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I have used this (in my own bash scripting)
From frames to DF timecode:
fps=30
D=$(( frames/17982 ))
M=$(( frames%17982 ))
frames=$(( frames+ 18*D + 2*((M - 2)/1798) ))
# Count frames, seconds, minutes and hours
frame=$(( frames%fps ))
second=$(( frames/fps%60 ))
minute=$(( frames/fps/60%60 ))
hour=$(( frames/fps/60/60%24 ))
It's based on the code provided by some SMPTE guy and works fine even up to 24H TC.
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