Purest limits of music playing in band (8)
I believe the answer is:
spectrum
'band' is the definition.
(eg a band of colours)
'purest limits of music playing' is the wordplay.
'limits of' suggests removing the centre.
'playing' is an anagram indicator.
'music' with its middle removed is 'mc'.
'purest'+'mc'='purestmc'
'purestmc' is an anagram of 'SPECTRUM'.
'in' acts as a link.
(Other definitions for spectrum that I've seen before include "Light split by prism" , "range of tones" , "Crumpets (anag)" , "A broad range, of colours say" , "Array, range" .)