An academic paper Music Lessons Enhance IQ provides some evidence that music lessons may improve general intelligence. This briefing from the Society for Neuroscience discusses the issues further.

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Training in musical skills

There is a lot of evidence that computer based training in musical skills, such as discriminating notes, is very effective. See this paper for some background. While this is often known as "ear training", it is, of course, really training the brain rather than the ear!

GNU Solfege is a good open source ear trainer, and works on most platforms.

YouTube channel of Eric Arceneaux who sells his approach to learning singing and offers many lessons for free in his earlier videos.

YouTube channel of Dizzi Dulcimer who sells hammered dulcimers (and other easy to learn instruments) and gives her lessons away for free on her channel.

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BrainTrainingGames - for other potentially IQ enhancing activities