Question Question about Tempo/Meter/Time Signatures

[mobius017]

I've been working to understand how tempo/meter/time signatures relate to one another since I first tried studying music a good number of years ago. I think I've recently come to figure things out; could someone who knows better what they're doing check my understanding please? ;)

Below are the notes I've put together explaining the 3 concepts.

Tempo

• The speed of a piece of music, notated using Italian words or in Beats Per Minute (BPM)

Rhythm

• The patterns of sounds and silence in a piece of music, notated with musical notes of differing durations
  • E.g., note names and durations (using American/British names)
    • Whole note/semibreve: 4 beats
    • Half note/minim: 2 beats
    • Quarter note/crotchet: 1 beat
    • Eighth note/quaver: 0.5 beats
    • 16th note/semiquaver: 0.25 beats
    • Etc.

Meter/Time Signatures

• Generally, musical compositions follow repeating patterns of stressed and unstressed beats.
• In music notation, bar lines are placed at the end of each instance of this repeating pattern. The area between adjacent bar lines is called a measure, or bar.
  • Beats being stressed/unstressed is achieved by changing the velocity of the notes that correspond to those beats
• The function of time signatures in music is to indicate the pattern of stressed and unstressed beats that the music follows.
• Time signatures are written in a fraction-like format. The upper number (numerator) indicates the number of notes per measure. The lower number indicates the duration/type of these notes.
  • For example, 4/4 time indicates that each measure contains 4 notes, and that each note has the duration of a quarter note. 2/8 indicates that each measure has two notes, and that each note is an eighth note.
• Every time signature can be categorized/described along two dimensions
  • The number of notes (or groups of notes, explained later) per bar - each note or group of notes represents a beat - corresponds to the numerator
    • Duple - 2
      • Has a beat pattern of strong, weak
    • Triple - 3
      • Has a beat pattern of strong, weak, medium
    • Quadruple - 4
      • Has a beat pattern of strong, weak, medium, weak
  • The number of notes per beat
    • Simple - 1
    • Compound - 3
• Simple meter
  • Has a straightforward, march-like feel
  • Has a note pattern directly corresponding to the time signature, e.g. 4/4 has 4 quarter notes and 2/8 has 2 eighth notes
  • Each beat can be divided into even divisions of 2 notes
• Compound meter
  • Has a lilting feel
  • Every beat is represented by a group of 3 notes; i.e., compound meters can be made by tripling the notes of simple meters
    • E.g., the simple triple meter 3/4 corresponds to the compound triple meter 9/4, which has 9 quarter notes
  • Each beat can be divided into even divisions of 3 notes
  • Compound meters retain the stressed/unstressed patterns inherent to duple/triple/quadruple meters, but those patterns are applied to the groups of notes
    • E.g., 9/4 is a triple meter whose 9 quarter notes can be grouped into 3 groups of 3 quarter notes, and the first group is strongly stressed, the second group is weakly stressed, and the third is mediumly stressed

 

[inactive]

One thing to keep in mind is that all of the above is very western in origin. Other cultures don't necessarily look at musical time in the same. A favourite example of western academics is Indonesian gamelan, which views musical time as a circle.

Additionally, not all western music uses bars. Divisions into measures emerged during the Renaissance period, but even up to the modern day cadenzas and cadenza-like passages often contain portions without barlines.

Another concept to be aware of is odd meters such as 5/4, which can be (but not exclusively) interpreted as 3/4+2/4; or 7/8 which can be (but not exclusively) interpreted as 2/4+3/8. More confusing is 8/8, which can be (but not exclusively) interpreted as 6/8+1/4. And there are countless others.

In case you're curious, a couple of famous pieces in 5/4 time are Mars The Bringer of War by Holst, and Take Five by Paul Desmond from the Dave Brubeck Quartet. (Dave Brubeck himself often experimented with odd meters.)

 

[AALLF]

Hi, I've just read though all of your information, and I believe it is almost all technically correct. If I may clarify a few things here, just to be completely sure:

Rhythm

• The patterns of sounds and silence in a piece of music, notated with musical notes of differing durations
  • E.g., note names and durations (using American/British names)
    • Whole note/semibreve: 4 beats
    • Half note/minim: 2 beats
    • Quarter note/crotchet: 1 beat
    • Eighth note/quaver: 0.5 beats
    • 16th note/semiquaver: 0.25 beats
    • Etc.

Just to clarify, this only applies to 4/4 time.

The upper number (numerator) indicates the number of notes per measure. The lower number indicates the duration/type of these notes.

• For example, 4/4 time indicates that each measure contains 4 notes, and that each note has the duration of a quarter note. 2/8 indicates that each measure has two notes, and that each note is an eighth note.

Again, it would be more technically correct to say "beats" instead of "notes". A measure can contain as many notes as you want, provided they all add up to the correct amount of beats. For example, 4/4 time, means that the quarter note gets the beat, and there are 4 beats per measure. 6/8 time means that the eighth note gets the beat, and there are 6 beats per measure.

Compound meter

• Has a lilting feel
• Every beat is represented by a group of 3 notes; i.e., compound meters can be made by tripling the notes of simple meters

Hmm, maybe it's more technically correct to say feel, or grouping, instead of beat. For instance in 6/8, the eighth note still gets the beat, but they are often grouped together in 3's to show the stressed beat (the first eighth note in the grouping).

Hopefully that helps some. It's been a while since I've had to think about this myself.

 

[inactive]

6/8 time means that the eighth note gets the beat, and there are 6 beats per measure.

6/8 = two beats per measure.

 

[mobius017]

Hi, I've just read though all of your information, and I believe it is almost all technically correct. If I may clarify a few things here, just to be completely sure:
...
Just to clarify, this only applies to 4/4 time.
...
Again, it would be more technically correct to say "beats" instead of "notes". A measure can contain as many notes as you want, provided they all add up to the correct amount of beats. For example, 4/4 time, means that the quarter note gets the beat, and there are 4 beats per measure. 6/8 time means that the eighth note gets the beat, and there are 6 beats per measure.

Thank you! I'm really glad to have the feedback from someone who knows better than me!

I think these comments gets back to one of the central things I've been misunderstanding. The thing I thought I'd figured out was that the time signature is actually completely separate from note duration. But judging from your comments, that doesn't seem to be the case--it seems like if you change the time signature, the actual durations of the notes changes. I.e., quarter notes get longer or shorter.

That's one of the things I've struggled to understand. How do musicians cope with this? As musicians play along, are they actually running up to quarter notes and saying, "Oh, a quarter note. I know what that is. Oh, wait--given the time signature, I have to multiply that by 0.125 and play that instead?"

(Edit: bear in mind, when I studied music before, I started learning using 4/4 time. So that's where I got my whole foundation for understanding how long a quarter note is, for example. Which is where I get this "multiplication" idea for adjusting note durations in accordance with other time signatures.)

Maybe the key lies in what you said about "get the beat." I've heard that phrase before. So, maybe tempo is indeed a fixed thing, going along predictably at, for example, 120 BPM. Depending on time signature, each beat is understood to correspond to a different note. So in 4/4, that note is a quarter; in 6/8, that is the eighth note. That should mean that 6/8 is slower than 4/4, correct, assuming that tempo is fixed?

Though, I'm not sure that changes anything about the difficult idea that musicians are completing complex fraction/decimal mental math in the midst of performing.... I don't mean to impugn anyone's intelligence, but that seems like too much of a mental load for anyone to carry....

 

[Älfa Dröttning]

I think it’s important to remember that the decision of which time signature you use depends upon how the music is accented (or how you perceive the accent). Like parallax_fifths said, if you’re looking at something in 6/8, it’s usually accented on beats 1 and 4, and that makes it feel like two dotted quarter notes instead of six eighth notes. If you’re looking at a measure of eighth notes in 3/4 you would have the same amount of eighth notes, but they would have different accents.

6/8: 1 2 3 4 5 6
3/4: 1 2 3 4 5 6

The groups of eighth notes are also counted differently ("1 2 3 4 5 6". for 6/8 versus "1 and 2 and 3 and" for 3/4), but that's not as important a factor to consider when looking at the differences between the two.

For how people adapt to tempos, it depends on what you're playing. For example, I'm currently working on a piece that, among other things, starts with a quarter note being at 72 bpm in 3/4 and then goes to the quarter note being 84 bpm in 6/4, and then has an entire measure of 9/8 being 60 bpm. Tbh I didn't even look at the tempo markings for weeks until just now because, unless I'm just starting learning the piece or am setting my metronome to a particular tempo, I don't usually do any math. After enough practice I don't pay attention to what the specific timing of everything is because it's just muscle memory, and since it's a solo with an accompaniment I can take liberties with the tempo.

Take movement 5 of Riverdance (Firedance) for example of a group performance: . With enough practice, you don't think about the fact that it's switching from 7/8 (4+3) to 6/8 to 5/8 (2+3 then 3+2) when you're actually playing since you just feel the music and you have more important things to think about (balance within your section and throughout the group, are we all in time and in tune relative to each other, etc). In practice, there is a bunch of work done on tempo and learning how everything fits together, but that's so you don't need to think about it as much when you perform (assuming everyone does what they've practiced and watches the conductor). With both tempo and meter, it basically comes down to how you feel the music and, in the case of performing in a group, how you relate to all of the parts around you.

And to answer your question about 6/8 with the eighth note at 120 vs 3/4 with the quarter note at 120, the 6/8 measure would take up a longer amount of time than the 3/4. I hope this helps!

 

[AALLF]

Hey, I'm glad I could help a little. This stuff can really get complicated when its explained, but its actually really simple in practice. Let me try to simplify all of this in the most practical way I can.

- All you need are the time signature and the tempo.
- All a time signature does (practically), is to make it easier to read music, by grouping notes together into measures.
- The tempo solely determines the speed of the music. (If you look at a musical score, it will have the tempo at the top, such as "quarter note = 120", "eighth note = 80", dotted quarter note = 60, etc)

Let me use a simple example:

I have a piece of sheet music I'm about to play. I see the time signature is 4/4. At the top of the page, it says "quarter note = 120". So, I get my metronome and set it to 120 BPM. I say to myself, "Ok, every beat I hear on the metronome is a quarter note." I look at the music and read along, figuring out the rhythm, measure by measure.


Let me use a more complex example:

I'm about to read a piece of sheet music. The time signature is 6/8. At the top of the page, the tempo says "dotted quarter note = 90". I set my metronome to 90 BPM, and say to myself, "Ok, every beat I hear on the metronome is a dotted quarter note." The composer intends to have the 6 eighth notes grouped into 2 groups.

So I listen to the metronome and divide every beat I hear into 3 eighth notes. I go from there and figure out the rhythm, measure by measure.

I hope I was able to simplify it for you. There are all kinds of conventions with time signatures and tempo, and it can get complex if you delve into it.

Though, I'm not sure that changes anything about the difficult idea that musicians are completing complex fraction/decimal mental math in the midst of performing.... I don't mean to impugn anyone's intelligence, but that seems like too much of a mental load for anyone to carry....

It IS really hard! . It takes a lot of practice to get a complex piece of music down to where it is apart of you. Back in my college days in the music building, performance majors had ONE piece that they focused on perfecting each semester, and that was their test at the end. They played in ensembles, and practiced other music, but they focused on getting one piece perfect.

I majored in composition, but I was still required to perform in various ensembles, and it never got easy to perform. It can be a nightmare figuring out the rhythm of some complex pieces.

 

[mobius017]

If you’re looking at a measure of eighth notes in 3/4 you would have the same amount of eighth notes, but they would have different accents.

6/8: 1 2 3 4 5 6
3/4: 1 2 3 4 5 6

In 3/4, there are 3 beats per bar, and the beat is assigned to the quarter note. 3/4 should be a triple meter, giving it a pattern of strong, weak, medium, right? If the notes listed above are eighth notes, wouldn't 1 be the strong beat, and then 3 would be the start of the weak beat and 5 would be the start of the medium beat? In that case, wouldn't 1 be the only note that is listed as accented?


Thank you very much to everyone for replying!

Having read everyone's responses, I'm thinking that in a way meter/the math involved isn't really so complicated, though it's more than I think one might want to do on the fly. And it would get more complicated for things like dotted notes or triplets.... Anyway, here's a revised bit of thought; does this look correct?

--Start of Revisions--

The numerator tells you how many beats per measure and what the pattern of stressed/unstressed beats is, and the denominator tells you which kind of note gets the beat. Tempo provides a constant stream of BPM. So at 4/4 with 120 BPM, the denominator and tempo tell us that there are 120 quarter notes per minute. If you switch to 4/8 at 120 BPM, you have 120 eighth notes per minute. So eighth notes in 4/8 are as long as quarter notes in 4/4; their duration (and the duration of all other notes) has doubled.

Also, it seems that the first note in a group (in compound meter) takes the accent, rather than the whole group. That's good to know.

--End of Revisions--

I'd been assuming that the goal for a musician would be to be able to just sight-read all the tempo stuff the same way they do pitches/etc., but that doesn't sound like it's necessarily the case. A lot of the tempo work, in particular, seems to be arrived at through practice of a particular piece of music. Though I imagine that once you've done certain conversions enough, sight-reading becomes easier. At any rate, some practice being required makes much more sense than the idea of picking up a sheet of music cold and mathing it all out as you go along.

I have another related question if you don't mind, this one regarding stressed and unstressed beats.

How do stressed/unstressed beats manifest in musical compositions? Like, where do they come from, and how would you make use of them? The only practical example I've seen is syncopation.

To be honest, I have difficulty telling the difference between stressed and unstressed beats. The explanations I've heard make it sound like the stressed/unstressed patterns just naturally arise as people listen, the way one of your two footsteps can sound louder than the other. But I'm not sure I hear a difference between my footsteps, if that makes sense.

My understanding before was that these stresses/unstresses will manifest automatically due to...human psychology? But now I've seen things that imply that velocity can be used to create them, or at least represent them. So I'm wondering if that's something I need to do. It seems like more work than I can imagine most people doing, going through every track in their songs and adjusting the velocity for the appropriate notes....

Thanks very much again--I know this is a lot of questions about what is probably critically fundamental stuff.

 

[AALLF]

The explanations I've heard make it sound like the stressed/unstressed patterns just naturally arise as people listen

That's the way I think of it. I think the stressed/unstressed beat stuff is something that is just a convention of the meter. Like in 4/4 time, the first beat is strong, 2nd weak, 3rd medium, and 4th weak. And in a meter like 6/8, depending on the grouping of eighth notes into 2s or 3s, the strong beat is at the beginning of each group.

I think that's just what sounds natural and how we naturally perceive it. Of course, syncopation is a whole other thing. Sometimes accenting weak beats as strong beats prolongs the rhythm, the groove, as we naturally crave hearing the rhythms eventually settling into a predictable downbeat and upbeat.

As far as velocity, I don't think you have to worry about that for every note, or trying to match it with any meter. I only touch that in the Vocaloid program when I want a particular line to have a softer, more delicate pronunciation, or a harder, more aggressive pronunciation. I leave most of my notes at neutral (I'm on V3 using GUMI, though. Never used any other Vocaloid or version).

For things like drums, I do use the velocity on the hi-hat, for example, to give it that groove in 4/4 time (strong, weak, medium, weak). But that's it. In quieter sections, I may bring the velocity down for all notes, and then back to max for all notes in the loud sections.

If you are using sampled instruments (piano, drums, strings, etc.), depending on the instrument, it may benefit from velocity changes in order to make it sound more realistic. The drums I use already kind of vary slightly in velocity from hit to hit, so I mostly leave it alone. Depending on your instrument, there may be an option to randomize the velocities to give it a natural feel. I use Reason for my DAW, and I randomize the velocities very slightly, as well as the timing of each note to give it a more realistic feel.

But as far as using velocity for every note to match some sort of inherent strong/weak accents in meter, I don't think that's necessary. Of course, that's from my experience. In my music, the drums and guitar have most of the groove, and I play the guitar myself. If you use drums in your music, just using them will give your music a natural rhythm/groove.

 

[Älfa Dröttning]

In 3/4, there are 3 beats per bar, and the beat is assigned to the quarter note. 3/4 should be a triple meter, giving it a pattern of strong, weak, medium, right? If the notes listed above are eighth notes, wouldn't 1 be the strong beat, and then 3 would be the start of the weak beat and 5 would be the start of the medium beat? In that case, wouldn't 1 be the only note that is listed as accented?

Yes you have the pattern of strong-weak-medium right. I was mainly listing all of the eighth notes just to show the difference of where the accents are placed between the two time signatures, and since the standard subdivision for 3/4 consists of 3 quarter notes, it makes sense to mark those as accented. Most of the time 3/4 has accents on beat 1 (and that can lead to each measure being felt in one instead of 3), but sometimes beats 2 or 3 are accented for effect. Plus there are different kinds of accents to look for, like accents due to pitch, volume, or note length (that last type is called an agogic accent), and those differences can help you tell where the strong and weak beats are. Even though the strongest accent is usually on beat one, that doesn't always mean the accents on other two beats can be ignored. If you're looking for an example, you could check out this waltz: . The strongest accent is on beat one since it's a lot lower in pitch and is louder than the other beats, but since some instruments repeatedly come in on beat 2, and the second beat has a large jump in pitch compared to beat one, I'd argue that the second beat has an accent even if it's not as strong as beat one.

 

[mobius017]

Ah, that's interesting--I didn't realize the accent was subjective to a certain extent, or could be manipulated in a few ways. Thank you!

 

[inactive]

Another thing to keep in mind is that accents don't have to be regularly spaced. "Dance of the Adolescents" from Stravinsky's Rite of Spring is a famous example where strongly marked accents are placed at irregular time intervals in order to create colourist effects.

 

[peaches2217]

Another thing to keep in mind is that accents don't have to be regularly spaced. "Dance of the Adolescents" from Stravinsky's Rite of Spring is a famous example where strongly marked accents are placed at irregular time intervals in order to create colourist effects.

I have nothing of use to add, I just wanna say Rite of Spring is one of my favorite pieces and seeing it here makes me immeasurably happy. Carry on!

 

[Cyana]

It may help for 6/8 to think of it more as two dotted crotchet beats, rather than six quaver beats, even though quavers matches how it's written. Sheet music will often write the tempo referencing a dotted crotchet (like how a standard crotchet is often used to denote the tempo for simple time), rather than the quaver. In his way, you can draw parallels between 2/4, 3/4 and 4/4 and 6/8, 9/8 and 12/8, as the stress patterns will line up between the beats. 2/4 and 6/8 have a strong first beat and weak second beat, with all the quavers in between (one quaver in between for 2/4, two quavers for 6/8) being even weaker than the weak beat.

It kind of works with the subdivisions too, with simple being subdivided in two and compound, three. In 2/4 we say there's two crotchet beats, which subdivides into four quavers, but we still count the crotchets for the actual beat. In 6/8, we say there's two dotted crotchets that subdivide into 6 quavers. Counting the quavers for the actual beat would make the tempo look very fast and mean you're trying to keep track of 6 different strong/weak/medium accents. Whereas counting the dotted crotchet (like how 2/4 counts the crotchet) is easier because then you've only got the two strong/weak accents to worry about, with the remaining quavers falling into "de-emphsised" territory like the off-beats in 2/4. Hopefully that makes sense lol

As for matching the accents with music, it occurs during the composition stage, no velocity tweaking necessary. I find it's easiest to hear with lyrics. English words have natural stress patterns just like music, so when they're set to music, it's best if they match up. Take the word "faster". When we say it, it's stressed like "FAST-er". So, to gel with the pulse (I'll use 4/4 bc it's easier lol), the "fast" should ideally go on the 1 or 3 beat, but can work on 2 or 4... but not on the off-beat. More importantly, the "er" should not go on a stronger beat than "fast". This would change the word stress to "fast-ER", which sounds odd and awkward. The same kind of thinking applies to instruments, but it's harder to tell than with lyrics because there's no natural stress like with words, and you can make cool grooves by emphasising the off-beat. It's the kind of thing that becomes easier with time

Edit: I think part of what makes simple vs compound so confusing is that the way the divisions are done isn't consistent. We say 3/4 is simple because the three crotchets divide into three lots of two quavers. But for 9/4, we don't divide the crotchets, we group them into three lots of three instead... the argument could be made that it subdivides into 9 groups of two quavers, making it a simple meter. It's a bit arbitrary, unless I'm missing something

 

[mobius017]

Thanks! That may end up being helpful, grouping the beats that way. I definitely see where you've coming from about the patterns of stressed/unstressed syllables; like you alluded to, once you've written or read poetry/music for awhile, that's probably the part of the whole thing that becomes most intuitive--when you're writing lyrics, you can feel when the lines aren't consistent with each other.

 

[mobius017]

I guess the next question, then, relatedly, is how to properly mesh lyrics with the meter? I'm probably uncommon among (aspiring) musicians in that I write lyrics first, because I'm better at it.

Maybe it's sort of self-explanatory. I'm thinking what needs to happen is that I write my lyrics first, and then choose a metric pattern that matches them best (There are only really three patterns to choose from; they're just applied differently.). The parts that don't match, I coerce into doing so--meaning notes get longer/shorter, or rests get added. That time signature can then be used to inform the time signature choices for the other tracks.

Though to some extent, I wonder if it has to be as formulaic as all that. Can't you kind of hear when things don't work?

(Says the guy who can't tell the difference between stressed/unstressed beats UNLESS they're words....)

 

[inactive]

If you're going for a pop aesthetic, lyrics are sung with all sorts of timings. They're nowhere near as metrically regular as 18th and 19th century western music, which works to pop music's advantage. A lot of pop music (but obviously not all) uses a very limited note range, which would cause serious creative issues if the vocalist sung in a metrically-regular rhythm. Instead, notes in pop melodies start and finish in all sorts of places with all sorts of note lengths. You can see an example of creative note writing in this unofficial piano transcription of "Take On Me."

As much as I love the common practice period, its melodic rhythmic patterns are far less adventurous than those found in pop/rock/etc. music.

 

[Cyana]

I guess the next question, then, relatedly, is how to properly mesh lyrics with the meter? I'm probably uncommon among (aspiring) musicians in that I write lyrics first, because I'm better at it.

Maybe it's sort of self-explanatory. I'm thinking what needs to happen is that I write my lyrics first, and then choose a metric pattern that matches them best (There are only really three patterns to choose from; they're just applied differently.). The parts that don't match, I coerce into doing so--meaning notes get longer/shorter, or rests get added. That time signature can then be used to inform the time signature choices for the other tracks.

Though to some extent, I wonder if it has to be as formulaic as all that. Can't you kind of hear when things don't work?

(Says the guy who can't tell the difference between stressed/unstressed beats UNLESS they're words....)

If you've already written the lyrics, just kind of say them out loud to yourself, and tap along with a regular beat, a slow one to start with. Notice which words/syllables fall on the beat and which don't. It might help to write your lyrics down, and put a little mark on every syllable that lands on a beat. For the most part, your voice will naturally want to put stressed syllables on beat, and you'll find yourself shortening/lengthening other parts as needed. But if not, marking it down gives you something to look at while you figure out which parts aren't working

 

[mobius017]

@parallax_fifths, @Cyana: Those suggestions make sense! Thank you both very much!