What temperament is a guitar tuned?

[Tim Keenan & Rebecca Counts]

John, Bill & List:


Billbrpt@aol.com wrote:

> The guitar's frets are laid out in a manner that would imply ET.  All
>  electronic guitar tuner's frequencies are based on ET. However, many players
>  will tell you that once they have tuned  according to the elctronic tuner,
>  they play some chords and "tweak" the tuning a bit to suit their own
>  preferences.  Many who do this are essentially converting the ET to a WT.
> 

Guitar frets on all modern guitars that i know of are laid out at a 
factor of 2^-12, just like an equal tempered piano scale. Because the 
guitar interface is a 2-dimensional matrix rather than linear and because 
the intervals are fixed in the dimension along the neck, you can 
only alter the intervals between the open strings. Any attempt at using 
other temperaments results in different harmonic results depending upon 
how you voice any given chord and which form (or "shape") of the chord 
you use.  Very few guitars I have played have perfect intonation, 
although inharmonicity is low compared to that of pianos because the 
tension is so much lower and the strings thinner and less stiff.  The 
intonation of any guitar is affected by the choice of strings (why most 
electrics have compensating bridges), the age of the strings (older 
strings are less elastic and go sharper when pushed to the fret than 
do new ones, and have higher inharmonicity) the action height (the higher 
the string is above the fretboard, the sharper it goes when it it pressed 
down to the fret) the height of the frets and the technique of the 
guitarist (how close the finger is to the fret, how far the string is 
depressed below the crown of the fret, and the amplitude of the vibration 
(if you watch with a visual aid, you can see that a loud note is sharper 
than a quiet one, especially in the bass).

Any time you tune a guitar, you try to make the best compromise for the 
piece you are playing, so that as many as possible of the actual 
intervals to be used will sound tolerable.  I have never seen an 
electronic tuner that will do a satisfactory job on a guitar. I don't 
know any accomplished guitarists that use them, although I know of some 
roadies that use them to put stage guitars "in the park" before a 
performer picks them up, and I know luthiers who keep one on the bench 
for analytical purposes. I am sure you could store a good average aural 
tuning for a given performer on a given guitar with a given set of 
strings of a given age on a SAT.  

When I tune, I set my open fourths to about 1 beat per second wide, the 
third between G and B to roughly 8 beats (no, I don't count) make sure my 
fifth-fret unisons (and 1 fourth fret) are tolerable, check the 
coincident 3rd and 4th partials of adjacent strings(7th and 5th frets), 
and the 4th partial of E against open e, and then play a bunch of chords 
to find any intolerable intervals.  And of course, all of this only 
applies to standard tuning (EADGBe)  There are many guitarists using 
non-standard tunings, a lot of which are tuned to an open chord, or 
something approaching one (such as DADGad) and in which it is possible to 
push the tuning (of the open chord) towards "just intonation", since most 
of the compositions played this way are strongly tied to the home key, 
and the occasional crunchy excursion is soon satisfyingly resolved.

Tim Keenan
Terrace, BC