After looking over the comments by Ron Koval regarding Bill Bremmer's EBVT and considering Bill's comments on the difficultly of achieving EBVT using 12 offset numbers from ET, I decided to recalculate the numbers that I had been proposing. When I calculated the offsets last year, I was using a model for inharmonicity that was not as good as the model I now use in TuneLab Pro. Using the new model, I come up with slightly different numbers (which are also now balanced to achieve an average of zero cents). C 4.06 (EBVT balanced for zero average) C# -1.47 D -0.11 D# -0.23 E -3.25 F 2.14 F# -3.42 G 4.13 G# 0.59 A -2.18 A# -0.03 B -1.17 This calculation is based on the inharmonicity of a Steinway D as described in Roberts, "The Calculating Technician". The EBVT is a difficult temperament to get right because the aural goals involve some pure 5ths and 4ths. Pure intervals are the most sensitive to differences in inharmonicity. By contrast, a temperament that is defined mostly by how fast the thirds beat would not be as sensitive. Also, there is the issue that the octaves as described by Mr. Bremmer are not all the same width if you follow his aural instructions strictly. What the above numbers ought to achieve is the core requirement of EBVT, namely: pure 5ths: F-C F#-C# A#-F equal beating thirds: F3-A3 = G3-B3 = C4-E4 equal beating thirds: A3-C#4 = A#3-D4 equal beats: G3-D4 = A3-D4 equal beats: G#3-D#4 = A#3-D#4 -Robert Scott Ypsilanti, Michigan
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