Intonation - what's it all about?
Intonation is that attribute of a string musical instrument that enables it to produce perfectly true notes - i.e., neither sharp nor flat - when the strings are stopped at every fret position. While at face value this would seem like an obvious statement as well as what is expected from a musical instrument, in reality it is a difficult goal to achieve and an expectation that is not always met. In order to be successful in this effort, there are several issues that must be considered.
The first is the complication of dealing with the various gauges of strings that are needed to provide the instrument with the entire range of notes it is designed to produce. Thinner strings are needed for higher notes, and thicker strings are needed for lower notes. As string gauges change, several things happen to keep them from noting true (why this happens will be discussed further in this article). Suffice it to say that to manage this range of string gauges, a compensation needs to be made for each different gauge's length, and this adjustment is made at the bridge in what is called intonation compensation or intonation correction.
Intonation correction is the process of positioning the contact point for each string on the bridge's saddle so that the string notes (intonates) properly at each of the frets up and down the neck. Different gauges of strings require slightly different string lengths because thicker strings tend to change pitch more quickly than thinner strings when they are pressed and stretched to the fretboard. (The string is being "choked" as it is pressed down and that causes its pitch to increase.) So, as the gauge increases, the "string scale" (not the "fret scale") needs to be increased slightly. This is why you see the small saw-tooth stepping on the top of the bridge saddle for each set of strings.
The bridge saddles on most solid-body guitars feature adjustable contact points for each string so that the optimum intonation can be fine tuned. But mandolins and banjos feature fixed intonation points and are basically an average contact point to enable the use of several gauges of strings. (In reality, perfect intonation is only accomplished by having a bridge saddle designed with specific intonation correction for each specific set of strings.)
One thing that complicates achieving the perfectly-corrected saddle is that there are several ways to make a wound string. Wound strings are comprised of a core wire with an outer wire wrapped around it. And, there are several combinations of core wire size and wrap wire size that can yield the same final diameter string. As this diagram shows, a .034˝ string (for example) can be made with a .014˝ core wire and .010˝ wrap wire or a .016" core wire with a .009˝ wrap wire or a .018˝ core wire with a .008˝ wrap wire. And, of course, there are many more combinations for this and other gauges of strings.
If you have a bridge that intonates perfectly for one brand of mandolin strings and you change to another brand that has different core/wrap wire combinations on its wound strings - even though the package states the same overall diameter - the bridge may intonate differently.
One question that often arises is "If the intonation position moves back as gauges get larger, then why is the intonation point for the third pair of mandolin strings (D) - which has a larger gauge than the second pair of strings (A) - closer to the nut?" Good question! While the third pair of strings (D) is a larger overall gauge, the third and fourth strings are wound strings in which the core or center wire is actually a smaller gauge than the plain (A) strings, so the intonation point must be closer to the nut.
We have two scale lengths at play here: the string scale and the fretting scale. The string scale is predicated on a particular gauge of string's intonated length; the fretting scale is predicated on the fret locations in a straight line on top of the frets. For example, the F5 mandolin has a 13-15/16" string scale but a 13-7/8" fretting scale (because the strings are raised at an angle above the fretboard, the distance from nut to top of bridge is longer than the distance from the nut to a point directly under the bridge in a straight line across the top of the frets). With guitars and mandolins, the string scale is usually based on the second string's length, and the fretting scale is based on the middle string's length.
Why don't fiddles have an intonated bridge? Another good question. First of all, the violin (fiddle) bridge wins the medal for the ultimate bridge design. In the violin bridge, there is no direct route of the strings' energy to the soundboard. The energy of each string is attenuated by an opening between the string's contact point at the top of the bridge and the bridge feet. But aside from bridge design, the intonation of the strings on a violin is controlled by the location of the musician's fingers. In the absence of frets, the musician locates and perfects the strings intonation as each note is played.
Some banjo bridges are made with intonation correction notches. For those banjo players who choose straight, non-intonated bridges, they usually turn the bridge slightly counterclockwise to create a pseudo-intonation correction.
Around 1918, Gibson engineers began working on bridge saddles with adjustable contact points. These were made in the form of inserts that fit into a groove on the top of the bridge and could be interchanged or turned around to achieve the ideal intonation. Aside from the fact that the parts were fragile and occasionally got misplaced, the movable insert system presented the musician with too many options as well as parts that were rather fragile, and frustration in using it caused the design to be very short lived in Gibson's accessory line.
Intonation correction first requires that the bridge is in the right place. Secondly, the action must be correct; too high an action requires that the strings are drawn further to the fretboard which "chokes" them and increases their pitch.
In the final analysis, there's a lot to think about in trying to achieve perfect intonation on all strings at all fret positions.
One major change we have made in the
bridges we manufacture is that the intonation notches, as a group, are positioned on the centerline of the saddle to keep the saddle from cocking at an angle on the bridge's posts. Another feature of our bridges is that rather than copying the intonation positions of the early Gibson bridges, the intonation corrections on our bridges are designed for today's strings with their unique elastic properties
