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Say you have an allegro marking on a piece. This is about 120-144 bpm. If the time signature is 4/4, that means that quarter note= 120 - 144. However, if the time signature on the piece is 6/8, does that mean eighth note= 120 - 144, or is it still referring to the quarter note?

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I would be very careful about assigning specific numbers to tempo names, where the composer did not specify those numbers. In general they don't match up that precisely, and its likely that the composer did not have that specific of a tempo in mind. "Allegro" for example, does not convey a specific range of tempos. It just conveys a brisk or lively mood (literally, "joyfully"). Tempo terms actually tend to be used as a mood indicator more than some kind of precise clockwork.

That said, while I wouldn't assume any particular tempo number, you should generally use the dotted quarter (not eighth notes or straight quarter notes) as the basis for the beat in a compound time signature. However, if a specific tempo number is given, it should make it clear (with a small note and an equal sign) which note is considered the beat (as mentioned in Shevliaskovic's answer).

See also: How to calculate the tempo of a song in numbers and find the Italian terms?

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What I have seen from pieces I've played is that they specify that. At the top of the score, there would be a quarter note = 140 or eighth note = 140 or dotted quarter note = 140 or half note = 140 or something.

To be honest, I think that in a 6/8 piece it would be odd to have quarter note = 140 it should be dotted quarter or eighth imo.

Per the related wiki article:

In compound time signatures the beat consists of three note durations (so there are 3 quavers (eighth notes) per beat in a 6/8 time signature), so a dotted form of the next note duration up is used. The most common compound signatures: 6/8, 9/8, and 12/8, therefore use a dotted crotchet (dotted quarter note) to indicate their BPM.

If I saw a score that said allegro with a time signature like 6/8 and there wasn't anything that makes it clear, I would play the eighth note on 140; I would see it as if there was a eighth note = 140 on the top of the score.

  • Yup. A mm marking that doesn't specify what note value is being counted is incomplete and meaningless. If a piece in 6/8 specified q=120 I'd either assume a misprint, or examine the note-groupings in the piece, and the context, to see if counting quarters might be appropriate. Today's music does not always follow the "6/8 is compound-triple, two dotted quarter beats to the bar" rule rigidly. – Laurence Payne Mar 8 '15 at 1:35

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