In theory any two primaries combined should create a secondary colour however broken colour involves two complimentaries, one colour which is primary and one that is secondary, opposing eachother on the wheel. Red and green, blue and orange and purple and yellow.
Broken colours can however be made pleasing if eachother a lot of one colour is added or a little amount to create more of a balance in the mix. Broken colours are often dull on their own, however they mix well with other colours as they are essentially "cousins" of many other colours.
Broken colours create an overall dull feeling to a composition whereas pure colours are a lot brighter and therfore influence the overall feel of the composition with this. An example of this would be painting autumn and spring, autumn is a much more subdued season, the leaves are changing colour and falling and the weather is a bit colder with gentle oranges, yellows and reds. Whereas spring would be much more bright yellows and greens and blues to create that feel of spring.