, 35" actual free string length. Feels taught Buzzard type bass with stop tailpiece and long headstock: 34" scale length, 41" actual free string length on top G. Feels loose. Removing the nut and keeping the same tension will lower the pitch. Removing the nut and keeping the same pitch will require higher tension. Buzzard feels floppier because the longer string is at a lower tension with less of the free vibration blocked off by the nut. Therefore it is dependant on the percentage of the taught string that is freely vibrating between nut and saddle. I have pondered this and never had the time to set it up on a test jig with a spring gauge and a calculator to experiment with exact values. My question: by how much does the extra meat between the nut and the tuners affect tension between a headless and a headed bass, assuming both are using identical strings? A whole gauge worth? This also has implications for people who like to downtune and dont want to fart around opening the nut out to .125, would a headless (or indeed a normal bass with an added locking nut) give enough extra tension to get away with .105 tuned to C? Quote Link to comment Share on other sites More sharing options...
ikay Posted January 17, 2011 Share Posted January 17, 2011 The formula for vibrating string tension/mass/frequency can be found here: [url="http://en.wikipedia.org/wiki/Vibrating_string"]http://en.wikipedia.org/wiki/Vibrating_string[/url] This formula applies to the vibrating part of the string (eg. between nut and bridge). From this it's clear that, mathematically speaking anyway, for a given string vibrating length, mass and tuned frequency, the tension will always be the same. However! This doesn't take into account the construction of the string itself which will affect the 'perceived' string tension or stiffness. For example round core strings have a softer feel than hex core which feel stiffer. I think there's probably some confusion here between the terms 'tension' and 'stiffness'. For a given vibrating length, mass, tuned frequency the string tension will be as per the formula but a hex string will feel 'stiffer' than a round core string. The free length of string above nut or below bridge has no bearing on the tension of the vibrating part of the string which will always be as per the formula. However (again), more or less downward pressure where the string passes over the nut and bridge saddle might well affect the perceived string tension or stiffness. The break angle over the nut or bridge is probably a more significant factor than the free length of string at either end. That's my tuppence worth anyway! Quote Link to comment Share on other sites More sharing options...
mart Posted January 17, 2011 Share Posted January 17, 2011 [quote name='Johnston' post='1092628' date='Jan 17 2011, 03:41 PM'].... The only way I could think above the nut or behind the bridge would make a difference is if you have a high action or doing some string bending. If you have more free length then you would get give over say your 41" rather than 35" for the headless. So it should have more stretchyness because there is more string to stretch. If that makes sense.[/quote] I agree with this in that when you displace the string (e.g. when bending a string) you are stretching it slightly, and the increase in tension will be proportionate to the increase in string-length [i]as a fraction of the total free length[/i], i.e., 41" instead of 35" in the case above. Of course, this assumes your nut is lubricated enough to let the string pass over it quite freely. But I don't think this only applies when you have a high action or are bending strings: I think you notice that difference whenever you fret a note, or whenever you pluck a note - since both activities involve displacing the string slightly. I've no idea how you'd exactly measure this effect, but Johnston's suggestion seems a good idea. Quote Link to comment Share on other sites More sharing options...
ikay Posted January 17, 2011 Share Posted January 17, 2011 OK I agree that free string length (and break angle) can make strings feel more or less stiff/flexible. The issue in question here though is to do with string stiffness/fexibility, not string tension which is always as per the formula. The follow is from a guitar forum but the same principle applies. POST: "lets say i have two identical guitars except one has an original floyd rose (set to float) and the other has a tune-o-matic, which will have higher string tension?" REPLY: "The tension for a given note on a given scale length is always the same. It MUST be, otherwise it wouldn't be the same note anymore. What you are looking for is the term "stiffness". The longer the additional string length BEFORE the nut and AFTER the saddles - those two being the two pivot points - and the smaller the break angle, the less stiff the string will be when you try to bend it or even just press it down. But as soon as you set a whammy bridge to float, it'll have a certain "give", so when you bend or fret the string with your fretting hand, the bridge might tilt forward, detuning the rest of the strings ever so slightly. But if the trem springs are strong enough or you block the trem and your strings are locked at both ends, you successfully eliminated the pivot points, thus your Floyd equipped guitar will feel stiffer under your fretting fingers than any other non-locking guitar with the same scale length." Quote Link to comment Share on other sites More sharing options...
ikay Posted January 17, 2011 Share Posted January 17, 2011 This lutherie article explains what's going on: Human Perception of String Tension and Compliance in Stringed Musical Instruments - [url="http://liutaiomottola.com/myth/perception.htm"]http://liutaiomottola.com/myth/perception.htm[/url] Quote Link to comment Share on other sites More sharing options...
EssentialTension Posted January 17, 2011 Share Posted January 17, 2011 (edited) [quote name='ikay' post='1092705' date='Jan 17 2011, 04:32 PM']This lutherie article explains what's going on: Human Perception of String Tension and Compliance in Stringed Musical Instruments - [url="http://liutaiomottola.com/myth/perception.htm"]http://liutaiomottola.com/myth/perception.htm[/url][/quote] That's an excellent article as is [url="http://liutaiomottola.com/formulae/tension.htm"]http://liutaiomottola.com/formulae/tension.htm[/url] There are several threads on this and related topics already, for example: [url="http://basschat.co.uk/index.php?showtopic=81825&hl"]http://basschat.co.uk/index.php?showtopic=81825&hl[/url] [url="http://basschat.co.uk/index.php?showtopic=64841&hl"]http://basschat.co.uk/index.php?showtopic=64841&hl[/url] [url="http://basschat.co.uk/index.php?showtopic=30385&hl"]http://basschat.co.uk/index.php?showtopic=30385&hl[/url] Edited January 17, 2011 by EssentialTension Quote Link to comment Share on other sites More sharing options...
robocorpse Posted January 29, 2011 Author Share Posted January 29, 2011 Lovely, thats sorted it out. "Compliance" was the term I meant, so I'm definitely sticking 35s or 40s on my next headless project. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.