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 <[email protected]> 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" <[email protected]> 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
>>
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