When you lower the pitch by releasing tension, there might be slack in the gears in the tuning machines, which might make the string go below the intended pitch.
By going further down and approaching the target note from below, there will be force applied to the gears and when you've reached the correct pitch the gears have less potential to move.
So your teacher is correct.
music.stackexchange.com/users/8682/Meaningful Username
Yes, as the strings are kept under tension better.
It works with all stringed instruments (inc. piano!), for the same reason.
Also, somehow, it seems easier to hear a note coming up to pitch rather than approaching it from above. '
We're tuning up'.
music.stackexchange.com/users/2808/Tim
There will often be some friction at various parts of the tuning linkage, as well as at the nut (where the string passes over).
At some points, including the nut, things may bind slightly.
Think about what would happens if the string is binding where it passes over the nut, both in the "tightening" and "loosening" cases.
If the string binds where it passes over the nut while the player is loosening it, then the portion of the string between the peg and the nut may be at lower tension than the main sounding portion of the string.
Each time the string is plucked, its tension will be momentarily increased.
Consequently, even if the tension difference at the nut wasn't sufficient to cause slippage while the string was resting, the act of playing the string might cause it to slip at some inopportune time.
If, by contrast, the last action was to tighten the string, then the portion of the string connecting the peg will if anything be tighter than the sounding portion.
If it's not "enough tighter" to overcome friction when the string is resting, it will be even less inclined to move when the main string is drawn more tightly (reducing the tension difference).
Although it's easiest to visualize the above behavior happening at the nut, it can also happen at other parts of the mechanical linkage.
For example, the peg might bind slightly such that it would stay put (at least for awhile) even if the worm cased to exist.
Ideally, the tuning gear would always ride against the worm, but if the peg binds, it might not turn to loosen the string unless or until the worm pushes it.
If one turns the worm enough to turn the peg 0.4 degrees, but the peg binds after turning only 0.3 degrees, then one would initially hear the string's pitch as though the worm had been tuned 0.3 degrees, but if the peg slips (as it likely would at some point) the tuning would change by an extra 0.1 degree.
As a principle, what's important is not whether the pitch of something is being raised or lowered, but rather whether one is pushing something in the direction opposite where it wants to be.
For most instruments, that would represent raising the pitch, but some electronic instruments which are tuned by adjusting inductors work in the opposite direction; I wouldn't be surprised if some mechanical acoustic instruments do so as well.
music.stackexchange.com/users/5603/supercat
Yes, because that is the way that the gears in tuning machines work best.
music.stackexchange.com/users/None/
Yes... on all the above.
Plus, in case it isn't mentioned in there somewhere, when a new string is a little sharp you might want to give it a gentle tug outward to make it flat, and then tune it up.
This way, if there's any looseness at the peg end, you can get rid of it.
music.stackexchange.com/users/10209/jackster12
Yes, your teacher is very correct there.
When you tune down, it outside slack on the strings, and gears!
This means your guitar's tuning may go below the level you wanted.
If you want to avoid tuning down, I recommend purchasing a chromatic/guitar tuner.
This helps you to reach near perfect pitch, so you should tune down less.
music.stackexchange.com/users/13675/telefan77
The easiest way to understand this is to consider the gears connecting the tuning knobs to the strings.
If you "tune up", the surfaces of the gears are in contact the entire time and cannot loosen.
If you "tune down" the gears engage in the oposite direction and could leave a gap that closes due to the string tension while you play.
This would cause the string to detune down.
Although this is a simplification, it hopefully demonstrates the concept...
music.stackexchange.com/users/23588/Memphis B Hound
The only time I would not tune up from below is if the string had been tuned way too high already for whatever reason.
In that case, after you tune the string down, it will tend to creep up a bit afterwards because of material memory.
Tuning it from above will help counteract this effect.
That said, this is only really applicable to certain materials- metal strings have practically no memory, nylon strings somewhat more, and gut strings a whole lot.
So the occasions when I would tune from above on a guitar are pretty limited.
The best general policy, as has been said here, is to tune from below.
I however do this quite often on the gut strings of my harp, and it helps considerably.
music.stackexchange.com/users/26744/Scott Wallace
There s backlash in the gears.
Poor gear meshing causes "slippage" although the teacher is correct its not strings per se but poorly machined, or fitted worm gears.
You tune up and its tight "in tune" hit the string or pull the string and the tuning pole will turn.
Slightly, but enough to cause it to drop out of tune.
Happens all the time on cheap keys you can even feel it if there s excessive backlash.
A gap on fine incremental movements if the key needs quarter turn to reach desired pitch when you know your pitch hovers at the threshold and it requires a large movement to get there.
Your tuning keys are the problem!
not the strings.
All other things being equal such as thermal coefficients, mechanical integrity plays a major role.
music.stackexchange.com/users/45439/tony
I used to have a guitar teacher that said you should always finish tuning each string by tightening/sharpening the string.  So for example if the top E is a little sharp, you should turn the peg to make it flat and  then  tune it up to the right pitch, as opposed to just turning the peg to the right pitch from above.  He claimed that the increase in tightness as opposed to loosening from above kept the string in tune longer.  Is this true?
When tuning a guitar, should you always end with tightening the string rather than loosening it?
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<guitar><tuning><strings><string-instruments>
music.stackexchange.com/questions/16587
music.stackexchange.com/users/6629/Alexander Troup
It is correct that you should always tighten the guitar string a little when you finish tuning it. Yes, you should always end string tuning by tightening rather than loosening it
Yes, you should always end string tuning by tightening rather than loosening it