In the odd chance you didn't catch every word of the Yahoo! Music API Terms of Service, here are some important rules you must abide by when using the API:
Usage of the API is limited to noncommercial use.
Make sure your locale is supported by the API and follow the internationalization rules. See Supported Locales.
Yahoo! reserves the right to include advertising, e-commerce links (such as a "buy" button), copyright notices, and other metadata in or associated with the content provided to you through the Yahoo! Music APIs (for example, within a video player or media player). You shall not interfere with any advertising, e-commerce links, copyright notices, or other metadata presented.
Otherwise, terms are basically the same as the standard Yahoo! APIs Terms of Use.