To interpret the plot below, observe that the zero crossings of the f[ ] function are equal to the frequencies in the spectrum of the sound. Below the plot are the exact frequency values at which these crossings occur (the plot stops at about 600 Hz for clarity, but the zero crossings are calculated out to highF (=2000) Hz.

addSynth[dur_,sr_,freqs_,amps_,decay_]:=Module[{},
tVec=Range[0.,dur,1/sr];
env=Exp[-decay*tVec];
envRise=ConstantArray[1,Length[tVec]];
envRise[[1;;8000]]=Range[0,0.9999,1/8000];
env envRise Total[Table[amps[[i]] Sin[2 Pi freqs[[i]] tVec],{i,1,Length[freqs]}]]];
ratio2cents[x_]:=(1200 Log[10,x])/Log[10,2];
mat[ki_,wi_]:={{Cos[ki wi],-Sin[ki wi]/(ki)},{ki Sin[ki wi],Cos[ki wi]}};f[w_]:=(mat[k1,w1].mat[k2,w2])[[1,2]];
highF=2000;mu1=0.0275591;mu2=0.00721785;
Manipulate[
w1=lam 0.9144;w2=(1-lam)*0.9144;t=2.05049*4.4484;
If[play==True,sndWav=addSynth[2,44100,ansKal,RandomReal[{-1,1},Length[ansKal]],2];EmitSound@SampledSoundList[sndWav,44100];play=False];
 k1=w Sqrt[mu1/t];k2=w Sqrt[mu2/t];sol=FindRoot[f[w]==0,{w,Range[75,highF,10]}];GraphicsGrid[{{Plot[f[w],{w,0,600},PlotRange->All],
ansKal=Select[Union[Round[100*sol[[1,2]]]/100.],highF>#>0&]},{ansCents=ratio2cents[ansKal/ansKal[[1]]],Round[100 Mod[ansCents,1200]/100]}}],{{lam,0.5},0,1},{play,{False,True}},SaveDefinitions->True]

When lam is at the left (lam=1), it is all the light guage. When lam is at the right (lam=1), it is all the heavier guage. In the middle (lam=1/2) is the 50-50 test case. Note how the fundamental (lowest frequency) covers an almost-octave from 122 Hz down to 62.5 Hz. This is a ratio of

122.14/62.5

This arises because of the particular mu1 and mu2 values (i.e., the string densities), which are in the same proportion:

Sqrt[mu1]/Sqrt[mu2]