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Rhythm

Rhythm in music generally

Tempo, and meter are both terms relating to the rhythm of music, but they are not synonyms. I will blather on about tempo in the next subsection, but for now, it has to do with how fast the music is moving. Meter controls how the beat is divided, affecting the fundamental feel of the music. Tempo is set by whoever has the dominant hand in driving the performance; meter is set by the composer and is written into the score in what is called the time signature.

Time signatures

1 Medieval and Renaissance music was written down with much less temporal precision, either in terms of meter or even note duration. This may simply represent a less developed writing system, but it has been suggested that it also reflects the performers' freedom in that area—that temporal variety was an expected part of the performance, particularly with traveling ensembles. Our desire to get everything as controlled as possible may prevent us from fully understanding this music. See Brent, 1998.

2 I like it! I think I am going to use that word, but don't go looking for it to show up in your dictionary. Other, more boring, people call it the 'beat unit.'

I introduced time signatures in the section on notation. The concept itself is, as one would expect, the product of its own evolution, but has become sufficiently ingrained in our thinking that some signature is virtually always imposed on music even when that music is imported from a time before time signatures (as with the refrain to "Veni, Veni, Emannuel").1 As you probably know, the bottom number in a time signature tells you, as with the denominator in a fraction (should we call it the 'denotinator'?2), what the unit of measurement is. That number is always a power of 2 (e.g. 2, 4, 8, etc.), for the simple reason that those are the notes we have to work with. There are no third or fifth notes in standard notation. The top note tells you how many of those notes (the one specified on the bottom) fit in each measure (although that note is not required to ever actually present itself). Now, when I say there are no fifth notes, that does not mean you cannot have five beat measures, it is just that they will be presented as five quarter notes or five eighth notes, etc.

One way of categorizing measures is by how many beats there are in each:

2 beats per measure = duple
3 beats per measure = triple
4 beats per measure = quadruple
5 beats per measure = quintuple

And so forth, although the number of beats per measure does not necessarily correspond to the top number, since the bottom note is not always one beat, as we are about to see.

Simple meter Simple meter

Time signatures are generally divided into simple and compound. In a simple meter that denotinator is also the unit of beat, and the division of the beat is always binary: if the quarter note is the beat, the eighth note is the half-beat; the 16th note is the quarter of a beat, etc. Pretty much, this is what you have if the numerator (top number) is a primary. ³ is still considered simple because even though the measure divides into three, the note values down from the beat are still binary.

Compound meter Compound meter
3 See if it divides easily by some other common primary.  is either a duple of quints, or asymmetric, for example. [Five duples would just be ⁵. For what it is worth, the only time I have seen this it was 3+3+2+2=asymmetric.] Some folks have argued for using actual notes on the bottom of the signature. This would save you having to do a bunch of math in your head, and make it real clear what the beat is. A composer could have, say, a double dotted half (= 7 eighth-notes) as his denotinator, with a three on top. This would give him a basic triple beat which would then subdivide into seven sub-beats each.

4 Playing with the contrast between the ³ and ⁶ rhythm was a common feature of renaissance madrigals, and more recently, has been popular in Afro-Cuban music. Note that in the sample (no particular piece) the measure in question is measure three. The violin is actually playing three quarter notes on top of a ⁶ meter. But in the score the second quarter is written as two eight notes tied together. This is a common courtesy to the player, who is expecting two triple beats per measure, and is most likely going to find this easier to read. However, writing this way is a courtesy, not a rule.

Compound meters subdivide the beat into three. So 6/8 may = ¾ in math, but ⁶³ in music. ⁶ actually has two beats per measure (+). Each of those beats subdivides into three eighth notes. It is a duple with a triple subdivision. ⁹ is ++: a triple with a triple subdivision. I am going to assume you can figure out . Each of these go duple below the eighth-note level. If you wanted three levels of triple, you would have to write that as 27/16, I suppose. I have never seen such an animal, but I'll bet you it exists. You probably have discerned the pattern. If the top number is not primary, divide it by three. If it divides evenly, giving you a primary number, that is your beat consisting of dotted notes. If not, do it again. If it still doesn't work, well, I'm glad it's you and not me.3

Simple meter (5/4) Complex meter

Complex meters can't be reduced to threes or twos. What makes them 'complex' is simply that in the western hemisphere, we find any beat bigger than four hard to hear, so we end up subdividing. We usually take a ⁵ measure and mentally subdivide it into three + two, or the reverse. ⁷ becomes three + four, or two + three + two, or something like that. It will seem strange the first time you try, but it will get more natural. Obviously, complex meters can also be simple or compound, or they can further subdivide into more complexity (25/16, for example).

3/4 measure in the middle of 6/8 3/4 inside of 6/8
If the audio button is screwed up, try the MIDI

But don't get your nose out of joint if the composer is not consistent. She should warn you if she plans to change the actual size of the measure, but if the piece is running along in ⁶ and you suddenly get a measure that is unambiguously ³, just play it; don't write and complain to the publisher.4

Meter in practice

Throughout the common practice period, the meters were dominated by ⁴, with a little ³ thrown in for good measure (no pun intended, well, OK, maybe a little). This continues to be true in mainstream pop.

Popular music makes occasional forays into ³: Cat Stevens' "Morning has broken" maybe doesn't count since it was actually a cover of a hymn by Eleanor Farjeon, published in 1931, set to an even older tune. Neil Young's "Only Love Can Break Your Heart" is perhaps a little less interesting, but is unambiguously modern pop. In the middle Ages and the Renaissance, ³ was considered 'perfect time.' It has certainly for a long time been considered perfect for dancing—the waltz being the most famous.

5 Some composers have played with traditional meters by introducing different kinds of complexity. Mozart and Beethoven both used polyrhythm occasionally (³ along with ⁴), and the Beatles played with it in "Mean Mr. Mustard."
Stravinsky changed meters frequently in Rite of Spring. (Here, from the 'Sacrificial Dance'). meter change in Rite of Spring
If the audio button is screwed up, try the MIDI

Modern composers and jazz players have experimented with other time signatures. ⁵ was made famous by Dave Brubeck's "Take five," and Blind Faith took most of an album side to make the same point to a generation of rockers in "Do what you like." Greater complexity rarely finds its way out of 'serious' music (academic and jazz), but brief meter changes are commonplace.5

Tempo and drums

6 In this statement I am taking 'instrument' as an external device used to produce sounds. The counter-assertion that 'voice is an instrument' is rooted in a competing, although equally valid, perspective.

At the beginning of the last section (Pitch, notes, and scales), I referred to the fact that there was some disagreement over whether melody or rhythm came first. I decided to side with melody, but only because I regard singing as music. There can be no doubt that the earliest instrument6 was a drum.

About three weeks after some cave-dude(tte) changed the future of the world by beating on a hollow log with a stick, one of the oldest jokes came into being. Q: How do you tell if a drummer is at your cave entrance? A: The knocking speeds up. Underlying this humor is the assumption that if the song speeds up, it must be the drummer's fault. I am going to guess that most of the time she has a better sense of rhythm than the other goons in the band, but admittedly, we need someone to blame it on.

7 This is not to imply that drummers have been the only victims of canned-instrument technology.

But it is actually more than that. Until the modern period, it was common practice for music to speed up and slow down during a performance. That is why we have the Italian terms, accelerando and decelerando. Check out Don McLean's "American Pie" sometime. One of the driving factors in this move toward mono-tempo has been the elimination of real drummers in favor of the variety you plug into your computer.7 It is possible to persuade these e-drummers to change tempo but it raises the level of complexity in assembly-line music production.

Still, the more energy you are generating in a real performance, the more likely it is that you will be speeding up a little. It is not necessarily something you need to 'watch out for.' If the audience is picking up on the energy, they are speeding up a little as well.

Who has the beat?

8 Historically, who drives the tempo in multi-instrument performance has changed over time. Orchestras in the 17th and 18th centuries received that sort of leadership from the first seat violinist. This is why that position is still called 'concert master/mistress.' Felix Mendelssohn, besides being a composer, made two contributions to the history of music. He rescued a largely forgotten composer named J.S. Bach from the obscurity into which he had fallen, and he introduced the concept of the 'conductor' (himself) which has been standard in orchestral music since. One of the functions of the conductor is to oversee the 'musicality' of the overall performance, to a large extent by controlling the changes in tempo.

Some players like to play 'in the pocket,' meaning that they have a strong sense of steady rhythm, and very little patience for on-the-fly tempo changes. Nevertheless, most of the time in a performance, the rest of the band does well to listen to, and conform to, the drummer. Better drummers will listen to, and conform, to the primary vocalist. This allows the vocalist to drive the organic expression of the song, but major changes should not be unexpected. Some modern bands may have someone who takes that role other than the vocalist (the song-writer, perhaps), but clearly someone needs to be in charge.8

Drum notation

Drum notation is still somewhat of a moving target. What approach to take frequently depends on who you are writing for, and how much control you want to have. The following notation methods are not mutually exclusive, and can easily be mixed and matched as needed. One thing they have in common, though, is the staff sign. Rather than the usual G (usu. treble), F (usu. bass), or C (usu. alto or tenor) clef signs you will see either the two parallel bars as in the next image, or a rectangle with more or less the same shape. This is called the 'neutral clef,' or sometimes the 'drum clef.'

Slash notation Slash notation

By far the simplest drum notation is called (descriptively) slash notation. This consists of a notification to the drummer of what the basic beat is, and very little more. It looks like the illustration to the left. The 'time' indication means that the drummer is simply keeping the beat. Other options might include (but are not necessarily limited to) 'fill' or 'solo.' Beyond that, this simplest form tells the drummer nothing more than that there are four beats per measure. If the piece were in ³, there would be three slashes per measure. You are giving her freedom (trusting her) to play in a style appropriate for the music.

9 As far as I can tell, as of this writing (2013), Finale® will not allow you to do this. The closest alternative I've seen looks like this: slashes w/cues in Finale
Slashes with cues Slashes with cues

Sometimes a time signature may be provided. In a somewhat more useful variation, a rhythm may also appear on the staff reflecting the dominant rhythm of the piece (slashes with cues). This allows the drummer to create her improvised part in light of the dominant rhythm (note that the stems are up; if you are using a software music editor, you may have a challenge figuring out how to convince it to do this).9

10 You may have noticed the missing time signatures in most of these samples (although not this one). In the world of pop and jazz, anything but ⁴ is so infrequent that writers will simply assume it. If you don't see a time signature, assume ⁴. On the other hand, if you are writing it yourself, please, don't do this.
Rhythmic notation Rhythmic notation

You can get a little more control by opting for rhythmic notation (Sometimes referred to as 'slashes with stems'). In terms of temporal notation, these work just like the standard oval notes we have already seen, except the heads are slashes. You can even have hollow slashes for half- and whole-notes. You use this form when you need to tell the drummer something specific about the rhythm, but still want to leave her the freedom to implement it using whatever percussive medium she wants.10

Using only one line Using only one line

If you are only using one of these methods, you probably don't need all five lines in the staff, and some people will work with just one to reduce some of the clutter. If you decide, however that maybe you actually want some more control, you will have to move on to the next level of detail, which usually does require the full staff.

The full staff

11 The PAS standard is described more fully, and with much higher authority, in Norman Weinberg's (2002) Guide to standardized drumset notation. If you want to read it, you pretty much have to buy it. More than ten years after publication, there are maybe six or seven libraries anywhere that have it.

This is where my earlier comment about this being a moving target becomes more meaningful. This method looks a lot more like standard music notation, but since drums aren't usually perceived as having notes (even when the set is tuned), the locations of the notes on the staff refer to specific drums, cymbals, etc. The temporal indications are the same. As a visual clue, but also to add to the amount of information you can squeeze into one five-line staff, note-heads are given several shapes. Regular drums get standard oval heads (), but cymbals get × shaped heads (), and miscellany (bells, blocks, tambourines, etc.) often have triangular heads (). Until relatively recently, there were only a few conventions regarding which line/space referred to which item in the set (bass drum on the second space and snare on the third are the oldest). It was expected that the writer would indicate at the start of the piece how the vertical placement of 'notes,' and various head shapes, corresponded to the expected kit. Late in the 1990s, the Percussive Arts Society came up with a standard to cover all this.11

12 That was not just a ridiculous random choice. I remember hearing about just such a percussion choice in a studio recording (where actual volume is not particularly an issue).
AC/DC: drum score fragment from "Back In Black" score fragment from AC/DC
If the audio button is screwed up, try the MIDI

Not surprisingly, people who had already learned to write and read in another format have still not all jumped on the bandwagon, and most high end software gives you the ability to override the standards in favor of your own preferred layout. Obviously, older printed editions did not comply, and it is not clear that music publishers were among the first to get on board after the standard was created. In addition, I have noticed that not all 'standards compliant' software vendors have agreed on how to interpret the same 'standards.' Some of this inherent to the medium; the PAS didn't think of everything. If you are writing a percussion part that requires a cardboard box as a drum, you may have to improvise.12 For some reason, the PAS didn't create a standard for that. Improvisation, in this case, means telling the reader how you intend to notate your unusual surface and sticking with it. The best options are to either make use of an unusual note-head, or, if your software will allow you, go below the staff using ledger lines (standard includes two above, but none below). Standards do facilitate long-term communication, so if you are considering creating your own layout for a standard trap set, please, let me discourage you.

A sample legend from Audio Graffiti A legend example
Another sample legend Another legend example

This also means that you need to verify right from the beginning, if you are looking at someone else's drum score, whether he has specified a system of drum to staff mapping that you do not expect. The PAS standard also recommends such a key (called a legend), even if you are sticking within the PAS standard. The designers of the standard recognize that there is a good deal of possible variation even among conforming scores. The above two legends are both acceptable. The first is more compact; the second more readable.

The standard layout

13 By this, I mean if your set includes those labeled in the following staff. If you have only one mounted tom, you don't use the note on the fourth line from the bottom.
If you are writing for a basic standard drum kit,13 PAS recommends the following layout:

Basic drum kit chart Basic drum kit chart

There are more performance specifics that I will discuss presently, but you should note a couple of things. As I mentioned earlier, the drums have oval heads, and the cymbals have ×-shaped heads (—you will sometimes see them looking more like a double-sharp [] with a stem). The drums move up the staff from low to high much like a standard musical score, just with the snare stuck in there in its traditional location. It is not clear to me that the same can be said for the cymbals, but these are not specifically tied to particular sizes, so that is up to you as the composer; I would recommend it.

Of course, if you are a long-time member of the drum-of-the-month club, you may need a few more note-heads up there to accommodate your growing implements of percussion collection. As you fill out your tom set, you should add the notes in the following order:

The order in which to add toms Order in which to add toms

There are few specifics provided with this standard. If you have particular head sizes in mind, or other details, they need to be specified in your legend at the beginning of the piece. In fact every surface you use should be specified there. Again, although it is not a rule, I would recommend sticking to the lowest to highest pattern where possible.

More cymbals More cymbals

Additional cymbals are notated as on the right. The 'more cymbals' group is unassigned, so be particularly sure to be specific in your legend. Things like Chinas, sizzles, etc. go there.

You have probably already noticed some overlap. The second hi-hat is in the same space as your seventh tom, for example. This is one of the functions of multiple note-heads; besides providing some useful visual categories, they allow you to stick more information within the space of one staff.

Blocks, bells, tamborines, shoe boxes... Blocks and bells

Were you hoping to include more than drums and cymbals? If you want to put them on the same staff, switch to a triangle head (). This is also how you would approach non-ordinary surfaces.

Obviously by the time you have multiplied your toms and added lots of blocks and bells, your single staff is going to start to look a little cluttered. If you have enough of these other surfaces, and assuming that you don't want your drummer to shoot you, the PAS recommends using a separate staff for this last group (on the top staff), in which case regular note-heads are preferable.

Getting some control

The hi-hat the hi-hat
Sticking modificatons sticking modificatons

If you want some input on how the heads are hit, you get that through another set of head modifications. It is also possible to use icons to specify sticks/mallets, and different striking locations on the head (although I don't have pictures for those). You will sometimes see the ghost note with a smaller note-head, instead of in parentheses as here; the meaning is the same. The hi-hat is generally closed, so specifically marking it that way, is not common.

Whole- & half-notes whole & half-notes

Whole- and half-notes are indicated with hollow notes, as with normal oval heads, although there is an obvious issue with hollowing out the x heads. Weinberg's guide suggests using diamond shaped heads, as in the illustration. As you can also see from the picture, that gets a little hard to read. Finale® uses the alternative hollow-x method (a circle around the x), which seems more legible, but Musink® uses the same symbol for any crash cymbal. Time will tell who wins. Once again, use your legend.

14 Frequently, user improvisations don't reflect a fundamental understanding of the pattern underlying the existing standard, which means they are less likely to be adopted. But even then, they exert pressure on the standards developers to respond to the obvious need.

Clearly enough, just as most standards have evolved as a result of pressure from users and the commercial sector, notation standards will evolve and follow observed practice. The more people do something the same way, the more likely it is to be responded to, or even adopted.14 If you need to add something new, look first to see if there is an emerging consensus on how to approach it before striking out on your own.

Repeats and expression symbols

Drum notation uses the same measure-repeat symbols as standard notation. '' tells you to repeat the last bar. '' means repeat the last two bars. Not surprisingly, in many drum scores these get frequent use. The standard and are obviously going to function the same as usual.

Common accents/articulations Common articulations

Accents are only slightly different. Marcato is, as you would expect, a noticeable accent; Tenuto a little less so. The upstroke (down arrow) is an anti-accent, meaning that note is played more lightly, although not so much as the ghost stroke mentioned earlier. Staccato is, well, staccato. The 'let ring' is not the same as a tie, although using a tie may be the only way to persuade your software to create such a symbol.

Stems

The rules for stem direction are slightly different than standard. If it is a solo part, or some situation where the drums are actually being treated as an instrument, stems should, according to the PAS, be written using the same standard as for other instruments:

1.Notes on or above the middle line are written stems down; below that they should be stems up.
2.Notes sharing a stem (played simultaneously) or beamed receive stem direction based on the note farthest from the center line.

If, on the other hand, the drummer is simply playing a beat in the background, notes are generally written stems up, particularly where that makes the flow of the rhythm clearer to the reader. If, however, notes played by the hands and those played with the feet are distinct, that should be clarified by having the foot-beats written with stems down.

Weinberg (2002) provides the following examples:

Solo: mixed stems Solo: mixed stems
If the audio button is screwed up, try the MIDI
Beat-keeping: stems up Beat-keeping: stems up
If the audio button is screwed up, try the MIDI

Limb clarification: separated stems Limb clarification: separated stems
Two drum voices: divided stems (slightly modified from Weinberg). If the audio button is screwed up, try the MIDI Two drum parts: divided stems
If the audio button is screwed up, try the MIDI

Finally, if it is written in two voices with both parts scored on the same staff, one has stems up, the other, stems down (as with any other mixed voice staff).

There is more in Weinberg's book that I have not covered here. If you are actually going to seriously write for drums, you should go there, rather than depending on this summary. There is also more information to be found on the excellent site, Audio Graffiti.

Percussion with pitch

Some percussion instruments actually have definite pitches—tympani, vibes, marimbas, etc. In those cases the instruments have their own staves and the notes are represented just as they would be with other note-producing instruments.

Musicianship

Ear training for rhythm

Being able to hear and recognize, and to produce more and more complex rhythms is also an important part of developing musical skill. It is not unusual to be able to reproduce a heard rhythm without having a clue how to turn it into notation. By this I mean just regular musical notation, not necessarily being able to write a pattern for drums (although the latter is clearly based on the former). Ear training works the same way here as it did for melody in the last section. America's "Horse with no name" is a place to start. The melody should be a breeze, so the work comes with figuring out the rhythmic pattern, both for the guitar and the vocals. This is not a complicated pattern, but it is a little more complex than "Frère Jacques."

Conducting

The other skill worth developing is conducting. You don't need to be thinking that being an orchestra director lies in your future to find this useful. I often find that it helps when I am trying to figure out a rhythmic pattern—more so than tapping your feet or something. Maybe I will get around to doing a page on this, but the basic patterns can be found at Music and Mind Games. It takes some practice, but you will probably find it is worth the effort.

Where to?

In the next section, we are actually going to start talking about chords. My guess is that a significant percentage of my (2) readers have been waiting for this.

Works Cited

Brent, Margaret (1998). "The Grammar of Early Music: Preconditions for Analysis." In Tonal Structures in Early Music (Criticism and Analysis of Early Music), ed. Cristle Collins Judd. New York : Garland Pub.

Weinberg, Norman (1998). Guide to Standardized Drumset Notation. Lawton, OK : Percussive Arts Society (Distributed by Hal Leonard Corporation).

© 2013 Alan Humm