Guitar tuning by ear - starting points

Yep we all have electronic tuners -what would I do without my trusty Snark?  I'm generally pretty lazy and haven't spent a great deal of time trying to tune my guitar without an electronic aide, but I figured it was about time.  So I dug out the notes I may have written down correctly (or not) last time I thought about it.  I remember struggling with it but I couldn't make it sound right - but that was then, this is now.  Here's what I did:

First I used the electronic tuner to tune the A string.  I know, it involves using an electronic tuner, but I'm not about to start banging a tuning fork around - knowing me I might hit my guitar!   (Interesting note if you are in Botswana with no tuner - the telephone dial tone worldwide is an A!)  In any case I don't suppose it matters if the A string is in tune if you are just playing solo: the guitar should end up in tune with itself.

As harmonics are the way I've been tuning, I figured it might be useful to know the actual notes when playing natural harmonics.  It turns out it's based on the ratio of the fretted string length (from the nut) to the total string length.  Unless you want to memorize the frequencies of the notes, figuring them out might be a mite cumbersome.  As I only intend to use the 5th 7th and 12th harmonics for tuning, it's far easier to remember them.  So here they are:

• the 5th fret harmonic is 2 octaves above the open string
• The 7th fret harmonic is an octave plus a fifth above the open string
• The 12 fret harmonic is an octave above the open string

nb.  This can be confusing - remember the harmonic note is calculated not above the fretted note but above the open string.

And for extra credit:

• The 4th and the 9th fret are both 2 octaves plus a major third above the open string

So how could we use this to tune?  (Disclaimer, I'm not an expert - I just tried this a few times and got my guitar pretty much in tune.  There are other, more accurate methods but I figured this would do for a start).

1. 5th string.  Tune your A string to 440 Hz (or to "A" on the electronic tuner)
2. 6th string. Tune the E harmonic on the 6th string  (5th fret) to the E harmonic on the 5th string (7th fret).
3. 4th string.  Tune the A harmonic on the 4th string( 7th fret) to the A harmonic on the 5th string (5th fret). 
4. 3rd string. Tune the fretted note A on the 3rd string (2nd fret) to the A harmonic on the 5th string (12th fret).
5. 2nd string.  Tune the fretted E on the 2nd string (5th fret) to the E harmonic on the 5th string (7th fret)
6. 1st string.  Tune the open E on the 1st string to the E harmonic on the 5th string (7th fret). 

UPDATE: When checking this method results against the electronic tuner - it was good except for the G string was flat, so perhaps fine tuning of that string in particular might be needed.

Having got the guitar roughly in tune, I understand the next thing to do is to cross check using intervals in the key you will be playing in.  As I don't actually know how to do that yet, maybe that will be a future post.  For the moment I'm just cross checking using 5ths on adjacent strings because they sound pretty similar to my ears.

The beauty of this system is that you tune everything directly to the A string.  Unlike the method I was shown when I first picked up a guitar: i.e. tune each string relative to the next one using 4ths, so that small inaccuracies get compounded as you tune each successive string.  I could never get that one to work. I guess in my case the small inaccuracies were not so small...

However, there is a drawback with this method.  Tuning one string with harmonics to another with a fretted note isn't perfectly correct because of the fretted notes not always being pure tones (there's that equal temperament tuning again).  Hence the 2 frequencies are not quite identical.  For more information this site appears to offer useful advice and recommends other methods that are likely more accurate, and the site here claims to have the perfect solution.  But for the time being, I'm just pleased I managed to get the guitar to sound in tune without using the tuner.

UPDATE: I tried the tuning method recommended by the  Guild of American Luthiers (see tuning method here) and personally I felt compelled to reach for the electronic tuner afterwards (!)  Probably because it requires you to rely upon one tuned string to tune the next and maybe my ears are not that good.  YMMV. 

And what started this train of thought?  An instructional video at classical guitar corner on Drop D tuning.  I could have done with that before last week's orchestra performance - though I don't expect it would have helped me remember to tune back up again afterwards :(     Who would have thought that tuning down to D then an additional 6 (yes 6) turns down then slowly back up 5 or so to D would be required to stabilize the tuning???  Watch the video - could alleviate a lot of the hit or miss nature of having to play in drop D!