The instructor will only be able to work with P3-P5 pupils in four of the more disadvantaged communities because of the limited pound;53,000 budget in the first year of the three-year scheme. Percussion is seen as a way to identify rhythm in children and a cheaper option than learning other instruments.
Like other authorities, the city complains there is no guarantee the scheme will continue beyond 2006, although ministers have suggested the pound;17.7 million funding will be incorporated into overall council spending.
Moray, Highland and the Western Isles have raised similar issues along with the instructors' national organisation. A national shortage means there are not enough instructors to meet the extra demand.
Aberdeen has written to the Scottish Arts Council, which is administering the scheme for the Scottish Executive, to register its "disappointment".
John Stodter, director for learning and leisure, wants to know how decisions were made on allocations to councils and what the pound;3.5 million retained by the arts council over three years will be used for.
Meanwhile, an analysis of the city's first year of swimming for all eight-year-olds has underlined the need for organised school programmes if all pupils are to become confident in water.
More than 2,000 children took part in the first year but only 290 pupils (14 per cent) have taken up the option of vouchers for lessons out of school hours. Half the parents said they would be keen to take advantage but few follow through their interest.
The city says its scheme has been highly successful in introducing primary children to the water, although concerns remain over access to pools and the "significant increase" needed in the number of teachers qualified to coach.
Aberdeen reintroduced swimming after a survey showed that one in three S1 pupils could not swim or could not swim more than 10 metres.
A survey by Win Hayes at Edinburgh University found that as many as one in two 11-year-olds in Scotland leaves primary unable to swim or is at risk in deep water. It echoes the Aberdeen finding that few pupils take part in swimming out of school.
Scottish Swimming, the governing body, has issued a revised swimming strategy backed by Frank McAveety, Sports Minister. It is pressing for an entitlement to swim for all primary children and a minimum level of achievement for all 10-year-olds.