EBVT: why numbers fail

[Ron Koval]

Hi everyone-

I've been busy lately:

swabbing out sousaphones
cleaning clarinets
tweaking trumpets
freshening french horns
altering alto saxes
pricing piccolos

well, you get the idea, I haven't been keeping up with piano stuff.  I did, 
however cruise through the archives to catch up on the last few days and 
found John, Bill, and Scott's posts on EBVT.  So... I crunched some numbers, 
tuned some pianos and came up with:

Robert Scott offsets, tweaked to get 4 pure 5ths and equal beat rates of the 
following thirds (F-A, G-B, C-E) (A-C#,Bb-D) (F#-A#, G#-B#)

A    0
A#   1.63
B    .58
C   5.35
C#   .98
D   1.81
D#  2
E   -.86
F   3.1
F#  -1.28
G   4.5
G#  2.49

This works out to a pretty strong temperament with an "apparent" bump for 
the E major triad. It does however, follow the aural directions posted by 
Bill Bremmer a while ago, without tempered octaves.

But more interesting, and maybe more to the subject line, John listed both 
his FAC offsets and direct measurements.  Using the direct measurements with 
a saved tuning of a Steinway M, I came up with different numbers from his 
FAC numbers.

        FAC    Direct factored into calculated tuning
A       0      0
A#      .4     -.76
B       1      -1.84
C       3.4    3.19
C#      .2     -.15
D       .2     .72
D#      1.2    -.21
E       -.9    -1.33
F       1.4    1.68
F#      -.1    -.29
G       2.8    2.42
G#      2.9    3.29

Now, it's not much of a difference, but my gut feeling points back to the 
machine tuneoff idea.  If you just use a 'out of the box' tuning from each 
of the different machines, I think you'll get a different tuning.  Probably 
the reason Bill didn't get adequate results, is that he didn't apply offsets 
to a good ET tuning in the first place.  So if you wouldn't use 'just' an 
FAC tuning for ET, it probably won't get much better when using offsets for 
alternate temperaments!

So with that in mind, here's my latest tuning with equal beating attributes. 
  This was developed from the equal beating Rousseau.  Just remember to at 
least make sure the octaves calculated work for that piano before starting. 
(Better yet, use a saved tuning that has been aurally verified) If you're 
not using a Verituner, everything from the tenor section down is suspect. I 
'balanced' this tuning, meaning I shifted the offsets to make the least 
amount of tension change to the piano.  If you must have A=440 dead on, just 
add one cent to all the numbers.

A  -1
A#  1
B   -1
C  2.5
C# -1
D  -.5
D#  1.7
E  -1.5
F  1.7
F# -2.3
G   .7
G#  1

This temperament progresses smoothly through the circle of fifths and is 
suitable for every day use on modern instruments.

enjoy!

Ron Koval
graphman





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