Zuni Totalism

Below is the complete transcription of part of a Zuni Buffalo Dance from Robert Cogan’s and Pozzi Escot’s 1976 book Sonic Design, one of the best books of musical analysis ever written. (Though long out of print, you can still get print-to-order copies on the web.) This is the book which introduced me to the practice of switching back and forth among different tempos in Southwest American Indian music. Combined with the rhythmic theory I already knew from Henry Cowell’s New Musical Resources, it elicited in me an interest in meters with denominators other than powers of 2, and, more significantly, led me to embark on a musical style which shifted among different tempos. Here’s the score, and you can hear the original recording from which Cogan and Escot worked here:



The meters, of course, aren’t given as 2/3 or 5/6, as they could be, but as 2 and 2/3 over 4 and 3 and 1/3 over 4 – a format Charles Ives also used. A somewhat similar Hopi Elk Dance song, in my own transcription, using dotted quarters and quarters instead of quarters and triplets, is given in my program notes to Desert Sonata, the 1994 piece that quotes the song.

Of course, the Zuni were not reading from sheet music, and one could quibble about whethere these incomplete triplets are the best way of rendering their music in notation – but as I saw it in 1977, this was a way of transferring that feeling of performance practice into music based in European notation. I wanted a musical basis that didn’t sound European, didn’t sound familiar, nor was rhythmic precision my aim. It has always seemed to me that dotted 8th-notes have an inherently syncopated feel, while triplet quarter-notes are much smoother, suspended over the felt beat, and I was interested in using the notation to induce different qualities, not only quantities, of rhythm. Performers who internalize that principle find my music easier to play than it looks at first. Steve Reich had arrived at his style by studying the Ewe drumming of Ghana, Riley and Glass by involvement with classical Indian music, Lou Harrison via Indonesian gamelan, and so on, and as someone who had grown up in the Southwest, I mined Zuni, Hopi, and Pueblo music for qualities that would help revitalize my tradition. During the 1990s there was a lot of criticism of white artists who “appropriated” music by people of color, and so I gradually backed off from the more programmatic aspects. Plus, increasing commissions from ensembles limited my style in rhythmic respects, while working with the Disklavier and electronics liberated it in other directions. This Zuni-Hopi influence survives in my music, but rather abstractly at this point. 

In any case, to anyone who claims that incomplete triplets can’t be performed, I can always counter, “The Zuni can do it – why can’t you?”


  1. says

    I think Cogan and Escot got their analysis of that piece totally wrong. . . The performers aren’t playing it as a quarternote pulse interrupted by 6th notes, and the rhythm of the melody isn’t dotted eighths and 16ths. The whole first section (drum and vocal line) is on an 8th note pulse, usually in groups of three, but occasionally in groups of two. I’ve added a drumtrack to the recording to illustrate what I mean. The claps double the attacks of the vocal line to demonstrate that it always stays with the eightnote pulse.
    Escot and Cogan’s quarternotes are actually dotted quarters, and the triplets are quarters, and there’s a steady eighthnote pulse all the way through. They didn’t just group things confusingly, but they actually transcribed the melody rhythm incorrectly.
    I haven’t done as thorough an analysis of the second part, but I think that there we have a steady 16th note pulse, usually grouped in twos, but occasionally in threes.
    The elegance, then, is that you have two sections, each with a steady pulse, but in the first the pulse is grouped in threes with occasional groups of two and in the second the pulse is grouped in twos with occasional groups of three. But it’s not a case of nonstandard denominators or fractional numerators.
    Incidentally, inspired by the recent discussions of non-standard denominators, I’m working on a section of a string quintet which switches between X/4 and X/6. Also, I’ve discovered that Lily Pond can notate those time signatures easily, if you don’t mind that it lacks a GUI.
    KG replies: I said you could quibble about the notation, but you decided to do more than quibble: you decided to start my day off by telling me that my entire artistic output is based on a utterly worthless analysis. You wrote in to tell me that one 3:2 notation is absolutely unacceptable, while your 3:2 notation is just fine. Of course your transcription stays within the 8th-note pulse, just as theirs would stay within a triplet-8th pulse. If you think there’s a difference between going from dotted quarters to quarters and going from quarters to triplet quarters, then you don’t understand how incomplete triplets work. Personally, I find the given notation intuitively right, having a very different feel than the Hopi Elk Dance I transcribed. In addition, there are other Hopi songs that bounce among three tempos, requiring either incomplete tuplets or dotted quarters tied to dotted 8ths as a unit. Have fun.

  2. says

    I have no comment re the analysis but I really like that buffalo dance clip and the post in general, very interesting (not heard much native american music before, will listen out for more now)
    Put links to it on my blog also, cheers/thanks :-)

  3. says

    Woah, I didn’t mean to offend you. Yes, I think Pozzi Escot and Bob Cogan mistranscribed this particular musical example, but that’s not the same at all as saying that your “entire artistic output is based on an utterly worthless analysis.” Obviously the analysis had worth, or you wouldn’t have been able to base an entire musical output on it. Plus, I know nothing about any other Hopi music and I’m entirely prepared to believe that lots of it is most accurately/usefully transcribed with unattached triplets, especially if you’re the person telling me that it’s the case. I did phrase my analysis in much more of a my-way-or-the-highway manner than I actually meant it, and for that I appologize–my hotheaded contrarianism gets me into trouble from time to time :)
    My serious problem with the Cogan/Escot transcription is that the dotted eighth followed by 16th rhythms in the vocal line imply that during the non-tripleted sections the feel of the meter has the quarternotes subdivided into 4 parts and that the rhythm maps to that grid, but that in the triplet sections there’s a whole new subdivision since triplet quarters are mathematically a subdivision of the quarter into 3 parts. But the vocal line of the first section in fact lines up exactly to subdivisions of the quarternote beat into three parts the whole way through. I’m sure we agree that a triplet quarter followed by a triplet eighth is rhythmically very different from a dotted eighth followed by a sixteenth–so the transcription is wrong, and it’s not the case that it “would stay within a triplet-8th pulse.” A notation which creates incorrect subdivisions of the beat seems significantly problematic to me. If you’re hearing the vocal line as subdividing the quarters into three rather than four, we’re hearing it approximately the same way–but that ain’t how Escot and Cogan notated it.
    If they had transcribed the piece with the vocal line consisting of triplet eights and triplet quarters, which would preserve the unattached triplet quarters in the 4/6 bars, I would have no objection at all. And if you think notating it that way, with the unattached triplet quarters, is truer to the way the music is felt by the performers than my X/8 solution you may well be correct–after all, you have much more famiarity with the Zuni idiom than I do.
    My reason for preferring the X/8 meter over triplets in an X/4 meter (which we agree is mathematically identical, so this is mere personal preference) is twofold. First, ordinarily when the dominant pulse in a piece is subdivisions of the beat into three, the custom is to use 6/8, 9/8, 12/8, etc. rather than a whole slew of triplets, since triplets imply conflict with the underlying pulse. So this strategy makes a little more sense to me, but I’m not claiming it’s the only way or even necessarily the best way. Second, my impression of the second section is that the pulse which Cogan and Escot notate as eighth-notes should actually relate (not exactly, but intuitively) to the triplet quarters of the first section, so I would like them to be notated with the same note type. By my count the pairs of triplet quarters in the second section are actually more likely dotted eights, so the 3:2 ratio there matches the 3:2 ratio between the quarternotes and the triplet quarternotes in the first section. The way Escot and Cogan have it, the implication is that the eighthnote pulse of the second section relates 2:1 (intuitively only, since it’s in a different tempo) to the quarternote pulse of the first section. By using an X/8 meter I can have the small subdivision represented the same way in each section, and simply group those subdivisions differently in each section as appropriate. Again, personal preference, and as I said it may be that the importance of emphasizing the unatached tripletiness ought to trump my objectives here.
    So two questions: First, do you think my assessment of the way in which the second section relates to the first makes sense? Second, if so, and given your preference for notating the first section with triplets in X/4 and X/6, how would you feel about keeping it that way but also notating the second section mostly in 6/6 (or 3/3) with the occasional 7/6, or X/6 and the occasional 2/4, and mostly as quarternote triplets in groups of two with occasional quarternotes? I think that would satify your desire for unattached triplets, and it would also create the implied rhythmic relationship between the two sections that I’m looking for. But it might also be too wierd.
    KG replies: Galen, Robert Cogan and Pozzi Escot are pretty smart people, and I’m no dummie, and you don’t look at something for 20 minutes and decide the three of us have been morons for 30 years. I’ve been lecturing about this Buffalo Dance, and showing the transcription, just about your entire life, and I’ve never had anyone complain that the transcription is inaccurate. You think the dotted-8th/16th rhythm is not exactly 3:1, which could be equally true in a million recordings of Baroque music. I admit the first one sounds like a triplet, but they all sound slightly different, and I wouldn’t vouch for the rest. It’s not a machine singing, and this isn’t a science. I don’t even *really* think the triplet quarter-notes are exact triplet quarter-notes, but they’re too fast for dotted 8ths, and that’s the nearest reasonable equivalent. I’ve transcribed dozens of American Indian recordings, and I’ve never once thought I got one perfect, because it’s an oral tradition, not based on European tuning or metric archetypes. It’s a translation process. It can’t be precisely captured in notation. The Buffalo Dance impressed me with the possibility of lurching back and forth between tempos. The Cogan and Escot use of incomplete triplets offered me an idea for how to transfer this concept to notated music, based in European notation as expanded by Cowell. If your point about 16th notes interferes with this narrative and/or leads to some new insight, then let’s have it. Otherwise, you’re presenting something very fuzzy and subjective as though it were easily quantifiable and self-evident. Make your own transcription, if you want, but don’t imagine you’ll be any closer to pinning down what was in the head of the people who sang this music.

  4. says

    First, the last think I’m saying is that You and Robert Cogan and Pozzi Escot have been morons for the past 30 years. And the idea you took from this and Cowell of using incomplete triplets to lurch back and forth between fractionally related tempos is very, very cool. And I agree, this piece does have the feel of periodically switching gears in to a new tempo at a 3:2 ratio, which is fascinating.
    To me, though, there’s a very significant difference between switching between those tempos by changing how you group a consistent underlying pulse versus changing the underlying pulse itself by a 3:2 ratio. If that difference doesn’t seem significant to you, then what I’m saying would indeed qualify to you as quibbling and I’ll be done. To me, notating the vocal line with dotted eights and sixteenths versus eightnote triplets makes a clear statment about which of those two things the notator believes is happening, but if it doesn’t seem that way to you then I’m quibbling and I’ll be done.
    But if you agree that those differences are significant I think I can persuade you that this is a case of changing the grouping of a consistent underlying pulse.
    KG replies: I do not concede that there’s anything more inaccurate about the transcription than there is in any such transcriptions. Just because something appears in my blog doesn’t mean it must be attacked and debunked, though it sure seems that way.

  5. says

    I find the notation perfectly reasonable, but it occurs to me that if I were performing this music (or something similar), I would probably end up ignoring the time signatures altogether after the first few readings — the bar lines themselves would be sufficient. So what if the bars change length once in a while, that’s the way the music flows.
    So that’s my player perspective. As a composer, this approach makes eminent sense as a way to express one’s metrical intention in idioms that use this kind of gesture.
    KG replies: Sure, when I write rhythms like this, I often leave out meters, which confuse more than clarify. I have it on good authority that the Zunis ignore the meter entirely. :^)

  6. says

    Thanks for posting this and the corresponding audio file. I ‘get’ Oleana even more (which I am working on finding an appropriate performance opportunity for.) I need to return to my graduate ethno materials and dig up all that Francis Densmore stuff and assimilate it even further to help.
    As to the transcription, it can be tricky to fit music that is conceived outside the concept of notation to fit into our expectation. Do what you need to make the round peg fit the square hole. You could just as easily write some of that as a 4/4 bar in a faster tempo. I know from transcribing Carnatic rhythms that no barline can adequately capture the nature of what is going on in an aural culture.
    KG replies: Thanks very much, Mell. Only it’s *Olana*, not *Oleana*. A vibe solo based on David Mamet’s play would have to be very different, I think.

  7. ged says

    Yeah, I’m thinking, looking at the two-and-two-thirds over four type of notation, that it requires less of a mental ‘gear-shift’ than a 2/3 meter; it seems a little bit more intuitive to me. Especially where, say, a quarter note pulse carries on into one of these unusual bars, and then the bar ends in an incomplete tuplet.
    I agree with what Dave Seidel said: I suppose the ‘funny time signature’ would become a sort of ‘Here be dragons’ sign, where one must not blithely assume that n-tuplets come in groups of n).
    (Well, for the sort of pop music I’m writing, the notation is more of an aide-memoire than a definitive text.)
    Though I do very much like the exotic look of a 2/3 or 5/6 meter on the page. And that odd-prime-in-the-denominator approach probably leads to some interesting ways of composing, when one is explicitly thinking in such terms. Like, if you were using meters based on a Farey sequence or something like that :)
    In such cases, I guess an x-and-a-bit over 4 notation would obscure things.