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I'm trying to understand how exactly we calculate tempos and how we assign their Italian names in written music. I've searched before asking, but I'm not 100% sure I've understood everything correctly, so I'd like someone to confirm or correct me in simple terms.

Say I have a melody that's composed of eighths and no pauses. In 1 minute, exactly 150 eighths are played. The time signature is 6/8.

  1. I assume that in this case the appropriate symbol (if written on a sheet) would be Q = 75 (or 1/8th = 150). Is this right?
  2. In the above example, is the BPM equal to 75 or 150? Is the conversion (from, say, 150 eigthths to X BPM) independent of the time signature or not? And if not, how?
  3. Wikipedia has a list of tempo ranges in BPM with their respective Italian names. Given the answer of question 2, if a different song is at, say, 135 BPM, is it always vivace or does this depend on the time signature?
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Good question, I wonder about this too. Things that seem plausible: if the time signature is known to be 6/8, then I'd say it would not be a good idea to denote it as Q=75, since the quarter is not the unit (the 8th is). And additionally, 6/8 is usually counted in 2 groups of 3 8ths, not as 3 groups of 2 8ths. So I'd prefer 1/8th = 150 over 1/4th = 75. I'm not sure about the "BPM" notation, but intuitively I'd say the beat is the unit of the time signature, so 8th in case of 6/8th. Regarding the "italian terms", those also denote a "mood", not just the tempo. So it's not always "vivace". –  Roland Bouman Jan 23 at 2:22
    
I find it important to note that most software and metronomes operate with a default value of Quarter note taking the beat. Depending on your software or metronome, this should be changeable or the settings can be changed to allow the click to fall with different accents and/or subdivisions. –  Basstickler Jan 23 at 13:35
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Very often in 6/8, the dotted quarter is the unit of measure for metronome markings. –  BobRodes Feb 6 at 22:04

4 Answers 4

up vote 5 down vote accepted
  1. Beats per minute (BPM) is dependent of time signature. The time signature tells which duration gets the beat. A song with a time signature 4/4 can have the same BPM as a song with as a song with a time signature of 4/8 or 4/2. They would also most likely feel the same and would be hard to differentiate without the music in front of you. Because the time signature is 6/8, the eighth note becomes the beat and the BPM would be written out as (eighth notes)=150 similar to as depicted below.

    enter image description here

  2. It is true that 75 quarter notes equal 150 eight notes, but because the beat is defied as eighth notes the BPM cannot be 75 it has to be 150. In 6/8 BPM refers to eight notes not quarter notes. If the time signature was 3/4 under the same conditions the BPM would be (quarter notes)=75. The time signature defines the beat.

  3. Yes it will always Vivace no matter the time signature because again the the time signature defines the beat. A song in 3/8 with a BPM of 135 will be Vivace just like a song with a time signature of 3/4 with a BPM of 135 or a song with a time signature of 3/2 with a BPM of 135. However, the Italian tempos more denote feel than actual tempo so not every Vivace song will have the same BPM.

EDIT: I was wrong in the comments for using the term hypermeter and as Pat Muchmore pointed out the term I was looking for was compound meter. The difference between compound and simple is in simple the beat(different then beats used in BPM) can be broken up into two subdivisions while compound can only be broken into three subdivision. Also another error I made in compound meters(like 6/8) the beat is mostly grouped by the three subdivisions which in 6/8 case it is a dotted eight note. That being said it if it a simple(2/x,3/x, and 4/x) and asymmetrical meter what I said above is still valid, but compound meters (6/x, 9/x, 12/x) deserves a separate answer set because it is not the same.

It could be expressed as (eighth notes)=150, but as pointed out in the comments it is usually grouped to demonstrate the compound meter. I.E. insted of being grouped in eighth notes, it is grouped in dotted eighth notes. It is commonly grouped as (dotted quater notes)=50.

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I have some reservations concerning the statement, that in 6/8 the beat would be 1/8. At least in classical music in this meter in nearly every piece there would be an emphasis on the first and the fourth eigth, so that the beat would be three eights or a dotted quarter. –  guidot Jan 23 at 8:58
    
That's different than any usage I've ever seen of hypermeter. Hypermeter, at least in the William Rothstein sense that I understand to be standard, is multi-measure groupings, not intra-measure groupings. 6/8 and 12/8 do indeed have the beat as the dotted-quarter, as evidenced by their conducting patterns. As always, there's room for different vocabularies, but I've never taught from a textbook that doesn't define 6/8, 9/8, 12/8, etc. as being compound meters with dotted-quarter beats in nearly all cases. –  Pat Muchmore Jan 23 at 19:22
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I've virtually never performed a piece in which the beat was felt as 1+1+1+1+1. The beat is uneven, shifting between quarters and dotted-quarters, which is why it's asymmetric. Stack exchange thinks this conversation is too long, so I'll stop. Obviously you and I define "beat" very differently, what you call "groupings" I call beat. Your usage is very strange to me, but perhaps we were just taught in very different traditions. –  Pat Muchmore Jan 23 at 23:04
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You're right, this is all straying very far from the OP. I would just point out that 5/4 and 7/8 are very different kinds of asymmetric time sigs. Your description of 5/4 is spot on, but 7/8 is fundamentally different--there are three beats in the measure, but one is an eighth note longer than the other two, e.g. 2+2+3. As always, there are exceptions, but almost always that's how it is conducted and felt by the performers. If I had a nickel for every rehearsal minute spent discussing where the long beat is... –  Pat Muchmore Jan 24 at 17:03
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I think you're confusing the purely pragmatic fact of metronome settings with beat. Again, I'm not talking about 7/4, I'm talking about 7/8, they are different. 9/8 has three beats, each 3 eighths long. 7/8 has three beats in which two have 2 eighths and one has 3. This is nothing like triplets, where the beat stays the same and you squeeze 3 notes in instead of two--the eighth speed is consistent. You're right that the long beat can shift metric positions, and that will be reflected by how the passage is conducted or how the musicians feel the beat together. –  Pat Muchmore Jan 29 at 17:06

If your piece is in 6/8, then the eighth-note is NOT the unit of the beat, it is the dotted-quarter note. Most time signatures with 8 on bottom are compound time signatures, not simple. Thus, in your example, if the eighth notes are happening 150 times a minute, then the dotted-quarter beat is 150 divided by 3, or dotted-quarter = 50. This is the same as the BPM, although in some programs it's easier to set the BPM to some subdivision like the eighth to make editing easier. 50 is relatively slow, akin to Largo in the old Italian terms--but you shouldn't feel beholden to those old tempo indications. I advise my composition students to just use their own language to describe the tempo and feel of the song, and then add an explicit metronome marking in parentheses afterward, i.e. Melancholy (DQ = 50) [replace DQ with an actual dotted-quarter note).

EDITED TO ADD: A lot of this depends on the feel of your actual song, I'm assuming you're describing it accurately as a proper 6/8 in "classical" terms. It's all about how many eighth notes are grouped within the pulse that you were naturally tap out with your foot. If it feels natural to tap every eighth-note, then I'm not sure that 6/8 is the best description. If it feels natural to tap every group of two eighth notes, then you should probably call it 3/4. Standard 6/8 should feel like there are three eighth notes for every beat.

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Beyond the consideration of the time signature and how many subdivisions there are of the main beat indicated by the time signature, please remember this:

The Italian names for different tempos were invented and were used in the centuries before there was such a thing as a mechanical device that could create a precise number of beats per minute (the metronome), and before there were accurate clocks that could measure seconds or fractions of a second. Therefore the important point is this: the Italian names for tempos are by their very nature approximate suggestions as to what tempo you should select. They are guidelines for how to interpret the tempo of a piece. They are not scientific measurements.

Beats-per-minute, however, is a scientific measurement of tempo.

The first metronomes were invented around the year 1815, and it was only in subsequent decades that it became common for composers and publishers to list a value such as "one quarter note equals 82 beats per minute" on a score in place of an Italian tempo name or a word like "moderate" or "fast" in some other language.

Whenever you see an "Italian" name for a tempo indication, or one in another language besides Italian, it means that the composer is suggesting an approximate tempo. You can and should choose your own tempo based on that suggestion.

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  1. The number is telling beats per minute. So whatever a beat is, that's it. The bottom number in the time sig. tells that. If it's 4, then a beat is a crotchet. If 8, then it's a quaver.Just like maths fractions. Thus if the tempo is 60b.p.m., and the bottom number is 4, there will be 60 of them in a minute, one a second.

2.In away the tempo is free from the time sig. in that any number of b.p.m. can be allocated to a crotchet, quaver.Watch duple time, though, as for example, 12/8 could be counted as 4/4, But the speed of playing would probably tell you if it's wrong !

3.The Italian names are just a broad idea, to give a clue as to how a piece will be; it's almost as much a guide as to how it's played as how fast it's played.

Tempos have been and are rarely stuck to rigidly. Dance tunes are probably the only ones which need adherence. Most others will have a guide, but how often do performers play a slow piece fast, or vice versa ? Pop songs are changed, tempo wise, after it's all been recorded, to 'improve' them.Try putting a metronome on against a tune, and it often becomes apparent that the tune moves, albeit slightly, in and out of tempo. That's music.

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