The Physics of Guitar Tuning

...as the string tensions change with differing tunings, so too do their "open vs. closed" lengths, ie: intonation lengths.

You'd do that at the bridge, in any case, right?

The machines still have manual knobs, too, because we all know that 99.9% of the people who pick one up will still fiddle with the tuning, no matter what.

Does this mean my Conn Strobe tuner is obsolete?

GA. I think the one aspect either I missed or you didn't explicitly mention is that tuning a string up increases the tension along the string (that's how tuning works), but the increased tension also makes it harder to deflect the string sideways as when you press the string down on a fret, even if the neck doesn't bow (due to the tension bolt that reinforces the neck). Your fingers can feel this. The extra force is stretching the string a bit more and this results in a slightly higher pitch. You are also right in your next post about tuning the higher strings a bit flat so that you hear a beat frequency. This is the basis of the 'tempered' vs 'natural' scale. Not only are the higher strings a bit flat, but the notes are also a bit flat as you go up the neck. If you only play the guitar by itself the difference is usually not much of an issue, but if you play with keyboards and spend much time up the neck it sucks noticeably.

I agree.

Great post AH.
Another classic case where the simple mathematical/physical model and a shed load of software still isn't as good as a human (with a decent ear) who's had some practice.

I may be mistaken but I vaguely recall hearing that all this stuff about tuning following exact mathematic intervals isn't exactly true anyway?
Del
(BTW I'm not into music, but the rest of the family is)

I think you are right about not tuning exactly on. At least on my 12-string guitars having a small or minimal beat frequency between strings actually makes the guitar sound fuller rather than sterile.

I am thinking that the same thing applies to pianos. Tuning is more of an art than science.

I always assumed that the frets were spaced at ratios of 1 over 12th root of 2 (chromatic tuning) to give a compromise for whatever key you're playing in. I could be wrong on that. Maybe it depends on the guitar.

Calculating Fret Positions

Thanks for the link. And I should have said tempered scale.

The frame of a piano on which the strings are mounted is made of cast iron and is designed [by engineers :)]to have nominally no flex at all since this is what will make the piano stay in perfect tune with perfect harmonics even tho the string tension is very high.

My '68 Les Paul standard which weighs 12#11oz. has adjustments on the bridge to allow for ultra-fine tuning set-up but I know of no one who resets them for different tunings, they usually have a roadie just hand them a different guitar, lol.

The action is the same height along the entire fretboard, roughly 2mm, and the ultra-light weight strings collectively have not enough tension it seems to my tin ear to affect the straightness of the steel reinforced neck no matter how far you bend.

You can do a vibrato by pushing on the head and base at the same time while bracing the body against your belly so there is flex in the neck but you have to force it.

You can pretty much play the thing with your left hand by 'hammering on' and using the volume and tone controls. It almost plays itself, lol.

I've never had it set up professionally because it would be wasted on my tin ear (trumpet and euphonium player consequently) so I use harmonics to tune it or an app on my Droid. Frets are mandatory and I can't play slide which drives me crazy. Tinnitis doesn't help either.

I like the Gibson necks because my digits are so short (hold the comments) so my collection now includes all Gibson Cherry Sunburst made between 1968-1972 and consists of a J-45, Custom Les Paul, A-4 Mandolin, a 3/4 size 12 string, and my first electric, an ES-125.

Staggers my imagination what they are worth now since I got them all for between $450 and $500 each over the past 40 years.

(My Yamaha 12 string has unbelievable good tone so it stays out in easy reach tho.)

This may be OTS, but your topic reminded me of something I read about a while back, a bridge that automatically keep a guitar from getting out of tune as a set of new strings stretches. It works by keeping a constant tension on the strings. http://www.popsci.com/diy/article/2010-05/invention-awards-plug-and-rock-out

Interesting but I doubt if I could ever bring myself to cut that big a hole in the back of an all original 1972 Les Paul...

Also, there is a point in a musician's learning curve when the ear overtakes the instrument whether it is fretted or not. (In some circles frets are considered a handicap.) People like these two seemingly have gone beyond the ability of commoners like myself and most others into a world innate ability far beyond the comprehension of most everyone.

http://www.youtube.com/watch?v=2gO7FI_ogvA