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- Brian Hoffman April 2017
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Language for describing positions in a measure of 4/4
Hi collective wisdom,
I have a easy question, mostly of an editorial nature, about referring to locations in the measure. I’m writing about rhythm in rap music, with a persistent 4/4 meter. Sometimes I need to refer to the last sixteenth note of the measure. Sometimes I need to refer to the final sixteenth-note position of every beat. Sometimes I need to refer to all the sixteenth note positions of the second beat. Sometimes just first sixteenth note of the beat.
I make these sorts of references several times per paragraph, so I’m looking for a consistent and intuitive way of doing so. I also want my writing to be approachable to humanists and social scientists who don't read music. I’ve been toying with using the takadimi rhythmic solfege, which enables for constructions like “4-mi” to refer to the last sixteenth of the measure, or mi to refer the last sixteenth of each beat. It also distinguishes between “beat two” for all of beat two and “2-ta” for just the downbeat. The downside is that it requires the reader to learn takadimi.
I’ve also considered using beat-class notation (e.g., bc 15 for the last position of the measure) when referring to specific positions and language like “beat two” for referring to ranges. This language has several downsides: zero-indexing isn’t intuitive, and referring to “the last sixteenth of each beat” requires something like “bc 3 mod 4,” which, while precise, is rather technical.
I’ve also considered Adam Krims’s 1-x-y-z-2-x-y-z, etc. This is essentially a rhythmic solfege, but it has no assigned symbol for the first position of each beat, and "1w" for the downbeat looks really strange.
If there was an obvious, correct answer, I’d have stumbled onto it by now. What would be your preference? Is there something I’m overlooking?
SMT Discuss Manager: smtdiscuss@societymusictheory.org
Comments
Hi Mitch,
I've recently run into this issue as well, also when writing about rap music. For what it's worth, I think both Krims's method and the takadimi tactic are about equally intuitive. Of course, they'd both necessitate a brief explanatory passage early on, but after that I think readers would be fine. In my own writing, I was imagining something like "4.1" to refer to the first sixteenth note of beat 4, but I'm not crazy about how easily that could be conflated with paragraph designations in, say, an MTO article.
To satisfy my own curiosity, I wonder: If you were using the Krims method, would you still use the word "beat" before the metrical designation? For example:
"The first syllable of the word 'money' falls on beat 4, while the second syllable arrives at beat 4y."
As opposed to:
"The first syllable of the word 'money' falls on 4, while the second syllable arrives at 4y."
Thank you very much for bringing this up--I was beginning to dread the prospect of writing phrases like "the third sixteenth note of beat three in measure four" over and over again, and I think all of the options you've listed are preferable (though I do imagine the beat-class notation could obfuscate things unecessarily).
-Robert Komaniecki
The approach that Robert suggests is actually pretty logical, I think--with the decimal separating the beat number from the beat division number. I've used it before.
1.1 = beat 1, division 1
2.3 = beat 2, division 3
4.4 = beat 4, division 4
Even if you were to further subdivide a beat, this approach would work:
1.1.2 = beat 1, division 1, subdivision 2, etc.
I think a non-musician (unfamiliar with rhythm syllables) would be able to intuitively grasp this approach. For musician audiences, 1 e & a would work fine, too.
I think that your takadimi intuition is correct, but why not use the ubiquitous 1-e-and-a as a more familiar version? "The and of beat four." "The 'a' of beat three."
At least, that seems to be the "obvious" solution that you may have overlooked. I'm not certain that it's the "best" solution.
-Brian Hoffman
1-e-&-a may be a little easier to read (with the ampersand instead of spelling 'and').
I'll put another vote towards the 1-e-&-a system. The only trick is differentiating between the beat location "a" and the letter "a". There are some easy ways to solve that: You could capitalize the "e" and the "a", put the letters in bold, put the letters in quotes, italicize them, etc. As long as you're consistent, I think it shoud be fine.
Me too, basically, I'd go with 1- 1e 1& 1a for the sixteenth subdivisions...
Hi Mitch. Good question.
I'll throw in with Robert and Brent, further agreeing that most audiences–including non-readers of music–will be able to grasp it quickly. I'll only add that with such a clear system for discussing rhythm and some musical examples to bolster your discussion, those non-readers will gain a certain amount of musical literacy from reading your work.
You might even recommend that readers try out the examples themselves, giving those 'ivory-tower humanists' another understanding of 'old school!'
I should have asked this a long time ago! I agree that 1-e-&-a is easily grasped and already widely known, but it doesn't make refering to "the & of all four beats" easy to refer to, and this is pretty critical for me. I like the 4.1, 4.2, etc. system, but I also frequently need to use actual decimals. Now I'm toying with 4•1, 4•2, etc., and this would enable the notation "•1" to refer to all on-beat positions, "•4" to refer to all just-before-the-beat positions, etc. And I don't the option-shift-8 character • for anything else. Since I never need further subdivisions, 16•4•1 could be assumed as "m. 16, beat 1, position 1."
Or I could force my readers to get on board with zero-indexing. Then musicians wouldn't go around thinking 2 (a second) + 2 (a second) = 3 (a third).
A counterpoint to the "1-e-and-a" camp:
One of the reasons why I prefer to not use "1-e-and-a" for my beat designations when writing about rap music specifically is that you're typically describing syllables of text. When pronounced aloud, "Ee," "and," and "ah," all sound like they could be syllables of text in their own right. It runs the risk of tripping up readers (or listeners, if you're giving a presentation).
Say, for example, you were describing the metrical placement of the lyric "amazing":
"The "Ah" of "amazing" falls on the "ah" of beat three, while the "ing" falls on the "ee" of beat four."
It's just a little clunky.
I agree with Robert, Brent, and Keith—2.3, 4.1, etc. is easy to grasp.
Zero-indexing does of course have a certain elegance though. For example, in a measure of 4/4, 8th notes occur at 0, 2, 4, 6, 8, etc. Starting at zero makes sense in that the "clock" also starts at zero. As Mitch points out, all the math makes much more sense, just as it does in dealing with pitch. Toussaint (A Geometry of Rhythm) zero-indexes rhythm, and of course Babbitt's time-point system does, which among other things allows him to use the same all-partition arrays for both rhythm and pitch (as in the 4th string quartet).
I put in a vote for the all-numbers camp, with the caveat that I would consider using superscripts for the sixteenth note positions. So 4^4 for the last position in a measure. That's often used in the form (measure number)^(beat number) but I take it you don't need to be including measure numbers with these. You could also use variables to indicate, say, all placements a sixteenth after the beat (X^2).
--Jason Yust
I'm in the number camp, with a preference for zero-indexing. Even your most math-phobic readers somehow managed to pass out of third grade, when they learned their times tables up to the level of 4 x 4 = 16. They can tell whether or not a number in that range is even or odd, and whether or not it is divisible by four. I would simply lay out a 4 x 4 matrix at the beginning of the discussion. The interface in which I'm writing won't allow formatting, so I'll describe it. You place 0, 1, 2, and 3 on the top row; then 4 5 6 7 in the second row, and so forth. Call attention to the first column, 0, 4, 8, 12, and say "these are the beats. They are all multiples of four." (Readers who run screaming for the exits at this point are probably unreachable by any standard.) You then circle the fourth column, and say "we are particularly interested in these sub-beats, 3, 7, 11, and 15, each of which is incrementally smaller than a multiple of 4, and each of which anticipates a beat by a semiquaver/sixteenth note." There is a small investment in overhead, with a big payoff that will carry over into any further work that you and other metric theorists do.
---Rick Cohn
Similar to Jason's post above, I was going to suggest subscripts, with the 1-e-&-a system -- eliminates the need for any dots/decimal-looking-things at all. I like the familiarity of these syllables, and I like the fact that it easily groups them into classes. The subscript (or superscript, as Jason suggested) helps eliminate the cumbersome wording of "...on the 'a' of beat 3," and you could easily deal with "...on all the 'e's in the measure" by something like X^e
In my own notes I've recently been using 1 (1)e (1)& (1)a to refer to the four sixteenth subdivisions. So, an event occurring on the last sixteenth of a 4/4 measure would be said to occur at (4)a. This takes the readability of the 1-e-&-a system but presents it in a compact form like the decimal system, so that you don't always have to type out "the e of 3" or whatever. I haven't needed to refer to the final sixteenth-note position of every beat at once, but it could be done with (-)a (the dash clarifying that there wasn't a typo by which the beat designation was left out).
I'm not a fan of 1.1 / 1.2 / 1.3 / 1.4 etc. because two separate duple subidivions / metric levels are conflated into one decimal location. If sixteenth-note triplets are suddenly employed, is what was 1.3 now 1.4? Zero-indexing runs into similar problems (as will any purely numerical system which doesn't embed fractions), but it does have an advantage over a quasi-decimal system in that it doesn't force us to bias one particular organization of the measure into beats. For instance, if 3/4 and 6/8 are simultaneously implied in a passage, zero-indexing tells us where in the measure an event occurs without committing to the framework of either meter.
In response to Jesse (previous post), who wrote:
Good point. However, the 1-e-&-a system has the inverse problem. If we move from sixteenth notes to eighth-note triplets, then the location of "&" changes. If we have sixteenth-note triplets, as suggested in the quotation, then who knows what the syllables are (choose your system, I guess). Even the syllables for sixteenth notes (1-e-&-a) and for eighth-note triplets (1-&-a) are far from being universal, whereas numbers would be widely understood.
Even though I still prefer the 1-e-&-a system, Rich's point is valid. It also reminds me of the challenge thatt comes up every year in aural skills class...what syllables do we use for quintuplets? (Takadimi might take care of that...I don't know the system.)
I use the 1-e-&-a system for this purpose but I find it awkward. The major advantage of the 1.1.1 system is that it's already ubiquitous in DAWs like Logic and Ableton Live.
. . . and different c!ock resolutions generate different rhythmic subdivisions (in current music software).
The following is a variation on some of the previous suggestions.
What about 1i 1ii 1iii 1iv ?
If subdivision is not needed one can just say 1, 2, etc.
If one needs "to refer to the last sixteenth note of the measure" (let's say it's measure 12) : "12, 4iv"
If one needs "to refer to the final sixteenth-note position of every beat" : "the iv of every beat," or just "every iv."
If one needs "to refer to all the sixteenth note positions of the second beat": "2i-iv."
If one needs "to refer to the first sixteenth note of the beat: "the i of the beat," or, if there's a specific beat in mind, such as beat 3: "3i."
Just a suggestion...