Today, the date corresponds to midnight today, so if you want to add dates from today, you also need something like
ColumnName >= select DATEADD(MILLISECOND, ((DATEPART(hh, GETDATE())*3600000)+(DATEPART(mi, GETDATE())*60000)+(DATEPART(s, GETDATE())*1000) +DATEPART(MILLISECOND,GETDATE()))*-1, GETDATE())
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