An Uneventempered Tuning Strategy and How to Use Electronic Tuners With It. 

by Paul Hawthorne

 

First, if you have not read Bill Palmer's tuning essay under this heading, it would be best to do so before continuing here.

 

The way I tune a banjo is only slightly different from his.  The logic that got me there, however, was not so much to spread the errors out as to have the lower and louder harmonics (the 1's and 5's) fit together, and to accept and get used to a higher open B note than called for by just intonation or even temperament.  I like the 1/5ness in a bluegrass context, and the perfect fourth holds on the first two strings (which tend to stand out in the overall blend) work well.  I like to have a slightly compensated third string.

 

Set the bridge carefully and straight across to have the 1st and 5th string harmonics match the fretted notes at the 12th and 17th frets.   After setting a string to reference, usually A440 from a fork at the 7th on the first string or the guitar G, tune the first and third strings a just fifth apart.  You can do this by matching the third string harmonic at the 7th fret with the 12th fret harmonic on the first string.  Continue with Bill's general tuning method until the open G's, D's, fretted d on the second string and fretted g on the first and second all really fit together with just intervals   The b and d come out a little high this way relative to a tuner(see below), so the effect is similar to what Bill talks about, that the higher strings are a little sharp. The d at the 7th fret on the third string will be a little flat in relation to the other d's.  It may be necessary to adjust the bridge a little until all the tuning conditions are met at the same time.

 

As an aside, once the bridge position is found, measure the distance from some fret to both sides of the bridge and memorize it, write it on the head, whatever.  Carry a tape measure in the case so that you can easily reset the top of the bridge to the correct position, if it has been moved while inside the case in transit.

 

For the analytically inclined, here are the nominal frequencies, starting with g reached by even temperament down from A440.  In actuallity, we usually don't tune to two decimal places and there are some intrinsic errors in the instrument, so the numbers are likely to be a little off these.  This serves as a guide.  Notice that the fifths are right on at the cost of only a slighly greater error in the third.

 

String                      Even temperamnent        This tempering             Just intonation

 

First        d                  293.67 Hz                       294.00 Hz                    294.00 Hz

Second    b                  246.94                            247.23                          244.00

Third        G                196.00                            196.00                          196.00

Fourth      D                146.83                            147.00                          147.00

Fifth        g                  392.00                            392.00                          392.00

 

I don't claim my tuning strategy is "best"; it's a compromise I like and can appreciate today.  Since all hearing skills such as pitch matching, relative and  absolute pitch are learned, I would like to think my ear will mature to the point where I'd prefer a slightly different tuning when playing in different keys out ot the G tuning format with even tempered scale frets.

 

You can use an electronic tuner to get to alternate tunings by using it to match the strings and/or harmonics.  The deflection of the needle will be the same if the pitches are the same, even if the indication is not at the center of the scale.  Once an uneventempered tuning is reached, you can measure it as indicated on your tuner and then repeat that indication to recreate the tuning.  If it is a tuner with a light indicator, it is sometimes possible to get inside and find trimmer pots that can be adjusted to give an indication at the uneven temperament tuning. If you do this, it would probably be best to mark the tuner as no longer adjusted to even temperament.  

 

My usual tuning for guitar is similar, with the same high b string to get a similar 1/5ness, and eliminate clash of the two b strings.  My guitar also has the first and second strings shortened .015 and .020 at the nut to improve intonation.

 

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I hope this submission is valuable to you..  Please email me any comments or questions you may have.

Paul Hawthorne