It could provide power to record, and harm one tenor by mistake (9)
I believe the answer is:
logarithm
'it could provide power' is the definition.
The definition suggests a singular noun which matches the answer.
'record and harm one tenor by mistake' is the wordplay.
'record' becomes 'log' (log is a kind of record).
'and' means one lot of letters go next to another.
'one' becomes 'i' (Roman numeral).
'tenor' becomes 't'.
'by mistake' indicates anagramming the letters.
'harm'+'i'+'t'='harmit'
'harmit' is an anagram of 'arithm'.
'log'+'arithm'='LOGARITHM'
'to' is the link.
Can you help me to learn more?
(Other definitions for logarithm that I've seen before include "Mathematical aid simplifying multiplication and division - a girl moth (anag)" , "It undoes power" , "Aid to mathematical calculation" , "Power to which base number must be raised to obtain a given number" , "Exponent" .)