EBVT numbers again

[Billbrpt@AOL.COM]

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In a message dated 11/1/01 7:46:37 PM Central Standard Time, rscott@wwnet.net 
(Robert Scott) writes:


> 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
>   n

Thank you so much, Mr. Scott, for looking into this further.  I will try to 
see if I can produce the EBVT with the FAC program and your figures.

There was one omission in your writing:  C#-A# is also a pure 5th in the EBVT.

I find your comment about inharmonicity being a difficulty in creating a 
calculation for creating pure 5ths very interesting.  All WT's have at least 
5 or six or more of them.  I really wonder if these HT's are really being 
represented well with deviation figures?

When tuning aurally, a pure 4th or 5th is the easiest interval to tune and 
use an aural check to verify.  It is the *tempered interval* with no exact 
reference which requires so much more skill to accomplish. Also, Equal 
Beating intervals can be easily tuned aurally to within very low tolerances.  
It is the slight differences and mismatching of ET intervals which are 
challenging.  It seems to me that the tuning curve programs which work for ET 
because the goal is an equitable compromise for all intervals may fail when 
scale irregularities and the program do not have pure and equal beating 
intervals as their goal, only a smooth spread.

Bill Bremmer RPT
Madison, Wisconsin

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