![]() ![]() The resulting equal divisions are a logarithmic function of the speaking length of the string, rather than pure fractions, and thus are not a true analog of the natural harmonic series. In chords, therefore, a C# might be sounded on one string, and a Db on another - this will be a very false octave unless the instrument is in equal temperament."Įqual temperament divides the octave into twelve exactly equal semitones. Back in 1581, Vincenzo Galilei (Galileo's father), explained the need for equal semitones logically and correctly - "since the frets are placed straight across the six strings, the order of diatonic and chromatic semitones is the same on all strings. There many alternative ways to do this on keyboard instruments, and it is only in the last 150 years that equal temperament has taken over as the accepted standard.Īs far as the guitar and other fretted instruments having 12 straight, unbroken frets to the octave are concerned, equal temperament is the only choice. A temperament is a specific way of dividing the Pythagorean comma among the intervals of the octave. To make a fixed-interval instrument with 12 notes in the octave useable in all the key signatures, the purity of the intervals has to be compromised. Finding a way around these problems has been the cause of much controversy and many bitter arguments among music theorists for two and a half millenia. There is another problem in that 7 pure octaves and 12 pure fifths do not add upp the same:ġ2 fifths = (3/2) ^12 = 129.74The discrepancy works out to 24 cents (almost exactly a quarter-tone), and is known as the "Pythagorean Comma". But Nature throws a spanner in the works by making the natural tone row irregular, so instruments tuned in this way cannot modulate to different key signatures without adding more intervals to the octave. ![]() The ancient Greeks and Chinese knew about the pure intervals, and constructed their musical scales around them. Real-world strings produce harmonics which are pure fractions of the speaking length of the string. The problem with equal temperament, though, is that it is artificial, a mathematical construct, and it conflicts with the physical properties of real-world strings. It is designed to play the equal-tempered scale, and it is perfectly possible to adjust and intonate almost any well-made guitar so that it plays this scale pretty accurately. It is not designed to play perfect intervals (except for octaves and unisons) in any position, or any key. No matter how good the instrument, and how well tuned and adjusted, it never sounds perfectly in tune in all positions and keys. Every guitar player - and every guitar builder and repairer - is familiar with the problem. Tuning has always been a bugbear for guitarists. ![]()
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