I recently started writing a string quartet recently and I want the cello to play two notes (B and C; G and A) simultaneously. How do I know if that is actually playable (not on the same string/reasonable hand span) on the cello? Obviously there are multiple strings on the instrument so multiple notes are possible, but does the specific interval determine if the notes are playable?
Whether these combination are possible depends entirely on where they are and which octaves the notes are. If the B and C are B2 and C2 specifically than it’s very easy, because C2 is an open string (the lowest one) and just about any note above (and including) G2 are possible to play at the same time because they are playable on the next string up. If the G and A are G2 and A2 it’s easy because G2 is an open string and the A2, and just about anything from C2 up, can be played on the lower string at the same time. G3 and A3 are easy as well, because A3 is an open string and G3 can be played on the string below.
In a sense, these are lucky notes, because at least one is an open string, and most intervals are possible when combined with an open string as long as it can be played on a string above or below.
General rules when open strings aren’t involved are a bit trickier, and there can be specific exceptions, but it is possible to give a general list. Remember: this list is specifically for double stops in which neither note is an open string.
Easy intervals playable virtually anywhere: Major and minor sixths Perfect fourths (though they can be a bit harder to tune due to the pure interval) Tritones
Slight amount of stretch for players with smaller hands and especially in lower positions (closer to the nut): Major thirds Minor sevenths But really, these are rarely a huge problem.
Fairly extensive stretch, though they start to be playable in higher positions. Some people with larger hands can handle them even down low: minor thirds Major sevenths
Requires the use of the thumb in all but the highest positions, BUT tend to be practiced a lot by pros: Perfect octaves
Requires the use of thumb and tend to be unfamiliar to a lot of players: Major and minor seconds Perfect unisons
Tends to require awkward hand position and difficult to tune: Perfect fifths
Major and minor sixths, major thirds, perfect fourths, tritones and minor sevenths tend to be pretty safe. Perfect fifths aren’t too terrible, but can be wearying and shouldn’t be overused. Perfect octaves are difficult but practiced often enough that they’re fine for more virtuostic pieces and when you give plenty of time for the player to get their thumb in position.
Everything else can be difficult and should be used very carefully. Again, unless an open string can be involved, in which case almost anything is doable.
ETA: For violin and viola, things are generally less restrictive. All the easy intervals for cello are also easy on violin and viola. In addition, both minor thirds and major thirds are easy, as are both minor and major sevenths. Violin and viola don’t ever use the thumb, but octaves and still possible and a good bit easier, though you don’t need to allow nearly as much prep time as for cello. Interestingly, perfect fifths are still kind of awkward and wearying if overused. This is because—just like for cello—violins and violas are tuned in perfect fifths, and mashing the finger down is less comfortable than normal performance. Major and minor seconds are, theoretically, no more difficult than minor ninths and octaves respectively, but they are less familiar to the majority of players. Unisons tend to be a bit of a pain, and aren’t super familiar, but are potentially usable in a virtuostic context.
A good reference source for this (and much else!) is Cecil Forsyth's "Orchestration"- available on line at https://imslp.org/wiki/Special:ImagefromIndex/107662/torat
This is now just over 100 years old and therefore doesn't include many modern "extended techniques" but it's a comprehensive reference to the basics.
See page 416 specifically for cello double-stops. I don't think it disagrees much with Pat Muchmore's answer, but it's worth noting as a more general reference for such things.