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Sometimes the same phonetic symbol is used when a slightly different sound is created (allophones). This depends on the other sounds surrounding it.

BlaCK kitten blaCK egg

the /k/ sound in black differs depending on the following word – why is this? Is it to do with articulation or assimilation?

This does not only happen with the /k/ sound. It also occurs in other words, why and how does this happen?

Old cOde

The /o/ sound?

Huge Hunt

The /h/ sound?

Beef puB

The /b/ sound

EAsy pEAce

The /ea/ sound?
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tjterry6Is it to do with articulation or assimilation?
I'm not sure what distinction you're trying to make here, but I'd say mostly assimilation, though both are involved. The mouth often takes the shape of the following sound. This affects the quality of the preceding sound. The "h" for example is articulated wherever the following vowel happens to be.

CJ
Comments  
Linguistics. A predictable phonetic variant of a phoneme. For example, the aspirated t of top, the unaspirated t of stop, and the tt (pronounced as a flap) of batter are allophones of the English phoneme /t/.

The English language words have many origins, i.e. Latin, Greek, French, etc., not to mention how the language began to unravel after settlers came and began America. Some educated, and many, not. Words began changing, new words evolving, etc. I'm not so sure there is a direct answer to your very interesting question.

Thanks!

K.
 CalifJim's reply was promoted to an answer.