The top number refers to how many beats per measure, the bottom number refers to which type of note (rhythmic value) gets a beat. If the bottom number were 4, it is referring to a quarter note, 2 = half note, 1 = whole note, or 8 = eighth note. We don't have a note that could be referred to by a 3. There is no 1/3 note. Not really. You might think that a triplet would be a 1/3 note, but if I wanted a triplet eighth note to be the note that gets a beat, we have time signatures for that -- 6/8, 9/8, 12/8 etc...So you see, there is no note / rhythmic value you could be referring to with the 3 in your hypothetical 3/3 time signature.
You could write in 3/3, but not all that many musicians would understand what you're doing.
Standard time signatures have a bottom number that corresponds to the note representing either one beat (called simple time or simple meter) or one third of one beat (compound time). If the number is 1, a whole note is the beat (or beat division); 2 means a half note is the beat or beat division; 4 means a quarter note, 8 for an eighth note, etc. Notice that whatever the unit is, it looks like a fraction "1/x", where x is the number of times you'd write that note to equal one whole note.
Time signatures that use other values for the bottom number - like 3 - are called *irrational meters*. In an irrational meter, the unit of one beat is still 1/x - so if the bottom number is three, one beat is represented by one third of a whole note.... which is a half note triplet.
So 3/3 is a triple meter, where each measure is made up of three half notes marked as triplets.
The reason you'll never see a time signature like that is that it's rather silly. It's a triple meter. It's going to sound exactly the same as any other triple meter - 3/4, 3/8, 3/2, etc. Because of that, the statement "would have lined up more attractively as 3/3 instead of 4/4 or 3/4 doesn't make much sense - I can't conceive of a rhythm that would be easier to represent in 3/3 than one of the more familiar triple meter signatures.
Thanks for the well thought out message. I'm probably just having a hard time explaining what I'm seeing in my software.. Again, not a music theorist here.. This is probably because I'm making music that is more like soundscaping or ambient and it doesn't really follow any traditional rules, so the software I'm using (which would be built for traditional music) isn't designed to do what I want.. This just led me to ask the question out of curiosity.. Think a droplet of water resonating off the wall and it has 9 echos. I wanted to divide that into 3 measures and then select my bpm off of that.
You can use any triple meter for that - three beats per measure, with any note you'd like as the beat. If you know how long it is between your echoes you can use that to find bpm - if they're 0.375 seconds apart, your bpm = ( 1 / 0.375 ) x 60 = 160
When the bottom number of a time signature is not a power of 2, that's called an **irrational time signature** (which is mathematically confusing because it's completely unrelated to irrational numbers, but oh well). 3/3 means you have three half note triplets in each measure, each of which gets a beat.
But this usage is extremely rare, to the point where a musician can probably go a full career without ever seeing it used. The reason? The bottom number is a notational convenience. There's no real difference between how 3/2 and 3/4 sound; it's just how its notated. A 3/2 measure with three half notes sounds exactly the same as a 3/4 measure with three quarter notes - and so would a 3/3 measure with three half note triplets. And because it's so inconvenient to keep notating triplets, we avoid time signatures like 3/3 in favor of 3/2 and 3/4.
But there is a case where you might want an irrational time signature: when you want it in relation to another time signature. For example, say that most of your song is in 4/4, but you want to have one measure that's truncated for an effect. If you wanted 3 quarter notes, you could have a measure simply in 3/4 before going back to 4/4. But what if you wanted a measure that's just two half note triplets long? Well, that's when you might use a 2/3 time signature.
For the record, though, you can alternatively notate this sort of measure in 2/2, with a marking "half note triplet = half note," and then when you switch back to 4/4 you'd note "half note = half note triplet." I think this is more common, but it's hard to say - this sort of truncated measure is already rare, no matter how you notate it.
Adam Neely did a video on this topic which I partially based this comment on: https://youtu.be/cQ9yI4dtuGQ
Now I’m no expert, but as I understand it the denominator tells you what counts as one “beat” and the numerator tells you how many of those beats are in a bar.
/4 is a quarter note which is most common. I think you could *technically* do a 3/3 time signature, but /3 would be a really weird length.
For fun, here’s a super mathy time signature, “[No. 41A](https://youtu.be/xPXJ7l-NkgQ)” from “study for player piano” by Conlon Nancarrow. The time signature is 1/(sqrt(pi)/sqrt(2/3))
So technically you can do anything, it’s a question of what sounds good
Can I ask what exactly you mean when you say that things would have lined up more attractively as 3/3? It's possible that a half note triplet quantization is what you're after.
Sure.. So think brian eno type stuff. I'm striking a note and then playing w/ the resonance of the note and this particular note, has a rising edge 3 times per measure and then after 3 measures fades off. So each time I strike that note, I have 9 measures to play w/ to be in sync with that resonance.. But in ableton, I can only do 4 measures, or 2 or 8.. Working around it, I did 3 / 16\* and it worked out fine fine.. This just led me to doing some reading and I realized what I was doing was unconventional and wondered if it was beyond a social "it sounds good" or if there was a mathematical reasoning on why you COULDN'T do 3 / 3..
There is no reason you can't have a pattern in 3/4 time signature that repeats every 3 measures. The lower number says nothing about how many measures a pattern must have before it can repeat. I feel like in your response you mix up measures with beats. The top number tells you how many beats there are in a measure, the lower number is more about convention than anything else. A 3/8 time signature with half the tempo of a 3/4 time signature will be technically the same, but a 3/4 time signature is generally regarded to have a specific 'feel' to it (a waltz) so most musicians will interpret them differently.
Best to just say: because we don't have "third notes" in Western music. (I know I know, the nonconformists on this sub think we theoretically _could_ or maybe even _should_, but practically speaking, almost no music software out there will support it.)
If your music divides neatly into divisions of 3 and 9, try 9/8. 9/8 typically subdivides into three _dotted quarter notes_ of three _eighth notes_ each.
I think a good followup question as an ambient composer, though, would be: can your software do away with time signature altogether and just work with raw durations in seconds, SMPTE timecode, or something equivalent? Why _wouldn't_ you structure your project that way?
It honestly seems odd to me that we don't have a third note. There's a pretty clear distinction between a half note and a quarter note, so you would think there's room for an intermediate.
Maybe it has something to do with the technical limits of human musicians?
I don't think it's that, as musicians slip in and out of triplets on a regular basis. It's the notation that's the hang-up.
My very rough understanding is, way back in early medieval times, music divided into threes was actually the norm (even called "perfect time"), and duple/quadruple divisions (called "imperfect time") were the interloper. The way of distinguishing between the two was complicated, sometimes involving the use of red ink vs black, and eventually the "imperfect" stuff became the norm, with the exception of the compound meters we now have. The real story is almost certainly messier than that, though.
That's actually very interesting. Sort of like how we use AM and PM because early clock makers couldn't make clockwork intricate enough to make a 24 hour clock that was a reasonable size.
This would be an excellent question.. What I like about the signatures is I at least have some structure I can click things into.. So if I want to line things up, it's nice to have them lined up this way.. I realized I have done everything in 4/4 for 8 years unaware there were even other time signatures out there and it has been working just fine by just changing tempos and expanding to my needs, I just wanted to understand this concept a little better and maybe move towards a bit more organization and streamlining as well as be better equipped to talk to others about music composition.
Although time signatures should not generally be thought of as fractions, if you think of 4/4 (for example) as
4 * 1/4
you can see that the total length of the measure is 4 times one quarter note (1/4). Thus, a whole note perfectly fills the measure.
The numbers that appear on the bottom of a time signature are 1, 2, 4, 8, 16, etc. because our modern note values are various levels of binary division of the whole note. An eighth note is 1/8 (or 1/2 of 1/2 of 1/2) of a whole note. While you can certainly have a note value which equals 1/3 of a whole note, a half note triplet, those values only make sense to use when you are breaking out of the usual binary division.
Notating 3/3 as a time signature would be needlessly complicated, since each measure would have three beats yet would still assumed to be a whole note in length, since each of your 3 beats is 1/3 of a whole note. Time signatures with bottom numbers that are not of the form 2^n exist theoretically, but are useless.
---------
As an aside, in medieval and renaissance musical notation note values were more flexible, so that you could have a half note, really called a "minim", divide into two *or* three quarter notes, or "semiminims", without messing around with dots. There were little symbols that told the performer what the divisions were at two different levels, usually "breve" and "semibreve", and one of the possibilities was two "perfect" levels of division, meaning 3. So in that case, your 3/3 signature could have communicated that info! Obviously that is a completely different application than how we use signatures today.
I love making stuff in irrational time signatures. If you have the means to do it, go ahead and call 3 third notes per beat and 3 beats per bar "3/3". I don't know if it's technically accurate, but it really helps my brain understand what it is I'm composing. (Like, why would I want to do 9/8? That doesn't explain to me that I'm doing 3 beats of 3 steps!)
I compose on a DAW, so I see everything as a grid. Even if I COULD do the songs in it, I don't ***want*** to see a grid of 9 beats split into 8 steps. it's annoying to me. I like to make stuff in a clean 3/3, And I think using that as a means of understanding your song is perfectly fine, though I will warn you that if you're making music for other people to play, you might want to do 9/8 since that's what people are used to.
3/4 and 3/3 would be the exact same time signature. You'd just have to invent a bunch of new note values to do the same thing that current note values already do.
x/4 only means a quarter of a measure in 4/4 time. Other than that, it's merely an abstraction.
As a lot of people have pointed out, 3/3 is a valid (albeit irrational time signature) but is generally only useful in specific circumstances, so I think that topic is pretty much covered, but here's my take on what you might try and use *instead* of a 3/3 bar and why.
However, I think it's worth outlining the difference between the *number* of beats in a bar and their *grouping*. So the bottom number of a bar tells you what kind of beat the bar is divided into, measured as fractions of a semibreve (whole note). There are also conventions about how notes are grouped based on the kind of note being counted in (this is usually about where the accented beats of a bar fall).
So, crotchet (quarter-note) beats are counted in twos or fours, and if a crotchet-counted bar (eg a bar of 4/4) is broken down each subdivision will be in 2s, 4s, 8s and so on. Quaver (8th-note) divisions (like 12/8) are traditionally grouped in threes (don't ask, western notation is old and a bit weird). This means that even when the bar is the same length, the notes are grouped differently: e.g. a 3/4 bar has 6 quavers in and so does a 6/8 bar, but the 6/8 bar implies that the quavers are 'felt' in threes, and are thus grouped in two groups of three in the music, whereas the 3/4 bar is 'felt' and grouped in three groups of two.
Based on some of your comments I think you are looking for a bar of three groups of three notes, for which 9/8 would be the normal time signature. This is obviously a super shallow look, and there are lots of circumstances where other choices would be useful (filling a 3/4 bar with crotchet-length triplets; a bar of 9 of some other note if the time signature or tempo was changing noticeably).
Ableton makes limitations based on how people commonly use their software. Software is hard and there aren't many people trying to write in 3/3. There isn't some music standard they're working from that says they only can support specific time signatures or that they have to limit you to m/(n*2) but that's what they've chosen to support.
You can possibly get the same effect (I don't have access to your music project, so I could be wrong), by writing your music in 9/8 at a tempo that's 112.5% of your original tempo. You might also be able to write it as 3 half note triplets in a bar of 4/4. It all depends on what other subdivisions are going to be going on at the same time.
The top number refers to how many beats per measure, the bottom number refers to which type of note (rhythmic value) gets a beat. If the bottom number were 4, it is referring to a quarter note, 2 = half note, 1 = whole note, or 8 = eighth note. We don't have a note that could be referred to by a 3. There is no 1/3 note. Not really. You might think that a triplet would be a 1/3 note, but if I wanted a triplet eighth note to be the note that gets a beat, we have time signatures for that -- 6/8, 9/8, 12/8 etc...So you see, there is no note / rhythmic value you could be referring to with the 3 in your hypothetical 3/3 time signature.
Actually there is allow me to introduce you to the half note triplet
Wouldn’t the dotted quarter get the beat?
1.5 plus 1.5 plus 1.5 equals 4.5
This would be 9/8
You could write in 3/3, but not all that many musicians would understand what you're doing. Standard time signatures have a bottom number that corresponds to the note representing either one beat (called simple time or simple meter) or one third of one beat (compound time). If the number is 1, a whole note is the beat (or beat division); 2 means a half note is the beat or beat division; 4 means a quarter note, 8 for an eighth note, etc. Notice that whatever the unit is, it looks like a fraction "1/x", where x is the number of times you'd write that note to equal one whole note. Time signatures that use other values for the bottom number - like 3 - are called *irrational meters*. In an irrational meter, the unit of one beat is still 1/x - so if the bottom number is three, one beat is represented by one third of a whole note.... which is a half note triplet. So 3/3 is a triple meter, where each measure is made up of three half notes marked as triplets. The reason you'll never see a time signature like that is that it's rather silly. It's a triple meter. It's going to sound exactly the same as any other triple meter - 3/4, 3/8, 3/2, etc. Because of that, the statement "would have lined up more attractively as 3/3 instead of 4/4 or 3/4 doesn't make much sense - I can't conceive of a rhythm that would be easier to represent in 3/3 than one of the more familiar triple meter signatures.
Thanks for the well thought out message. I'm probably just having a hard time explaining what I'm seeing in my software.. Again, not a music theorist here.. This is probably because I'm making music that is more like soundscaping or ambient and it doesn't really follow any traditional rules, so the software I'm using (which would be built for traditional music) isn't designed to do what I want.. This just led me to ask the question out of curiosity.. Think a droplet of water resonating off the wall and it has 9 echos. I wanted to divide that into 3 measures and then select my bpm off of that.
You can use any triple meter for that - three beats per measure, with any note you'd like as the beat. If you know how long it is between your echoes you can use that to find bpm - if they're 0.375 seconds apart, your bpm = ( 1 / 0.375 ) x 60 = 160
When the bottom number of a time signature is not a power of 2, that's called an **irrational time signature** (which is mathematically confusing because it's completely unrelated to irrational numbers, but oh well). 3/3 means you have three half note triplets in each measure, each of which gets a beat. But this usage is extremely rare, to the point where a musician can probably go a full career without ever seeing it used. The reason? The bottom number is a notational convenience. There's no real difference between how 3/2 and 3/4 sound; it's just how its notated. A 3/2 measure with three half notes sounds exactly the same as a 3/4 measure with three quarter notes - and so would a 3/3 measure with three half note triplets. And because it's so inconvenient to keep notating triplets, we avoid time signatures like 3/3 in favor of 3/2 and 3/4. But there is a case where you might want an irrational time signature: when you want it in relation to another time signature. For example, say that most of your song is in 4/4, but you want to have one measure that's truncated for an effect. If you wanted 3 quarter notes, you could have a measure simply in 3/4 before going back to 4/4. But what if you wanted a measure that's just two half note triplets long? Well, that's when you might use a 2/3 time signature. For the record, though, you can alternatively notate this sort of measure in 2/2, with a marking "half note triplet = half note," and then when you switch back to 4/4 you'd note "half note = half note triplet." I think this is more common, but it's hard to say - this sort of truncated measure is already rare, no matter how you notate it. Adam Neely did a video on this topic which I partially based this comment on: https://youtu.be/cQ9yI4dtuGQ
Now I’m no expert, but as I understand it the denominator tells you what counts as one “beat” and the numerator tells you how many of those beats are in a bar. /4 is a quarter note which is most common. I think you could *technically* do a 3/3 time signature, but /3 would be a really weird length. For fun, here’s a super mathy time signature, “[No. 41A](https://youtu.be/xPXJ7l-NkgQ)” from “study for player piano” by Conlon Nancarrow. The time signature is 1/(sqrt(pi)/sqrt(2/3)) So technically you can do anything, it’s a question of what sounds good
Can I ask what exactly you mean when you say that things would have lined up more attractively as 3/3? It's possible that a half note triplet quantization is what you're after.
Sure.. So think brian eno type stuff. I'm striking a note and then playing w/ the resonance of the note and this particular note, has a rising edge 3 times per measure and then after 3 measures fades off. So each time I strike that note, I have 9 measures to play w/ to be in sync with that resonance.. But in ableton, I can only do 4 measures, or 2 or 8.. Working around it, I did 3 / 16\* and it worked out fine fine.. This just led me to doing some reading and I realized what I was doing was unconventional and wondered if it was beyond a social "it sounds good" or if there was a mathematical reasoning on why you COULDN'T do 3 / 3..
The lower number doesn't affect how.many measures you can have
There is no reason you can't have a pattern in 3/4 time signature that repeats every 3 measures. The lower number says nothing about how many measures a pattern must have before it can repeat. I feel like in your response you mix up measures with beats. The top number tells you how many beats there are in a measure, the lower number is more about convention than anything else. A 3/8 time signature with half the tempo of a 3/4 time signature will be technically the same, but a 3/4 time signature is generally regarded to have a specific 'feel' to it (a waltz) so most musicians will interpret them differently.
Best to just say: because we don't have "third notes" in Western music. (I know I know, the nonconformists on this sub think we theoretically _could_ or maybe even _should_, but practically speaking, almost no music software out there will support it.) If your music divides neatly into divisions of 3 and 9, try 9/8. 9/8 typically subdivides into three _dotted quarter notes_ of three _eighth notes_ each. I think a good followup question as an ambient composer, though, would be: can your software do away with time signature altogether and just work with raw durations in seconds, SMPTE timecode, or something equivalent? Why _wouldn't_ you structure your project that way?
It honestly seems odd to me that we don't have a third note. There's a pretty clear distinction between a half note and a quarter note, so you would think there's room for an intermediate. Maybe it has something to do with the technical limits of human musicians?
I don't think it's that, as musicians slip in and out of triplets on a regular basis. It's the notation that's the hang-up. My very rough understanding is, way back in early medieval times, music divided into threes was actually the norm (even called "perfect time"), and duple/quadruple divisions (called "imperfect time") were the interloper. The way of distinguishing between the two was complicated, sometimes involving the use of red ink vs black, and eventually the "imperfect" stuff became the norm, with the exception of the compound meters we now have. The real story is almost certainly messier than that, though.
That's actually very interesting. Sort of like how we use AM and PM because early clock makers couldn't make clockwork intricate enough to make a 24 hour clock that was a reasonable size.
This would be an excellent question.. What I like about the signatures is I at least have some structure I can click things into.. So if I want to line things up, it's nice to have them lined up this way.. I realized I have done everything in 4/4 for 8 years unaware there were even other time signatures out there and it has been working just fine by just changing tempos and expanding to my needs, I just wanted to understand this concept a little better and maybe move towards a bit more organization and streamlining as well as be better equipped to talk to others about music composition.
Although time signatures should not generally be thought of as fractions, if you think of 4/4 (for example) as 4 * 1/4 you can see that the total length of the measure is 4 times one quarter note (1/4). Thus, a whole note perfectly fills the measure. The numbers that appear on the bottom of a time signature are 1, 2, 4, 8, 16, etc. because our modern note values are various levels of binary division of the whole note. An eighth note is 1/8 (or 1/2 of 1/2 of 1/2) of a whole note. While you can certainly have a note value which equals 1/3 of a whole note, a half note triplet, those values only make sense to use when you are breaking out of the usual binary division. Notating 3/3 as a time signature would be needlessly complicated, since each measure would have three beats yet would still assumed to be a whole note in length, since each of your 3 beats is 1/3 of a whole note. Time signatures with bottom numbers that are not of the form 2^n exist theoretically, but are useless. --------- As an aside, in medieval and renaissance musical notation note values were more flexible, so that you could have a half note, really called a "minim", divide into two *or* three quarter notes, or "semiminims", without messing around with dots. There were little symbols that told the performer what the divisions were at two different levels, usually "breve" and "semibreve", and one of the possibilities was two "perfect" levels of division, meaning 3. So in that case, your 3/3 signature could have communicated that info! Obviously that is a completely different application than how we use signatures today.
I love making stuff in irrational time signatures. If you have the means to do it, go ahead and call 3 third notes per beat and 3 beats per bar "3/3". I don't know if it's technically accurate, but it really helps my brain understand what it is I'm composing. (Like, why would I want to do 9/8? That doesn't explain to me that I'm doing 3 beats of 3 steps!) I compose on a DAW, so I see everything as a grid. Even if I COULD do the songs in it, I don't ***want*** to see a grid of 9 beats split into 8 steps. it's annoying to me. I like to make stuff in a clean 3/3, And I think using that as a means of understanding your song is perfectly fine, though I will warn you that if you're making music for other people to play, you might want to do 9/8 since that's what people are used to.
3/4 and 3/3 would be the exact same time signature. You'd just have to invent a bunch of new note values to do the same thing that current note values already do. x/4 only means a quarter of a measure in 4/4 time. Other than that, it's merely an abstraction.
you're probably looking for 9/8
As a lot of people have pointed out, 3/3 is a valid (albeit irrational time signature) but is generally only useful in specific circumstances, so I think that topic is pretty much covered, but here's my take on what you might try and use *instead* of a 3/3 bar and why. However, I think it's worth outlining the difference between the *number* of beats in a bar and their *grouping*. So the bottom number of a bar tells you what kind of beat the bar is divided into, measured as fractions of a semibreve (whole note). There are also conventions about how notes are grouped based on the kind of note being counted in (this is usually about where the accented beats of a bar fall). So, crotchet (quarter-note) beats are counted in twos or fours, and if a crotchet-counted bar (eg a bar of 4/4) is broken down each subdivision will be in 2s, 4s, 8s and so on. Quaver (8th-note) divisions (like 12/8) are traditionally grouped in threes (don't ask, western notation is old and a bit weird). This means that even when the bar is the same length, the notes are grouped differently: e.g. a 3/4 bar has 6 quavers in and so does a 6/8 bar, but the 6/8 bar implies that the quavers are 'felt' in threes, and are thus grouped in two groups of three in the music, whereas the 3/4 bar is 'felt' and grouped in three groups of two. Based on some of your comments I think you are looking for a bar of three groups of three notes, for which 9/8 would be the normal time signature. This is obviously a super shallow look, and there are lots of circumstances where other choices would be useful (filling a 3/4 bar with crotchet-length triplets; a bar of 9 of some other note if the time signature or tempo was changing noticeably).
It's an irrational time signature made up of 3 half note triplets. It's not commonly used though.
Ableton makes limitations based on how people commonly use their software. Software is hard and there aren't many people trying to write in 3/3. There isn't some music standard they're working from that says they only can support specific time signatures or that they have to limit you to m/(n*2) but that's what they've chosen to support. You can possibly get the same effect (I don't have access to your music project, so I could be wrong), by writing your music in 9/8 at a tempo that's 112.5% of your original tempo. You might also be able to write it as 3 half note triplets in a bar of 4/4. It all depends on what other subdivisions are going to be going on at the same time.