tuning narrow and wide

[Ron Koval]

Tony added to David's response:

>I'm sorry, I'm coming in on the middle; what measurements?
INHARMONICITY MEASUREMENTS.
>
> >> From this one would assume that the narrowing and widening of a piano =
> > should only happen above and below those notes.
> > <snip>
>I don't agree with this at all; in my world, everything is stretched.

YES, EVERYTHING IS STRETCHED. BUT MY QUESTION IS FROM WHAT
snip

Ok, what starts out as simple quickly gets more confusing as we try to get 
more precise.  I think what Tony was first pointing out as narrow and wide 
referred to a tuning chart.  The numbers there aren't really inharmonicity 
measurments, they are cents measurements when compared to the mathematical 
model of tuning.  The first step is to realize that because of 
inharmonicity, any piano needs to be tuned wide of the mathematical model, 
which doubles frequency to get to the next octave. (110, 220, 440, 880....) 
How much wider depends on both the piano AND the tuner.  In the chart that 
he had, he noticed that the middle of the piano's tuning remained the same, 
while the ends were shifted sharper or flatter to achieve the narrow or wide 
tuning style.

The second step is to realize that there are different amounts of stretch in 
each range of the piano that are percieved as acceptable by different 
technicians.  Because in most pianos, there is a range of where the octave 
is percieved as beatless, there are varying conflicting published methods 
for testing an octave. (4ths=5ths, 4ths >5ths, 3rd=10th, 3rd<10th)

The people that developed the machines realized this variation of tuner 
preference and came up with different methods to customize the machine to 
the technician.  RCT has different OTS numbers, SAT has the double octave 
beat control, Tunelab uses graphs to predict beat rates, as RCT can.  Even 
the 'lowly' Korg tuner had variable stretches built in to the M1200, similar 
to the Peterson, giving the tuner some options to try and match the machine 
to the piano to the technician's preferences.

I used the term 'organic' to represent a tuning style where the 10ths will 
beat faster than the 3rds, as suggested by Virgil Smith.  Maybe 'resonent' 
would be a better choice, because the result of this kind of tuning adds a 
resonence, suggesting a tuned duplex effect as the upper, unmuted strings 
match what is being generated below.  Some of the Verituner users have been 
able to experience this, using the custom styles to allow the piano to 
dictate the stretch based on varying setpoints and balancing of octave 
types.

Ron Koval
Chicagoland

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