It is already known that reducing the distance between the ball end and saddle improves tuning stability, hence the deep trem block holes in modern designs by companies such as Fender and PRS that contrast with the original shallow trem block holes of the original vintage Fender design. The experiments outlined in this post provide confirmation that deep trem block holes do indeed improve tuning stability.
It should be noted that drilling the holes even deeper than those used in American Standard Strat would mean the string knots would catch on the bridge plate (causing further problems). It is of course a matter of taste whether players prefer the authenticity of the vintage shallow trem block holes or the improved pitch stability of the modern deep trem block holes. I suspect that the difference in tone on deep drilling the holes on the block is negligible (while the mass of the block is significant to tone) but that was not the subject of this experiment.
In order to test the effect of the depth of trem block holes on tuning stability, experiments were carried out on my Fender Stratocaster (Oiled Ash 10 for 15 Limited Edition, but functionally the same as the American Standard) fitted with Kemp Strings Standard 10s and modified with Graphtech String Saver Saddles, Trem Block by Callaham Guitars and ESP Arming Adjuster. The pitch of the strings, given in cents (percent of a semitone) relative to the nearest chromatic note, was measured using the ReaTune plugin (200 ms window size) in Cockos Reaper software in the following sequence:
- – The “Before” tuning measurement was performed with the guitar tuned initially using the “train your trem using pull ups” method as described in my YouTube video: https://youtu.be/lNB0NeC12LY
- – The “Up” tuning measurement was then performed with the trem bar pulled up (and supported by putting metal objects between the trem block and body) and the tuning measured again
- – The “Release 1” tuning measurement was then performed with the released back to rest again and the tuning remeasured
- – The “Down” tuning measurement was performed after the tremolo bar was pressed down (and supported by placing metal objects between the bridge plate and body) and the tuning measured
- – The “Release 2” tuning measurement was then performed with the tremolo arm bar released back to rest again and the tuning remeasured.
- – The “Reset” tuning measurement was then performed after the trem was quickly given a full pull up and released (to reset the pitch)
The “Net” value in the tables is the pitch instability experienced by the player between pull ups and dives on the tremolo arm. This is calculated using the difference in pitch after a pull up and release (the “Release 1” column) and after a dive in pitch and release (the “Release 2” column).
The first measurements were carried out with the “vintage correct” shallow holes on the trem block (so that the string ball ends are almost flush with the back of the guitar). The results were as follows:
“Vintage correct” shallow holes (distance between ball end and top of saddle = 46mm)
Next the holes were deep drilled in the mechanical workshop of the School of Physics and Astronomy at the University of St Andrews. The resulting trem block then had identical hole depth to the American Standard trem block. The result were as follows:
Deep drilled holes (distance between ball end and top of saddle = 26mm)
The results show that the tuning stability is improved by deep drilling the holes in the trem block as the numbers in the “Net” pitch column (that show the difference in pitch between a pull up and relase and a dive and release) are closer to zero after deep drilling. The pitch drop after a dive in pitch was an average of 18 cents for the vintage style shallow trem holes (with a standard deviation of 10 cents). After deep drilling, the pitch drop after a dive was an average of 8.5 cents (with a standard deviation of 6 cents).
Making deep trem block holes (in the style of the standard American Strat) approximately halves the distance of string between the ball end and the top of the saddle and approximately halves the tuning errors (measured in cents) in comparison to “vintage correct” shallow trem block holes.
It is likely some alternative designs such as the Sophia 2:22 Tremolos by Coherent Sound in Light may also be effective in further improving pitch stability in comparison to the modern American Standard trem design (by reducing the ball end to saddle distance and angle around the saddle), but I have not yet used one in order to check for myself. Pitch stability with floating trem use can of course be optimised by eliminating the distance between ball end and saddle altogether by cutting off the ball end and using locking bridge designs such as those of Floyd Rose.
In terms of the physics of the situation, the cause of tuning differences between pull up and release and dive and release is friction between the guitar strings and the saddles at the bridge (assuming the knife edges, nut and string trees etc. are in good condition). Such friction is the subject of a journal paper on the Applicability of the Capstan Equation to Guitar Strings by Tom Groves (a student at the University of St Andrews) and myself (Jonathan Kemp of the University of St Andrews and Kemp Strings). The results indicate that the typical tension differences either side of the bridge are determined by the angle that the string forms either side of the saddle, and this tension difference does not depend on the distance of string behind the saddle. The smaller the distance of string behind the saddle, the smaller the distance of string that displaces over the saddle for this given tension change behind the saddle. This means that the tension change (and pitch differences) in the sounding length will be minimised by reducing the distance behind the saddle.
In addition to confirming the benefits of reducing the distance between ball end and saddle, it is notable that the Kemp Strings used meant that the relative tuning of the low E, A, D, and G strings are in good agreement for both pull ups and dives for both deep drilled blocks and vintage shallow holes.