Cutoff frequency for unknown woofer/tweeter pairs

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Hey there,

I plan to build a pair of active monitor speakers from a broken Yamaha keyboard (all speakers magnetic) :
Woofers: 283 Yamaha / XJ999 / 8Ohm 20W
Tweeters: 281 Yamaha / XK000 / 8Ohm 20W

On the original board, the speakers are wired in a "not so crossover fashion" with the woofers connected directly to the amp and the tweeters fed through a 3.3uF bipolar electrolytic capacitor. If I got the math right, that gives us a 1st order Butterworth high-pass around 6000Hz.

Considering a 2nd order Linkwitz-Riley crossover, is it ok to aim for a 3000Hz cutoff frequency (from a 6000Hz at 6dB rolloff (1st order) to a 12 dB rolloff (2nd order)) ? That would mean C=3.3uF and L=0.85mH.

Thanks for your time.
 

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