Are there coefficients of elasticity for the two different materials (gut, metal) that must be taken into account?
Leonard On 12/20/13, 11:48 AM, "David Smith" <d...@dolcesfogato.com> wrote: >Hi Alexander, >Thank you. Since my question is unrelated to fretting and is only related >to tuning Pythagoras's relation does not apply. The Mersenne relation >does apply when tuning and the derivative of > F ~ sqrt(T) >Is > F'(T) ~ 1/sqrt(T) > >This is where my thought that increasing the a higher tension string will >be less sensitive to changes in tension than a lower tension string. > >When I plot the partial derivative of F'(T) using the values for this >string I find that the sensitivity is actually quite small; less than >1/10th of a hertz per Newton. This is why I was wondering what people's >experience has been with gimped gut strings and if changing the nominal >tension of the string (by changing the diameter) would make a >difference. The general answer is no and that changing the density of the >string, by going to a different material is more effective. Or changing >the length by going to a bass rider was another suggestion. > >The engineer in me is trying to understand this numerically. Probably >more useful to get back to playing and enjoying my instrument and live >with its personal characteristics. > >Thanks all for the discussion. > >Regards >David > >Sent from my iPad > >> On Dec 20, 2013, at 3:09 AM, alexander <voka...@verizon.net> wrote: >> >> >> David, >> >> according to Pythagoras, When the tension on a string remains the same >> but the length L is varied, the period of the vibration is proportional >> to L. >> >> According to Mersenne - When the length of a string is held constant >> but the tension T is varied, the frequency of oscillation is >> proportional to sqrt(T). >> >> When the string is pressed down to a fret, both its' length and its' >>tension are increased. Increase in length produces more effect, as the >>effect of tension is square-rooted. >> >> At the low low octave, from G (98 Hz) to A (110 Hz) are just 12 >> (twelve) notches (or however one would like to describe the little >>Herzes) >> At the next octave up, from G (196 Hz) to A (220 Hz) are 24 notches >> >> When we consider, that the length of the string (since we use the same >>instrument, just drop or raise the pitch of the string in question) will >>increase by the same value, let's call it a "6", >> >> That "6" in the low low octave will increase the Frequency almost by a >>half tone, while in one octave up - just by a quarter. >> >> Therefore the string deformation of a low tension string at the lower >>pitch will change that pitch noticeably much more then at any higher >>pitch. >> >> alexander r. >> >> On Thu, 19 Dec 2013 21:17:49 -0800 >> "David Smith" <d...@dolcesfogato.com> wrote: >> >> >>> Thanks. I really appreciate the feedback. If Alexander gets a chance >>>to post >>> his formulas that would be great. I think I will continue to live with >>>it >>> since I have for many months so far. >>> >>> Regards >>> David >>> > > > >To get on or off this list see list information at >http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
