Richard Jernigan -> RE: Eventual end of guitars structural intonation issue (May 19 2015 20:07:13)
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What I see in this thread, besides the usual ill-tempered snarling of some of the participants, is a certain lack of clarity. Nothing is to be done about the snarling, but I will attempt to clarify a little of what I think I have read. To correct the intonation of an instrument, one must have in mind what the objective of the correction is. As I understand Michael Ruhe, his objective is to bring the guitar closer to equal temperament. Equal temperament was not always the objective of tuning instruments. In fact, the temperament used by Bach was not equal temperament. It was one of the temperaments developed by Werckmeister http://en.wikipedia.org/wiki/Werckmeister_temperament and advocated by Bach's great predecessor Buxtehude. But Werckmeister's temperaments approximate equal temperament more closely than previous tuning systems used for keyboard instruments. ("Johann Sebastian Bach, the Learned Musician" by Christoph Wolff, pp. 228-229.) Before Werckmeister at the end of the 17th century, North German organs were tuned by a variety of methods which improved the consonance of intervals, but sacrificed the ability to play in keys with more than four sharps or flats. Here is a keyboard of such an instrument, with 15 notes to the octave. As you can see, D# and E-flat are two different notes, and so on. You can hear such organs on CDs. Look for those built by Arp Schnitger, for instance. Schnitger was born in 1649, and lived until 1719, when Bach was 34 years old. Bach is known to have played on some of Schnitger's organs. These organs sound much sweeter than modern equal temperament organs, as long as you stay within the keys to which they are limited. That's because the intervals are small ratios of whole numbers, not multiples of the twelfth root of two =2^(1/12), as in equal temperament. By Bach's time, composers were writing music that was highly chromatic, modulating into distant keys. Beethoven went even further. Sacrificing consonance for versatility became a good tradeoff. Our ears are accustomed to the slightly discordant sounds of modern organs and pianos. In other cultures, such as Balinese or Javanese gamelan, even wider discords are intentionally produced. But modern harpsichord players of European Baroque music seldom tune to equal temperament, and the difference is easily heard. The older tunings sound sweeter. Even in more recent music, the string sections of symphony orchestras do not play in equal temperament. Typically they tend toward just intonation for the particular key they are playing in. Wind players are taught to adjust via embouchure, even though their instruments may be equally tempered by design. Practical limitations have led to twelve frets per octave on the guitar, and twelve keys to the octave on keyboard instruments. In old school flamenco the harmonic vocabulary was more limited than in modern times. This is not to say that Ramon Montoya, Niño Ricardo and Sabicas never employed "extended" chords. They did, but they employed them less often than Paco or Tomatito. Montoya's and Sabicas's playing can be quite consonant. One suspects that they may have tuned to make prominent chords sound good, departing from equal temperament. Guitars tuned to equal temperament can sound pretty good. Skilled players will adjust intervals of long duration to sound sweet, or cover the dissonance by vibrato, or both. The question arises: For a flamenco guitar with very low action and properly laid out frets, is compensation necessary, or would a skilled player make it play consonantly with no more effort than if it were uncompensated? Some in this thread say, "Yes." Another question would be: Is equal temperament the proper objective, even for modern flamenco, or are the number of keys used few enough to make a different objective practical, as in the North German organs? People are playing flamenco in more and more keys, so maybe this tilts the table toward equal temperament. There is no question in my mind that making a badly intonated guitar play closer to equal temperament will usually make it sound better. The methods that I have read for doing this have maintained the fret spacing of 2^(1/12), but compensated nut and saddle for each string. It is certainly conceivable that changing the fret spacing, still with compensation for each string could produce the same effect, but I have not looked up Michael Ruhe's patent, nor worked out the math myself. No personal attacks, please. RNJ
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