I tot up minutes perhaps in modest study of scores, etc (10)

'study of scores etc' is the definition.
(musical scores)

'i tot up minutes perhaps in modest' is the wordplay.
'tot' becomes 'sum' (synonyms).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'minutes perhaps' becomes 'log' (a meeting's minutes are a log of the meeting).
'in' indicates putting letters inside.
'modest' becomes 'coy' (I've seen this before).
'i'+'sum'='isum'
'isum' reversed gives 'musi'.
'log' placed inside 'coy' is 'cology'.
'musi'+'cology'='MUSICOLOGY'