time signatures
the confusion continues...
I'm going to break from the pattern here to talk about an issue that appeared on my radar this week, dealing with notation, specifically time signatures. I don't write much about notation here because I’m trying to keep this open to a wide variety of music making purposes. Most of the world's musicians do their thing without notation. It is not an essential tool for making music.
That said, notation can be a very powerful tool. Powerful tools become more useful with experience and attention. Think of the difference between the way you wield a knife, for example, and the way a chef wields a knife, a whittler wields a knife, a butcher wields a knife, and so on. The knife is still useful to you as a quotidian user, but you do not automatically gain all the benefits that a chef has without the practice and attention that a chef has put into using a knife.
Notation is a quirky tool, too, because like the relationship between language and writing systems, some things change and others stay the same and it can be difficult to say why. Why, for example, do the British still spell neighbor and color as "neighbour" and "colour"? Why do they accent words from French like garage and René and Godot on the first syllable? And, really, why is there still a gh in neighbor or neighbour? Western European music notation has many of these similar kinds of vestiges hanging around in its notation and theory. Some things change (like dropping that u) and some things are old habits that are perhaps too old to fail (like that gh).
Fellow musician/educator/substacker Ethan Hein had a post about time signatures and how they are confusing and difficult to teach. They are indeed confusing and difficult to teach! We often just teach it through brute rote and memorization. Especially if you are working with younger children, it often seems simply more efficient to get everyone to nod and say yes and move on with making music, than to go into the gorey details. Dr. Hein points out that the confusion often remains with people well into adulthood.1
And I'll admit that going into all the gorey details may create more confusion, but I'm going to do my best to clear some of the cobwebs and mystery surrounding time signatures.
One of the first things to know is that there are enrhythmic time signatures — they are like time signature synonyms, different ways of saying the same thing. One of the first issues Dr. Hein brings up is why one song is in 7|4 and another is in 7|8. In a purely technical sense, there is no real difference. One could notate either song in either time signature. Here's just the opening rhythm of Jingle Bells2 in a variety of enrhythmic settings:
All four of these examples could sound the same because our notation system is proportional. A half note is twice as long as a quarter; a quarter is twice as long as an eighth. So depending on how you set the tempo, all of these could sound the same. Obviously this begs the question, why have all these different time signatures? I'm going to answer this circuitously and beginning with a question.
Have you ever wondered why a whole note is called a whole note? Nowadays, people often say because it takes up a whole measure. That, however, is only true if we are using 4|4 or 2|2 as a time signature. The real reason a whole note is called a whole note is because it used to be one whole beat. And we didn't have measures. And our time signatures were complete or broken circles, with or without dots in them! Fun times.
The complete circle and the dot meant "perfect" and the broken circle and lack of dot meant "imperfect." In the Catholic, mystic mindset of the day, perfect meant 3, because Joseph+Mary+Jesus = 3 and God+Jesus+Holy Spirit = 3. Imperfect meant two. It gets a lot more complicated from there and transcribing medieval notation into modern notation is harder than sudoku. But the thing to notice here is that the whole note was actually divisible into threes as the default. Putting this into Gordonian terms and avoiding modern time signatures for a moment, you get something like this:
𝇇 = the macrobeat is divided into three microbeats; the microbeat is divided into three subdivisions.
𝇈 = the macrobeat is divided into three microbeats; the microbeat is divided into two subdivisions.
𝇊 = the macrobeat is divided into two microbeats; the microbeat is divided into three subdivisions.
𝇋 = the macrobeat is divided into two microbeats; the microbeat is divided into two subdivisions.3
What I want you to remember from this is that the dot means there are three subdivisions. This will become important.
The people developing notation were the privileged, educated classes — the church and the state. It's not like no one ever played a really long note and no one danced. Those things of course were going on, but they weren't necessarily notated. Notation developed because the church wanted some uniformity across its vast jurisdiction. What was the church notating? Chant, whose rhythms were largely a heightened form of speech. Musical rhythmic notation used to be based around poetic ideas of rhythm — the classic ancient Greek poetic meters, like iambs, trochees, dactyls, and so on. Basically they were combinations of long and short sounds, again like you have in poetry, not necessarily mathematically proportional. But the church was not isolated from life outside the church; there was always influence from other musical practices both formal and informal, not to mention from outside Europe.4 Eventually, those composing for the church and the court (who also want dance music, not just religious music) found themselves finding ways to get more specific about rhythm.
One of the issues was that as instrumental music became prominent in the life of the court as well as the church, there was a need to notate faster rhythms. It stopped making sense to use the whole note as the beat unit and to use what was originally a smaller subdivision instead. When exactly that happened and what piece first started using 4|4 instead of C with no dot is hard to find on the internet. I don't have access to Grove's but that's where I'd look first.
So that explains to some extent why we now use a quarter note as our default beat unit. But theoretically we can use any note as our beat unit, and we indicate that by putting the denominator of the note value in the bottom of the time signature — which looks like a fraction, but isn't a fraction. It's more of a code or a symbol, like the chord indications lead-sheets use. If we wanted to use the whole note as the beat unit and have four whole notes grouped visually (and aurally) we'd have the time signature 4|1.
Now we run into a problem. Everything is now duple. We split the whole note to get two half notes, we split the half note to get two quarter notes, we split the quarter to get two eighths, we split the eighth to get two sixteenths, and so on. Our system privileges duple notation. This is fine when we are in 2|1, 2|2, 2|4, 2|8, 4|4, and so on. Lots of music is duple. But! Some music is still triple! What do we do?
And when I say some music is still triple, I mean that this is still in play, though perhaps less common in pop music du jour:
𝇇 = the macrobeat is divided into three microbeats; the microbeat is divided into three subdivisions.
𝇈 = the macrobeat is divided into three microbeats; the microbeat is divided into two subdivisions.
𝇊 = the macrobeat is divided into two microbeats; the microbeat is divided into three subdivisions.
Sometimes our macrobeat is divided into threes; sometimes our microbeat is divided into threes. Sometimes both! (c.f. Rocky Road to Dublin and other slip jigs) Now according to Gordon, it's only when our macrobeat is divided into threes that we have a sense of triple meter; it doesn't matter what the subdivision is. Gordon ran tests on pre-verbal toddlers to come up with his ideas about how musical nomenclature should change. That doesn't mean some of you out there are not freaking out right now. Pax, my friends. I think one of the biggest issues of music notation is that different people perceive the same things differently. One of the other biggest issues is that your perception of music will affect how you choose to notate something AND how something is notated will affect how you perceive the music. This idea will come back.
We backed ourselves into a notational corner a long, long time ago — centuries ago! In some ways we never had a nice way to notate threeness, despite it being held in such high esteem in Catholic Christian European culture and mysticism. Remember our friend the dot? Let's talk about the dot some more.
Nowadays when you learn notation, you are told that a dotted half note is three beats, because the quarter note gets the beat. Fine. That's easy enough. When you get to the dotted quarter, you are told that the dot adds half of the note value to the note. This is totally and completely mathematically true! But musically, it's a terrible explanation. This is where music literacy often falls apart and if that doesn't kill it, the dotted eighth note will do the job quite nicely, because who is audiating an eighth plus a sixteenth? And if you, like me, started learning about dotted eighths when you were eight and hadn't learned fractions yet, it's that much harder to conceptualize and audiate. This is one of the points where people quit lessons.
I am on a mission to restore the threeness to the dot! Its original concept never changed! Yes, the math is the same, but it's much easier to musically conceptualize (that is, audiate) three subdivisions connected into one sound than to add 3/8 plus 1/16 in terms of sound. But we were talking about time signatures, weren't we? Ah, yes. We'll return to the dot again in a moment.
So here's the thing about time signatures: they basically only tell you that everything in the measure adds up to a certain duration, expressed in a number of notes. They don't necessarily tell you how to audiate what is going on. That information you gain through the experience of listening to, reading, and playing from notation; and, of course, music teachers helping you out, hopefully. A time signature of 4|4 might actually be something more like two macrobeats that are divided into 3 plus one divided into 2, in which the microbeats are the same length, but the macrobeats are not. Regardless, everything adds up to 4 quarter notes.
Well, if four quarter notes equal one whole note, why isn’t the time signature 1|1? Again — what works best in math, doesn’t always work best in music. Most of the time, 4|4 is there to tell you that there are four beats (the top number = the number of beats) and the quarter note (the bottom number — the 4 is a synecdoche for ¼) is the beat reference note, that is the symbol that lasts one beat. All the other durational symbols will be determined in proportion to the quarter note’s duration of one beat. A time signature of 1|1 would mean that the whole note is one beat and all the other durational symbols are determined in proportion to the whole note’s beat — this is originally what that C time signature meant.
Because our note duration system prefers twos as the default, we use the dot when we want something divided into threes — just like the good, old medieval times! However, that division is only down one level; after that it's back to twos. For example, you can have a dotted half note as the macrobeat, which will give you three quarter notes as microbeats, but those microbeats will default to duple eighth note subdivisions. You can have a dotted quarter as a macrobeat, which will give you three eighth notes as microbeats, but those microbeats will default to duple sixteenth note subdivisions.
And because our time signatures use the duple nature of our note duration system as part of the code, there is no way to nicely show triple meter with those numbers in a way that makes easy, obvious sense, because the bottom number will always correspond to duple durational system — that is, other than using 1 for a whole note, the bottom number will always be an even number.5 So in this way, 3|8, 6|8, and 12|8 are enrhythmic because they are all ways of showing paired triple meter. This is precisely the kind of thing where you just get students to nod and say yes and move on. It's been going on for centuries. And yet…
There was one person who did try to fight this and came up with a simple, clear way of doing so. Why? Because not only was he a professional composer, he was also interested in teaching children. My guess is that he also ran into the problem that many students found time signatures to be a stumbling block to notational reading comprehension. That man was Carl Orff and together with Gunild Keetman, they came up with a whole pedagogical system, that may not be perfect (what pedagogical system is?), but is pretty rad overall. Orff simply replaced the bottom number with an actual note. So instead of the cryptic 6|8, he'd write 2|dotted-quarter — with an actual dotted quarter note. Now it's very clear that there are two macrobeats in the measure and they are divided into three microbeats, because we know that the dot means things are divided into threes.
I'd make a notational example, but for some really weird reason the major notation software programs — who all actively court educators — do not have Orff-style time signatures as a native thing. I can tell you that every time it's brought up on the Finale forum there are two responses: The first response is from a helpful but disillusioned person who says, "Oh yes, you can do that! Here are the 50 steps it takes to make that happen! See? So easy!" The second response is from a troll who makes fun of you for not understanding how "real" time signatures work.6 Ah, the joys of music. But I digress. I highly recommend the Orff-style time signatures. Ah, here's an example from the internet:
The truth is that 6|8 does not have six beats in it and the eighth note does not get the beat. It has two beats and the dotted quarter note gets the beat. Because we have this inelegant way of notating that, we started teaching that there are six beats (what the top number ostensibly means) and the eighth note gets the beat (what the bottom number ostensibly means), so that it matched up with the way we teach 4|4, which is there are four beats (top number) and the quarter note gets the beat (bottom number). There is something to be said for consistency, but it does require you not to think too hard about it and ignore the kinesthetic response you are having to music to some extent.
But still: Why do we have so many ways of expressing the same basic metric feel? Part of it has to do with the surface activity — the busy-ness of the rhythms you are reading and playing. Yes, 128th notes can exist, but you don't want to be reading that all the time, it's tiresome; put it in a different time signature. Part of it is a combination of tradition and feel. When you read a lot of notated music in a lot of different styles, you do get a sense of what works better than other things. Rock reads better in 4|4; samba reads better in 2|4. Some marches read better in 2|2 than 2|4. It's weird, but again, it's a little like language. There are word orders that just sound right and if you change it, you don't sound like a native-speaker anymore and communication is hindered.
And sometimes it's just a matter of preference. How do you know that you are hearing 6|4 or 6|8? You don't — you hear paired triple meter. You can choose to notate that in either 6|4 or 6|8 — or 2|dotted-half or 2|dotted-quarter, to continue my promotion of Orff-style time signatures.7 How you make that decision will depend on what's happening rhythmically and what you like to look at. I can tell you 6|4 is far less common for notating paired triple meter — that might factor into your decision. Might someone disagree with your choices? Yes, absolutely. But now, I hope you have some arguments to support your choices with.
As does fellow substacker Stephan Kunze in the comments.
With a simplified rhythm — often the words "all the" are sung to a different rhythm than what I present here.
If you are noticing this looks a lot like the common abbreviation for 4|4 time and are wondering if this is where it came from, your hunch is correct. You may have been told that C stands for “Common Time” because 4|4 is so common. Somebody made that up way later. It’s actually from medieval mensural notation.
Brian Ferneyhough fans can hold their horses. If you don’t know what I’m talking about, it’s okay. This is not the time or place for so-called irrational time signatures.
Here's a nice example from a MuseScore forum, in which you have the work-around suggestion (which never looks good, btw) and the people who are like "whaddya need THAT for?" Apparently, it is native in Dorico! It should be native in all notation programs.
3|4 and 3|8 are also possibilities, natch…
👏🏼 YES! The dot means three, and Orff time signatures should be standard. Love your Substack!