In a message dated 12/17/99 6:11:42 AM Pacific Standard Time, pianotoo@imap2.asu.edu (Jim Coleman, Sr.) writes: << Hey, for all practical purposes the 5/4 ratio works just fine. >> Jerry, After trying all of the suggestions, especially Jim's, consider this: It will be much easier to know that the relationship is not correct than when it is. It is that kind of off-balance feeling just like when you have five against four in music. But when you have the A3-A4 and the F3-F4 octaves sounding good and your 3rds F3-A3-C#4-F4-A4 all seem to progress proportionately, you'll have it. You'll also have the best framework for avoiding the most common error in temperament tuning today known as the Reverse Well error. When looking for the error, you will never change your A4. You could have too wide or too narrow an octave between your A3 and A4. The usually best recommended compromise is somewhere between a 4:2 and 6:3. Using the untuned (as of yet) test note, F3, the 3rd, F3-A3 should beat slightly slower than the 10th, F3-A4 (the test for a 2:4 octave), proving that it is wider than a 4:2. Then, using the untuned (as of yet) test note C4, the minor 3rd A3-C4 should beat slightly faster than the 6th, C4-A4 (the test for a 6:3 octave), proving that it is slightly narrow of the 6:3 octave type. This is a very fine distinction. You have to be able to discern the Rapidly Beating Intervals (RBI) to a very fine degree. If both tests seem about right, the octave is about right. Sometimes there is not much difference between the 4:2 and 6:3 at this point, particularly on a low inharmonicity piano. You should be able to hear this difference more clearly on a high inharmonicity piano such as a Steinway. Once you are satisfied with your A3-A4 octave, ( it sounds more or less "pure" when played but the RBI tests are also satisfactory), if the A3-C#4 & C#4-F4 is inverted (faster-slower) [which would also be the rock solid foundation for a typical Reverse Well error], it means that your F3 was too flat, thus causing your F4 to be too flat. Try sharpening your F4 to see if the A3-C#4-F4-A4 relationship is then satisfied. You may still have to flatten the C#4 a little too but once you have the top of this correct, see if you can then make an acceptable F3-F4 octave. As Jim pointed out, the low end of the tenor on a piano with plain wire on a hockey stick shaped bridge will be skewed. Your 3rds will be a little slower than expected. Your 5ths may even end up a little wide. It is very important to the harmony of the music that will be made on the piano that you do not have 3rds that are way out of proportion. This is where closely voiced chords are played. It is easy to make the piano sound disharmonious by concentrating on favoring 4ths, 5ths and octaves and ignoring the 3rds. Moreover, the 3rds are pretty important all the way down to F2 but lose their importance after A3. After A3, you can let them become faster as you stretch the octaves to get more of the "singing tones" out of your 10ths. Bill Bremmer RPT Madison, Wisconsin P.S. Speaking of Reverse Well, I found a particularly exaggerated example of it yesterday on a nice Kawai KG-2D. The F#3-A#3 and Ab-C4 3rds were nearly pure, the F3-A3 and G3-B3 3rds very fast and sure enough, the C4-E4 3rd was the very fastest 3rd in the entire temperament. To me, all music would sound like a nightmare on such a piano even though at standard pitch, I could still recognize in which key the piano would be being played because of the pitch alone. To me, the "color" (which I personally do not associate with the colors we see, i.e., blue, red, green, etc.) would be completely inappropriate even though the pitch is more or less standard. It seems to me that people are calling two entirely different perceptions of musical tone or tonality by the same use of jargon, namely the word, "color" and that is what is causing the confusion about hearing "color" in ET.
This PTG archive page provided courtesy of Moy Piano Service, LLC