In a dichotic listening task where participants listen to different (frequency-wise) musical tones through headphones, is cross talk to the contralateral cochlea of each ear through bone conduction a source of noise to be taken into consideration, or is it insignificant? If it is a source of noise, are there any ways to eliminate physically or computationally any such effect?
Crosstalk needs to be taken into consideration, but with reasonable controls it can be made insignificant. Interaural attenuation can vary between less than 40 dB to over 60 dB depending on frequency, the type of headphone, and how well it is coupled to the head. If you have 40 dB of interaural attenuation and present the sounds at less than 40 dB SL (sensation level) the cross talk will be inaudible. The further below threshold, the better off you are.
If you need to present the sounds at a level greater than the amount of interaural attenuation, crosstalk will still not matter if the other sound provides sufficient masking or you introduce sufficient masking noise. For dichotic speech tasks, the speech masks the crosstalk. For musical tones, you might need to introduce a masking noise depending on the frequency content of the tones.
It may be easier to simply spatially separate the stimuli by either presenting them over loudspeakers or using head-related transfer functions (HRTFs) and presenting them over headphones. In the original work of Broadbent (1954) he used a number of different configurations while Cherry (1953) only used headphones and presented each stimulus monaurally.