In a message dated 3/5/01 7:48:00 AM Central Standard Time, thepianoarts@home.com (thepianoarts) writes: << Any "C" fork users care to exchange temperment checks and patterns etc? I have been trying to evolve the 'Up three thirds, down a fifth, up two thirds" etc. temperment taught from the Aubrey Willis course 25 years ago. Anyone on the list using this pattern? BTW, after 25 years with the fork, I moved to the Sanderson Accu-fork. It has some advantages. Their beat-rater is also a nice tool for checking contigious thirds. >> As Tom Cole did, I also learned from Bill Garlick RPT that it really shouldn't matter which starting note you use to tune Equal Temperament (ET). Since all intervals are tuned *equally* you may use virtually any note to start. The late John Travis suggested in his book, "Let's Tune Up" that you could get your temperament to be "more equal" (sic) if you started on a black key such as F# or C#. I often hear technicians talk about "different temperaments" when they are really only talking about one: ET. What they are really talking about are different temperament *sequences*, that is, the order in which the temperament octave is constructed. This is often called "the Bearing Plan". The sequence you mention, "up a 3rd, up a 3rd, down a 5th" was conceived by Oliver Faust and is one of the better ideas. What is most important, however, is the diagnostic check afforded by the contiguous 3rds. In order to tune a really good ET, you have to make lots of good *estimates* first, then verify and correct your intervals using the contiguous 3rds (the well-known 4:5 ratio) and other interval tests. You can use Faust's idea starting with virtually any note, not just C or A. There really is no one temperament sequence which is fool proof. Inharmonicity and irregular scale designs will also force some kind of distortion of the way the temperament may be expected to sound. This is why the study of other kinds of temperaments than ET is important. In the end, you'll want your piano to give the most pleasing harmony possible. If you know that getting the temperament to be truly equal is not quite possible, at least in the way it is usually expected to come out, you'll want to know what is best to do to make a compromise. Even with the best pianos using the best temperament sequence, you can expect that after tuning your first 13 notes, C3-C4, F3-F4, A3-A4 or any others, you will have to make slight corrections to get true equality by using the contiguous 3rds and other interval tests. Many technicians seem to believe that making the 5ths be as pure as possible while ignoring the resultant irregularity of the 3rds would make the piano sound best. Actually, quite the opposite is true. The 3rd, 4th and 5th octaves of the piano is where all of the *harmony* occurs. Widening 5ths (making them be closer to pure) and/or the octaves will cause all Rapidly Beating Intervals (RBI), the 3rds, 6ths, 10ths and 17ths to beat faster. When choosing to compromise intervals in the low tenor, the bottom of the 3rd octave, it would be far better to make the octave less stretched and the 5ths sounding more tempered. When a full chord is played, the tempering in the 5th virtually disappears. It is very rare in a true musical context to have an open 5th with no 3rd. Thus, the slightly impure sound of a tempered 5th which sounds dissatisfying to the technician who plays it outside of a musical context when tuning, ceases to be of any concern when actual music is played. You can still get a true ET where contiguous 3rds and other interval checks are *proportionately* correct even on the "poorest", most irregularly scaled pianos. Yes, this means that you really can tune an Acrosonic, Kimball, Wurlitzer spinet, etc., in ET and make it sound sweet and pleasant if you really understand your interval checks and how to make compromises. A skilled technician who knows other kinds of temperaments can actually make these instruments have a sweet sound and largely avoid the kind of harshness that many people fear from the use of Historical Temperaments (HT). Bill Bremmer RPT Madison, Wisconsin
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