A Chord Sequence You’ve Never Heard

I’ve said it before, and I’ll say it again: one of the thrills of composing microtonally is the ability to write logical chord progressions and feel virtually certain that no one has ever heard them before. When I was young harmony was a nightmare for me, and for good reason: I’d been taught to use pitch sets like everyone else, which were not conducive to good voice-leading or subtle nuance. Circa 1983 I decided to break a well-trained taboo and go back to triads and sevenths chords, on the grounds that it was insane to deny myself musical materials that had worked so effectively for centuries: like a playwright trying to excise overly familiar human emotions, or common words. I just decided harmony wasn’t going to be a point of innovation for me. This is what other composers seem to hate most about my music; a comment I’ve gotten frequently, with an undercurrent of disapproval, is, “I’ve never heard such complex rhythms with such simple harmonies.” I quit caring. But then when I got into microtones, I became able to squeeze those harmonies up against each other in so many possible permutations that the unlikelihood of any other microtonalist ever having come up with one of my exact progressions before is astronomical. It’s such a relief to write a series of chords that makes sense and actually be surprised by the way they sound, not being reminded of any other music I’ve ever heard. In the chord progression linked above, I couldn’t even tell you what the chords are without looking them up; I just generated a tuning via my usual voice-leading rules, put the notes together, and they came out even better than I expected. 

Researching 4’33”, I ran across a statement about harmony by Cage which I think bothers me more than anything else he ever said:

I now saw harmony, for which I had never had any natural feeling, as a device to make music impressive, loud and big, in order to enlarge audiences and increase box-office returns. It had been avoided by the Orient, and our earlier Christian society, since they were interested in music not as an aid in the acquisition of money and fame but rather as a handmaiden to pleasure and religion. (“A Composer’s Confessions,” 1948)

Geez, John, just because you had “no ear for harmony,” those of us who do have one aren’t supposed to use it? And if we use harmony to make our music “impressive,” that’s automatically for money and fame rather than pleasure? Isn’t giving pleasure what sometimes tends to bring money and fame? I’ve never read anything else of his that left such a bad taste in my mouth.


  1. says

    Of course his view changed later in life; certainly there’s a lot of harmony in his music (even from around that period!). But I’ve always thought he’s talking most of all about principles of voice leading that give music continuity, ‘dragging’ the listener on through the spectacle of the piece (doesn’t he say something like “I like to be moved, I don’t like to be pushed” somewhere?), and that’s not quite in line with Cage’s more static giving-attention-to-every-little-mushroom sensibility.
    Not sure if that would lessen the bad taste in your mouth though…
    KG replies: Well, unlike a lot of David Byrne fans, I don’t mind disagreeing with my heroes from time to time.

  2. says

    So I found this post really interesting. I agree with just about everything you say – and in the musical atmosphere lately, your comments on Cage, harmony, and the fact that there’s nothing wrong with using what’s tried and true (obligatory hat-tip to originality, of course) – but I was a bit confused by the MP3 you put up in support. Some of the chords I found beautiful and the chord changes natural, but other chords just seemed harsh on the ear, and other changes completely out of place. I’ll confess to being a bit of a curmudgeon w.r.t. classical music (I love Bruckner and Mendelssohn and disdain Cage, I probably fit an easy typecast there), but my tastes are wide and I enjoy just about any music that could rightly be called “beautiful” (and if you’ve heard cante flamenco, my favorite singing, you’ll know my definition of “beautiful” includes a lot) so I’d like to understand this – is it really just about developing an ear for dissonance and atonality, or does music like the progression you posted fundamentally stem from an aim besides beauty, emotion, energy, etc.?
    KG replies: Well, to each his own. Objectively speaking, they’re all just purely-tuned seventh and ninth chords (with a couple of eleventh harmonics), connected by pretty consistently tiny pitch increments. As I’m always telling my theory students, you may not like the way it sounds, but if you’ve followed the rules, it can’t be wrong.

  3. Bill says

    Some of these comments sound like pure Cage though…
    “I couldn’t even tell you what the chords are without looking them up” !
    “…actually be surprised by the way they sound, not being reminded of any other music I’ve ever heard” !!
    I think you’re using harmony pretty broadly here, wouldn’t most purists be shocked by your ‘harmony’?

  4. Owen Gardner says

    I’m not at all a fan of harmony and, in fact, I’d tend to agree with Cage on this point. That said, I greatly appreciate your implicit defense of JI against the tired argument of it’s stopping off harmonic progression. I remember Partch having written a wordier rebuttal in which he rightly claims that JI doesn’t stop off anything but rather promotes a subtler art of dealing with it.
    P.S.: I think these chords are all lovely.

  5. says

    “I’ve never heard such complex rhythms with such simple harmonies” sounds like a great compliment to me – you’ve done something new. And it takes a lot to come up with simple harmonies – why, anyone can make complicated harmonies (well, I’m oversimplifying a bit:)).

  6. Bob Gilmore says

    I don’t think we need take that Cage passage too seriously. I think it’s one of those moments when he’s trying to be provocative more than anything else. And besides, it’s nonsense. Just because great minds come out with nonsense from time to time doesn’t mean we need to lose sleep!

  7. says

    I find it amusing that in a world allegedly obsessed with the new and different, musicians are not falling all over each other clambering onto microtonality.
    Of course, it’s imitative abilities rather than creative abilities which are recognized and fostered when it comes to child musicians, so the funnels and sieves a young person goes through before and during musical education have already ensured that the deck is stacked in favor of preserving a status quo. This means that sticking to a theatrical representation, or a tiny ritualized subset, of musical intervallic relationships by using only 12 equal tones per octave rather than using whichever of the infinite possible intervals are appropriate to the music could very well be due to the limitations of the musicians rather than the audiences.
    Anyway, one of the wonderful possibilities of microtonal music is illustrated in your audio example: the wild (and “Wild”, as in, it reminds me of things in Nature) possibilities of movement which can happen in apparent contradiction. Tight and tiny voice movement with huge harmonic movement, simultaneous movement and stillness at the same time, things like that.
    -Cameron Bobro

  8. kraig Grady says

    The other great thing about JI is melody. It equally creates the space for touching on emotions that have been suppressed by the intonations of the past.
    KG replies: Amen. (Kraig, when I saw your name come up, I thought, “Shit, Kraig’s going to tell me he wrote that same chord progression back in 1987.”)

  9. says

    Kyle, I like the chord progressions. One thing that struck me is that the instrumental sound was kind of thin, sort of like tuning forks. What does it sound like using instruments with different harmonic profiles? I’d be curious to hear the progression using different instruments.
    KG replies: Well, it’s Kontakt. I’ve got the samples I have, and I no longer apologize for them. I first did it on a piano sample, which sounds cleaner, but you don’t get the delicious voice-leading of the tones merging into the next chord.

  10. says

    Kyle, I wasn’t criticizing the sounds – I really am curious. I understand why you used the ones you did, and from your comment, it seems that they complemented your voice leading aims better than the piano samples (which I’d be curious to hear, as well as, say, clarinets, to hear how they differed). :-)
    KG replies: Yeah, but the Kontakt clarinets sound even worse.

  11. says

    As you stated above, your chords are just purely tuned seventh and ninth chords, and they sound very beautiful. But I don’t think your example is an example of a microtonal chord progression; the functionality of these chords is based totally on what their functionality would be were they built with tempered intervals. The microtones seem to simply add a “sheen” to an otherwise tonal (with a small “t”) progression. Thus it strikes me as a variation on a chord progression I have heard before, rather than a chord progression I’ve never heard before, as though you were to play a tonal chord progression in the highest register of the piano, for example.
    Also, I’m wondering about your use of the word “logical”. I think you should change it to something like with “related to tonality”, because I think that’s what you mean by logical. I know this might rub you the wrong way, but a serialist or fan of serialist music hears his or her chord progressions as extremely logical. Unless you mean only logical to your ears, which is totally understandable, but since you are posting the work as an example of a more general “logical”, I’m assuming that wasn’t really what you meant.
    KG replies: In harmonic terms, and in my own music, I invariably think of “logical” as referring only to voice-leading, though root movement can sometimes reinforce or interfere. If you think there’s nothing really microtonal about this chord progression, I’d like to see you take it down in dictation.

  12. says

    Can you clarify your working definition of a “logical” chord progression? Are you talking about functional or quasi-functional harmony? About following a set of voice leading rules that are derived from the ones we get out of 16th century counterpoint and traditional harmony? About each chord relating to the next by a certain degree of relatedness through the harmonic series? I’m curious.
    Your chord progression is lovely, and one of the things I found especially interesting about it was that to my non-microtonally-trained ears it sort of eased in an out of functionality in a way that usually you can’t do. Functional harmony interrupting atonality is jarring, and atonality interrupting functional or apparently functional harmony is similarly jarring, but this progression seemed never quite functional and never quite not, but moving back and forth on the spectrum between the two. I’m also reminded (conceptually, not aesthetically) of some spots in Schoenberg where he writes progressions of what I think are pretty ugly chords but which work anyway because he’s basically following traditional voice leading rules.
    That Cage quote is complete bull, but it is interesting how he seems more opposed to impressiveness than to harmony per se. He’s mangling the means/ends distinction, and it makes me wonder how he would feel about a composer using Cagean compositional techniques for the sake of writing impressive music to make money.
    KG replies: For use of “logical,” see previous comment (posted after yours arrived). What makes me most queasy about Cage’s statement, in retrospect, is the negative value he attaches to “increasing the audience” – almost Schoenbergian. And we new-music types have worked so hard to increase the audience for the last 25 years, after our predecessors were so blithe about decreasing it.

  13. says

    “What makes me most queasy about Cage’s statement, in retrospect, is the negative value he attaches to “increasing the audience” – almost Schoenbergian.”
    Ah, Kyle, but then we should distinguish
    between “increasing the audience” as such and using “devices” in your music merely to “make it more impressive” so as to increase the audience. Cage definitely was not against increasing the audience or he wouldn’t have been on TV all the time. What he says he’s against here is pandering to the audience on the level of musical language. That makes perfect sense, if the musical language you actually are defending so happens not to make use of those particular “devices”.
    KG replies: Oh….. OK.

  14. says

    Thinking some more about that Cage quote, I’m also struck by the foolishness of his claims about the music of “the Orient” and early Christian society.
    In the first case, he seems primarily to be engaging in ignorant exoticisation and Orientalism–I would be very surprised to find that the music of any Asian country evolved outside of an economic system that placed value on audience size. This sort of fetishization of non-western culture as somehow more pure, innocent, and spiritually authentic is a pretty ugly element of the music history of the past century. To be clear, I’m not talking about borrowing ideas from non-western culture because the ideas themselves are interesting and useful–the problem is exoticisation. It’s always made me uncomfortable that one of Cage’s chance procedures was the to use the I Ching. If he used it just because it was a useful tool for generating chance outcomes, that’s fine, but if he used it for reasons of spiritual Orientalism I have a big problem.
    In the case of early Christian society, it seems rather naive to think that using music as a “handmaiden to. . . religion” isn’t at least in part a case of using music to accrue money and power, and to increase the size of the church.
    KG replies: The “Christian and oriental” thing is inherited from Ananda Coomaraswamy, whose book “The Christian and Oriental Philosophy of Art” came out about that time, and who regularly discussed the aesthetics of India, China, and medieval Europe as though they were all part of a unified world from which Europe departed in the Renaissance. Certainly Coomaraswamy idealized the aesthetics of that world as part of The Perennial Philosophy.

  15. says

    Wow, that’s very interesting. I just did a little digging around on Wikipedia to find out more about Coomaraswamy and Perennialism–was Cage in fact a Perennialist and part of the Traditionalist School, or was he merely borrowing this one idea? Or should I wait for the book because it’s complicated and you explain it all there?
    KG replies: Well, I don’t know whether Cage ever got his official Perennialist Card and Decoder Ring. :^D David Patterson has a great article on what Cage took from Eastern thought in the 1940s (David W. Patterson, “The Picture That Is Not in the Colors: Cage, Coomaraswamy, and the Impact of India,” in David W. Patterson, ed., John Cage: Music, Philosophy, and Intention, 1933-1950 (New York, Rouledge, London: 2002, Routledge)), and it’s easy to trace some ideas he got from Aldous Huxley, Coomaraswamy, R.H. Blyth, and Sri Ramakrishna in his writings, sometimes virtually paraphrasing them without very clear attribution. I think those ideas became less important to him from the 1960s on as he went on to Buckminster Fuller, Thoreau, Norman O. Brown, and others.

  16. says

    “In harmonic terms, and in my own music, I invariably think of “logical” as referring only to voice-leading, though root movement can sometimes reinforce or interfere.”
    Do you have your thoughts on what voice-leading is posted anywhere online or would you mind explicating your thoughts on voice-leading a bit more?
    KG replies: Geez, explicating how I think about voice-leading is sort of asking how I feel about my mother – entirely right-brain, nonverbal, and purposely never examined. All I can tell you, as I once told Phil Glass, is that I’m still trying to write the Bed scene from Einstein on the Beach. And by the way, I used the wide-ranging and intentionally vague word “logical” to prevent people from writing in with totally random chord progressions no one’s ever heard before. I have no definition for “logical” beyond what makes sense to me while I’m writing music. I’m a composer, not a theorist, or at least, I would never try to make up theories about how my own music works.

  17. mclaren says

    Yowie zowie! Ain’t it cool?
    Once you make a jailbreak from 12 equal pitches per octave, there’s just no limit on the amazing new emotions and striking new melodic modes and exotic new harmonies you can conjure up. And not abstruse incomprehensible ones either, but plain straightforward yet really different melodies and harmonies, easy on the listeners’ ears but without being jejune or trite.
    Microtonality really seems like the way to get “something familiar, yet excitingly different” in terms of melody and harmony in contemporary music.
    Rhythm, Nancarrow already gave us new resources for — we’re all still working that one out, and there’s probably centuries worth ‘o good stuff for new music left in that gold mine. And as for timbre, Ussachevsky & Luening and Max Mathews and Jean-Claude Risset and Pierre Schaefer and Pierre Henry gave us a whole treasure trove of new musical resources for tone-colour. But exploring new pitches outside 12 equal…that’s been slow to enter the mainstream. Still, little by little, serious contemporary music seems to be getting xenharmonized.
    Mind you, microtonality isn’t the only way of writing exciting new music. But it’s an important one, and no contemporary composer should entirely ignore this new musical resource (all puns intended, ahahaha!).
    JI is particularly megabitchin’ because there is literally no limit to how far you can explore. You can cruise right up the overtone series and it just…doesn’t…stop. There will always be fresh new harmonies and melodies. You can put the pedal to the metal and go up into the hundreds or the thousands in terms of prime numerators and denominators, and the ear doesn’t have any problem assimilating ’em as long as they’re used adroitly.
    JI melodies rock particularly hard because when you transpose ’em, you get this wonderfully iridescent change in the entire mood of a melodic motif.
    In ordinary 12, transpose a melody up a major second, blah, big deal. Same-old same-old. But in a JI tuning, if you transpose a melody up by a major second (and you have to specifiy what kind of major second, because there are different flavors!) you get a brand new melody with small intervals where there used to be large intervals and large intervals where there used to be small intervals. It’s like watching rainbows shimmer across a butterfly’s wing: the effect of even a “simple” arpeggiation transposed up or down by successive scale degrees in JI can be mesmerizing.
    You also get expressive nuances courtesy of small pitch-shifts like the 81/80 that let you write down with exact specificity the kinds of variegated emotional shadings previously only used intuitively by skilled performers who “bent” the notes to add more feeling, but couldn’t detail exactly what they were doing using the limited pitch-set of 12 equal. It opens up a whole new wealth of emotional hues that’s like moving from a black-and-white world into a technicolor polychrome universe of strangely beautiful new emotions, exotically gorgeous new moods.
    Plus, you’ve also got exotic voice-leading that you just can’t get in any other way. JI chords can thread through vertiginous paths along the edge of an harmonic precipice, only to settle down placidly in a nice sensible cadence…that comes at you out of nowhere. Once again, completely different from 12 equal.
    And last but not least, you can do exotic things like transfer from one JI limit to another, or jump from one subset of a JI tuning (say, 17 note Pythaogrean) into a larger JI tuning (say, 29 note Pythagorean) which contains the previous tuning like a nested Russian doll. That’s an additve JI example, but for a divisive JI example, you can take a tuning like the Greek enharmonic modulated up by an 11/8 and merged with itself, then collapse back down to the plain old 7-limit Greek enharmonic. Both additive and divisive JI tunings offer these kinds of scale-nested-inside-scale resources.
    It’s all just too cool for school.

  18. Joe says

    Can I ask what your usual voice-leading rules are?
    KG replies: I try, as often as possible, to have two voices moving in opposite directions by intervals no smaller than 25 cents and no larger than 60. It’s great when it works. Partch called it tonality flux:
    (Ordinarily I wouldn’t refer you to Wikipedia, but it’s an article I wrote – and no one’s ruined it yet.)

  19. andrew violette says

    I’m enormously conflicted about microtonality.
    To my own ear it always sounds merely out of tune. For instance, the series of chords that you wrote sound beautiful to me but I relate to them as out of tune chords I already know. This is how I hear Harry Partch and other microtonalists. It’s not because I don’t hear the intervals microtonally but because I have a natural tendency to place those intervals within a functionally tonal system. Can it be that we as a species naturally gravitate toward the lower partials of the harmonic spectrum? Is that why, after thousands of hours of listening to atonal music I still dream tonally? Maybe it’s me, maybe I’m blind. I don’t know.
    Not only that but it would seem to be a nightmare to get players to accurately play the microtonal intervals that I would put on the page. In my experience it is extremely difficult to get players to play just plain in tune–no matter now good they are. Microtonal minimalism would be horrendously difficult to rehearse and perform. It’s easy to smudge a piece of Elliott Carter intonation-wise (who hears it? I do, but that’s another story)but try playing Steve Reich with anything but perfect intonation and it sounds awful. A microtonal process piece for strings, unimaginable difficulty in performance!
    For these reasons I don’t think microtonality will ever be accepted as the norm, but I’m so glad Harry Partch and others don’t agree with me.
    KG replies: I love the weirdness of it. But after a few listenings my own microtonal pieces start to sound all too normal to me, and I have to keep adding more pitches to get the thrill again.

  20. mclaren says

    I hear what you’re saying. In my experience, efforts to “detwelvulate” classical 12-equal pieces by putting ’em into 5-limit or 7-limit just intonation usually fail and typically produce music that sounds badly out of tune. The fault is not the tuning, but the fact that the composition was originally written for one tuning but it has now been wrenched out of shape into another entirely different tuning. In general, compositions written in a given tuning should be played in that tuning. Trying to “improve” ’em by performing (say) a Beethoven sonata in some JI tuning ruins it and makes it sound sour, especially when you get commas during modulation.
    That said, a large part of your discomfiture may simply be that you’ve been listening to the wrong kind of microtonal music. Very little of the microtonal music composed today is done in JI: virtually all the microtonal music composed and performed today uses either non-just non-equal tunings, like Barbara Benary’s gamelan pieces, or various equal temperaments, like William Sethares’ music. I’m curious: do you really hear Barbara Benary’s gamelan music as sounding out of tune? How about Sethares’ music — do you really hear that as sounding out of tune?
    There’s a huge disproportion in the new music community between talk and reality when it comes to just intonation. Huge amounts of talk go on about JI nowadays, but virtually none of the microtonal music composed today is done in JI. Only a tiny minority of the microtonal composers practicing today work in just intonation. If you’re judging by the talk and the theory, you’re making a huge mistake, as Brian Eno did when he dismissed microtonality as “producing beautiful theory and ugly music.” The reality of microtonal music has no relation to the theory and the discussion about it on various online forums, which is overwhelmingly dominated by mathematicians and programmers who cannot play a musical instrument and have never composed any music.
    The best example of this bizarre disconnect twixt theory and practice in microtonality involves the recent article in Perspectives Of New Music on the alleged musical structure of the various equal divisions of the octave. That article represents an exercise in numerological set theory which has absolutely no relationship to anything any actual microtonal composer is doing today.
    It’s also important to note that some ostensibly microtonal tunings prove problematic. As Ivor Darreg constantly pointed out, 24 equal isn’t a fair test of microtonality because it simply splits the tuning up into 2 different circles of 12 fifths per octave offset from one another by 1/24 of an octave. Most microtonal tunings are integrated — that is, they have a single circle of fifths, viz., 19 equal, 17 equal, 37 equal, and so on. With 24, you haven’t really escaped from 12. You’re still hearing all the familiar chords and melodies, just with alien pitches interspersed between ’em. As Buzz Kimball has aptly pointed out, almost all the new harmonic resources in 24 equal merely add ugly-sounding dissonances to conventional 12-equal harmonies, with the exception of the neutral third and sixth. So the problem may have been that you’ve been listening mainly to music in 24 equal, which is not a fair test of microtonality at all.
    You mentioned that you “…have a natural tendency to place those intervals within a functionally tonal system.” It’s important to bear in mind that just intonation tunings are more functionally tonal than equal divisions of the octave. A JI tuning reinforces the tonic more strongly, to the extent that modulation within a JI tuning introduces noticeable pitch shifts which communicate a departure to a different tonal center much more powerfully than in a conventional 12-equal tuning. In a just intonation C major scale, for example, if you modulate to the key of D major, the A above D is now a different pitch from the A in the original C major scale. Thus, a JI tuning much more strongly emphasizes the tonal center of the scale than does the conventional tuning of 12 equally spaced pitches in the octave. So it’s unlikely that you hear microtonal music as sounding out of tune because of issues with lack of tonal center.
    As for the alleged “enormous difficulty” of playing microtonal music with conventional instruments, Johnny Reinhard and his group with the American Festival of Microtnal Music seem to have no difficulty doing it. You might want to listen to Johnny’s polymicrotonal piece Cosmic Rays for string quartet. It doesn’t appear to present “unimaginable difficulty” for the performers.
    In any case, your assumption here seems to rest on the peculiar notion that most new music today will be played on traditional 19th century acoustic orchestral instruments. In reality, most new music today uses either percussion instruments, or synthesizers, often softsynths on laptops. Performers using instruments like a microtonal marimba or a microtonal xylophone or a microtonal steel drum or a microtonal celesta or a microtonal vibraphone have no problem at all with playing highly microtonal pitches. Synthesizers of course eliminate the problem entirely. Since these kinds of performances represent the overwhelming majority of new music performances today, while new compositions for orchestra represent only a tiny microscopic minority of the new music being composed and performed today, it’s peculiar that you’d fixate on the problems an orchestra might have performing microtonal music. Orchestras are simply not a significant part of the new music scene today compared to small ensembles which use percussion and synthesizers, and what’s more, orchestras haven’t been a significant part of the new music scene for quite a few years now. Perhaps back in the 1950s orchestras dominated the new music scene: but certainly not today.
    You asked: Can it be that we as a species naturally gravitate toward the lower partials of the harmonic spectrum?
    This belief was aptly summarized in an anecdote from Nicholas Slonimsky’s Encyclopedia of 20th Century Music:
    “The American pedagogue Percy Goetschius used to play the C major scale for his students and ask them a rhetorical question. `Who invented this scale?’ and answer it himself. `God!’ Then he would play the whole-tone scale and ask again, `Who invented this scale?’ And he would announce disdainfully, `Monsieur Debussy!'” [Slonimsky, Nicholas, Encyclopedia of 20th Century Music, 3rd Edition, 1984, pg. 1168]
    However, the available evidence from the peer-reviewed scientific literature done on listening tests shows no tendency for listeners to prefer, or even recognize, “lower partials of the harmonic spectrum” (I think you mean lower overtones of the harmonic series).
    “Scales are highly artificial, and the laws of acoustics may be quite unconnected with their construction. The number of possible scales is incalculable: provided that a scale forms a basis for viable music, there is no reason to claim that any one scale, like our diatonic scale, is superior. (..)
    “Many varieties of scales have been used in different parts of the world and at different periods of history. A pentatonic scale, which only uses five notes within the octave…is the basic scale of music in many non-Western cultures throughout the world, as well as being the basis of Celtic folk music. The whole-tone scale, used extensively by Debussy, consists of six notes within the octave, each a tone apart from the next. Hindu music uses scales in which the octave is divided into intervals less than a semitone. Javanese music uses two different systems: slendro, which divides the octave into five nearly equal intervals, and pelog, which divides the octave into seven, using a mixture of small and large intervals.” [Storr, Anthony. Music and the Mind. Ballantine Books: New Yorks, 1992, pp. 54-55]
    “As we have seen, the harmonic series is by no means `universal.’ Harmonic sounds are only one kind of common sound: there are as many kinds of sounds as there are distinct kinds of vibrating objects. Musical systems have been built on many of these, and many others are undoubtedly possible.” [Sethares, William. Timbre, Tuning, Spectrum, Scale. Springer-Verlag: New York, 1997, pg. 273]
    “It would appear that a person’s preference, in scale construction, is determined more by the individual’s history of listening and performance that by a priori mathematical consideration.” [Ward, W.D. and D. W. Martin, “Psychophysical Comparison of Just Tuning and Equal Temperament in Sequences of Individual Tones,” Journal of the Acoustical Society of America, Vol. 33, No. 5, 1961, pg. 588]
    “[The] object was to determine if people who sing tend more to equal temperament or to just intonation. To this end, it was only necessary to have the same melody sung by a number of people and to register their tones by a measuring instrument, such as an oscilloscope.
    “The result of these measurements was highly unexpected. It went so far beyond the limits of the original question as to render it meaningless. What appeared was that the singers sang neither in just intonation nor in equal temperament–they simply sang unimaginably off pitch. And this was equally true of all the singers, trained and untrained, unmusical and highly musical. (..) …The questions posed by the investigation were, for example, Does the singer at this place tend to produce the tone 300 or the tone 316, at this other place the tone 500 or the tone 493? The answer given by the merciless instrument, from which there was no appeal, was neither 300 nor 316, but 238; neither 500 nor 493, but 586. Tones which lay far closer to the adjacent tone of the chromatic scale than to the tone actually to be sung! Such facts can no longer be discussed in terms of poor intonation; the singers simply sang different notes from those which the test prescribed.
    “As an answer to the original question, then, the result was valueless. Instead, it brought a very different and much more interesting situation to light. It became evident, that is, that the great discrepancies always appeared where a rise or fall of the melody was clearly marked, and that, in the majority of cases, the direction of the discrepancy followed the upward or downward direction of the melody. (..)
    “But the most significant thing about the result of this experiment is the fact that it required the intervention of the measuring instrument to reveal these grotesque distortions of pitch, these false tones. The audience, which included experienced musicians, had not noticed them at all.” [Zuckerkandl, Victor. Sound and Symbol. Pantheon Books: New York, 1956, pp. 79-81]
    “Experiments have repeatedly shown that musicians such as singers and violinists, who are not tied down to a fixed set of intervals (as keyboard players are) consistently vary the size of their intervals; indeed, most singers and violinists are perfectly aware that they do this. However, there is no generally accepted rationale for how it should be done; people have these adjustments ‘by ear.’ Empirical studies have not, as yet, revealed the basis of the practice. But they have demonstrated that no explanation in terms of a fixed intervallic scale will match the facts; violinists do not play in just intonation, or mean-tone intonation, or Pythagorean intonation, any more than they play in equal temperament. In other words, they determine their intonation in accordance with the individual musical context.” [Cook, Nicholas. Music, Imagination, and Culture. Clarendon Press: Oxford, 1990, pg. 236]
    “Another, more recent, study (Keefe, Burns & Nguyen, 1991) presented an identification task to a Vietnamese musician who is also a musicologist and thus quite familiar with Western pitch nomenclature. (..) Some well-defined interval categories were found, but for certain interval regions, the musicians was unable to respond consistently and the boundaries between some interval categories did not match measurements of his own tuning behavior. The authors concluded that the `Western concept of interval does not exist in Vietnamese music’…” [Perlman, Marc and Carol L. Krumhansl, “An Experimental Study of Interval Interval Standards in Javanese and Western Musicians,” Music Perception, Vol. 14, No. 2, 1996, pg. 99]
    Three of the major non-Western musical systems (Indian, Chinese, and Arab-Persian) have inclusive scales approximately equivalent to the western 12-interval scales and, hence, have the same propensity for the`perfect’ consonances (octaves, fourths, and fifths). There are, however, a number of musical cultures that apparently employ approximately equally tempered 5- and 7-interval scales (i.e., 240 and 171 cent step-sizes, respectively) in which the fourths and fifths are significantly mistuned from their natural values. Seven-interval scales are usually associated with Southeast Asian cultures (Malm, 1967). For example, Morton (1974) reports measurements (with a Stroboconn) of the tuning of a Thai xylophone that `varied only plus or minus 5 cents’ from an equally tempered 7-interval tuning. (In ethnomusicological studies measurement variability, if reported at all, is generally reported without definition.) Haddon reported (1952) another example of a xylophone tuned in 171-cent steps from the Chopi tribe in Uganda. The 240-cent step-size, 5-interval scales are typically associated with the `gamelan’ (tuned gongs and xylophone-type instruments) orchestras of Java and Bali (e.g., Kunst, 1949). However, measurements of gamelan tuning by Hood (1966) and McPhee (1966) show extremely large variations, so much so that MePhee states: `Deviations in what is considered the same scale are so large that one might with reason state that there are as many scales as there are gamelans.’ Another example of a 5-interval, 240-cent step tuning (measured by a Stroboconn, “variations” of 15 cents) was reported by Wachsmann (1950) for a Ugandan harp. Other examples of equally tempered scales are often reported for pre-instrumental cultures (although in these cases, the concept of scales may be of doubtful validity). For example, Boiles (1969) reports measurements (with a Stroboconn, `plus or minus 5 cents accuracy’) of a South American Indian scale with equal intervals of 175 cents, which results in a progressive octave stretch. Ellis (1965), in extensive measurements of melodies in Australian aboriginal pre-instrumental cultures, reports pitch distributions that apparently follow arithmetic scales (i.e., equal separation in Hz). Thus, there seems to be a propensity for scales that do not utilize perfect consonances and that are in many cases highly variable, in cultures that either are pre-instrumental or whose main instruments are of the xylophone type. Instruments of this type produce tones whose partials are largely inharmonic (see Rossing, 1976) and whose pitches are often ambiguous (see De Boer, 1976).
    b. Intonation in Performance. A number of measurements have been made of the intonation of musicians playing variable-tuning instruments under actual performance conditions (e.g., Greene, 1937; Nickerson, 1948; Mason, 1960; Shackford, 1961, 1962a,b). The results of these measurements have been summarized by Ward (1970). They show a fairly large variability for the tuning of a given interval in a given performance ranges of up to 78 cents, interquartile values of up to 38 cents. The mean values of interval tunings, in general, show no consistent tendency to conform to either JI or PT in either melodic or harmonic situations. The general tendency seems to be to contract the semit and slightly expand all other intervals relative to ET. There is also some evidence of context-dependent effects [e.g., to play F# sharper than Gb (Shackford, 1962a,b). Those results mirror, to a certain extent, the results of the adjustment and identification experiments using isolated intervals (discussed in Sections III,A and III,B, which showed a tendency to compress the scale for small intervals and stretch the scale for large intervals, in both ascending and descending modes of presentation. above measurements were obtained for Western classical music, but the same general tendencies are evident in measurements of intonation from a military band (Stauffer, 1954), Swedish folk musicians (Fransson, Sundberg, & Tjernland, 1970), and jazz saxophonists (Owens, 1974). Measurements of intonation in performance for Indian (Hindustani) classical music Jhairazbhoy & Stone, 1963; Callow & Shepard, 1972) show similar variability. There are even large variations in the intonation (ranges of up to 38 cents) of a given interval in the single performance of a composition by one musician. Callow and Shepard analyzed these variations in terms of melodic context and found no significant correlations. Large variability (plus or minus 50 cents) was also found in the intonation of a Thai vocalist whose frame of reference was presumably an equally tempered 7-interval scale (Morton, 1974).
    There is no evidence from any of these studies that suggests that the performers tend to play intervals corresponding to exact small-integer ratios, either with reference to the tonic or to preceding notes, for either melodic or harmonic situations.” [Burns, Edward M. and W. Dixon Ward, “Intervals, Scales and Tuning,” in The Pscyhology of Music, ed. Diana Deutsch: Academic Press Inc., New York: 1982, pp. 257-8.]
    “These results seemed to be paradoxical, given the fact that the same musicians tuned the octave, fifth, major third and their inversions within a field of variance close to a semitone, as previously observed by Kubik [20]. This apparent contradiction does not appear to be inherent in the Central African system or in the experimental results, but rather in a Western definition of consonance. This definition is refuted by the practices of these musicians, who tune intervals, step by step. Our experimentation verified that `perfect’ consonances are not a constituent of a Central African concept of the scale. These musicians do not judge a strict octave (1200 cents) to be better than a large major seventh (1150 cents) or a small minor ninth (1250 cents). On the contrary, the Banda Linda musicians prefer the small “octave” (1150 cents) in any register, probably because of the roughness it creates on the octaves that are always played simultaneously with double sticks in each hand.” [Voisin, Frederic, “Musical Scales in Central Africa and Java: Modeling by Synthesis,” Leonardo Music Journal, Vol. 4, 1994, pg. 89]
    “…It has been asserted again and again that the reason why certain intervals are `consonant’ and give the impression of a very close musical relationship is their prominence in the `chord of nature,’ which is the term sometimes used for the harmonic series.
    “Now we are bound flatly to say that all this is a piece of pure mythology, and that musical relationships have nothing to do with the chord of nature. Musical relationships do not depend upon the physical properties of the sound wave or the physical action of the ear, but upon the integrating, organizing and selecting activity of the mind. And to regard the harmonic series as a determiner of basic musical effects is to fall into a primary psychological error, the error of attempting to explain an experienced whole in terms of the sum of its parts. (..)
    “For both [Heinrich Schenker and Arnold Schoenberg] it appears that tonality rests ultimately upon an appeal to the harmonic series; and if we ask, `Why do we feel loyalty to a tonic?’ the ultimate answer would presumably be that it is the fundamental of the harmonic series, the `chord of nature.’
    “This answer is unsatisfying from a world music standpoint. There are cultures whose music appears to have little relationship to the harmonic series. Worldwide there is a multiplicity of scales and harmonies hardly expressible in the small number ratios that might relate them to the harmonic series, even roughly equidistant scalar schemes, and harmonies that owe no allegiance to the triad, that entity so prominent in the thinking of Schenker and Schoenberg.” [Erickson, Robert, “New Music and Psychology,” in The Pscyhology of Music, ed. Diana Deutsch: Academic Press Inc., New York: 1982, pg. 522.]
    “It has been shown experimentally that intervals which do not occur at all in the harmonic series have valid…musical possibilities. And, of course, in many exotic musical systems various `non-harmonic’ intervals are constantly in use. (..) …The possibilities of harmony do not depend upon the chord of nature. Moreover, modern experiments in harmony often seem to look towards the use of intervals which not only fail to occur often in the harmonic series of partials, but which are not there at all.
    “Music, to reiterate the point once more, depends on the mind and not on the ear. The proper road to take in analyzing its foundations is not a discussion of the conditions of auditory sensations, but rather a treatment of auditory perception. That is, we are not dealing with the effects produced by external physical causes upon the ear, the auditory nerves, etc., but rather with what happens when these externally-produced effects are taken up and interpreted by the mind.” [Mursell, James L. The Psychology of Music W. W. Norton & Co. Inc. New York: 1937, pp. 55-57]
    In fact, it is quite certain that a musical preference for the harmonic series cannot be engraved in our genes, for if it were, we would hear all of conventional western music as sounding horribly out tune — since all of the instruments used in Western orchestras produce partials which actually depart quite significantly from the harmonic series:
    “The growing gulf between the discoveries of physics and the traditional theory of musical harmony became embarrassing by the beginning of the nineteenth century. Musical theory ignores the fact that vibrating strings have inharmonic partials as well as harmonic ones because of such physical factors as degree of stiffness, placement of the bridge, and method of securing the string for tightening. Piano strings, for example, tend to produce out-of-tune partials. They become inharmonic to the extent that by the 15th partial they are so sharp that the 15th is near the ideal pitch of the 16th partial. Strings on fretted and other string instruments display peculiar characteristics in their harmonic content that are dependent upon the physical nature of the instrument. Brass instruments tend to produce flat harmonics, and the vibrational behavior of a simple tube, like that of a simple string, is considerably modified in musical practices, both in performance and manufacture of instruments, to overcome the problem of inharmonic partials. Brass tubes have bell-shaped ends fixed with specially shaped metal to control the harmonic partials, for example.” [Walker, Robert. Musical Beliefs: Psychoacoustic, Mystical, and Educational Perspectives. Columbia University Press: New York, 1984, pg. 92]
    “As is particularly evident…the frequencies of the partials [of the piano] are not harmonic. (..) It is seen that the partials are progressively sharpened, indeed to the extent that the 15th partial has just about the frequency of a 16th harmonic. True harmonics of the fundamental frequency could not be found.” [Schuck, G. H., and R. W. Young, “Observations on the Vibrations of Piano Strings,” Journal of the Acoustical Society of America, Vol. 15, No. 1, pg. 4, 1943]
    “The resonance frequencies [of wind instruments] appear to constitute a harmonic series, but this is not true in reality. The frequency distance between them is successively reduced, the higher the number of the resonances. This is due to viscosity losses along the tube walls. Viscosity losses occur because the mobility of the air is not perfectly the same along the tube walls as farther toward the center; the rubbing along the walls slightly reduces the motion of the air particles.” [Sundberg, Johan. The Science of Musical Sounds. Academic Press, Inc.: San Diego, 1991, pg. 111]
    “As the amplitude of the reed oscillation increases (by increasing the blowing pressure), the nonlinear character of the feedback from the air column [of a reed instrument] destroys the harmonic, sinusoidal vibration of the reed, upper harmonics appear with increasing strength (in generally the intensity of the nth harmonic grows proportionally to the 2nth power of the intensity of the fundamental), and the resulting sound becomes `brighter.’ At the same time, the fundamental frequency readjusts itself so that the upper resonance peaks are somewhat inharmonic.” [Roederer, Juan G., Introduction to the Physics and Psychophysics of Music, Springer-Verlag: New York, 1973, pg. 118-119]
    The prejudice that humans naturally gravitate toward music based on the lower members of the harmonic series goes back a long ways:
    “When Fetis, again around 1870, stated that white people (i.e., Western Europeans) had alone succeeded in creating a music worthy of the name, his basis was supposedly objective and unquestionable argument. Only in [Western European] music, he explained, were found reunited all the elements of the art of sounds: melody, rhythm and timbre, known to all races, but also polyphony, unknown to yellow and black races. Obviously, the discovery of artful and varied polyphonic methods, often close to our own, in Africa and Asia, sank this reasoning.” [Brailoiu, Constantin, Problems of Ethnomusicology. Ed. and Translated by A. L. Lloyd. Cambridge University Press: New York: 1984, pg. 120]
    An extreme example of this claim comes from Sir John Hawkins circa 1770:
    “Even the best music of the barbaric peoples of the earth is said to be hideous and astonishing sounds. Of what importance then can it be to enquire into a practice that has not its foundations in science or system, or to know what are the sounds that most delight a Hottentot, a wild American, or even a more refined Chinese?” [Sir John Hawkins, General History of Musick, 1776]
    “Much of this musical mathematics is a matter of convention and has no deep significance. Although the octave is common to most types of music worldwide…ways of subdividing the octave vary enormously. Many cultures do not use the Pythagorean intervals in their scales, and there is no reason to think that that their music is worse for that.” [Pacey, Arnold. Meaning in Technology. The MIT Press: Massachusetts, 1999, pp. 27-28]
    “The Musical Scale is not one, not `natural,’ nor even founded necessarily on the laws of the constitution of musical sound, so beautifully worked out by Helmholtz, but very diverse, very artificial, and very capricious.” [Ellis, Alexander James, “On the Musical Scales Of Various Nations,” Journal of the Royal Society of the Arts, Vol. 3, 1885, pg. 536]
    “Acoustic phenomena, auditory physiology, and cognitive processes may impose constraints on the class of possible musical scales. Nevertheless, a great variety of scales can be found among the world’s musical traditions. This fact, established by Alexander Ellis more than a century ago, (Ellis, 1885), has been confirmed by subsequent ethnomusicological research (.e.g., Berliner, 1978, pp. 63-68; Hood, 1966; Morton, 1976, pp. 232-237; Tracey, 1970, p. 125). The most obvious dimensions of difference across cultures are the number of scale steps within an octave and the size of of those steps.” [Perlman, Marc and Carol L. Kumhansl, “An Experimental Study of Interval Interval Standards in Javanese and Western Musicians,” Music Perception, Vol. 14, No. 2, 1996, pg. 96]
    “That superb and aprioristic scorn is finished that allowed Berlioz to write about their music that the Orientals are still `sunk in the deepest shadows and in an infantile ignorance;’ that `they call music what we call charivari’ and that their song is made up of `nasal, guttural, moaning, hideous sounds, similar to those of dogs when, after a long sleep, they stretch their limbs and yawn strenuously.’ Such sarcasms can only make one smile at their author.” [Brailoiu, Constantin, Problems of Ethnomusicology. Ed. and Translated by A. L. Lloyd. Cambridge University Press: New York: 1984, pg. 120]
    Humane and highly educated Western musicians often seem remarkably oblivious to the racist implications of the claim that the lower members of the overtone series are mandated by the genetic structure of the human organism. If you think about it for a moment, this is really tantamount to the claim that the peoples of every other nation on earth aside from Europeans and Americans are either genetically defective, or demented, or simply stupid. If someone in everyday life were to raise the suggestion that the peoples of every other nation on earth other than Europeans and Americans are producing literature or art which is in some basic way defective, it’s safe to say that a stentorian hue and cry would arise. But when Western musicians make the offhand suggestion that only Westerners are doing music right (i.e., using the lower members of the harmonic series in their music), this somehow escapes comment and is not even noticed by otherwise sensible observers.
    It’s fascinating to note that the claim that humans naturally gravitate toward the lower members of the harmonic series represents the exact mirror image of the comments just a few of Kyle Gann’s posts ago by musicians claiming militantly that there are no cross-cultural universals in music perception, and that all the effects of music are entirely due to cultural conditioning.
    The available evidence from the peer-reviewed scientific literature, as well as from music history and ethnomusicology and psychomusicology and cognitive neuroscience, appears to show that both of these extreme beliefs contradict observed reality.
    The preponderance of the available evidence suggests that musical perception is not entirely a matter of behaviorist cultural conditioning, and that humans are not merely musical blank slates; but, at the same time, such hardwired cross-cultural universals of musical perception as appear in the human ear/brain system only show themselves under relatively extreme conditions and in the kind of musically simple and isolated examples (such as very loud long-held acoustically rough dyads played on a pipe organ) which limit their general applicability to new music composed in the real world.
    For example, C + C# played in the midrange fffff on a pipe organ for 20 measures straight at a metronome marking of 60 is going to be pretty tough on the listeners. But the exact same C + C# played by a flute and a vibraphone using rapid eighth notes at a metronome marking of 120 will likely be very easy on the audience’s ears.
    The upshot is that the reality of music as it is performed and heard in the real world seems to lie somewhere between the extreme “nature” claim (viz., humans have an innate preference for lower members of the harmonic series) and the extreme “nurture” claim (viz., all musical perception is entirely a matter of cultural conditioning with no internvention by the hardwiring of the human brain or nrevous system).