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My professor wants us to explain the range of a song by stating, for example, "range of an octave plus a 4th" rather than "the range is D to G"... because it may be different if transposed.

My question is if it ranges from F4 to G5, does that mean I can say it has a "range of an octave plus a 2nd"?

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Yup. If you would like to get specific (pun not intended), the song has a range of an octave plus a major second, since there are many qualities of seconds (but octaves are assumed to be perfect in this context). Getting even more technical, you could also use compound intervals to describe the situation, saying the song has a range of a major ninth, though that's not as common once you get beyond two octaves.

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    You should, of course, ask your professor exactly how they want the range stated if you get the opportunity, but my suggested conventions hold within most musical discussion. – user45266 Dec 9 '19 at 6:04

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