In theory, the mass of the string, the tension and absolute pich are irrelevant as things are expressed in ratio.Michael Lazar wrote: ↑Sun Nov 05, 2017 3:16 pmThis is a question about saddle compensation. Does anyone here know how many cents a note fretted at the 12th fret will be flattened (lowered) for each millimeter of saddle setback using medium tension nylon strings tuned to A440, a 650mm scale and an action height of 4mm at fret 12? I can appreciate that the values may differ among the different string diameters and other variables but any sort of theoretic answer would be helpful.
The simple answer, in the real world, is 3 cents per millimetre.Michael Lazar wrote: ↑Sun Nov 05, 2017 3:16 pmDoes anyone here know how many cents a note fretted at the 12th fret will be flattened (lowered) for each millimeter of saddle setback using medium tension nylon strings tuned to A440, a 650mm scale and an action height of 4mm at fret 12?
Doan's answer is technically correct and responds directly to Michael's (over specified) question. You don't need to know the action, the material properties or the tuning to figure out the answer, as Doan correctly points out. However, in practice, Doan's response is problematical. The reason is that when you apply compensation at the saddle, it applies to all the notes on the fretboard and the open string. So the compensation will flatten the open string as well as the note fretted on the twelfth fret. Usually, the open string will then be tuned back up to pitch, which will also sharpen all the fretted notes. At the twelfth fret (half scale length) you get exactly half the tonal change that you might have thought you were going to get, so the "real world" answer is half of what Doan calculated.bacsidoan wrote: ↑Sun Nov 05, 2017 4:20 pm
In theory, the mass of the string, the tension and absolute pich are irrelevant as things are expressed in ratio.
The frequency of a vibrating string is calculated by this equation:
where:
l is length of the string
T is tension
Mu is mass per unit length
In this case l = 325 mm (at 12th fret)
Let's call f2 is the original frequency at 325 mm and f1 is the frequency at 326 mm
One can easily see that the ratio f2/f1 is 326/325 = 1.0030769230769230769230769230769
From this one can derive the cent calculation between two frequencies according to this equation:
Plug in the number. The interval between f2 and f1 is 5.32 cents. In other words, each mm of saddle setback will drop the pitch by 5.32 cents at the 12th fret.
This is just a simplified calculation for 12th fret. If one goes up the register, the compensation will be progressively more and vice versa, progressive less for the lower registers.
Of course you are correct. I'm aware of that. I just tried to answer the OP's question directly. My calculation is based on the premise that if you keep everything the same and just move the saddle back 1 mm, the pitch at the 12th fret will drop by 5.32 cents. The pitck at the open string will drop half of it which is 2.66 cents. After the saddle compensation, if the player turn up the tension of the string to negate the 2.66 cent drop to keep the guitar open string back in tune then the fretted note at the 12th fret will drop 2.66 cents from the original frequency.Trevor Gore wrote: ↑Sun Nov 05, 2017 11:44 pmThe simple answer, in the real world, is 3 cents per millimetre.Michael Lazar wrote: ↑Sun Nov 05, 2017 3:16 pmDoes anyone here know how many cents a note fretted at the 12th fret will be flattened (lowered) for each millimeter of saddle setback using medium tension nylon strings tuned to A440, a 650mm scale and an action height of 4mm at fret 12?
Doan's answer is technically correct and responds directly to Michael's (over specified) question. You don't need to know the action, the material properties or the tuning to figure out the answer, as Doan correctly points out. However, in practice, Doan's response is problematical. The reason is that when you apply compensation at the saddle, it applies to all the notes on the fretboard and the open string. So the compensation will flatten the open string as well as the note fretted on the twelfth fret. Usually, the open string will then be tuned back up to pitch, which will also sharpen all the fretted notes. At the twelfth fret (half scale length) you get exactly half the tonal change that you might have thought you were going to get, so the "real world" answer is half of what Doan calculated.bacsidoan wrote: ↑Sun Nov 05, 2017 4:20 pm
In theory, the mass of the string, the tension and absolute pich are irrelevant as things are expressed in ratio.
The frequency of a vibrating string is calculated by this equation:
mersenne_eq1.png
where:
l is length of the string
T is tension
Mu is mass per unit length
In this case l = 325 mm (at 12th fret)
Let's call f2 is the original frequency at 325 mm and f1 is the frequency at 326 mm
One can easily see that the ratio f2/f1 is 326/325 = 1.0030769230769230769230769230769
From this one can derive the cent calculation between two frequencies according to this equation:
cent3.gif
Plug in the number. The interval between f2 and f1 is 5.32 cents. In other words, each mm of saddle setback will drop the pitch by 5.32 cents at the 12th fret.
This is just a simplified calculation for 12th fret. If one goes up the register, the compensation will be progressively more and vice versa, progressive less for the lower registers.
As expected, Frank gets it right here: http://www.frets.com/FretsPages/Luthier ... pcalc.html. Check his "extreme" example at the bottom of the page.
That's 'easy' for you to say!bacsidoan wrote: ↑Sun Nov 05, 2017 4:20 pmIn theory, the mass of the string, the tension and absolute pich are irrelevant as things are expressed in ratio.Michael Lazar wrote: ↑Sun Nov 05, 2017 3:16 pmThis is a question about saddle compensation. Does anyone here know how many cents a note fretted at the 12th fret will be flattened (lowered) for each millimeter of saddle setback using medium tension nylon strings tuned to A440, a 650mm scale and an action height of 4mm at fret 12? I can appreciate that the values may differ among the different string diameters and other variables but any sort of theoretic answer would be helpful.
The frequency of a vibrating string is calculated by this equation:
mersenne_eq1.png
where:
l is length of the string
T is tension
Mu is mass per unit length
In this case l = 325 mm (at 12th fret)
Let's call f2 is the original frequency at 325 mm and f1 is the frequency at 326 mm
One can easily see that the ratio f2/f1 is 326/325 = 1.0030769230769230769230769230769
From this one can derive the cent calculation between two frequencies according to this equation:
cent3.gif
Plug in the number. The interval between f2 and f1 is 5.32 cents. In other words, each mm of saddle setback will drop the pitch by 5.32 cents at the 12th fret.
This is just a simplified calculation for 12th fret. If one goes up the register, the compensation will be progressively more and vice versa, progressive less for the lower registers.
Alan Carruth wrote: ↑Mon Nov 06, 2017 6:00 pm...and we're back into the endless discussion of the deficiencies of Equal Temperament.