HT enthusiasts: Based on aural tuning directions that Bill Bremmer provided, I have calculated the following offsets for his EBVT temperament: F 3.10 F# -1.28 G 4.50 G# 2.49 A 0.00 A# 1.63 B 0.58 C 5.35 C# 0.98 D 1.81 D# 2.00 E -0.86 or, if you prefer offsets that are more zero-centered: F 1.41 F# -2.97 G 2.81 G# 0.80 A -1.69 A# -0.06 B -1.11 C 3.66 C# -0.71 D 0.12 D# 0.31 E -2.55 In finding these offsets I developed a software tool called the Temperament Designer which can hopefully help to translate aural tuning instructions into offsets from ET for other "historical" temperaments as well. One difficulty in translating aural instructions is that they depend somewhat on inharmonicity. So the computer program that I designed uses an ET tuning file and an inharmonicity file on which the calculation of beats is based. Then it provides the ability to modify the ET tuning according to aural instructions based on interval beats. Once the program was written, it took me about 10 minutes to follow the aural instructions for Bill's EBVT and derive a "virtual tuning". Then the offsets for a temperament octave are written out to a file which can be read into TuneLab, or manually entered into an SAT or RCT. The effect of inharmonicity in this process, while noticeable, is small. Therefore I have every hope that the offsets derived based on the "typical" inharmonicity data that I used will apply equally well to most pianos. I also investigated the effect of starting with two different "ET" tuning curves using different partials. That also did not affect the outcome very much, as long as the ET tuning curve was a reasonably good match to the inharmonicity. I have a little more clean up to do on the program before I make it available on my website, but I wanted to get this preliminary result out because of the interest in the EBVT numbers. -Robert Scott Real-Time Specialties
This PTG archive page provided courtesy of Moy Piano Service, LLC