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For a personal project I was trying to transcribe a part of the flute solo in this piece. However, I am unsure at what speed I should transcribe the piece. I could either transcribe the piece at 250 bpm or 125 bpm. If the piece is transcribed with 250 bpm the transcription may be significantly less complicated, but 125 bpm may fit the piece better. I have transcribed the first few seconds of the piece at 250 bpm and 125 bpm respectively in the image below.

What BPM is would be considered more fitting? Or is this a subjective matter?

This question is often subjective, but there are some objective rationalizations that make things easier.

I would strongly recommend transcribing this in a way that doesn't use so many small note values. Not only does this match the feel of the music better, it will also be easier for a performer to read; those 64th notes in the 125bpm transcription are pretty gnarly.

With that said, remember that you can transcribe something into a form of cut time. In this case, I'd use the 250bpm transcription but with a 2/2 time signature, signifying that the half note receives the beat instead of the quarter note (and thus it's really 125bpm).

Transcribing it in cut time is really the best of both worlds: you get the notational simplicity of the 250bpm transcription with the half-time feel of the 125bpm transcription.

What I do in these cases is to listen to the drums. Listen to what the drummer is playing and you can easily deduct the tempo. In this song, the Kick Drum and the Snare Drum are being played on the beats 1,3 and 2,4 respectively and they are quarter notes. These quarter notes are on 125bpm, no matter how fast the flute is playing.

This is really common for the drummer; to play the kick and snare drums on quarter notes (this is the pulse of the song) and the hi hat on eighth notes, which is exactly the case in the song.