Duplex

[Overs Pianos]

Carl, Ron N and other interested folk,

You were right Carl when you wrote about the formula I posted last night;

>Well, this gets me longer length, lower pitch than either given length,
>with what would seem the right interval mirrored around the lower one.

The formula that I devised for calculating a detuned duplex length 
between two adjacent harmonic lengths, was actually posted last night 
as incorrect, it was supposed to be;

>Detuned length option = (((lower harmonic length)/(next higher
>harmonic length))^(0.5))*(HIGHER harmonic length)

Sorry about the misinformation Carl. This can happen when it's after 
midnight. Things can go wrong when writing off the top of the head 
when tired.

Let's go through an example. Let's assume that we have a speaking 
length on a certain note of 100mm. We wish to find a duplex length of 
between 20 to 25 mm.

The two nearest tuned harmonic lengths would be the quarter length - 
25 mm, and the fifth length - 20 mm.

Now let's look at the formula. The 'Detuned length option' (DLO) is 
the length we intend to derive by solving the right hand side of the 
equation.

The 'lower harmonic length' will in this case be 25 mm, while the 
next higher harmonic length will be 20 mm.

Substituting these into the equation we get;

DLO = ((25/20)^(0.5))*(20)

DLO = ((1.25)^(0.5))*20

DLO = 1.1180 * 20

DLO = 22.3 mm

For the next shorter detuned length option we would use 20 mm as the 
longer harmonic and 16.66 mm as the shorter.

DLO = 18.25 mm

There, the piano should sound a whole lot cleaner tonight.

Ron O
-- 
______________________________

Website:  http://www.overspianos.com.au
Email:        mailto:ron@overspianos.com.au
______________________________