Koval 1.2 [long update]

Ron Koval drwoodwind@hotmail.com
Tue, 16 Mar 2004 16:13:31 +0000


Hi all -

I've been out of the loop this last week, and am just trying to catch up on 
the pianotech reading.  Thanks David, for giving the KV 1.2 a try; I'm glad 
you've found it usefull.  For the 'new' people out there here's a little 
background:

I created the Koval variable temperament series to take advantage of some of 
the strengths I had found studying a wide range of historical and modern 
temperaments.  What I wanted, was a temperament that would provide a good 
range of color while keeping the individual offsets from equal temperament 
small.  I had always experimented with 'morphing' temperaments; the dividing 
or multiplying offsets to strengthen or weaken the effect of the 
temperament.  While this works on all temperaments, I was dissapointed by 
the outcome many times.  With some help from other 'temperament adventurers' 
I was able to use a spreadsheet to not only look at the width of the third, 
but also chart the projected beat rate for the different intervals in a 
chord.  Yet there was still something missing,  some effect that I could 
hear, but couldn't predict on the computer.

What I ended up charting was the relationship between the beats of the major 
third and the minor third in a chord.  This beat syncronicity, (I think 
Robert Wendell came up with that one...) where the beats are at a simple 
relationship can be found in many of the historical examples, especially in 
the remote keys.  Aha!  This is the effect that Bill Bremmer used to go on 
about, trying to explain why the rough keys didn't play as rough as 
expected.

So, I worked up this temperament, which allows dividing and multiplying the 
strength of the effect.  After much tuning, I've settled on the three 
"stopping points" that seem to play the best.  These give the effect of a 
quasi-equal, a Victorian, and a Well temperament.  Since the same number set 
is used, going from one strength to another doesn't involve moving the 
strings too far.  The naming of the KV series relates to the offset for 
C,(and F) so you can know the amount for the largest ET offset.
I'll try to type this so it should come out clear.  Here are the offsets for 
the KV1.2 , KV2.1, and the KV4.4


note__1.2_____2.1_____4.4
C_____1.2_____2.1_____4.4
C#___-.16____-.28_____-.59
D_____.48____.84_____1.76
D#____.72___1.26_____2.64
E_____-.48___-.84_____-1.76
F____1.2____2.1______4.4
F#___-.32___-.56_____-1.17
G_____.8____1.4_____2.93
G#___.32____.56_____1.17
A_____0______0______0
A#___1.04___1.82____3.81
B____-.6____-1.05____-2.2

(boy, I really hope I typed them right!)

Remember that these are spreadsheet numbers, trying to come up with a 
precise target for tuning.  We would all be lucky to work on instruments 
that allow us to tune this close. The reality, especially if we're talking 
about smoothing out spinets, is that we're doing pretty good to get the 
string to stay within a half a cent of where we're aiming, for a normal 
tuning.  SAT owners, don't sweat over the hundreths, just round them off an 
give it a try!  These numbers won't match what's on the rollingball.com 
site, or even what's in your VT today, since I've made some further 
adjustments.


Ron Koval
Chicagoland

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