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I've seen tempo sometimes denoted like "♩ = 120 BPM" instead of using something like "Adagio". In cases like this where it has a number, the actual size of the note seems irrelevant since I could just say then "dotted-half-note = 30 BPM" and it would mean the same thing.

So let's suppose I'm in 3/4 time signature, which means my measure is made up of quarter notes in a pattern of 1-1-1. Is it customary to use the same size note as in the bottom of the time signature? In this case, it would then be "♩ = 120 BPM". Or can I just put any size I want as long as it means the same thing, e.g. "dotted-half-note = 30 BPM"?

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  • You could also give the length of a beat in time as s, ms or ns. However that wouldn‘t help much. What you feel, or what you might dance to, is, in your example: 123 123 etc., not 3 3 etc. So it‘s more a specification of feel, rather than tempo alone.
    – MS-SPO
    Jan 6 at 9:45

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Generally, the bottom note (of simple time such as 3/2, 2/4, 3/4, 2/2, or 4/4), the bottom note is used to represent the beat. Compound time may be a bit more complex (but the composer ought to indicate what's wanted); times like 6/4 or 6/8 or 12/8 may indicate grouping by triplets. Sometimes the actual notes are used as in "quarter note = 120."

However, some care needs to be taken with dancers or music intended for dancing. Often dances are indicated in "measures per minute" rather than "beats per minute." In waltzes vs foxtrots, there is a difference. As some older sheet music was written in 2/4 but with an eighth-note beat, measures per minute would equalize 4/4 with 2/4 (rags, tangos, foxtrots, cha-chas...). There's always some "performance culture" that must be considered in figuring out tempi. (Not to mention the speed changes needed to compensate for venues with long reverb times, but that's not notated except for computer.)

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  • I second the advice to consider the "performance culture". If the score you're writing is in a well-established tradition, you can probably look at other scores and figure out what makes the most sense that way. Otherwise it's a good idea to ask relevant performers. They can figure out lots of things, but you want to make their lives as easy as possible, so you want to put whatever is clearest to them/easiest to count.
    – Zoë Sparks
    Jan 4, 2021 at 3:31
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A metronome mark doesn’t always match the bottom of a time signature, but neither should it be whatever you want.

A metronome mark is most properly a number of beats per minute. So the note value used for a metronome mark should be the value taken by a beat, not an arbitrary note value. Normally the bottom of a time signature indicates the beat directly, as in 3/4, or 2/2.

However, when the top of the time signature is divisible by 3, it often indicates compound time, especially when the bottom number is 8 (note that 3/4 would not normally indicate compound time, 12/4 might indicate it, and 6/8 does indicate it). For most compound time, a dotted quarter note gets the beat, which should be reflected as such in any metronome mark. Including a metronome mark with a note value along with an unusual time signature is one way to clarify how the time signature is to be interpreted.

Other cases where the metronome mark would not match the bottom number would be time signatures that are slightly changed forms of other time signature. For example, many cases of 7/8 time are meant to be played as 4/4 with a dropped 8th note. The tempo is best indicated with a quarter note value even if traditional metronomes could never play those clicks. Partly to be clear about the intention of the music and today also because there are digital metronome and apps that can click on quarter notes in 7/8 time.

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BPM stands for Beats Per Minute, so the note used in the tempo indication should have the duration of one beat.

In a simple time signature like 2/4, 3/4, or 4/4, you should use a crotchet note (quarter note), because this is the duration of one beat.

But in a compound time signature such as 6/8, or 9/8, or 12/8, a quaver (eight note) is the duration of a pulse (which has less emphasis than a beat), a dotted crotchet (dotted quarter note) has the duration of a beat, and so this is what should be used in the tempo indication.

In a 'larger' compound time signature such as 6/4 or 9/4 (again compound time signatures), the beat duration is a dotted minim (dotted half note).

Irregular time signatures are a bit more difficult because the duration of a beat is not constant.

[where S = strong beat, M = medium beat, w = weak (pulse)]
5/8 has the beat structure of SwwMw (but could also be SwMww)
7/8 has SwwMwMw (usually)
and 8/8 is SwwMwwMw

These irregular time signature should probably be denoted with dotted crotchets because this is the duration of a strong beat. (The second option of 5/8 should use a crotchet).
But, it would also be reasonable to instead uses a quaver in the tempo indication and write a PPM (Pulses Per Minute) instead of BPM.

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  • Dave Brubeck's Unsquare Dance - SwSwSww.
    – Tim
    Jan 3, 2021 at 12:54
  • @Tim Hmm strange piece, sounds like SwSwSMw to me, which is a type of 7/4.
    – Elements in Space
    Jan 3, 2021 at 13:32
  • That song is really groovy!
    – Elements in Space
    Jan 3, 2021 at 13:39
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The most usual case is to give the tempo in the units of the bottom of the time signature. For fast tempi it might be given in multiples of that, and for very slow tempi it might be given in a subdivision.

For example in 4/4:

  • quarter=120 works well
  • quarter=200 might be better expressed as half=100
  • quarter=50 might look better as eighth=100

The tempo of a Viennese waltz could be given as quarter=180 or dotted-half=60. Both are common.

It's up to the composer to choose something they think will help the performer.

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Since the lower number is supposed to denote what a 'beat' is, that should be the beat that is shown in 'bpm'. Otherwise, nothing would make sense. So your crotchet=120bpm should be ?=40bpm, in 3/4 time, I guess. Although only the composer knows what '?' represents.

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