Sometimes you need yield translators for inter-converting meaningful, mathematically valid yields. But then again, sometimes you need dirty translators, which switch away from the realm of valid yields and into the realm of historical convenience. In other words, sometimes the market convention with some yields is simply mathematically not justified, and perhaps that market had its origin in a time before the real mathematics was widely understood. Once a convention has a real human practice and history associated with it, it is difficult to make a big-bang switch away from the inferior formalism. Best just to think of these dirty expressions as market quotes. And the process of packing/unpacking the market quote as a bit like taking your shoes off or putting them on when entering a house. Once cleaned, then the rules on yield translation can be applied for your specific purpose.
When we come to looking at specific markets we'll see some of this going on. But a second point I'd like to make just now about yield conversions is the possibility that the nominal rate time basis - the time period within which you understand your $n$ and $r$ - isn't yearly. It can be any period. It mostly is nominally expressed as a return for a 1 year period, but it could be a rate expressed for a multiple year period, or a half year period, or quarterly. Day count conventions, which I'll be getting to soon, can be thought of as a digital-to-analogue signal converter for time, embedded at the level of the market quote (taking your shoes off at the door).
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