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On my Mac, there is a font that contains the BEAMED EIGHT NOTES Unicode character, but there are no fonts that contains the MUSICAL SYMBOL PLUS NOTEHEAD or the MUSICAL SYMBOL QUARTER NOTE Unicode character.
Are there fonts that contain such characters?
After you choose the character go to the Font Variation section you might need to click on the triangle at its left side to expand this. This shows the fonts that include the glyph.
OS X normally will not display a character in the Private Use Area unless you manually set the font in the app. I understand this is intentional, since every font could have a different glyph at the same PUA code point, and it only makes sense to display something when the user specifies the font.
I think it should also work when the right font is selected via CSS or other markup in a document being read.
Some earlier versions of OS X did not have this "feature" and did display PUA stuff. I don't know how they chose which font to use when more than one had something at the code point selected.
Best Answer
(The links to the Musica typeface don't seem to lead anywhere useful.)
Uptake of the Musical Symbols in Unicode has been very limited: there were already fonts that allowed music symbols to be incorporated into text blocks, such as the Bach Musicological Font (which is now hard to find); and notation applications use their own fonts, whose symbols tend to use the 'ASCII' glyph range.
However, over the last few years, a standard for music notation symbols in Unicode has been formulated, called SMuFL. SMUFL-compliant fonts will also include glyphs in the Unicode reserved locations that you are after.
The SMuFL reference font, Bravura, comes in two versions, one for notation software, and the other, Bravura Text, for use in text. Either of these will include the characters you want. You can download the fonts here.