mysql test if time is within a time span over midnight

I am working on a mysql query that will search a database of entries that each have a time span to see if a user input time or time span falls within the entries spans.

Ex user can input "13:00" or "13:00-16:00"

the database has entries like so:

id    startTime    endTime  
1     08:00        12:00  
2     20:00        03:00  
3     14:00        01:00  
4     16:00        21:00  

Searching is easy enough against a time span that is during a single day (startTime < endTime). The issue is testing when a span goes across midnight (endTime < startTime). For this application these values can not have a date attachment (they are stored as time only), so timediff etc will not work.

UPDATE:

The time spans will never be greater than 24 hrs so startTime of 1 and endTime of 3 will always be a 2 hr item, not a 26 hr item.

The reason I am not using dates is this relates to something more or less like business hours (but not exactly t开发者_如何学编程hat use case). The items the spans represent have daily hours, so it is not practical to add datetime stamps for every day.

I would check if endTime

1. totaltime = startTime + (24 hours - endTime)

The problem I see with this is if the endTime is the next day and endTime>startTime. For example you start at noon and end at 1pm the next day. There is also a problem if the time spans more than 2 days. For example start on day 1 and end day 3 or longer. I would recommend using dates.