In a world of magic, spells are songs. They aren't easy to sing and becoming truly proficient requires a similar amount of time and effort as it does to become an opera singer on Earth. Of course some people are just naturally talented singers and in fact this is how magic was originally discovered by someone singing away as they worked.
Simple songs can help people lift things. A more complicated song can light a fire. An operatic aria in co-operation with a swordsmith could help to forge a powerful magical weapon. (see note at bottom)
Spells are not permanent - they only occur whilst the singer is actually singing.
Anyone who is tone-deaf (4% of the population) simply can't do magic, and magic isn't fine grained enough to perform any kind of 'healing' on them. In any case, being tone deaf isn't an illness - it's just a lack of a particular musical ability. Remarkably, people who are simply deaf can learn to sing perfectly well given either healing or the right feedback unless they are also tone-deaf.
The benevolent chief wizard wants everyone to be able to practise magic but she and her advisers simply don't know how to go about it.
This is a medieval society in terms of technology so there is no recording equipment or anything like that. People have tried playing the tunes on musical instruments by rote but it simply doesn't work without the words.
How can the tone-deaf people be allowed to perform magic in a world where the only magic available is through singing?
Many high wizards have tried to come up with a magical answer to this and failed so ideally I am looking for a non-magical solution.
There is a complex relationship between the words of a spell and the melody. It takes a lot of study and understanding to create new spells. Most people simply memorise existing songs that have been found to work by others or that have been especially created by gifted 'composers' (i.e. wizards). Of course only very talented people can sing some of these more difficult works.
It is important that the correct pitch is sung (different octaves are equivalent). Thus people who have perfect pitch have an extra advantage. Those who are musical but do not have perfect pitch must carry a tuned whistle around to get them started. Unfortunately tone-deaf people can not pick up the pitch or sustain it.
Important - To use a magical device such as the powerful sword, the user must sing whilst using it. The magical item simply acts as an amplifier.
At the risk of being somewhat controversial I present the final verse of the original British National Anthem. We don't often hear this being sung!
Lord grant that Marshal Wade
May by thy mighty aid
May he sedition hush,
And like a torrent rush,
Rebellious Scots to crush.
God save the Queen!
This anthem has a very simple tune and so leaves a lot to be desired in terms of effectiveness. However we can imagine the average soldier being able to sing it and march in time to it as they go into battle. The combined low-grade magic of all the troops could be backed up by an intricate descant from a trained opera singer equipped with a megaphone.