EBVT - the numbers

[Avery Todd]

Bob,

    Thanks for all your work. One question. What do you mean by
"zero-centered". Maybe I'm showing my ignorance but I've never
heard that term before.

Avery

At 03:21 PM 10/26/00 -0400, you wrote:
>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
>