Setup Specs

[bausin]

>> ... the axis between the string and frets needs to be increased to accommodate for this elliptical orbit of the string, which is why relief is so dependant (sic) on the player.

Why would you need to increase the action, via relief no less, because of a horizontal component of the string motion?

[charles Tauber]

Originally Posted by bausin

Why would you need to increase the action, via relief no less, because of a horizontal component of the string motion?

The concept is simple.

A string is stretched between two end points: the nut and the saddle. They define the height of the string at the end points relative to a reference plane.

When at rest, the stretched string forms a straight line between its end supports. A force is exerted on the string that displaces the string to one side of the string's at-rest position. When the force is removed, the elasticity in the string causes the string to be displaced to the opposite side of the string's rest position by an amount (about the same as) the initial displacement. The vibrating string then oscillates back and forth on each side of the string's rest position. The greater the initial displacement, the greater the magnitude of its oscillation. Practically, if one plucks/strikes a string harder, the amplitude of the oscillation is larger.

The displacement (amplitude) of the vibrating string is (theoretically) zero at the end-supports of the string - the nut and the saddle - and is a maximum at mid-span of the string. For a fretted instrument, such as a guitar, sufficient space is required to allow the string to oscillate without interference from the frets. There are two ways to achieve that. The first is to raise the end supports of the string sufficiently high that when the string is plucked - displaced from its rest position - the maximum amplitude of the string - at the string's mid-span - still clears the frets. Doing so, makes the guitar more difficult to play because the strings need to be depressed further to fret a note due to the higher initial position of the strings relative to the frets.

The second way to accommodate the maximum amplitude of the vibrating string is to have the surface of the frets assume a curvature that is similar to that of the vibrating string. Practically, this is achieved by introducing a curvature into the playing surface and frets that is known as "relief". Having the surface of the frets assume a curvature that accommodates the amplitude of the string, allows the strings to be closer to the frets, reducing the effort required to depress the strings against the frets, fretting notes.

Ideally, to ensure the greatest ease of depressing a string to a fret, the strings would be a uniform height above the frets over the entire length of the string. Introducing a curvature into the playing surface (neck/frets) results in some frets being closer to the strings than others. A playing surface that is concave will have the greatest distance from fret to string at the midspan of the curvature. Conversely, a playing surface that is convex (back-bowed) will have the greatest distance from fret to string at the ends of the playing surface (e.g. the nut). Thus, in some cases of excessive curvature - convex or concave - where the nut and saddle heights are correct, a simple adjustment of the curvature is all that is needed to restore ideal playability.



To recap, there are three things at play: the height of the string at one end support - the nut - the height of the string at the other end support - the saddle - and the amount of curvature in the playing surface (relief). The three of these work together to minimize the height of the strings relative to the surface of the frets while ensuring the frets do not interfere with the amplitude of the vibrating strings .

[lar]

Originally Posted by bausin

>> ... Why would you need to increase the action, via relief no less, because of a horizontal component of the string motion?

Bausin,

Probably because the string vibration always has a vertical component. It's never plucked purely horizontally (parallel to the top). And the harder it's plucked, the greater the vertical component. And each player is different: for the same string displacement (volume), some players may give the string more or less vertical motion (related to individual 'technique').

On another note: it's interesting that Dan's book says that relief is all in the first 7-8 frets of the neck. The rest of the neck remains flat. So with .01" relief, the neck is flat from fret 14 up to fret 7, then curves away from the body (up, if it were lying on its back on the floor) to the nut. This means we are measuring relief just where the the neck starts to curve. And what you measure as 'relief', at the 7th fret, isn't the total amount of neck curvature. It's just a convenient way to measure neck curvature.

I've done mathematical modeling all my working life. I have to believe this has all been modeled by someone - and calibrated to actual results.

Larry

[bausin]

>> The second way to accommodate the maximum amplitude of the vibrating string is to have the surface of the frets assume a curvature that is similar to that of the vibrating string.

That makes sense for an open string, but I often like to play notes up the neck for variety. :-)

If you look at the concave diagram, you will see that playing a note on the lower frets will give some extra space for the string to vibrate at its midpoint. However, playing in the middle of the neck, say at the 8th fret, the string will have less room to vibrate at its midpoint than with a straight neck.

A straight neck will give a constant clearance from any fretted string to the next higher fret.

[charles Tauber]

Originally Posted by bausin

That makes sense for an open string, but I often like to play notes up the neck for variety. :-)

If you look at the concave diagram, you will see that playing a note on the lower frets will give some extra space for the string to vibrate at its midpoint. However, playing in the middle of the neck, say at the 8th fret, the string will have less room to vibrate at its midpoint than with a straight neck.

A straight neck will give a constant clearance from any fretted string to the next higher fret.

Seems like this might be your answer, under Thoughts on Neck Relief: http://www.bryankimsey.com

[Rodger Knox]

Actually, there are two waves going in opposite directions on the string starting where it is plucked, so the maximum amplitudes occur at the plucking point and the same distance from the nut(or fret on a fretted string) as the distance from the plucking point to the saddle. It starts out that way, but since strings have mass and stiffness, it doesn't stay that way long.

[bausin]

The only reason I can see for having a very small amount of relief is that you can be sure the neck is not back-bowed.

[mirwa]

Originally Posted by bausin

The only reason I can see for having a very small amount of relief is that you can be sure the neck is not back-bowed.

Some very good explanations have been given.

Many times we have to accept certain points even though we personally cannot comprehend it.

Example. With my eyesight I can see the world around me is flat, but science has proven to me the earth is round, I just have to accept that fact even though I cannot physically see it.

Good luck with your repair adventures

Steve