...or, the Two-Level Rhythmic Parsing Rule
The transcript for the above video follows here.
So, let's talk about this. There's this rule in music notation that you should always break rhythms to show the "Middle of the Bar". Usually, when sensible people debate this obviously true and right axiom, they are talking about rhythmic notation in a bar of 4/4 time and it usually goes something like this:
[Posh British:] It is common and proper to show the third beat of the bar, id est, rhythms should be notated in such a way as to make it immediately obvious where the third beat starts, and to not have any rhythmic figuration cross this threshold to avoid metrical obfuscation.
[Normal:] ...except when it's a half note… but let's not get off-track.
People often assume this convention is some arbitrary rule, one which must be followed with absolute diligence. To break it means the engraver ought to be tarred and feathered, drawn and quartered, and then their body burned up with the heat of a thousand suns!
However, showing the Middle of the Bar of 4/4 isn't actually arbitrary, just the most obvious effect of a much more interesting and more nuanced set of rules built right into how music notation works. It is a convention for rhythmic notation that allows for parsing of rhythm to be much easier on the player.
The rule is:
Notes should be grouped together by divisions of the bar no longer than a note length two rhythmic levels larger than the smallest note in said group.
- Book of Gould, Chapter 69: Verse 420
That sounds super confusing. Let’s try and make sense of it.
First I want to establish what it means by “two rhythmic levels.” In music notation, different types of notes will take up different lengths of time. These are usually grouped together into beats to build a rhythm, but we’re not going to get into that right now. All the different types of notes are related to each other in an exponential binary system of rhythmic durations. Just…
Here. look. This diagram is at the beginning of every method or theory book ever made. The note lengths arranged from longest to shortest. At the top we have a whole note. Below that, we have half notes, which are, well, half as long. Then below that we have quarter notes, which are half as long as the half notes, or a quarter of a whole note. And so on. Each additional beam on a black notehead will half the value again. Quarters twice as large as 8ths, which are twice as large as 16ths, which are twice as large as 32nds, which are twice as large as 64ths….[fade out]
[Michael Palin:] Anyway.
When the rule mentions rhythmic levels, it just means a specific type of note, and then moving two levels larger. So when we’re concerned with 16th notes, we go two levels up to quarter notes.
Now, with that prolegomenon out of the way, let’s look at this rule in practice.
Say we have a whole bar of 4/4 filled with 8th notes. This would be 8 notes altogether. The note length “two rhythmic levels larger” than an 8th note is a half note, which is equivalent to four 8th notes. In 4/4, there can only be two half notes since an entire bar has four beats in it, with each half taking two beats. Using this as a starting point for grouping the 8th notes, we can substitute those halves with the groups of four 8ths each. This causes the convenient and happy consequence of an invisible division right in the middle of the bar.
Note that it isn’t possible to combine just any four 8th notes here. The groups have to respect the divisions of the time signature by the larger note value. So these four 8ths that span beats 2 and 3 can't be beamed together. The half note divisions of the bar don't fit here as they have to sit on beats 1 and 3.
Interestingly, this lines up with the typical "strong" beats of a measure of 4/4. While I think that helps make this rule even more useful, I don't think that's the reason why it exists or should be followed. In all sorts of music, the sounding meter’s beat stress can shift around contrary to the default stress of the written meter, which remains constant. The whole point of written meter and time signatures is to give the musician a consistent framework of breaking up time into beats that are easily grouped together. Good notation will follow that intuitive grouping. Of course, sometimes it makes sense for the written meter to completely deviate from the time signature and show more clearly when the sounding meter totally breaks with the written meter... But we're getting off track here…
Going one level smaller than 8th notes, the same logic applies. Say there are eight 16th notes, then they should be grouped as four and four, since two levels up from a 16th note is a quarter note, the same length of four 16ths. In 4/4 there are four quarters available, so those two groups of four 16ths would have to fall exactly within two entire beats. If they don't, the groups should be broken up to respect the longer note value.
Notice here that the eight 16ths are grouped in groups of four as expected, but since they don’t fit into the beats of the larger note value, we have to come up with a different solution, namely to group together the middle four since they line up exactly with one of the quarter note beats.
Note too, that if a rhythm contains 16ths at all, the rhythmic figure surrounding those 16ths cannot be combined beyond the quarter note pulse. This is the "smallest note" provision of the rule we established at the beginning. Take this rhythm of two 16ths, then an 8th, then another 8th, then two more 16ths. We can't just beam these all together even though they add up to a half note, which would be two levels above the 8ths. The groupings must be only quarters and would have to be written as two 16ths and an 8th, then an 8th and the other two 16ths. This neatly shows the beats of the meter and allows us to parse the 16th notes practically instantly.
The whole point of this rule is to show the inherent binary nature of the different levels of note values, and marry it to the concept of the meter (in this case a duple meter). It makes smaller notes much easier to parse when there's a flood of them happening all at once. That two-level higher thing also does a really good job of limiting the size of groups that the musician has to contend with because any group for a given rhythm level is capped at four notes. For example, it is much easier to parse 8 16ths in two groups of four rather than a single group of eight.
It also limits the number of valid combinations of positions for symbols. For instance, a 16th note cannot be followed by a half note, since that would break the 16th note level parsing rules.
The logical result of these rules is that a half note in 4/4 only has three possible locations, on beats 1 2 or 3, and literally nowhere else. So if you see a half note, you can use it as an "anchor", if you will, for parsing the rest of the bar.
Obviously there are exceptions to these rules, and we haven't even talked about rhythm dots and syncopations to allow for simplified notation, but let’s save that for another time.
As a side note, all this logic applies in triple meters too, you just add another beat to the equation so the groups are a maximum of six notes long. It does make things a little bit more complicated, but it doesn't cause the system to fall apart. Triple meters can have some weird quirks that aren't the most obvious. Let me know down in the comments if you want to see a video breaking down triple meter rhythm as well.
Let's go through some examples of this rule in practice:
Here we have five 8th notes followed by a quarter. If we beam all five 8ths together, the musician could misread them at a glance, perhaps thinking it is only a group of four, and then assume the following quarter falls on beat 3. That would be incorrect since it actually is a syncopated quarter on the and of three. Given the parsing rule, we can group those 8ths up to the size of a half note, or four 8ths, and the extra one is given a flag on it's own.
Here's an example of syncopated quarter notes surrounded by 16ths. We won't get too deep into the syncopated part, because we'll save that for another video… but in between the two quarters are four 16ths. Now, according to the rule, we can group two levels higher, or a quarter note. Great, so those four 16ths can be beamed together right?! Not so fast. The groups must respect the divisions of the bar of the larger value. For our case here that's quarter notes. Since this is in 4/4, it can be divided into four quarter notes, each on the beat, pretty straightforward. Then each group must fall within those same groups. Therefore those 16ths must be broken to allow the first two to fall within the beat 2 group, and the last two to fall within the beat 3 group. Perfect! We can write the syncopated quarters as quarters or tied 8ths depending on how strict you get with syncopation rules. Feel free to fight about that in the comments.
[Pedant:] But that's obvious, duh! You just have to break the middle of the bar! Isn't that just a super complicated way of describing the same thing?
[Normal:] Yes… but also no, because this logic applies in all sorts of interesting ways that go way beyond the middle of the bar tomfoolery. The point here is to understand the logic and meaning behind the system.
Here, look at this example. Remember, anchoring? This is a 16th note followed by a quarter note. This is exceptionally difficult to read since the quarter notes are never placed on the quarter beat… I mean, on the e of the beat… I mean … on the second or fourth quartile of the beat. [ding]
Since the first beat of the measure contains 16th notes it must be broken up into a group by the parsing rules for 16th notes. So, that group should be no longer than a quarter note which means that following quarter note gets broken down into smaller notes tied together. Notice too how the 16th note on the beginning of beat three also gets grouped with the existing 16th notes, making the position of those 16ths, starting on the e of beat 3, much clearer.
This is the same reason why notating consecutive dotted 8ths in 4/4 is not allowed either. All dotted notes are parsed based on their smallest division, or the amount the dot adds, so a 16th note for a dotted 8th. This example violates the 16th note level grouping of quarter notes.
Colloquially, of course, this is to "show all the beats" but the reasoning behind it is far deeper and really has nothing to do with the specific time signature, only the binary rhythm system of simple meters.
[Pedant:] But wait, that music looks way more complicated, surely the consecutive dotted 8ths would be better!
[Normal:] No. It may look more complicated on the surface, but it actually is much easier to read since it follows the expectations of the rhythm sy stem that musicians are fluent in. Its sort of like spelling. You wouldn't spell words in this way in normal writing:
Thuh kwik brauwn fawks guhmpz ouver thuh lehzee dawg.
That's just not right!
There's a really absurd one, but shows how this logic cascades up the chain of rhythm sizes. The rhythms are beamed incorrectly all over the place, so let’s correct that.
See how the 16th notes in beat 1 are beamed together? If there were no 32nds in that beat, that would be fine, but since there are, it is proper to break the secondary beam in order to show the 8th note pulse there rather than the quarter note pulse, as 8th notes are two levels above 32nds. Sibelius actually does this incorrectly by default and you have to force it to display the correct rhythm. Notice too (and this is my favorite) that the primary beam is for the 8ths level and it is still beamed together to show the quarter note beat! By engraving the beams this way, musicians can very quickly parse the rhythm and find out where all those itty-bitty notes lie in the measure without thinking too hard.
Let’s throw some 64ths in the mix, just for fun.
That double dotted note is completely in the wrong place. It has to be broken up into a few tied notes. Notice how in beat 2 with the 64th notes, there’s actually *two* secondary beams. [point] Sibelius doesn’t do this by default, it actually has to be faked with line objects. This way the 8th note divisions of the 32nds are still respected while the 16th note divisions of the 64ths are also respected. If you follow the top level beam on this rhythm, you can easily see where the quarter note pulse is at all times, and the 8th note pulse, for that matter, by following the double beams.
In fact, here's the complete system all in one image from whole to 128th notes, or five beams. You can see how a single beam indicates the secondary grouping at the correct position for 8th notes at 32nd notes an d smaller. 64th notes not only have secondary but tertiary groupings with the two beams showing the 16th note groups, and 128th notes have quaternary groupings to show the 32nd notes!
Notice too that for quarters and halfs, which have no beams, they still have a visual definition that is functionally equivalent to beams: that is, the color of the notehead. You could easily pretend there was an invisible beam for those levels and it cascades up the list just like all the others.
It’s an ingenious system that musicians learn when reading music, but it never really is "explained", probably because few teachers would be able to articulate it; even most music engravers wouldn't be able to. It really is remarkable that this system is so logical and neat. Gould knows, not everything in music notation is.
All this is to say, using this system of rhythmic parsing correctly and consistently is of the utmost importance in your engraving. It’s one of the most fundamental elements of music notation that musicians will look at a lot. And, if they can easily parse your rhythms, they will learn to trust your notation and not second-guess themselves.
Thanks for watching this music engraving tip. Did you know about the rationale behind rhythmic parsing before? Let us know in the comments. If you liked what you saw or you feel like you learned something, be sure to hit that like button. For more videos, be sure to subscribe and smash that bell.
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