Duplex

[Clark]

Hi, Rons;

> Things can go wrong when writing off the top of the head when tired.

Sure! (insert bad pun here)

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

Yes, but it's like for pitches and this would simplify, where

dlo = sqrt(lower/higher)*sqrt(higher^2)
dlo = sqrt(lower*[(higher^2)/higher]) 
dlo = sqrt(lower*higher)

Less entry is nice, but I prefer less clutter, too (despite which, most
of my spreadsheets barely are parsable). The quadratic I posted takes
the form

n^2+n+(l^2)/(tdl^2) = 0

where [n] is a partial, [l] speaking length, and [tdl] is a target
length as permitted by design constraints and preference, has a positive
solution 

n = (-1+sqrt[1-4*([l^2]/[tdl^2])])/2

To be useful, this needs to be a whole number, so adjacent cells might
read

[r1c1={l}]
[r1c2={tdl}]
[r1c3=int((-1+sqrt[1-4*((r1c1^2)/(r1c2^2))))/2)]
[r1c4=r1c1*sqrt(1/((r1c3)*(r1c3+1)))]

where the third column shows the lower partial closest to the target
length entered to the second column, and the fourth column shows the
corresponding detuned length option.


I wonder, what would be the results of making front duplexes
proportional to strike lengths? Research I've encountered looks farther
back.

Did I post already about that Taskin fp at Cité de la musique?


Clark