Macho Meters

Anyone ready for another year of music theory talk? I did my annual shtick this week on odd meters. You can anticipate me: Holst’s “Mars,” the ancient Greek “Hymn to Apollo,” and Brubeck’s Take Five for quintuple meter; Pink Floyd’s “Money” for seven; a long passage from Roy Harris’s Seventh Symphony, plus a Bulgarian “Krivo Horo” for eleven; the “Blues” movement of Ben Johnston’s Suite for microtonal piano for thirteen; Waylon Jennings’s “Amanda” for fifteen; and the end of the first movement of my Desert Sonata for a long passage in 41/16 meter. Only this year, I have a student, Benjamin Bath, who grew up in a Greek family and going to Greek weddings and all that, and every meter I’d start to mention, he’d reel off all the traditional Greek and Macedonian and Bulgarian songs, and already knew the couple I played. So Monday he brought in a book, The Pinewoods International Collection selected by Tom Pixton and published by NightShade, and let me copy some examples. Try humming through this little number:

And here’s another, much easier to play, but impressively in 22:
A little more chromaticism, and these melodies would look like I wrote them. From my readers’ previous very informative debate, I know that some will object to the very notating of these traditional tunes, claiming that they can only be learned orally, and I reiterate the most relevant comment left by someone who knew this music:

[T]he Bulgarians DO NOT count out every “8th” or “16th” note while performing their music. They express them as long and short beats. They actively discourage trying to count it out, and expressed that the only way to hope to begin to play it accurately would be to feel the long and short beats.

Doubtless true, making the whole topic an excellent entrée into teaching students that there’s more than one way to scope out rhythms, and entire societies in which consecutive beats are not assumed “steady,” but can be different lengths. Helpfully, Pixton’s edition marks out the underlying rhythm on the top left of each example. But since I do teach the blackboard theory class and am pretty reliant on notation, I’m thrilled to have more than just a couple of token examples of 7, 11, and 13 – and not only examples by weird avant-gardists like myself, but by normal people who play at weddings. 

In fact, I’ve got to move to Greece or Bulgaria – out someplace where I can teach some real man’s theory. I’ve had it up to here with this pusillanimous 2/4, and 3/4, and hidden fifths, and D# equalling Eb.


  1. says

    The point about long versus short is exactly the same for the Arabic rhythms in the music of Rabih Abou-Khalil. It may look a bit difficult on paper, but it really swings. As long as one knows the difference between two and three, it’s quite playable.

  2. says

    Hi Kyle,
    I think the biggest challenge in notating odd and irregular meters is that we don’t have a way to indicate the lilt that often accompanies them. When they really flow, it’s beyond math and it’s just… GROOVE. Anticipate a hair of a beat here, lay back a tad on another one there. Like passion, or a love of dark chocolate or single malt, you can’t teach groove. Either people get it, or they don’t.
    Lots of “straight” music shares the same problem: take any Chopin Nocturne, for instance. Even in one of those common time pieces, no one would ever play the ink just as it’s written on the page; that would be… ew! It’s like jazz, or music from Bulgaria or Greece: there’s an aural/oral tradition we immediately grasp if we grew up with the music. I was tempted to give one of my private students the task of doing a take-down notation from a lovely, if soupy, recording of one of those Nocturnes, just for the fun of seeing what bizarre meters would be necessary to literally capture the essence of the music as heard! It would end up looking like some kind of Crumb score, methinks.
    When notating my electroacoustic pieces, I find I’m in that predicament all the time, except in this case there’s no grand tradition to which anyone can refer. The musician needs to be able to follow the score and play against it, but the electronic track might be very ambient and without a discernible beat. So I do a reverse-Chopin: I compose the thing freely against a steady and usually unheard pulse, then when I’m done I find where the natural lilt is, create downbeats with whatever Western music meter works best, and then often, still need to add rubato, ritard, or poco accel markings to even approximately notate the rhythm. Ultimately, I’ve got to trust that the player will feel the groove. That’s all that matters in the end.
    So I’ve concluded that there is no way to accurately notate rhythm. It’s all interpretive, like that Bulgarian or Greek music. This is why I don’t follow recipes, either. It’s much more fun to create food with a lilt, and see what it ends up tasting like!

  3. says

    Since you mentioned Johnston’s suite, I have a tangential question. I seem to recall once seeing a tuning chart for said suite either on this journal or at your site, but I can no longer find such a thing in either location. I was particularly interested as I recently wrote a piano piece which I think would benefit from such a pure overtone tuning, and I wasn’t sure which overtones he used to fill out the last two or three pitches. Was I simply mistaken about the existence of the tuning chart?
    KG replies: I don’t recall putting up the chart, but I can give you the tuning off the top of my head. It consists of the following harmonics:
    C 1st 0 cents
    C# 17th 105 cents
    D 9th 204 cents
    D# 19th 297 cents
    E 5th 386 cents
    F 21st 471 cents
    F# 11th 551 cents
    G 3rd 702 cents
    Ab 13th 840 cents
    A 27th 906 cents
    Bb 7th 969 cents
    B 15th 1088 cents

  4. says

    I wonder how much of this has to do with the failings of traditional Western notation to accurately capture the feeling of “the groove” in various folk musics, must as it falls short in capturing non-tempered scales.
    If the classical mind keeps segmenting time equally like the ticking of a second hand, sure, it’ll come out the way these examples showed. It, the tradition, doesn’t seem to allow a lot of room for the elasticity of a pulse within a measure.
    I mean, certain calypso music, in 4/4, could be accurately be rendered in 7/8 by the way the beat is pushed in the second half of the clave. Certain listeners who had heard Chopin himself play his own mazurks, written in 3/4, could have sworn they were hearing 4/4 by the way he held onto the first beat longer than traditionally written.
    Notice how the meters in the examples do not change meter. They stay in the groove.
    Sure, there are indeed odd meters everywhere but I’d hold a lot of these up to higher scrutiny and see how much of it has to do with the elasticity of time within phrases and how this is compounded when indigenous ornamentation is involved.
    Like the Bulgarians, we could also step back from the microscope of 8th notes and see how it all falls into the larger phrases.

  5. says

    I may be stating the obvious, but re. odd meters: how about all those jazz-rock and prog-rock grooves in the 70’s? How about King Crimson and Meshuggah moshing together compound odd meters? And can someone in the house scream “Zappa?” Odd meters come from two directions: above the neck and below the neck. The most successful ones – even the Chopin lilt – appeal below the neck.
    Thanks so much, Kyle, for your refreshing blog. You da shizzle!

  6. says

    “Like the Bulgarians, we could also step back from the microscope of 8th notes and see how it all falls into the larger phrases.”
    Yes, and I believe this is the key to real musicality, anyway (unless one is consciously going for a purely mechanical sound). My best composition lessons may have come from my piano teacher, Marshall Kreisler, when I was growing up. As I plodded through whatever repertoire he was trying to fit under my young and often heavy-handed fingers, he often talked about the arc of a phrase. He admonished me not to count the 16ths or the 8ths with which I was struggling, and rather, understand the intent of the musical line from Point A to Point B. And: magic! Keeping that in mind, I played the phrase far better.
    Composing is the same, as far as I’m concerned (I suspect a number of my peers may disagree): what matters most, what the listeners’ ears hear, is the arc from Point A to Point B. It’s the wash of the music over us that effects us, not always the intricate detail. Especially in a piece with a fast tempo, unlike composers who neurotically slave over every note choice because hey, we have to, the audience really doesn’t hear all the piddly notes in the run. What they hear is the beautiful swoosh of it, the gesture.
    I like to remind myself of that on the occasion when I hear a… uh… less than definitive [she writes diplomatically] performance of a piece of mine. Every composer has been here: the reaction from the audience is wonderful, yet all you can think of were all the botched notes. In these moments I remind myself that not only would the audience never know what notes were actually intended, but more to the point, the gesture of the music, even if inexactly executed, was enough to get the emotional point across.
    And this brings me back to rhythm. We all know that in anything other than the stiffest of beats, it’s the swoosh, the gesture, the effortless glide, that makes it so beautiful and makes the groove… groove (I like nouns that are verbs). So in addition to whatever little black dots we place on a page to indicate something only approximating the intent, it’s important that the aural/oral tradition is carried on. Otherwise, when looking at a fake book lead sheet with straight 8ths and the little word “swing” in the corner, who the heck would know that what it really means is eighth-sixteenth?!

  7. says

    Whoa! Surreal, I was in fact listening to Sandansko Horo at the very moment that I saw your example of it. What are the odds?! I play that tune in a Balkan-ish band I play in (mixed up with some klezmer, free jazz, and drum ‘n bass), and I was listening to the CD we just finished recording. It’s true, this tune seemed incredibly difficult when we were first learning it, but now it grooves totally easily and intuitively and feels completely natural. And when we play for the right audiences, people dance to it.

  8. richard says

    In regards to the whole “groove” thing and asymetrical pulse pattern I thought I’d bring up the problem of rhythmn in jazz. Many neophytes “swing” 1/8ths as triplets (1/4 note 1/8 note) which is ok for some styles of jazz, but beginning in about the ’50s 1/8 notes tended toward being quintuplets ( dotted 1/8 note, 1/8 note). I don’t know if this has been talked about much.

  9. Daniel Wolf says

    What is often bypassed in discussions like this is the fact that the music under discussion is dance music, and often closely related (if not identical) to vocal music which reflects the long and short syllables of the language (something quite different to English verse, based on stress accents rather than duration). The musicians and dancers do not count the underlying subdivisions, they count steps, which translate immediately into long and short metrical feet. Melodies overlaying these metres may often subdivide the feet in ways which contradict the obvious subdivisions. A single foot, may thus be divided into two or three equal parts, regardless of the count suggested by a single running pulse.
    I disagree with those in this thread who would exclude western music from this phenomenon. Jon Barlow (a wonderful pianist whose repertoire focused on Viennese classicism, Ives, and Cage), inspired by the experience of Karnatic music, insisted that “movements” in the classical style be taken literally, with unequal beats (i.e. feet), and embracing the whole range of posibilities from strict regularity to the near-random inequality of the Wiener espressivo. If the Waltz does have swing and/or groove, I don’t know what does.

  10. says

    Also, you could try music by bands like Dream Theater and Symphony X (beware the ‘heaviness’ there). A lot of different metric going on, with some entire sections in odd metrics like you’ve chosen (Mars, Money, etc).
    Really liked your last sentence, btw. :)

  11. Cory Parkinson says

    Take a look at Brian Ferneyhough’s pieces. His British “New Complexity” style is just that: complex beyond belief. His piece for solo piccolo (yes it is as agonizing as one would expect) entitled “Superscriptio” includes such times signatures as 66/1, 10/3, 6/10, and many other seemingly impossible meters. He assures us that they ARE possible, by some sort of logic like this. If we look at septuplet eighth-notes, if we take all seven of them, put them on the BOTTOM of the time signature (giving us a 7) then use the standard definition for the top (the # of ‘beats’), like 10, we come up with 10/7. The only thing is that this is all dependent upon a standard unit that we are making tuplets out of to represent the bottom of the time signature, which in the case of “Superscriptio” is the eight-note. It’s quite a stretch, I know–but I didn’t make it up. He did. So take it up with him. But I think it’s interesting nonetheless. Performances of his works usually are “guessed” as opposed to actually taking the time to figure out all the formulas, as the meter changes every bar. It comes down whether the 100% accuracy is as important as the effect he’s going for. We talked about this a lot in a composition seminar I did with Roshanne Etezady at Interlochen. Fun stuff! Hope this intrigues you as it did me…CP
    KG replies: Hi Cory. Well, I certainly know Ferneyhough’s music, and I was aware he uses some of those meters too. It detracts a little from my enjoyment of it that you can’t really hear their effect in that complex context.