Hi folks, I've been building for awhile and came across something I hadn't noted before. It appears the distance between the 12th fret and the saddle of the high E string is about three to four millimeters longer than the distance between the nut and the 12th fret.
I've been using an IBEX ruler with the various fret scales to locate bridges so haven't really paid attention to actual string length. I've checked this on the 25.4 and 24.9 instruments as well as a classical guitar with a 650mm scale. I should note there isn't any intonation issues on this string.
I'm really sure some of you may have some thoughts about this...
Most fretted instruments have "compensated" saddle positions that make up for the intonation error caused by the string stretching as it is fretted.
Here's more on that:
I'm aware of everything in the links you referenced on your website. I'm looking for a more basic explanation. i.e. in the "perfect world" the basic vibration of a string at when fretted at the mid-point should be twice the frequency of the unfretted string, however it's not a perfect world and is there something else (diameter and mass) of a the string that means the next octave of the open string is not exactly at it's center...
From what I understand, strings of different mass and different tension vibrate differently but the issue with intonation is that we stretch the string when we note it, thus increasing the tension slightly and raising the pitch. The bridge is slightly further away because we need that distance to compensate for the stretching.
In my college physics classes we had fun in a lab with lengths of string and weights. The string was long enough to actually see the nodal points as it vibrated. A weight on the end of the string allow us to vary the tension and thus the "pitch" of the string. The changes in tension were reflected in changes in the number of nodes as the string vibrated which, in turn, reflect the shortening or lengthening of the wave length/frequency. It all boils down to the idea that we have three ways of determining the pitch of a string, density/size, tension and length. To make playing practical, we establish a set density/size and tension then vary the length to change notes, Unfortunately, our method for changing the note also interfers with the tension thus we have compensation at the bridge
Besides that, our scale of "equally tempered" intervals between notes leaves us with a scale that insures that our instruments are never really quit in tune. It means that a noted string will always play a bit out of tune in relation to that same string played open or even on another fret. This can be "fixed" in part with the compensation and the fret spacing. In essence, the fret spacing we use is a compromise between the notes we want and the reality of our temperament. I'm told that it is possible to build a guitar with frets that fix this issue but the examples I've seen are extremely complex and appear to have been designed by Dr. Suse. In other words; It doesn't appear to be worth the trouble.
I think we may be talking about different things. FRETTING the string in the center means to press it to the fret, and the result is always to stretch the string, causing it to go sharp. So, the saddle is moved to compensate for that, and we add an appropriate distance for that.
Now, if you mean that the open string is not precisely in tune with its octave harmonics, that might be partially explained by air friction of the bending vibrating string or by air friction.
Thanks Frank! We have the same understanding of fretting but the stretching of the string I did not take into account. Your explanation (and Ned's) points out the need for compensation for the string stretch while fretting.
Ned, we had the same physics class(es) but I didn't get to do the cool lab you described!
Thanks again guys!
Sorry for the long winded lecture. I guess I didn't get what you were asking.
The lab was, well, a long time ago but, as a guitar player, it made a huge impression on me. We has to do all sorts of unfun math to figure the weight and tension on the string ( which was actually connected to an oscilator at the end.) In the case of the experiment, we fixed the vibration and the length and varied the tension. When the tension was just right, the node points in the string appeared to be perfectly still while the string oscilated widely between those points.
We first had to get the string to vibrate in two clean sections with one node, as we added weight, the number of nodes doubled with vibrating string between. If the tension wasn't right, the vibration was not clean and the nodes were "muddy" rather than stable. It made me understand why A4 is 440 hz and not "around" 440hz.
I spend a year in that man's class and that's all that I remember clearly of his teaching. He was a very poor teacher but some of his labs were fun.