Four characters, and the last two are plural

♩ is U+2669 QUARTER NOTE and ♪ is U+266A EIGHTH NOTE. Both are a single note. ♫ is U+266B BEAMED EIGHTH NOTES and ♬ is U+266C BEAMED SIXTEENTH NOTES — read those names again, because both are plural. Each is a pair of notes joined by a beam. If you want one note in a sentence, ♩ or ♪ is the one you want; ♫ and ♬ draw two.

The same four notes go by different words in British and American terminology: quarter note is crotchet, eighth note is quaver, sixteenth note is semiquaver. Unicode uses the American set in the official names, so search the catalogue for QUARTER NOTE, not for crotchet.

There is no rest in this block

A rest marks silence, and none of the four characters here is one. The rests exist in Unicode, but they live in the Musical Symbols block from U+1D13B MUSICAL SYMBOL WHOLE REST onward, above U+FFFF, where each one needs four bytes; anywhere that accepts a maximum of three bytes per character will refuse them. That is covered on sheet music symbols.

Two characters below U+FFFF do carry the word REST in their official Unicode names, and neither is musical: U+3241 PARENTHESIZED IDEOGRAPH REST and U+32A1 CIRCLED IDEOGRAPH REST are Japanese signage meaning closed. If a symbol list hands you one of those as a musical rest, the list is wrong.

Two characters share a name

The official name of ♩ is plain QUARTER NOTE. There is a second, separate character called MUSICAL SYMBOL QUARTER NOTE at U+1D15F. Searching a character database by name returns both, and they are not interchangeable: only U+2669 encodes in three bytes of UTF-8. When you copy from a reference, check the U+ number, not the name.

Width is not consistent across the four

East Asian Width is a Unicode property that a terminal or a monospace layout uses to decide how many cells a character occupies. ♩, ♪ and ♬ are Ambiguous; ♫ is Neutral. Where Ambiguous is configured to render double-width, three of these four take two cells and ♫ takes one, so a fixed-width list of them will not line up in a column.

In HTML

Only ♪ has a named character reference, and it is not the name you would guess: ♪. The other three have no name at all, so use numeric references — ♩ for ♩, ♫ for ♫ and ♬ for ♬. All four are general category So, other symbol, so a validation rule written around \p{L} or \p{N} will reject every one of them.

These four and the three accidentals on sharp and flat symbols are the complete set of music characters that paste anywhere; music symbols is the index for the wing.