OFFTONIC THEORY
   Part I: Preliminaries
      Chapter 2: Rhythm


2.1 Meter and Time Signatures

Meter is the rhythmic framework for the music. That may not make sense right away, so let's look at some examples.

Section Contents

2.1.1 4/4

.Here is a simple example, Frère Jacques (which you should definitely try singing/playing yourself before listening to my version):

Example 2.1 — Frère Jacques

Example 2.1

In 4/4, we have four beats each measure, each of which is a quarter note. But the downbeat, beat 1, is stronger than the others, and beat 3 is stronger than 2 and 4. So you have something of a strong weak medium weak pattern with the beats. I added dynamics to the recording above so that you can hopefully hear this pattern.

Do I have to play 4/4 this way?

See Chapter 0! No, you don't have to play 4/4 this way, and if you write 4/4 you don't have to mean for it to be played this way either. But it's the natural way to do it, and unless you indicate otherwise, it's just the way it will come out. You can use accents to change the stresses; when the stressed notes don't correspond to the stressed beats, that's called syncopation. Here are some examples of that:

Example 2.2 — syncopation

Example 2.2

I know you're gonna ask, so: the clef is just an alternate version of the percussion clef. I didn't know it existed either, but Sibelius has it. Whatever. The double bar line is used to separate sections of music, and it doesn't have any actual effect on the music. It's just for the reader to visually distinguish one part from another. And the last measure shows that you can beam rests to notes! That's not by any means required, but isn't it easy to visually distinguish the beats now? How would it look with a bunch of individual 16th notes?

Now, in each of these measures, there's some syncopation going on. In measure 1, the half note on beat 2 is strong and there's nothing on beat 3 (other than a continuation of the half note), but beat 2 is weak. In measure 2, the quarter notes are on the offbeats.

Offbeats?

Yeah, see how they're not on the beats? Those quarter notes are on the and of 1, the and of 2, and the and of 3 (remember how to count rhythms from Chapter 1). This kind of thing is really popular in marches and similar music, where there's some sort of "oom-pah oom-pah oom-pah" beat going on. The "pah" of "oom-pah" is the offbeat.

Measure 3 is a very common rhythm. Try clapping that rhythm while tapping your foot on 1 and 3. The second note comes early, before beat 3, so this is an example of syncopation as well. Measure 4 is an interesting case. The non-funky version of this rhythm would just be straight eighth notes, but to make it funky, a bunch of those eighth notes are hit a 16th note early. Syncopation is funky. BUT. Unless you want to give up the funk entirely, don't funk up the timing on the last two eighths. A bunch of stuff is early, sure, but those two eighths have to be on time.

Why?

Fool. The funk is not explained. It is felt. Seriously, though, the magic of jazz, funk, etc. is when it all clicks together, and if you're early on notes that are supposed to be on time, you're rushing. If you rush the funk, it no longer has that precision and togetherness.

Another important thing about 4/4: while the strong beats are 1 and 3, the high beats are 2 and 4. So, if you have a low action and a high action, you put the low action on 1 and 3 and the high action on 2 and 4. A simple way to see this is to tap your foot and snap. Tapping your foot has a low pitch; put it on 1 and 3. Snapping your fingers has a high pitch; put it on 2 and 4. So you get something like "boom snap boom snap boom snap boom snap". Here's a simple drum beat that illustrates this concept:

Example 2.3 — basic 4/4 beat

Example 2.3

Sweet beat! But, uh, what's going on in the third measure? I really don't get it.

First, B.D., S.D., and Ride Cym. are Bass Drum, Snare Drum, and Ride Cymbal, respectively. Bass and snare are actually always at those spots on the staff, but the other percussion is less standard; still, it's always good to label. If you just look at the bass and snare, you can see that the bass goes on 1 and 3 (though not just) and the snare goes on 2 and 4. In the second half of this beat, you can see that this thinking is taken to a higher level: the ride cymbal is higher than both the bass and the snare, so you get low-high-medium-high-low-high-medium-high. Of course, you don't have to stick to this kind of pattern, but it is the most natural way of doing it. There's also the fact that the ride cymbal is a weaker sound than the snare, so if you had the snare on the offbeats and the ride on 2 and 4, your music would sound very lopsided.

Wait, no, you still didn't answer. I mean, what's with that random eighth rest? How do you even read that?

Ah, that's what you meant! My apologies. Look at the stem directions in the first two measures, and now look at the stem directions in the last two. What's happening in the last two measures is that there are two voices on the same staff. So you have the bass/snare thing with the stems pointing down in the lower part of the staff, and at the same time, at the top of the staff, you have the cymbal with stems pointing up. You're supposed to read both of these voices at the same time. So that eighth rest applies only to the upper voice.

And why are they X's instead of regular notes?

Meh. Convention, I guess.

Also: C?

Where? Oh, right, there! That's the time signature. C stands for Common Time, which is 4/4. I personally don't like to use it just because I don't think there should be anything special about 4/4, but some people do use it.

Now, 4/4 is generally considered to be a simple quadruple meter. Quadruple means that there are four beats each measure, and simple because each beat is divided into two. We'll very soon see meters that do something different. 4/4 isn't the only simple quadruple meter, but as we'll see, it depends on how it's played. 4/8, 4/2, 4/1, etc. are also simple quadruple meters (recall that in 4/8, there are 4 beats, each of which is an eighth note; in 4/2, there are 4 beats, each of which is a half note; in 4/1, there are 4 beats, each of which is a whole note).

2.1.2 2/4

So let's go to 4/4's closest cousin (again, you should try singing the example yourself before listening to the recording):

Example 2.4 — Escravos de Jó

Example 2.4

What's a side drum?

It's essentially big snare drum. The reason why a snare drum makes that rattle is because there are these little beads held against the lower drum head, so when the head vibrates, so do all these little beads. That said, for some people side drum is just another term for a snare drum.

Also, why does this sound so high? I played it on the keyboard but this was an octave higher!

Ah, yes, the piccolo sounds an octave higher than written. Yes, I know, it makes no sense, but that's how it goes. You just need to know that information. There are several instruments that actually sound in a different octave from the one written. Remember when I said that guitar uses tenor clef (not the C clef, I mean the treble clef with an 8 below it that tenors actually sing from)? That's not usually true. The guitar usually just reads regular treble clef. It just sounds an octave lower than written, so the written C5 actually sounds like C4, Middle C. With the piccolo, it's the other way around; the written C5 sounds like C6.

Anyway, Escravos de Jó is a Brazilian children's song that's sung as part of a game involving passing objects, and it can also be sung as a round (with different people starting the song at different times). I'm not exactly sure how that game works, but you smack the object on the table on the downbeats. What this means is that beat 1 is always strong, and beat 2 is always weak. In 4/4, beat 3 is medium, but there is no medium beat here, just strong and weak. Hopefully the drum part helps you understand that. In fact, beat 2 is possibly too weak, and maybe this should have been written in 1/2 instead of 2/4, but that's actually just not something that's done.

What is actually preventing me from writing this in 1/2?

Literally nothing, though you will confuse people. If there's a conductor, the conductor may conduct this piece in 2 — that is, actually mark 2 beats per measure — or in 1 — mark just the downbeat. It's really going to be up to the conductor how to interpret this music.

And why can't a piece in 4/4 actually just be in 2/4 with twice as many measures?

That's a good question, and the answer is that it can. However, 4/4 is conventionally interpreted as having a strong-weak-medium-weak pattern, while 2/4 is conventionally interpreted as having a strong-weak pattern. The 4/4 pattern is longer. Strong beats in 4/4 happen every 4 beats, but strong beats in 2/4 happen every 2 beats. Also, 4/4 is easier to read, in my opinion.

Is there a way to tell by listening whether a piece is in 2/4 or 4/4?

NO! There is not! In fact, you can't tell the time signature at all by listening! A piece that sounds like it's in 4/4 may actually be in some completely off-the-wall time signature with lots of tuplets or syncopation, or it could be in 4/2 or 3/8 with very small subdivisions or really anything. The only thing you can tell by listening is what time signature makes the most sense for the piece. But the composer might well not have had any sense! Time signatures are purely written phenomena. The meter is not. You can listen to a piece of music and tell that it's in duple compound meter or triple simple meter or what have you. But you can't know what is actually written in the sheet music until you look.

In any case, 2/4 is duple simple meter. Simple because beats divide into two eighth notes, and duple because there are two in each bar. These terms, by the way, almost never come up in real life. Still, it's good to know them. Let's now go to 2/4's closest cousin, 2/2!

2.1.3 2/2

In the following score, you may want to try to sing through every line, but the important one is the melody in the clarinets. Just pick an octave.

Example 2.5 — Stars and Stripes (0) Example 2.5 — Stars and Stripes (1)

Example 2.5

I hope this song is familiar! The Stars and Stripes Forever, America's national march! (TIL: Sousa himself wrote lyrics, and I actually knew one of the verses already.) For all of the examples, I've just been writing things by ear, but for this one I actually found the score on IMSLP. Please allow me to stress how great IMSLP is. Of course, while IMSLP is great, some of the publishers are not so great, and on IMSLP are two scores, a condensed score and full score in Sousa's original hand. The condensed score was missing the drum part, and the manuscript score is completely illegible. Luckily there is also a set of complete instrumental parts, and I copied the drums from there. (Note that I didn't bother labeling the bass drum and snare drum for you; they should be obvious by now. Also, Sibelius's sounds are pretty great but not perfect; I had to make some compromises with the drums to make things sound OK, and the bass drum you're hearing here is actually a floor tom. Oh well.)

I AM SO CONFUSED! First, 2/2? That's a ¢, a cent sign.

Just like the C means Common Time, 4/4, the C with a vertical bar means Cut Time, 2/2, also known as alla breve. This is a simple duple meter: two beats per measure, so it's duple, each of which is a half note that gets subdivided into two quarter notes, so it's simple. Next question?

What's the little p? And the weird angle thingies at 15 and 16?

We will get to those! The p means "soft", and the weird angle thingies, also known as hairpins, tell you to get gradually louder or softer, depending on whether they get wider or narrower. By the way, why is a march soft, anyway? Well, this is just an excerpt. It was a lot louder right before this section, and it gets a whole lot louder right after it. I picked this section because it has less stuff going on so it's easier to transcribe. I recommend finding a recording of the whole thing on YouTube, ideally by a band, not an orchestra. Ain't no strings in Sousa's score!

There are so many notes at one time! How can I play/sing them all?

Each one is a different instrumental line. There are four separate horn parts, for example. The horn players are divided into these four parts, and some play Horn 1, some play Horn 2, some play Horn 3, and some play Horn 4. Actually, there are other instruments in addition to horns playing those notes; I just didn't bother showing them here. Same thing for the clarinet part; flutes and piccolos are an octave higher, there's a solo cornet (it's basically a trumpet — get mad at me later for saying that), saxophones, euphonium, etc. I just wanted to keep the size down so that you could actually read it. By the way, when you have a bunch of notes at the same time, that's called a chord. I already mentioned that earlier. In a few chapters' time you'll be able to identify each of the chords here as well as their harmonic functions, but just to give you a taste, the chord in the horns at measure 1 is an Ab major chord, and at measure 7 it switches to an Eb dominant 7th, and back to Ab major at 13. Don't worry if that made no sense to you right now. It will. Believe me, it will.

In the drum part, what are those little notes with the slashes?

Those are called grace notes, and they come just before the note they're attached to. On a snare drum, a note with a grace note before it is called a flam, and it's one of the fundamental rudiments of the snare drum. If you know how to make a flipped R sound, like in Spanish, the pattern employed in this piece goes "tra-ta-tum trum". Notice, by the way, that the flams happen regularly on the offbeats. Actually, let's talk about the meter of this piece, since that's what we're supposed to be talking about in the first place.

Up top, you may notice that I gave the tempo marking as half note = 120. That's not in the original score; that's just a tempo I thought was comfortable for this piece (some marches, like circus marches, are faster; on the other hand, British marches tend to be a bit slower and more stately). But the important thing is that the beat is no longer the quarter note. It's the half note. Try listening to the example and tapping along to the beat while following the melody line (the clarinets have the melody here). You might be used to counting the half note as two beats, but here it's just one beat.

So why not just write it in 2/4?

To be honest, I don't know. I personally get a more subdivided feel out of 2/2 than I do out of 2/4. Let me try to explain. In 2/4, there are two beats and that's it. In 2/2, I feel like the beats are fairly heavy, but you can still hear a bit of emphasis, not very much but just a little bit, on the quarter notes, that you don't feel with the eighth notes of 2/4. It might be just me. In fact, it probably is just me. I'm not sure Sousa himself would have thought this way. Ultimately, it's an arbitrary choice, and marches just happen to be written in cut time a lot of the time, so why not? So I get this somewhat indescribable feeling of broadness with 2/2 that I don't get with 2/4. Whatever. Maybe you feel it differently! It's up to you!

Why are the bar lines weird? Like, they join the three middle instruments but not the ones on the outside; what's up with that?

It's to make it easier to read scores. This score doesn't need it, to be honest, but full scores do. The idea is that the woodwinds are all bracketed together, the brass is all bracketed together, the percussion is all bracketed together, etc. (Some composers write for strings, too. Silly composers.) There's a standard order in which the instruments are listed called score order, and it's generally woodwinds from high to low, then brass from high to low, then percussion in whatever order, then strings from high to low. There are a lot of caveats here. First, it's also standard to keep instrument families together, so you'll have oboes and bassoons before you have clarinets and bass clarinets. Second, for some odd reason it used to be the fashion to put horns over trumpets, possibly because trumpets and trombones are in related families. Wind orchestra scores tend not to do that, but symphony orchestra scores still do.

2.1.4 3/4

Let's move on to a very different-feeling meter. Before listening to it, you should try playing/singing it on the syllable "ay", like "ay-ay ay ay, ay-ay ay ay", rhyming with Bill Nye (the Science Guy).

Example 2.6 — Niggun Habesht

Example 2.6

A niggun is a melody without words, popularized by Chasidic Jews. I couldn't find a lot of information about this one, but one video on YouTube claims it's by the Besht, the Baal Shem Tov, the founder of Chasidism himself. Niggunim are a major component of Chasidic practice; Chasidim believe that while words bring God's understanding down to our level, melodies elevate our spirits to his. (I'm not a Chasid so I may be getting some of this wrong.) Every strain should be sung twice; there's some mystical reason for that too. For this purpose, even though 17-24 and 25-32 aren't identical, 25-32 counts as a repetition of 17-24, and same for the last two phrases.

It's pretty, but why does it sound sad?

Later on we're going to learn about major and minor modes, which are part of the answer to your question. However, the rest of your answer is simple: it's soft, it's slow, and it's played by a single (synthesized) violin. Recipe for sadness right there. The niggun itself isn't particularly sad, and if you were to have four hundred black-hatted Chasidim singing this at a tish, it would sound a hell of a lot happier!

This niggun illustrates 3/4. 3/4 is a triple simple meter: three beats per measure, and each beat is divided into two eighth notes. The basic pattern is strong weak weak, but how much stronger is the strong beat than the weak beats? In a slow tempo, you can really feel every beat, but speed it up a bit and beats 2 and 3 kinda stop being so pronounced. Here's a great example (that will be a lot harder to sing):

Example 2.7 — Valsa Choro

Example 2.7

This is the opening of Villa-Lobos's Valsa—Chôro, from his Suite Popular Brasileira. A suite is generally a set of dances — well, a classical composer's idea of what dances might sound like, anyway! This particular suite has five dances, but they all resemble one of Brazil's most characteristic genres of music, the choro (Portuguese for "cry", often in the diminutive, "chorinho"). Many pieces of music are broken into mostly independent parts; these parts are called movements. Most symphonies, for example, have four movements, and most sonatas have three. The Suite Popular Brasileira, being a suite rather than one of these other forms, happens to have five movements: Mazurka—Chôro, Schottish—Chôro, Valsa—Chôro, Gavotta—Chôro, and Chôrinho. Other than the last movement, the other four are all fairly old and established dances in the realm of classical music, but the waltz (Valsa—Chôro) is the one that's the most danceable in real life. I highly recommend that you find a recording of this on YouTube and listen to the whole movement; I only gave you the beginning, and my synthesized recording is crap compared to even any amateur guitarist, much less a good one.

Wow. There's a ton of shit going on here. What's this, three voices at once?

Yeah, but you already know how to deal with that, don't you? The difference here is that all of these voices are played by the same player, so if one drops out or all of a sudden there are more voices, it's not a big deal. These voices just help the player figure out the different things going on at once in the music.

How can I compose something with so many things going on? That must take genius.

Believe it or not, it's actually not so hard. I mean, yeah, it's pretty hard, but if you learn all the shit I'm teaching you, you're basically halfway there, and then it's just practice. I happen to like Villa-Lobos's music, maybe because I'm Brazilian myself and he captures some of the national essence in my opinion, but he's not any more of a genius than the many fine composers who live today, composing in all genres.

So, measure 24... What's that weird hat thing with a dot? Also, rall? A tempo?

We'll get to all of them in some more detail. The weird hat thing with a dot is called a fermata, and it means WATCH THE CONDUCTOR. ...Sorry, force of habit. It means you hold that note for longer, as long as you feel like holding it. Though, if you're playing in an ensemble with a conductor, it's as long as the conductor feels like holding it, so WATCH THE CONDUCTOR. The "rall..." is a rallentando, and it means to get gradually but dramatically slower, like a car getting to a stop sign (yes, I understand the irony). You may also see "rit...", which can stand for ritardando or ritenuto (the former will often be referred to as a ritard, which is not a slur against those with mental disabilities); that means the same thing but is generally less dramatic. If you're going from a faster tempo to a slower tempo gradually, you use a ritard. If you're essentially approaching a stop, you use a rallentando. That said, Villa-Lobos didn't do that here, so whatever. The opposite of a rit or a rall is an "accel...", accelerando, where you gradually get faster. You may also see stringendo for the same. Note that the Italian words for "a little", "poco", and "a lot", "molto", get used too, so if the slowdown is really dramatic, you may see "molto rallentando", while if the tempo is tightening just a little bit, you might see "poco stringendo". If the tempo changes with one of these, "a tempo" will get you back to the original tempo. By the way, I happen to like this piece at quarter = 108. That wasn't written in the score I copied from (though "Valsa lenta", meaning "slow waltz", was); it's my interpretation. So after the rallentando at 24, 25 goes back to quarter = 108. 32 is the end of the excerpt and it doesn't, but the piece does go on at the original tempo.

Let's pay attention to the meter, though. In a waltz, beat 1 is usually much stronger than beats 2 and 3. You can see how there's a strong bass on almost every single downbeat, and there's mid-range stuff on beats 2 and 3. Remember the "oom-pah" stuff we talked about earlier? In a waltz, it's "oom-pah-pah oom-pah-pah" instead of "oom-pah oom-pah oom-pah". Beats 2 and 3 are the equivalent of the offbeats (but they still are on the beats; we'll get to the meter when this changes).

Now, the tempo in 3/4 can actually get really fast, at which point you'd feel that every measure only has one beat. In the following example, you should try singing the upper line, and when there are weird notes with lines between them, sing the upper one, not the lower one.

Example 2.8 — SMB Underwater

Example 2.8

Heyyy! Mario music! This is pretty chill. And WTF are those things?

This is the underwater theme from the original Super Mario Bros. on the NES. The tune was transcribed exactly, except that I wasted a lot of time today trying to find a way to get chiptune sounds into Sibelius and I failed, so I figured I'd change the vibe entirely. In the original there are pulse and square synths as well as a noise synth for the percussion (don't worry if you don't understand what this means; we'll get to it in a much later chapter), but here I used steel drums, a harp, and a hi-hat. That weird thing at measure 5 is called a tremolo, and the way it works is you quickly alternate between those two notes for the duration of either note. So, in this case, you have a dotted half note G and a dotted half note E, so you quickly alternate between the G and the E for the duration of a dotted half note. It's easier to do on some instruments than on others, and the steel drum is one where it's a common and characteristic sound, so I decided to use it (it's definitely not in the original). Tremolos and rolls, where you just hit one note very quickly over and over, are the way percussionists have to make their notes longer. Once you hit the note, it goes away, so if you hit the note again and again, it won't go away. (Note: do not attempt this technique on your significant other.)

How come we got faster than in the previous piece but this one sounds more relaxed?

That's odd, isn't it? Take a look at the tempo marking first. This says dotted half note equals 72. So even though we're in 3/4, which generally means three beats per measure, each of which is a quarter note, this tempo marking appears to be saying something different: one beat per measure, each of which is a dotted half note. It would be nice to use a time signature that conveyed that, but unfortunately, we don't have a denominator for dotted half notes. I mean, you could have 1/(4/3), since a dotted half note is three quarter notes (and it's in the denominator so you take the reciprocal), but that would be weird. Nobody does that. (People do plenty of weird things with time signatures, but that's not one of them.) We don't need to do any such thing because we have a tempo marking that tells us how to feel the music: in 1, not in 3. So each measure still has a 1-2-3 thing going, but beats 2 and 3 are much weaker than beat 1, weaker still than in the Valsa—Chôro. There's still that "oom-pah-pah" feel, and from measure 5 on, we have the low note on the downbeat and higher stuff, including the hi-hat, on the upbeats.

This piece has one beat per measure, and it's subdivided into three quarter notes. It's actually our first example of a beat that isn't divided into two parts, but since there's only one beat per measure it kind of straddles the line.

2.1.5 6/8

Let's look at a much clearer example in 6/8! The lines to sing are the top or bottom voices in the accordion (the middle voice is not very interesting). Actually, maybe sing the bass too. It's really easy.

Example 2.9 — Tarantella

Example 2.9

I know you have questions, but first things first: let's look at the time signature. We're in 6/8, which means 6 beats per measure, each of which is an 8th note. So why does it say dotted quarter = 144? Shouldn't it be eighth = something? 6/8, the vast majority of the time, is a compound meter: the beat is the dotted quarter, subdivided into three instead of two, unlike in the simple meters we've seen so far. You should be able to clearly feel two beats per measure here, not six (though do note the pickup, which is one full dotted quarter note beat). You should also note how the eighth notes are beamed in thees, like, for example, at measure 9. Eighth notes no longer come in pairs but in triples.

About the piece itself, this is the most well-known tarantella. The tarantella is a folk dance from southern Italy, and many composers have written their own takes on it, but this one just happens to be famous. I'm not sure if that's even the right name (Napoletana should mean that it's from Naples, but I don't know if that's actually true). The instrumentation is something I made up from the melody, though they do use accordions and tambourines (maybe not bass guitars, but then again maybe they do use those). Italian folk music actually uses compound meters quite often.

What's the weird dragon thing in the middle? And what's up with these repeats?

What dragon thing? ...Oh. Heh. Yeah, I guess it does kinda look like a dragon. I put wings on the repeats. Why? you may ask.

...

...You literally want me to ask?

It would be nice.

Oh, fuck you. OK. Why?

I'm glad you asked!

Fuck you.

I put wings on the repeats to make them more visible. The "weird dragon thing" in the middle is just an end repeat and a start repeat back to back; they just blend in together. Now, I don't normally put wings on my repeats, but Sibelius has an option for it and I figured you should see what that looks like, because some publishers do use these symbols. I haven't mentioned it until now because it's probably not relevant, but whenever you're at any sort of rehearsal, you should always have a pencil so that you can take notes in the music. It's an irresponsible waste of time to be told something by the conductor and then forget it at the next rehearsal because you didn't write it down. People write all sorts of things in their music. But if you forgot to take a repeat, you would definitely not be the first person to ever do so, and these wings help the repeat signs stand out. In your own music, you may add these wings so that you don't forget, or write a big "TAKE THE REPEAT YOU IDIOT" on the margin or something. (I've definitely done that before.) Speaking of taking the repeat, did you notice how, on the D.C., the repeat at measure 8 is not taken? Performance practice varies, but generally, it's understood that you don't take repeats on a D.C. There are a few different musical forms that work this way. For example, the classic minuet has a form that goes |:A:| |:B:| |:C:| |:D:| A B, where the A and B sections repeat on the first time through the piece, but on the D.C. at end, they don't repeat. This is mostly just convention, so you can feel free to write a piece that repeats on the D.C. Just mark it clearly!

What are those weird lines in the tambourine part?

That is called a roll. Technically speaking, it's a single-note tremolo and it means to divide the note into that many smaller divisions, so a quarter note with the three lines would actually be eight 32nd notes, a half note would be eight 16th notes, etc. In percussion, though, it just refers to a roll, which is when you hit the note as quickly as you can to make a longer sound. On the tambourine, there are two ways to do something like this: you can shake it, or you can run your thumb over the head, making it vibrate. This way is hard and hurts your thumb, but you get a more even sound.

Here's another piece in 6/8; sing/play the soprano line (the other lines are much less line-y).

Example 2.10 — Beren and Lúthien first four lines

Example 2.10

Beren and Lúthien is actually an original composition of mine, for solo/tenor duet and piano (well, more baritone than tenor, but whatever). It was unfortunate that we never got it performed, so if you want to record a performance, let me know and I'll send you the music! The words are from Tolkien, a poem in The Fellowship Of The Ring about Beren and Lúthien (hence the name, of course). Lúthien is also called Tinúviel, which is what the tenor interjects with here. This excerpt is the first half of the first stanza, out of nine stanzas. It's a long poem. For more, including a (synthesized) recording of the entire piece, you can check my music page. Note that the entire piece is in various forms of 6/8, with only one measure in 9/8 to highlight a particular crucial moment in the poem.

You wrote that? It's pretty. Will I learn to compose like that in this book?

I'm glad you like it! But no. You will not. You're responsible for your own imagination. I hope to give you the tools you will use to understand the components of such a composition, but you have to put them together yourself. For example, this section of the piece is in the dorian mode, which to me is associated with English countryside, medieval forests, that sort of thing. The constant rising motion in the bass, as well as the rising 16th note motif in the piano, help give this section a kind of ethereal feeling. I'm also fairly particular about which notes I use in those 16th note figurations; I'm careful with my harmonic implications there, and I also avoid straight arpeggios (that's when you play a chord one note at a time instead of all together; we'll talk much more about that eventually) in order to keep it complex. All these are things you should be able to think of yourself while writing a piece of music, even if you write EDM or ska or hip-hop instead of... whatever you call this. Western art music, usually.

This piece is an example of the slow kind of 6/8. You still feel the pulse in 2, but it's a subdivided 2. You feel all 6 beats in the measure, but the dotted quarter note is still the most important. Later in the piece things get faster, and it becomes a more traditional 6/8 at those faster spots. Note that the 16th notes are each an entire half of an eighth note beat here — don't rush!

Why does measure 4 have a dotted rest in the tenor? You said not to use dotted rests!

It's not just a dotted rest — it's a dotted rest followed by two eighth rests! Why not use a quarter rest? The answer is something we'll talk about in a bit: separation of subdivisions (also known as "the invisible bar line"). The dotted quarter rest is an entire beat. In 4/4, a dotted quarter rest is a beat and a half, so if you look at it, it's confusing. But in 6/8, that dotted quarter rest is a neat half of the measure, and when you look at it, you know that it's a complete beat. The eighth rests following are the subdivisions of the beat. The quarter rest is usually a beat, so if you saw it here, it would be confusing since it's no longer a beat. On the other hand, two eighth rests make it clear that the beat is divided into three.

But there are quarter notes, though.

Eh. Yeah, there are. I don't know. I guess it's just convention. We're all familiar with the quarter-eighth rhythm in 6/8, (and the same thing backwards, like in the second beat of measure 3), so we understand that, but the quarter rest would be contrary to our expectations.

The big picture here is that the most important job of music notation is to communicate the music to the reader. There's a lot of different stuff that goes into music notation, which is why we're spending so long talking about it, and somehow the reader needs to be able to scan it quickly and play it correctly without much effort. For that, the notation needs to be clear. If you need to sit there and think for a few seconds before you know what a chunk of music is supposed to be like, the composer (or the typesetter, or whoever) is wrong.

Dude. Rule 0.

OK, not "wrong". Merely "a jackass". How about that?

That's better.

That said, there are times when confusing notation is OK. One example is in music designed to confuse the musician to achieve some sort of artistic goal. Believe it or not, this is a thing. In the middle of the 20th century, composers would pull shit like this. They'd have a score that's just, like, a circle or something, and there'd be some vague directions for the musician (if you were lucky) that would be completely unhelpful in interpreting whatever abstract embodiment of whatever ended up on the page.

Anyway, back to the subject of meter.

2.1.6 Other (Regular) Meters

Are there other time signatures?

Yes, plenty! But our examples have been getting way too long, so I'll be briefer about them. First up, 12/8. 12/8 is just like 6/8 except that the measures are twice as long, so you'll have four dotted quarter note beats per measure: it's quadruple compound meter. You can also have 9/8, which is similar: a triple compound meter.

How do you know if a song is in 6/8 or 12/8?

By looking at the time signature. Duh. Because there's no way to tell by listening. There's never a way to tell by listening. But that's a bit too technical: how do you know if 6/8 or 12/8 is more appropriate? The answer is in the emphases. Remember how 4/4 has strong-weak-medium-weak? 12/8 is the same. 12/8 is like 4/4 but the beats have three eighth notes instead of two. And 6/8 is similar to 2/4, where the beats are strong-weak. However, you can always change the emphasis at will.

You can also have 3/8, which is usually a one beat per measure thing. See, we have such a strong association with the quarter note as the beat, or the dotted quarter, that 3/8 is generally much lighter than 3/4, even at the same tempo. But this is up to the composer. Technically speaking, there's no difference whatsoever between 3/8 with dotted quarter = something and 3/4 with dotted half = the same thing. Again, it comes down to how you want to communicate the feel of the piece to your reader.

In addition, you can go in the other direction: 6/4, 3/2, etc. What's the difference between 6/4 and 3/2? Generally, 6/4 is grouped as two sets of three quarter notes, while 3/2 is grouped as three sets of two quarter notes. You could have the quarter note be the beat for 3/2. I know it says it's three half notes, but the beat is actually whatever you want it to be. Say quarter = whatever and that's what the beat is. And, on the smaller end, you can do stuff like 9/16. I played a piece in 9/16 once... The fourth movement of Chabrier's Suite Pastorale. That's a crazy clarinet part! That has a kind of interesting meter, where it's kind of in 1 and kind of in 3. We think of 16th notes as very quick, so those runs of 16ths make sense as 9/16 rather than the heavier eighth notes in 9/8. JS Bach's Art of Fugue has a canon in 9/16 as well.

2.1.7 Irregular Meters

But are there other other time signatures?

There sure are! The melody to sing here is the top line on the piano:

Example 2.11 — Reiach Tapuach

Example 2.11

This piece, Reiach Tapuach, is in 7/8. It's a (modern) Israeli folk song about cute birdies and the smell of apples. I picked it because it has a very clear rhythm, and I arranged it for piano just now to really bring out that rhythm in the left hand. In this piece, the measures each have three beats, but... they have different lengths! The first beat has three eighth notes, while the second and third have two each. I wrote the tempo as dotted quarter = 104, but I could have done quarter = 156 or eighth = 310. I figured that going by the first beat in each bar made more sense, but the truth is that a simple metronome won't be able to keep time for you very well since the beats are irregular. On the other hand, they're not that irregular; every measure does it the same way. We say that each measure here is 3+2+2 — those are the lengths of each of the three beats, in eighth notes — but it could just as easily be 2+2+3 (2+3+2 is more rare). Hell, it could even be 3+2+2 in one measure and 2+2+3 in the next!

Just a quick little thing I noticed: in the last measure, the first eighth note has a Bb in the right hand, and the next eighth note has a B natural in the left hand. This is a neat little example of a cross-relation, where different versions of a note appear near each other in different voices. Much later we'll talk about why we care about cross-relations.

That's... really cool, actually. Question: what's up with the p, ff, etc.?

I swear I'll get to dynamics eventually! p means soft, ff means very loud, mf means medium loud. Generally, p's mean soft, f's mean loud, and m's mean medium.

Example 2.12 — Mars rhythm

Example 2.12

This is just the rhythm of a very famous piece that's mostly in 5/4 (there's a slow section in the middle that's in 5/2, and some noodling around in 3/4 at the very end), Mars, the Bringer of War, from Gustav Holst's famous suite The Planets (look at the score to get a sense of how scores are organized). If you haven't, you'll really want to listen to this. If you think it sounds a little bit like Star Wars, well, all of the great movie composers (like John Williams and, um... just John Williams, actually) lifted directly from The Planets, especially for space movies, since The Planets was already somewhat associated with space (Holst intended the astrological planets, not the astronomical ones, but so it is).

Didn't Hans Zimmer rip off The Planets too? Mars in general is remarkably similar to the battle music from Gladiator.

I did say great movie composers, didn't I?

Ooh. Sick burn.

5/4 generally (but not necessarily always) consists of quarter notes either grouped 3+2 or 2+3. In this case, it's clearly 3+2, so we get something like strong-weak-weak-medium-weak.

Is that timpani part in percussion notation? Why isn't there a percussion clef?

Timpani actually have pitch, and they read in bass clef. I picked an A for these (I think the actual piece uses G's, but whatever). I know it looks like a bass drum part, but no, they're actual pitches. You use a pedal to change the note by changing the pressure of the drum. If you're lucky, anyway. Some older timpani don't have a pedal and you need to tighten the drum head manually, which is, to say the least, a total bitch.

Sing this one:

Example 2.13 — Hoy, Nazar Eem

Example 2.13

Whoa! It shifts!

I love 5/8, partly because you can do this! It's an Armenian folk song. Actually, it's the melody from the third movement of Alfred Reed's Armenian Dances Part I, which isn't the same thing: the original folk song's in 6/8! You want to watch the Tokyo Kosei Wind Orchestra do this piece. The third movement starts at 3:47 with a cool 2+3/3+2 percussion thingy. The TKWO, if you don't know, is one of the premier wind orchestras in the world, and it used to be led by the great Frederick Fennell, the guy who invented the wind ensemble as a concept (I was lucky enough to have been conducted by him when he was still alive, at a Florida All-State Band, when I was in high school).

But are there other other other time signatures?

Le sigh. Here are some. Of not-so-special note are ones with fractions in the numerator, like (1 1/2)/4. Many pieces just don't have a meter at all, or there are breaks from the meter (like a 2/4 bar in the middle of a 4/4 piece). Often you just need an extra eighth note in a bar. Percy Grainger wrote a (1 1/2)/4 bar in his Lincolnshire Posy for that reason; he had a quarter note and a half of music that he needed to put somewhere. That's a little strange: today the sensible thing to do is to just write it as 3/8.

The really weird stuff is when the denominator isn't a power of 2. Like, for example, a bar of 2/6.

WTF? How do you even count that?

You'd have to be crazy to do this, but some people are totally crazy enough. The key is to realize that the whole time signature is basically a fraction of a whole note, so 2/6 would mean that the bar fits two quarter note triplets (we'll get to what that means shortly, actually). Let's say, just for example, that you have some piece in 4/4. Now, you start playing quarter note triplets. A quarter note triplet is basically splitting a half note into three instead of two, so there are six of them in a bar, right? You're playing those quarter note triplets. Now, all of a sudden, you need a bar with just two of them. What do you do? There's actually no easy answer. One possibility is to make it 2/4 but change the tempo for the length of that measure, but you're already doing the triplets so why change everything? So you write a measure of 2/6. Sibelius can't handle those at all (not without some serious font trickery, anyway) so I can't show it to you, but you probably don't want to see it anyway. There's more explanation on Wikipedia; these are somewhat misleadingly called irrational time signatures, even though they're still, you know, rational numbers if you read them as fractions.

But are there other other other OTHER time signatures?

Oy! You could always have time signatures that are actually irrational. Like, using square roots or transcendental numbers or whatever. But those aren't going to be human-playable, so why even bother? For art, that's why! But I'm still not going to bother to talk about them, mostly because there's really nothing to say. If you're going to do that, you might as well just use precise time stamps instead of measures at all, which is common in modernist scores (like George Crumb's Makrokosmos, Vol. I; take a look at some of this craziness). That doesn't mean that there isn't really cool stuff you can do with irrational time, but expressing it via time signatures is just not going to help anybody.

2.1.8 Meter Variation

Time signatures can change. Let's look at a little bit of that. Sing the following (should be easy):

Example 2.14 — Symphony No. 1 - IV

Example 2.14

WEIRD, why does the time signature change every single measure?

This piece doesn't have much of a consistent meter. I wrote three movements of a four-movement symphony for wind orchestra where the bar lines were dictated by the music and not the other way around; this is the main theme of the unfinished fourth movement (I think I last worked on this in 2010...). From the second half of measure 6 on, it's actually a reworking of a theme from the first movement with a different rhythm.

The thing to notice is that the quarter note is the beat, but in measure 3, beat 3 is one 16th note short. Same thing in measure 5, and measure 6 has both beats 3 and 4 missing a 16th note. This is actually fairly common. Often, a section of music will have normal quarter note beats but some of the beats will be a bit shorter or longer. A 4/4 bar with a missing 16th note might be written as 15/16, for example. From the time signature, you can't tell if there are five equal dotted eighth note beats or if it's a 4/4 bar with a missing 16th note. I've seen 3/4 bars where one of the beats got a little longer; that becomes 13/16. It's important to understand that we're not talking about entire pieces here, just one beat here or there.

You may know this, but one of the big things I do is transcribe Jewish liturgical music for the Offtonic NusachDB. There are two kinds of music with lyrics, loosely speaking: melogenic and logogenic. Melogenic music takes a melody and slaps lyrics on top of it. So you could write a fun metrical tune, in 4/4 if you wish, and make the words fit. Logogenic music, on the other hand, has the music fit the words. If you start with metrical poetry, you may end up with a metrical tune, but if you start with prose, you very, very much don't. Prose doesn't have meter!

So I'll show you two examples of logogenic music from vastly different traditions. First, the Moroccan chanting of the Song of Songs:

Example 2.15 — Yishakeni

Example 2.15

Where did the time signatures go?

I deleted them.

You what? Why?

Um, they were ugly?

You can do that?

Looks like it!

So how do you know how long each measure is?

You could count. Or... you could not. Why do you need to know, anyway? What you do need to know are where the beats are, and that's pretty clear from the way the notes are beamed. I wrote the number of eighth notes in each beat above the start of each beat. But remember how the goal of musical notation is clear communication? Audience matters. In my symphony, I carefully notated each time signature because it actually matters when dealing with a large ensemble. Here, you mostly just learn by rote anyway and the written music is just a reference, so time signatures provide less benefit than removing the visual clutter does.

Another very interesting feature of this particular chant (which applies to the entire megillah, about 20 minutes' worth, read on Friday afternoons before services start) is that it's in the locrian mode. Don't worry if you don't know what this means, but if you do know what it means, it's pretty cool. We'll get to modes in a few chapters, and we'll probably revisit this example then.

The other example is from the Ashkenazic evening service on Shabbat (well, the popular chant in the US for it, anyway):

Example 2.16 — Ushmor Tzetenu

Example 2.16

This sounds really... mechanical. An actual chazan would stretch the time much more and make it sound more natural and more fluid (listen for example to this version, beginning at 2:24, which uses the same motivic chant but in a different way). In that respect, my transcription is only a fairly rough approximation of how the nusach (that's the Hebrew word for this kind of liturgical chanting) goes. I also thought that time signatures would be unhelpful here. Both here and in the Moroccan example, the word is king when it comes to the melody. Here, for example, we squeeze a bunch of words together at "hapores sukat shalom aleinu". A similar thing happens at "l'chayim ulshalom", but there are fewer syllables so it takes less time. The rhythm fits the words.

What I want to make clear is that, for all our talk of meter, meter isn't actually necessary in a piece of music. Of course, if you're writing EDM, you're probably going to want to have a meter, because people have to be able to dance to it. Non-metrical music exists; that doesn't mean that you have to write it (or even like it). You don't have to play with time. You can keep things in straight 4/4 until you're bored (which might be fairly quickly). I love playing with time, but it has a place! For example, it can be nice to have a piece in a consistent time signature except for one important measure. I wrote an arrangement of a Jewish prayer that has "now, quickly" (in Aramaic) in the lyrics. The last time through the chorus, I paused after these words, as if to wait for a response: "...now! (pause) Quickly! (longer pause)" Having some metric irregularity is a nice way to wake people up, just to throw people off of their groove.

While we're on the subject, let's talk a little about the purpose of music. People write (or make) music for all sorts of different reasons. It could be for its own sake as art, for people to listen to it critically and appreciate it. It could be to fill silence in a commercial or a movie. It could be to get people to sing along. It could be to make people dance. It could be to make a political statement. It could be some combination of these goals, or something else. How you approach the music will depend a lot on how you mean for it to be played (if at all), who would play it, who would listen to it, etc. Something that would be great in one context may be absolutely terrible in another. For example, writing a march in 5/8 might make for a piece that's lots of fun to play and to listen to, but don't expect anyone to actually march to it! And similarly, the repetitive nature and slow changes of techno might be hypnotizing at a dance party, but don't put it on stage at a concert hall. So, it's good to know that you can lengthen or shorten measures at will as if they were clay in the hands of a potter, but it's not always a good idea to do it.

Anyway, we've talked a lot about meter. The only thing left to do is to acquire enough of a repertoire of music that you've seen different meters much more. For example, I'm not going to give you another example, but there are compound signatures, which look like two (or more) signatures side by side, maybe with a + between them, and what that means is that the measures alternate. Example 1.21 in the previous chapter, Lamah Haketz Nistam Na, could have been written in 3/4+4/4+3/4, and then I wouldn't have had to explicitly mark the time signature every bar. Honestly, though, I think it's easier to read with the explicit time signatures and you don't get confused, and besides, Sibelius doesn't do those time signatures automatically so it would have been annoying to set it up. Well, with a bit more experience, you would know about it. Some schmuck telling you stuff isn't going to substitute for actual experience with music. I'm trying to go as broad as possible with my examples, but it's not going to be enough. So, do yourself a favor and acquire a repertoire on your instrument, playing (or singing, as the case may be) music from as many different genres and time periods as you can find. That's how you learn. Especially if your main interest is popular music in any of its many, many forms, whether EDM or hip-hop or death metal or bubblegum pop or what have you, going outside your genre is the only way to really learn. As a bonus, you'll understand and appreciate your preferred genre better when you come back. So, let's move on!

Huh? Sorry, I zoned out there for a sec.

Never mind. We're moving on, to: