A Publication of R.W. Green Enterprises Reg'd         June 1987
Internet Editon
Page 2
frequency. The cause of this phenomenon is the stiffness of the string, which is generally neglected in theoretical discussions, and leads to problems when attempting to tune strings of different stiffness (i.e. different gauge, usually) to each other using harmonics. This problem is compounded when double-octave harmonics and higher harmonics are used, because the stiffness of the string becomes greater for shorter wavelengths (i.e. higher frequencies). Of course, any good guitarist or guitar repairman knows that one does not tune using harmonics, not because of inharmonicity, but because then the tuning would not be "tempered" in such a way as to play equally well in all keys (see also second-next paragraph). But if it were not for inharmonicity, then one could "temper" a guitar using harmonics in a similar way to that in which the piano tuner (myself included) "tempers" using beats. This is not advisable however, because of inharmonicity, and piano tuners must even compromise their octaves at times (Reblitz, pp. 54-55) in accommodating the same inharmonicity which makes "tempering" using harmonics inadvisable on the guitar.
   Now that that little-understood fact has been disposed of, we may throw light on some common myths regarding guitar tuning.
   Tuning using harmonics, a method just mentioned in the context of discussing inharmonicity, is not acceptable for two reasons. Firstly, the musical scale which we know and love is based on the twelfth root of two (a fact well-known to guitar builders or luthiers, and the reasons for which I will leave to another article or to my book) and not on simple integer multiples as are the harmonics, and secondly because of the inharmonicity of the strings just discussed, which makes the harmonics higher than exact integer multiples, making it exceedingly difficult to relate the harmonics back to our musical scale in any practical way.
   The method of the fifth fret, as I call it, which is almost invariably the first tuning method every guitarist learns, has a good foundation in theory, since the construction of guitars is based on knowledge of our musical scale, incorporating the twelfth root of two (or an approximation) into its fret spacings. However, even if we ignore errors which are introduced by using a "rule of eighteen" or another non-exact formula to determine the fret spacings, the fifth fret method is still plagued with problems. For example, no matter how accurately one calculates the fret spacings, the actual placing of the fret can never be this accurate and must have an error associated with it. In addition, when tuning each string to the one adjacent, there is an associated human error in detecting beats, no matter how skilled the tuner. There are two more sources of error worthy of (continued on p.3)








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