Johnson on Harmony, Soderberg on Theory (& Yes, I Get in a Lot of Words Edgewise)

The estimable Tom Johnson has just published a book on harmony, Other Harmony, "other" here indicating. heterodox to the mainstream of contemporary music theory and history teaching.  I haven't yet read the book, but some of the names sticking out from the online summaries — Euler, Hauer, Forte, Messiaen — make it appear very interesting indeed, in particular as ways of arriving at a greater diversity of voice leadings.

I think about theories of harmony a lot — perhaps too much for my own good — as both a practical and an intellectual concern.  A useful theory has got to do a handful of things at once:  It has to offer a taxonomy of resources within a given tonal system or environment, first among them managing the diversity of chords available (which need not always be simultaneities and need not always be complete and may sometimes be visited by guests or non-chordal tones, yet retain their identity) in terms of both their own content and their distance/relatedness to other chords and larger collections of tones but also in terms of the movement between chords, which is voice leading (which need not always be elegant or "parsimonious", a current term of art (I can't emphasize enough how important I think voice leading is; voice leading is a strong distinguishing quality among repertoires and I believe that it's the useful bridge between counterpoint — which I believe should be taught first — and harmony.))

That distance/relatedness exists in terms of both quality (yes, chords can be located qualitatively on a continuum of sensory consonance and dissonance (and yes, you have to consider things like registration and voicing and timbre and dynamics and duration (and yes, chords can be puns, simultaneously being identifiable in two or more ways)); yes, two major triads share a quality independent of their root relationship) and function within larger tonal contexts (scales, keys, and systems or networks, or collections and aggregates; yes, chords can be functionally dissonant independent of their sensory qualities (and yes, there's that punny business))   Finally, a theory of harmony should have the capacity to distinguish and describe individual and local harmonic practices, the things that an individual piece, an individual composer, or a particular repertoire do distinctively.  (These typically emerge not only in the choice of materials but in their temporal orderings.  Example:  in much repertoire, dissonances typically resolve forward to consonances. Example: the western classical, or "common practice", tradition allows IV to come before V but generally not V to come before IV; popular repertoires often do not share this prohibition.)

Ultimately, a theory of harmony is a tool that helps composers make more interesting or compelling works, helps players and musicians to engage with the works both practically and more deeply and is also a tool in discovering — or negotiating, as the case may be — the aesthetic foundations of our practices as composers, performers and listeners: not just what are our harmonic practices but what are our harmonic preferences?  

Stephen Soderberg is currently in the middle of a very thoughtful series of blog items about theory and its feedback relationships to practice.  I believe that hovering behind these relationships are, however, some psychoacoustic or neurological considerations and some private or social preferences that mix together and form or contribute to aesthetic criteria.  The entire twelve tone and set-theoretical project (from which tradition Stephen is working)  has a lot to admire about it, but attention to sensory considerations was not a prominent feature and, inasmuch as the tradition was or is pre-compositional or speculative theoretical, there was precious little said about the criteria with which musical works produced on the basis were to be appraised as successfully musical or not.

I was very impressed by the concern expressed by the late Heinz-Klaus Metzger that we are operating in a criteria-free era, but I suspect that we do, in fact, operate with criteria, but that we are almost painfully inarticulate about them.  (Yes, there were/are local and underground rules — they might be about octaves or starting rhythmic figures on downbeats or forbidding exact repetitions — but those are usually cloaked by the doctrine of deniability that governs things like admissions committees and awards panels.)  I will even go so far as to assert that we tolerate a lot of bad musical production because of this avoidance or even loss of the ability to be articulate about what we like and don't like (dare I go even further — this being aesthetics after all —: about what we find beautiful and not beautiful?.)

Composing Under Constraints & Musical Escapology

In one way or another, I've always composed under some set of constraints. I do so because the musical results have reliably both surprised and satisfied me, and have taken me through both comfort zones and previously unimagined places.  Many of these are tricks of the trade, widely shared in the community of composers; others may be uniquely mine.  Some are open and obvious, others are under the surface, some secrets, some puzzles, some cast away and irretrievably lost.  Working with a pre-compositional gamut of tones (sometimes a tuning) or noises is pretty common, as are using drones, ground basses (I'm very fond of ostinato basses but not so fond of repeated harmonic sequences), and hockets.  I like to take both random, constrained, and freely composed walks on pitch lattices, a practice related to an early, deep study of musical intonation.  I've used Hauer's harmonic band technique, through which any sequence of tones can be wrestled into a sequence of harmonies with smooth voice leading and often surprising local suggestions of globally a-functional tonalities. Formally, I like to use Gray Codes, Beckett Gray codes specifically, for example to control scoring patterns; this is an area where I'm probably a genuine pioneer.  I like borrowing forms from poetry, both in terms of metres and rhyme schemes (I would like to do more of the same with dance forms, perhaps especially because they're so out of favor.) I also like to use Square Root forms, following John Cage's model, but sometimes broken square root forms, in which some chunk of the pattern is missing, whether lost or intentional erased, as suggested by Lou Harrison. Harrison's phrase systems (described in his Music Primer, a beautiful small book rich in potent ideas (I received a copy as a 16th birthday present from the composer Douglas Leedy*))  are extremely useful, as are his interval and rhythm controls, the former of which anticipate Elliott Carter's methods. I like to cycle a rhythm within and through a sequence of measures and I also like increasing and decreasing series of icti over such sequences, and sometime I combine the two. I like logical sequences of numbers (here's my contribution to mathematics.)  I am also very fond of using perfect shuffles — yes, just like card shuffles — to order and reorder sequences of musical material; they are usefully rich in both familiarity and variety. And that's just from the top of my bag of tricks...

The question of whether a player or listener can or should dis- or recover these constraints and methods is unresolved, and usefully so, I think.  Not least because music works best when it works at several levels of entrance or retention: at the surface, for those just passing by, and deeper, ever deeper, for those with the time, skills, patience, imagination to go deep.  There is some music, like much of that of early Steve Reich or almost all of Tom Johnson's remarkable catalog, in which the methods are either immediately present or easy to puzzle out, but this does not make either the music or the method any less mysterious or profound for the accessibility. In such cases, knowing the local system simply makes the occasion more engaging, and ultimately removes distractions from attending intimately to either or both the underlying ideas and their physical expression in sequences of acoustic events. The flip of the coin comes with work like that of Milton Babbitt, in which aural recovery of the underlying array and the immediate rules for its projection into a score is really not on the agenda. The array itself insures a maximally even (or, by Jim Tenney's terms, ergodic**) distribution of event classes such that, statistically seen, any given sample of the surface should be more or less like any other, so that the extemporaneous process of composing out form the array is one of largely creating atypical events that defeat that evenness, emphasizing, for example, near similarities at the surface created by accident-like conjunctures found deep in the array. I would characterize this more as composing against the array rather than with it, and playing or listening to such pieces is definitely less about recovering the structure than enjoying the emergence of such playful anomalies.

I happen to find constraints like these advantageous; other composers disagree, and sometimes with something approaching anger.  Some advance the argument that composing with constraints is unnecessarily accepting unnecessary constraints on the musical results.  I would counter simply that this is mistakenly assuming that the imposition of constraints leads to a severely limited range of musical results.  In fact, in the huge vector space of possible musics, a reduction to a manageably smaller but still very large number (as with the 10^14 possible combinations that lead to my recent clarinet pieces***) is more than useful and with the huge variety of parameters, values, and contexts that can come into play for any given constraint, we are inevitably dealing in realms of finite, but still ridiculously large fields of possibilities. In any case, most anyone who claims to be composing without constraints is most likely doing exactly that — using a modality or tonality or a metre is a constraint, row tables and other pre-compositional means and tactics are constraints.  Hell, using five line-staved manuscript paper or just using a particular set of instruments and sticking with them is a constraint: be honest, how many times have you been listening to a string quartet when suddenly a Wagner tuba, a drum machine, and the Mormon Tabernacle Choir enter in?

ALL THAT SAID, the ultimate utility of recognizing a constraint is that a situation or scenario is created with authentic opportunites, among them tensions or conflicts, built into it.  And once you begin working with such a situation or scenario, the possibility or option to resolve the tensions or conflicts, and take or refuse opportunites becomes a lively presence in the work, whether tantalizingly left unaccomplished or relievedly resolved, by escaping, whether gently or through brute force, whatever limits one imagined the constraints to have set. And the question of whether this escape act is, ultimately, compositional or in the hands/mouths and ears of performers is also — and usefully so — open.

And of course, this:  My freedom will be so much the greater and more meaningful the more narrowly I limit my field of action and the more I surround myself with obstacles. Whatever diminishes constraint diminishes strength. The more constraints one imposes, the more one frees one's self of the chains that shackle the spirit.  — Igor Stravinsky, Poetics of Music

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* About those phrase systems: I recall Brian Ferneyhough, at the chalkboard in Darmstadt, appearing to dazzle his audience with a series of transformations to a series of measures. He was practicing notihing more or less than a species of Lou's system.
** It one of those paradoxes that John Cage seemed to have understood remarkably well: maximum variety leads to maximum maximum leveling.
*** That piece is indebted to a collections of poems coming out of the Oulipo, that famous cabal of writers exploring techniques for potential literature.(1) I'm a long-time admirer of the group, and not only the technical output, but the actual literary output of several of its members, first Harry Mathews, then Georges Perec and Raymond Queneau, most recently Jacques Roubaud whose novel Mathematics: is a wonderful thing, very close to my own sympathies, full of amplifications and interpolations and built of a linear expression of a branching structure (parentheses, dots) which is so flexible that it seems obviously the ideal one for an intellectual autobiography. 
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(1) I concur with Charles Shere about Daniel Levin Becker's Many Subtle Channels: Im Praise of Potential Literature; it should sit on everyone's little Intros-to-Oulipo shelf next to Mathews and Brotchie's The Oulipo Compendium and Motte's Oulipo: a Primer of Potential Literature).  As long as I'm at it, this year has been good for accounts of experimental literature in general, and I've enjoyed Charles Bernstein's Attack of the Difficult Poems, and really admire David Antin's  Radical Coherency.

Same and Different, again

ONE MORE THING about this fluid dynamic between identity and difference and the whole space of resemblance in-between those poles:  This can often depend upon a confusion of identities and I'm not altogether certain it's usually an honest confusion, instead it is often a voluntary entry into a contract to agree to mistake A for B.  One the one hand, this is just playing the game, agreeing, in musical terms, to hear a little more or a little less into the music so that two stretches of music fit into the same memory cache. On the other hand, this could be a little more ethically suspect, nefarious even, a suspension of honest estimation and judgment in favor of bending the evidence to suit the purpose of musical continuity or even unity, an act of some misplaced generosity, or even worse when a confusion of the kind is simply due to not listening and/or not remembering, which certainly happens much more than composers or performers ought be comfortable.

And this, too: Isn't this confusion often really, truly implausible?  There is a huge tradition in myth and literature of assumed and mistaken identities: think of Twelfth Night, or the Martin Guerre story, or any of those Hollywood films in which a thin layer of shiny latex turns person M into person N, or that classic hard-boiled detective formula in which person X mistakes person Y for person Z.   Of course the purpose of these mistaken identities is to set a target for the story which follows, and that target is the removal of the disguise, the restoration of proper identities. In some of these cases, one can well imagine that the mistaken identity is accepted knowingly (i.e maybe Martin Guerre was a creep and a lousy provider, so if this guy was affable enough and able to do the job well, well then Mrs Guerre was happy to play along) but in others, it can't really work unless there's some form of mass hysteria about (which might well be the case in Twelfth Night.) The frequency of these stories does make one wonder, however, if there wasn't once some time in which people regularly slipped into other identities and got away with it, people just accepting that you were who you said you were, even if you looked and sounded somewhat or even substantially different from how you used to look and sound (modern identity theft, which is an almost exclusively electronic information-based phenomena, is something altogether different, without any need for physical resemblance, indeed any physical presence, at all.)

So, in that space between a theme and its last variation or an exposition and its recapitulation, or along the hiccuping returns of a rondo, what is the nature of our confusion?  Do we enter in playfully, voluntary participant in a game with evolving rules, parameters, and other constraints?  Will identities be satisfactorily resolved in the end, like the denouement in a mystery, or can we satisfyingly be left without resolution?  Or do we simply all go a little bit mad when listening closely to music?

Rules: morals, games, music

A thoughtful post (here) by physicist Sean Carroll on the rules of morality and games.  His argument that rules of these sorts are not based on the laws of the universe nor handed from some deity but are nevertheless not arbitrary, invented and refined over time by real, fallible human beings is usefully applicable to music as well, with musical repertoires and styles hewing closely to the received rules but receiving a shock of  invention from time-to-time with extensions and refinements of the rule.

Now music does play against a certain immutable physical and physiological background — sensory consonance and dissonance, for example, with fairly clear correlates in physical and neurological domains — but the evidence presented by the diversity of existing musical repertoires suggests that there are plenty of alternative strategies for optimizing local musical rules to take into consideration these aspects to a greater or lesser (including no) degree. And yet, for all this diversity, there is a remarkable consistency to our ability to order an acoustical performance into broader or narrower categories of the musical and, within those categories, remark on the degree to which they follow or avoid the known rules.

Personally, what interests me most in music — "interests" here meaning "provokes my ear and aural imagination" — are those repertoires, forms, styles, pieces, parts of pieces, and moments of music in which it is thrillingly unclear whether the music is breaking the rules or discovering a new configuration or reading of those rules.  It is thrilling in the way a Rene Thom-style catastrophe or biphurcation is thrilling, a sudden and major shift due to a small change in circumstances. It is thrilling in the same way that a Wittgensteinian language game can be when suddenly, after an extended conversation, it becomes clear to both speakers that they weren't talking about the same thing at all.

Eventful Words

Word Events : Perspectives on Verbal Notation, edited by the composers John Lely and James Saunders has just been published.  It's both an anthology of word/text/prose/verbal scores and a significant bit of thinking-through-writing about prose scores and the general nexus of composition-notation-performance, with writings both by anthologized composers and, in particular the substantial new introduction and essays by the editors.  The composers included encompass both the usual suspects (Cage, Wolff, Young, Brecht, Bryars, Corner, Oliveros, Johnson, Cardew, Stockhausen), many who have built upon their work (Beuger, Pisaro, Walshe, Werder, even a certain wayward Californian), and a few important composers whose works with prose scores have been unjustly neglected.  I'm particularly grateful that work of Kenneth Maue is here; so grateful, in fact, that I've decided to perform one of Maue's pieces and put my copy of Word Events in the kitchen freezer and leave it there. (But not, of course, until I've read it once more through.) 

Curses & Snake Oil, Practice & Theory

Alex Ross has a pair of posts (here and here) about a harmonic progression with some significant history, moving, for example, from F# Major to d minor, two chords with no common tones.

As it happens — the lattice of coincidence being what it is —, in Budapest last week, I picked up a copy of Ernő Lendvai's Verdi and Wagner, a volume intended to be the first of several on "Bartók and the 19th century". Lendvai is best known to musicians for his thesis that major structural divisions in Bartók's music correspond to Fibbonaci proportions and the golden section. I've never been convinced that this thesis is precisely true, but find it unremarkable that such proportions in a rough form are present as it simply makes sense that major events in the course of a musical work would be successfully programmed to maximize our attention by appearing somewhere between the half-way point and the end, and a sequence like 1:2, 2:3, 3:5, 5:8, 8:13, ... hovers right in that region.* I suspect that a great deal of hovering around these ratios has been and will be tolerated in the exact divisions of a single musical work, so much so that an over-obsession with precision is probably unneccessary; moreover, in Lendvai's own accounting of Bartók's actual proportions, there is enough variability — particularly due to tempi — that considerable fuzziness in the ratios of real elapsed time are inevitable. This series of books, however, was intended to focus on Bartók's relationship to a harmonic tradition, in particular that of the major later 19th century opera composers, Verdi and Wagner. (It's worth adding here that the two more immediate influences on the younger Bartók's practice were Richard Strauss and Franz Liszt, who could be considered as mediator's between Bartók and those operatic styles.) I bought the book with nothing more in mind than having some streetcar riding material, but it did turn out to be fascinating reading, although in ways Lendvai certainly did not intend. What Lendvai did intend was to describe later 19th century harmonic practice in terms of the interraction between the diatonic and the chromatic, the one irregularly, assymmetricly, divided, the other evenly and symmetrical. So far, so good. But Lendvai's treatment rapidly goes beyond this, constructing an elaborate system with idiosyncratic terminology and then going well beyond his system proper by associating literal "meanings" for particular harmonic relationships with excourses into topics like key characteristics. The bulk of the volume is given over to a description of Verdi's Falstaff.

As far as I'm concerned, music theory of this sort is close to snake oil, with its effectiveness as analysis approximating a placebo effect more than a real account of what our ears and brains do with musical sounds. That said, the fact that real musicians have taken and do take such constructions seriously, as an impetus to the production of real — and often very fine — music, means that it is a real part of the culture around the music and, at the very least, we have an ethnographic obligation to take it seriously as well, at the very least as a locally coventional — if, ultimately, in terms of the psychoacouctical and neurological foundations of musical perception, arbitrary — means of giving constraint and order to musical materials. Lendvai's "theory" is, ultimately, a doctrine, positing for the late 19th century an extension and equivalent to the earlier doctrines of musical figures and affects.

Now, the chord progression which Ross has noted might be described in terms of any number of theoretical "systems" — Lendvai's among them — and individual composers may well work productively with such systems, and it has certainly established itself in the repertoire as a recognizeable figure with an associated affect, but there is probably no real need to call up either an elaborate theoretical apparatus or an existing repertoire of usage to identify the salient qualities of the progression: the two chords are connected by a smooth ("parsimonious" is the term of art) voice leading,** yet — depending upon how one deals with "enharmonically equivalent" tones — do not come from a common diatonic collection. Most tonal music bops along within the same diatonic collection, venturing from time to time to collections that share most tones, so a sudden jump like this one plays with our habits and expectations. The effect — and possibly, affect — is thus both smooth and startling.

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* When one traces the development of the Sonata form, one finds a similar refinement of proportions, successively moving the point of furthest harmonic remove from the center of the simple AABB Sonata further back into a development section.
** It is not a coincidence that the examples here are taken from vocal ensemble and opera, in which changes of texture, i.e. not maintaining a constant four-voice ensemble, are frequent.

Not-so-casual Observation

Voice-against-voice counterpoint is very much like tying knots, specifically like tying ties.  Like a bit of two-voice modal counterpoint, which can only begin with unison, octaves, or fifths, a tie knot can only begin with the two ends outside-out or inside-out, that is to say, in the sartorial equivalent of perfect consonance.   Thomas Fink's Encyclopedia of Tie Knots is a very cool and quite useful site, and Fink's work on designing tie knots by random walks comes uncannily close to using random walks to generate counterpoint.  

Layer Analysis

This is the season which is marked, in this part of Germany by the Zwiebelkuchen and, across the border in Alsace and Lorraine, by the quiche, and a very good season it is. For better or worse — mostly better, but let's face it, fingers have been cut and tears have been shed — the onion, Allium sepa, the lowly, bulbed, garden onion, the center of both these closely-related savory pastries, is the center of European cooking, indeed, virtually all of the world's cuisines. Sure, wheat and rye and milk, butter, and cheese and olive oil and salted cod and all manner of things that rise, rot, ripen, cure or ferment or take astonishing form or flavor when smoked, fried, baked, grilled, or boiled are each and all important. The truffle and the saffron thread, capiscum, ginger root, and the cardamom pod are miracles. But the onion provides a uniquely useful bulk and range of flavors upon which good things become better. What would Hungarian cooking, for example, be, without the countless recipes which begin: "fry a kilo of onions in lard"?

The onion is an object deserving some serious contemplation and reflection. As you peel, and slice, and dice, accidentally or purposefully allowing cell walls to open, breaking down amino acid sulphoxides and converting them into sulphenic acids, may your tears accompany the pleasure of exploring a structure of astonishing consistancy and integrity. We may joke, with ethnological wisdom, of a universe composed of elephants "all the way down", but onions really are all the way down, shoots composed of multiple, self-similar layers. I find that the appeal of this structure is less cosmological than aesthetic, and musically aesthetic in particular: works of musical depth reveal themselves to extend in time — much as each layer of the onion extends the bulk of the shoot — via rather elementary processes. This is true of form in Javanese music with the irama system uniquely relating tempo to density, or the prolongation and diminution techniques of early music or the classical tonality described by Schenker (or Stockhausen's formulas, as long as we're at it), and it's true of the self-similar structures ranging from Cage's square root form to numerous works by Tom Johnson.

From Materials to Music

I've been working in just intonation since my freshman year in high school, in 1975 or 76, when the music of Lou Harrison and Harry Partch first registered.  The beauty of the pure intervals was the first attraction, but soon, the whole business of organizing tones into scales and systems became an attraction of its own.  But a scale or a system is not yet music, but rather material with potential to be used musically.  The diagram (or lattice — German Tonnetz — or manifold) describing a tuning system is a static entity, rather like a map from which a useful route has not yet been discovered.  

My first lattices were all at right angles, following the models of Martin Vogel and Ben Johnston, with chains of fifths (ratios of 3:2)  running horizontally and major thirds (ratios of 5:4)  vertically.  Adding ratios of higher primes, especially 7, 11, and 13, was an on-going problem, solved with transparencies or other kludges.  I literally stumbled into a way of animating my lattices, turning the static information on the lattice into information about successive events in a score, when I came across an article by Shohei Tanaka (1862-1945), a Japanese scientist who wrote a dissertation in Berlin in the late 19th century on Just Intonation, in which he advocated a 53-tone equal temperament for the approximation of a just intonation based on pure thirds and fifths.  Tanaka used a lattice in which the lines of fifths and thirds were at a 60-degree angle to one another, and added lines indicating the minor third relationships as well, thus presenting major triads as upward pointing triangles and minor triads as downward.  This started to look more like music to me, and quickly, all of the moves that characterize smooth voice leading in tonal music started to appear as simple moves on this hexagonal lattice.  The tones connected directly to a single tone were the fifth above and below, the major thirds above and below and the minor thirds above and below.  The vertical mirror of a major triad was the minor on the same root, horizontal neighbors sharing the central tone were in a dominant-tonic relationship, and triad described by triangles sharing one face had mediant relationships.  At the same time, I started to recognized that the most compact voice leadings I was learning simultaneously in my study of figured bass realization were compact moves on the lattice, while progressions that were more exotic tended to be represented by greater distances on the lattice.

In the spring of '78, I went to San Diego to visit the Partch instrument collection then housed at SDSU under the watch of Danlee Mitchell.  I showed Mitchell my attempts at latticing Partch's scales and Mitchell said immediately that I had to visit Erv Wilson, a name I had recognized from the second edition of Partch's Genesis of a Music (Wilson, a professional draughtsman, had done the diagrams for Partch and had also suggested the layout for one of Partch's instruments, the Quadrangularis Reversum).  Wilson lived in East LA, and I soon arranged to visit his house, one of the oldest in the city, located at the edge of the arroyo into which the oldest — and now, almostly quaintly small — freeway in the city, the Pasadena, had been dug.  Wilson was in his front garden when I arrived, sorting bags of corn hybrids collected from his ranch in the mountains of Chihuahua, Mexico.   He looked through my collection of lattices and scores and at an adapted hawai'ian guitar I  had brought along and immediately took me in to his dining room, where he sat me down at the table and started to teach some more economical, elegant, and tonally suggestive ways of mapping tones on paper, or in the three dimensional models of dowels and spheres suspended throughout his house.  It was a total revelation to see how Wilson could accomodate far more than the lousy two or three dimensions I could capture on paper, as he casually drew examples with four, five, even eight dimensions represented.  But these examples were not Augenmusik, but acoustically immediate and vivid, as Wilson's house was filled with re-fretted guitars, a collection of flutes, and a number of keyboard percussion instruments, of metals, wood, and bamboo, each apparently to a different tuning system, with alternative keyboard layouts of Wilson's own exquisite and ergonomic designs.  (Wilson's ear is amazing: once, while using his scalatron out in his garage to tune up some aluminum tubing, I was periodically interrupted by his shouting out the ratios of each new tube "256/243! 16/15!, 13/12!"). 

My use of collections of pitches related by just intonation remained rather unadventurous for some time, as I was essentially replicating the most familar moves in tonal music. This was hard to square with my attraction to more experimental music.  Working with La Monte Young  provided one decisive step in this direction.  The harmonic motion in La Monte's pieces is very much understood as motion around a lattice, with formal sections of works restricted to subsets of the total collection of pitches (incidentally Xenakis is up to something similar in Herma) , but La Monte's avoidance of ratios involving the number five whether as tones used directly or as combination tones creates very different tonal environments, and a number of works allowed performers to improvise within the constraints of rules which effectively constitute the voice leading rules in these new environments.  These rules are related, also, to the "cuing" pieces of Christian Wolff, which have also been very important to me.  I made a number of pieces in which performers moved by a small set of rules through pitch materials, including a set of just intonation Mazes and equal tempered pieces, the best and most-played of which was Multnomah Riffs of 1981.  In Multnomah Riffs, the players worked through a score of four repeated measures or frames, from which pitches could be selected, and played at any time within the frame, omitting or repeating any tone so long as the sequence of tones was preserved.  My friend Jonathan Segel, known perhaps best as a member of the band Camper Van Beethoven, contributed an ostinato for celesta to keep track of the frames.

A second decisive step was provided by a small piece by the mathematician and composer David Feldman called Going Places, for two violins.   Going Places is essentially a canon for the two fiddles, chasing each other in a random walk (run, actually) across an open-ended lattice of major and minor thirds.  Encouraged by David's example, I soon wrote a number of pieces involving random walks across both open-ended and closed lattices of various dimensions, and eventually started trying different sets of constraints and changing the lattice, sometimes quite dramatically, in the course of a piece.  These lattice moves were also related to Lou Harrison's "interval controls"  (Elliot Carter, famously, uses a related technique).  

I would later encounter works by Yuji Takahashi and James Tenney that use similar techniques; I am particularly fond of Tenney's principle, in Changes for six harps, of establishing a tonic, jumping to someplace tonally distant from the tonic, and returning by the simplest possible root motion, often a descending series of fifths, thus recapitulating very familar harmonic territory.  As my own strategies for working with tonal motion had generally been symmetrical, even dualistic, Tenney's example was an important one, in that it better resembled the assymetry of real tonal musics, for example in the German tradition in which I can go to IV or V and IV to I or V but V can only go to I.   (For some great counter examples, with their own assymetries, from non-German traditions, consider the V-IV of the blues, or the extended subdominant chains in Berlioz's Marche Troyenne.)  

In Charles Seeger's breathtakingly prescient little treatise on Dissonant Counterpoint, he introduces the principle that the structure of an existing tonal system can be maintained, but the precise content be changed, in his case changing the hierarchy of consonant and dissonant intervals in a contrapuntal texture.  Following Seeger's example, in these unfamilar tonal environments, whether in just intonation or mapped to an equal temperament, there is plenty of opportunity to experiment with both the rules and material hierarchies, while still preserve qualities that are clearly tonal.  (The musical and mental agility on display in this and other examples of Seeger's writings has provided a decisive spark for experimental music for several generations past and will continue to provoke for several generations to come.  If anyone asks, I'm a card-carrying Seegerite.) 

(I haven't let go altogether of my youthful dualism:  when I come across the so-called half-diminished seventh chord in classical works (Bach and Mozart, especially), it still makes a lot of sense to think of it as a subharmonic chord, the exact inversion of a dominant seventh chord, and I think that it is sufficient that this chord is arrived at melodically, by voice leading and counterpoint (the Tristan "chord" is another example), without having to argue about the physical and psychophysical status of the subharmonic.) 

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At the moment, I am mostly interested in the relationship between the group of tones in play locally and globally,  and especially our sense that a tone belongs or doesn't belong to a moment in a piece or a whole piece.  Erv Wilson's ideas about moments of symmetry come into play here, in that subsets of a tune system can exhibit similar properties of coherence.   Classical diatonic tonality, with its matruschka-doll construction of chords, diatonic scales, and chromatic scales, is one example.  Recently David Feldman demonstrated that there are only a small number of distinct and connected graphs of a diatonic scale onto a 3,5 lattice.  (I'll let David publish his own result, but the number should be easy enough for you to figure out on your own.   He has also figured out the distinct graphs for sets of 12 pitches on this and on other lattices, a calculation which is not so easy).  This was very interesting to me because I have made a number of pieces that could be considered "pan-diatonic" and Feldman's lattices suggested something  more to the point, in that each graph, while preserving the letter names, had an alternative harmonic profile, much like individual moments in real tonal music.  Sometimes an A is the fifth above a D, sometimes it's the third above F, but not necessarily both at the same time.  The graphs could be realized in just intonation, or mapped to an equal temperament, or to an unequal temperament designed to best represent a particular graph or set of graphs.  Moreover, these graphs suggest particular melodic paths, rows, if you will, with built-in harmonic properties.  This line of working strikes me as very rich and, possibly, very musical. 

(from a talk in California, January, 2009).

Backgrounds

The figure in a clearing is a rich musical topic or texture.  Something happens occurs before, or against, or within, a background.  That background may be somewhat atmospheric or suggestive (musically or extra-musically), but it must also be somewhat neutral, audible but not listened-to. How is such a background made in a work of music?

(1) silence (Cage's rhythmic (metrical), and — later — time bracket (ametrical) structures.

(2) a scattering of small events (Berlioz: "intermittent sounds"), distributed irregularly and unpredictably. 

(3) erdodic form (Tenney):  completely and randomly filling the available time with events, so that no orientation, temporal or otherwise, on the basis of the background is possible.

(4) events occuring in absolutely regular and preditable intervals of time, providing a strict temporal reference, possibly references for pitch, timbre.

(5) a drone, a continuous sound providing a pitch, but no temporal reference.

(6) a contrapuntally independent stream of music, speech, or environmental sounds.

I love the coincidence here of completely full and completely empty backgrounds.  [Is a blank canvas white or black?  The complete physical spectrum of light tells us one thing (white is a broad spectrum of light, black is an absence of light) while the real experience of visible light, the colors with which a painter works (with a spectrum that our mind folds back up on itself, connecting reds to blues) suggests the opposite: white is the absence and black is completely full.]  This figure usefully focuses on the issue of audibility/inaudibility. While the figure and ground idea is, at root, contrapuntal, the immediate compositional issue is whether or not the listener should be aware of the counterpoint, and this audible/inaudible quality (now you hear it, now you don't)  is determined by the material relationship, the similarity or dissimilarity, between the figure and ground.

See also these Notes on Continuity and this post on Ives and Mahler.

     

Events, not Waves

Current reading: Sounds: A Philosophical Theory (OUP 2007) by Casey O'Callaghan offers a — to my ears,  musically suggestive, if never musically explicit — new approach to sound and our experience of sound, based, for a change, not in the traditional models of perception derived from vision, but in a model unique to sound and framed no longer in terms of waves in a medium but rather of events in our own environment located at or near objects or events which cause objects to sound.  The writing style is lively and makes some heavy matter refreshingly accessible to non-philosophers.

A Hard Day in Analysis

Here's a physicist's analysis, via FFT, of the opening chord to A Hard Day's Night.  (Hat tip Tyler Cowen.)  As the pop era's moral equivalent to the "Tristan chord" (an ambiguous event in a work of tonal music which continues to create great puzzlement and a regular stream of authoritative pronouncements), I'm sure music theorists will be busy with this for years to come.

Altogether, Now

John Cage disliked the word "texture" when applied to music; he thought that use of the term was an appropriation from a physically tactile domain that made no sense in the description of music. And while one could argue with Cage on the somewhat peripheral case that some sounds exert a presence which actually is tactile, sounds that one can feel through the skin as well as hear with ears, Cage's critique stands, usefully, pointing to a convention which is, indeed, vague. "Texture" is, in talk about music, used for a number of things, including — rather vaguely — the density or level of activity, and — more precisely — the quantitative and qualitative state of ensembles. In fact, our vocabulary for describing ensembles is quite good; it is both clear and vivid. Unfortunately, we've acquired some habits with this vocabulary which are not so good.

I recently volunteered to help a Gymnasium student prepare for a music exam. I managed to get him into real trouble, and it was trouble with a capital "T" and that stands for Texture. You see, on the exam he was being asked to reproduce a certain narrative in which "music history" (unqualified by many particulars of where or when) began with monophony, in the form of chant and monodic song, got mucked about by some non-westerners into heterophony, which was busy but not so sophisticated as that which followed in the West, albeit in a now-quaint and antiquarian way, as polyphony, and the story of textures ends with all of us singing Lutheran chorales, which are identified as homophony.

All the sins of this narrative — and it happens to be a standard entry-level academic narrative on both sides of the pond — aside, the sin that immediately alarmed me and led me to getting the kid in trouble was the fact that he was being forced to abuse some perfectly good terminology. These terms are useful for describing ensembles, but they are not really a set of four distinct terms but two very different pairs of terms. The first pair, monophonic/polyphonic is quantitative, a simple binary opposition between a single voice or line and and an ensemble of more than one voice. One may well go on to further distinguish polyphonic ensembles in terms of the numbers of lines, but the basic opposition remains that between one and more than one. The second pair of terms, homophonic/heterophonic is qualitative and applies only to ensembles, that is, to polyphony. These terms are not in a simple binary opposition but rather describe relative positions on a continuum between similar and differentiated voices or lines.

When the face value of this ensemble of terms is recovered as I describe here, their application to real, existing music becomes much more subtle, and, I believe, interesting. With, for example, musical ensembles that practice the simultaneous variation of a single melodic idea, a practice common throughout much of the world, an analyst is required to apply the pairs of terms in different ways within almost every musical parameter. The use of a single, core melody is, indeed, a symptom of homophony, but local details — in the form of simultaneous variations and ornaments — exhibit a tendency to differentiation, i.e. heterophony. The question of the number of lines active in the ensemble becomes one of perspective: how closely does one examine the music? From a certain distance, that of the Schenkerian Urlinie or the Javanese Lagu, it may well sound like one line, but from other distances, an adequate quantification demands a number greater than one.

If it sounds like I'm praising these terms for their precision only then, in their application to real, existing music, to let that precision slip away, like sand between fingers, it's because that's precisely what I want to be doing. Terms like these are useful not only because they make some features of music more clear, but also because they restore some of the mystery of music, by underlining aspects of the musical experience which are anything but clear.

If you have any doubt how central the act of making the familiar strange again is to the aesthetic experience then just try, for a moment, to remember the face of the loved one you know best. I guarantee that the more you try to reproduce that face in your memory, the less satisfied you will be with the quality of your memory. You can know and treasure all the broad features as well as a wealth of details from that familiar face, but you can never recover all of the texture of that face, in its unique ensemble complexity. And the proof of this is that each time you see that face again, you experience simultaneously the delight of recognition and the surprise of the unfamiliar, a most musical condition.

Imaginary Lands

More than a few composers — from Ligeti's Kylwiria to Kraig Grady's Anaphoria — have invested formative time, whether in childhood or as adults, in the invention of imaginary lands. Once one starts imagining a land, all of the details start to emerge: maps, languages and writing systems, mythology and literature, customs and rituals, postage stamps and passports, poetry and music. These newfound countries tend to be more systematic, more orderly, than any real, existing messy and conflict-prone places, which shouldn't be much of a surprise, as these are often refuges from bright and creative people who don't quite fit into the world as it is, and imagining utopia is certainly one of the functions that artists and writers and composers can often perform superbly well.

Ron Silliman has a pair of posts (here and here), contemplating the relationship between "grand theory" and practice (in his case, poetry and left politics) and this bit of text stands out:

... author, whether the Ur-situationist Lefebvre or Charles Olson writing in his most telegraphic critical mode, saw their work, these specific books, as making contributions to practice(s) whose hoped-for fruition existed principally away from the university, whether writing in writing poetry or making a political revolution. They are not contributions to a professional debate.

Professional music "theory", as practiced in universities and conservatories, is largely an account of practice in music already made, recipes for synthesizing new music that is similar to old models, or suggestions for the interpretation of existing music through the articulation or projection of particular features, but speculative music theory is the domain of composers, the work done in preparation for and during the composition. A speculative theory inevitably has the same utopian qualities that the grand theories Silliman discusses and many composers spend their creative lives, in effect, building imaginary worlds that follow their own sense and logic, accumulate their own habits and histories, and, as they grow, undergo all the successes and failures, consistencies and contradictions, tragedies, comedies, and farces that real lands experience. You create music to put it into the world, but it inevitably lives two lives, one in that real world, cruel or kind as it may be, the other, private, and cruel or kind as your own imagination.

pf

When future musicologists, should we survive the next century or two, turn to the reconstruction of late 20th and early 21st century art music, I reckon that dynamics are going to be something of a problem for those advocates-to-come of historically-informed performance practice.

The historical evidence is not particularly rich when it comes to dynamics, and contemporary written accounts of performance practice are rare.* While written scores may contain a large number of indications, it's far from clear what kind of range is intended, and whether dynamics apply equally to all instrumental resources. One composer is content with piano and forte, another might have 12 or more adjectives in play: are these terms to be applied only locally and/or relatively, or do they belong to some absolute scale of values? While the Italian marking remain widely used, many composers prefer a local language or an alternative lingua franca, and a small number of composers have used graphic or numerical notations for amplitude, so translation is an issue. The other important evidence, sound recordings, is, at this point in the cricket match, a source to be used with great caution, as the prevailing recording style is based upon a hot but rather compressed signal, with which dynamic differences are largely flattened. Digital recording and playback should, with increased available bandwidth, change this, but we're not quite there yet technologically and the flattened sound — identifiable with pop music — may be with us for a while, as it carries some degree of aesthetic inertia.

[Ironically, one minor source of direct information about contemporary performance practice may prove to be very useful in reconstructing the various dynamic styles of the day, and that is musicological research about historical performance practice in times earlier than our own, for the subtext of all of that research is, of course, how we do it now and how it differs from the past. The connection, for example, between the "terraced dynamics" discovered by certain twentieth century reconstructors of Baroque repertoire and a similar approach to dynamics in contemporary music, from Stravinsky to Nancarrow is real and instructive.]

All that said, I would not be surprised if future musicologists happen to look back and assign us into competing dynamic styles. There will be traditionalists, whose practice is as continuous as possible with the dynamic practice in conservatory-style 19th and 20th century music; this is the style in which the Italian terms will probably have the most stable exchange rates. There will be the amplificationists, plugged-in, usually mixed, and tending towards a loud and flat dynamic profile, sharing much with the production values of popular music genres. A subculture among the amplificationists will be that of the microphonists, whose interest in not in the loud, but in elevating the most quiet of acoustical phenomena into the world of the audible. There will be the as-soft-as-possiblers, pushing below the lower limits of traditional acoustic performance practice. ** There will probably be an all-acoustic loud-as-possible counterpart to the quietists. And finally, there will be a radical center, content with the dynamic possibilities of of a restricted set of signs, mostly soft and loud in whatever language, but never getting too close to either extreme.
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*Rare but not totally absent. The Morton Feldman discussion list, MF, has recently had some interesting threads on dynamics, for one.
**For the record, I happen to think that while Feldman was influential if not critical to the development of this style, his own music's dynamic style was relatively soft, but entirely within the framework of traditional "quality" classical performance, such that the substance of the sound produced was never sacrificed to an absolute low volume. This is also in keeping with his style of articulation, which was not excessively tender, but rather more in the tradition of the pianism associated with the Skryabinistes.

In Analysis

As part of a group project, I've recently been analyzing my favorite Mozart Piano Sonata (the F Major, K533/494). Going off on my own, beyond the confines of the project, I've been trying to get at the piece from as many analytic angles as possible (all the usual suspects -- scale-step, functional, tuning lattice, motivic, Schenkerian, rhythmic, topical -- plus an idea borrowed from Virgil Thomson and John Cage about pitch gamuts).

Without going into any specific results -- which would be premature anyways -- I've been struck by the contrast between those analytic methods which are more objectively descriptive and those -- Schenkerian techniques especially -- in which each analytic decision is negotiated in a process uncannily like that of setting a human subject down on a couch and asking about dreams or the subjects relationship to his or her mother. While one is fascinated by such an image -- after all, Schenker's work and psychoanalysis were both products of fin de siècle Vienna, if coming from very different neighborhoods of that complex cultural/intellectual town -- the high degree of subjectivity is troubling. And this subjectivity, reinforced by an insistence that each decision represents a form of belief, is not limited to Schenker-style analysis (One of my college teachers was a student of Boulanger, and his approach, directly following that of Boulanger, was to insist on the same sort of commitment, which the student had to demonstrate through rigorous musicianship exercises, often turning music class into something more like an old fashioned catechism lesson (no lisping nuns, but complete with back-of-the-knuckle slaps with a ruler whenever something was done wrong)).

One of the things that music handles well but music analysis deals with poorly is the exhibition of ambiguity. Real music can say two things or be two places at once, and sometimes more than two, while the preference in analysis is inevitably to pin things down. And most forms of music analysis are based on some aesthetic and stylistic preferences that are generally left unstated, particularly those concerning the "unity" of a movement or whole work of music. The idea, for example, that a piece of music starts and returns to the same place, or is an expansion or elaboration of a single idea or structure, is an aesthetic preference, not a law of nature, and music can very well start here and end up in some very different place, an unexpected there, or fail to relate entirely to a single generative idea and still be successful, interesting, attractive, or whatever...

However, if that if the student of analysis is aware and wary of any aesthetic assumptions underlying an analytic technique, these techniques can become valuable, in listening, performing, or in composing. Harmonic functions and Schenkerian prolongations are extraordinarly rich in descriptive and compositional power, but there is no object to these forms of analysis precisely similar to the object of psychoanalysis. A musical work may well be problematic, if not a puzzle, but it is not an ailing organism and will not be made well by analysis. The final Schenkergram, with a work reduced to a tonal skeleton common to all works also satisfying the same aesthetic critieria, is not interesting in and of itself, but the process of arriving at that skeleton is both very revealing and suggestive of alternate possibilities for interpretation or for new composition.

The known analytic practices are, as far as we can tell, only provisional, especially as long as our knowledge of the neuroscience of music is so limited. These analytic procedures can be put in reverse, as it were, and used to synthesize new musics; but the evidence from real composition is that many roads lead to Rome: although one algorithm or another may exhibit virtues of logic, elegance, or efficiency, there is no compelling evidence that real human composers operate on the basis of logic, elegance, or efficiency, so there is no slam dunk argument for any existing technique but strong hints that musical diversity is served by a diversity of approaches to musical synthesis. And while there are strong suspicions that our perception of music uses analytic techniques bearing some real relationships to known methods of music analysis, this is still such a young area of research that one is wise to be prepared for more surprises.

We're not out of analysis yet and that, my old (but not John McCain old) friends, is far from a bad state of affairs.

Harmonielehre

More than a few composers arrive at a moment when it seems useful, if not urgent, to assess their relationship to one element or another of music in a more systematic, sometimes formal way. It could be an assessment of rhythm or form or orchestration, but it's more often about pitches, and a composer's relationship to counterpoint/voice leading/harmony is not only a moment for producing teaching materials to share with others, but a moment for clarifying ones own practice and identifying resources and paths with potential for new music. For many composers, this is carried out within the context of a piece of music -- I think of Glass's Another Look at Harmony or Jo Kondo's Threadbare Unlimited (which the composer refers to as his own Harmonielehre) -- but for others, it takes the form of a written text: Schoenberg's Harmonielehre, Partch's Genesis of a Music, parts of Cowell's New Musical Resources, Charles Seeger's Dissonant Counterpoint. James Tenney's Changes for Six Harps and Klarenz Barlow's Çogluotobusisletmesi are interesting examples in which a composition and a theoretical/practical essay were produced simultaneous. Other composers who have more recently turned to major projects of the sort include Wolfgang von Schweinitz and Hans Zender.

Harmony, as a subject, is not precisely that which a scientist would identify as a theoretical discipline.* Sure, the taxonomy can be developed in a rigorous way (in fact, in many different ways), and the perception of harmonic and voice leading structures is a serious area of research in music perception and cognition, but a harmony text is more akin, in the worst cases, to an etiquette book, and, in the best cases, a cookbook, a collection of rules or recipes for describing a range of tone relationships and for replicating certain sounds or sequences thereof. There is clearly a program of taste, of aesthetics, behind every harmonic prescription. The German word that titles many a harmony textbook (and, of course, a nice work of symphonic dimensions by John Adams), Harmonielehre, captures this better than the English phrase "theory of harmony", as Lehre is teaching or doctrine as much, if not more than theory. As far as I'm concerned, the discipline of studying harmony is largely one of absorbing just enough of an existing doctrine in order to remake it -- accepting some aspects, rejecting others, introducing new concerns -- for ones own purposes. And then, as with any other form of doctrine, the greater spirits among us will proceed to ignore their own system in fascinating, productive, and yes, musical ways.
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* There is an argument that harmony is only a consequence of voice leading, a view that is taken up, for example, by James Cook at Mathemusicality. Although I am personally a voice leading oriented musician, I disagree with Cook & Co. entirely: there are many ways for composers or listeners to arrive at or to hear the same piece of tonal music, and while a strong voice leading approach may be construed as more efficient or logical or less complex than a strong chordal approach, (1) I don't believe that efficiency, logic, or simplicity are always going to be the chief criteria through which we approach or should approach music, (2) there are simply too many counter-examples of fine musicians who think in terms of sequences of chords rather than simultaneous melodic lines, and (3) there are many real musical contexts in which the music succeeds precisely because the balance between vertical and horizontal is dynamic and/or ambiguous.

Rationale

We know the world is round, but local daily life is carried out with flat-earth coordinates. Music is much the same: we navigate among our pitches and rhythms as if they were related by the simplest of ratios and proportions while knowing, all the while, that their simplicity is largely a conventional approximation, hiding all of the errors of human sound production as well as subtle compromises intended to create additional tonal possibilities. We live quite well and make music even better with our blissful decision to ignore the further decimal places of the measurable world. And yet this: the damnable effectiveness of that simplicity does make one wonder if it is in fact our execution that is flawed, the inherent error of being human, and that the music that is really real is some kind of platonic ideal.* Recent research in the neuroscience of music also seems to point to a preference, in the brain, for processing musical intervals as simple ratios, those found among the low-order harmonics of complex sounds, a capacity useful to both speech and music.


My own musical faith, however, is not that of a platonist, but something rather more constructive or intuitive. I believe that this is a more pragmatic viewpoint, one more immediately connected to the experience of music as it is made in real time. An example: in many of my pieces, beginning in the '70s, I use some form of just intonation, a term familar to many musicians. But defining what is meant, precisely, by just intonation is not an simple matter. If we define it as rational intonation, then we have the problem that every rational interval can be approximated by an irrational (and vice versa). If we want to limit our definition to ratios of small whole numbers, then we have the problem of defining "small". If we wish to define the intervals by minimal beating, then we have problems with timbres including spectra in non-harmonic relationships, which may well find minimal beating with intervals other than those of small whole number ratios. Moreover, as La Monte Young was wise to note, tuning is a function of time, and the accuracy of intonation will depend directly on the length of the sample. But the more pragmatic viewpoint is to examine the immediate musical context and worry less about decimal places of tuning accuracy or the natural wobbles of a man-made sound and evaluate intervals as the complex phenomena that they are: what is the intended relationship? what is the melodic, harmonic, and timbral context? what is the -- entirely subjective -- quality of the interval in question? In such a broader, contextual viewpoint, not only can more conventional just intonation be understood, but it is plausible that intervals and chords related by rather more complex ratios -- as are found in recent music by Young or by Kraig Grady -- are processed by the listener through attention to phenomena like the reinforcement of shared partial tones and difference tones in simple harmonic relationships.

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* Plato had us living in a cave with familiar reality being a reflection on the walls of that cave of the ideal reality from without; musically, I suppose, he'd have us in an echo chamber, in which the music we hear is the distorted echo of the ideal sounds outside.

What musicians want from science

Like many other musicians, I keep an ear out for recent research in the sciences on music and topics related to music. Stories about music and science appear quite regularly in the media and while many of the results are interesting, very little is immediately useful to a musician, aside from those results which get implemented immediately -- and, as far as I'm concerned, invisibly -- in commercial audio technologies. It occurs to me that the situation might be somewhat different if musicians helped to frame the questions explored in the research more specifically towards immediate musical problems. I can recognize that otoacoustic emissions or the relationship between tonal languages and the fascinating anatomy of human hearing, in which music is, at least in part, piggybacked onto organs used for language and balance, have great potential to reveal more very interesting things about music, but I, for one, would like to know much more about musical timing. What is the relationship between the "present" in music as it is played and the "present" as registered in the brain? How can ensembles of individuals coordinate rhythmically? How long are the chunks or stretches of music that our brain processes, and how does the brain sequence them back together? And, of course, as a composer, I really want to know how much I can play with these phenomena in order to make interesting new music.

Be Galant

For some reason, I get asked a lot to recommend textbooks for composition. I've compiled a list of books that have been useful to me, personally, as a composer, but that list doesn't include much in the way of common practice western repertoire except for Morley's Plaine and Easy Introduction (which is a bit too early music-ish for most) and de la Motte's extraordinary Kontrapunkt (which is too German for many anglophones). I like both the Morley and the de la Motte as they are built around real repertoire of really great music and they cover a number of areas not featured in conventional instruction: Morley, for example, the rhythmic system, and de la Motte for going into depth on Josquin rather than Palestrina, a really good move, as well as going back to Notre Dame polyphony and forward to Wagner's network technique.

But now there's a superb book in English to recommend: Robert O. Gjerdingen's Music in the Galant Style. While this is boxed as a musicological essay, it's really a composition handbook for composing with the VARIOUS SCHEMATA common to a style widely used in the period you probably called the late baroque and early classic back in school ("baroque" and "classic" as terms identifying their musical practice would have been unknown to the composers concerned). Schemata are snippets of music, figure, patterns, routines, or formulae, many of them named, that appear pretty much intact on the surface of a piece of music and are re-encountered again and again in the real repertoire. As Gjerdingen wisely points out, the use of these schemata are precisely analogous to the use of lazzi in Commedia dell'Arte or of figures in modern figure skating. (One of the musical schemata is the Monte, which immediately made me think of routines in card tricks, another performing craft with an elaborate body of self-referential tropes that can be recombined and reworked into countless new compositions).

There are many ways, indeed an undetermined number of ways, of achieving a particular musical surface, a score. In general, in the academy, we have come round to teaching the composition of tonal music as a matter that begins with an abstraction -- i.e. a harmonic progression or, more fashionably, a tonal structure that is prolonged and given detail through processes that can be loosely grouped together under the term diminution -- rather than the assembly of concrete bits of musical material. Of course, this has never been the case in the teaching of vernacular musics, Jazz in particular, where training is closely associated with the acquisition of an ever-larger personal catalogue of possible chords, scales, and riffs, and there have been a number of heterodox theoretical projects: David Cope's experiments, for example, have coalesced into a study of how bodies of musical surface "signatures" can be recombined to replicate compositions in the style of a given work, composer, or repertoire. One is struck, however, by one contrast in these two styles of theory instruction and that is the degree of intimacy between the theory-making and a particular body of music.

In learning music, we need to go both broad and deep. There is a place an expansive and abstract theory-making, as this is how repertoires are fruitfully connected and this is where many new musical ideas are cooked up. As a composer, it's obvious, but for performers and listeners, it's essential, as it is a way of connecting with unknown musics. But there is also a place for depth, and this -- again, largely outside of vernacular music instruction -- is a real and present deficit in contemporary teaching. I can easily imagine a semester spent productively with Josquin and de la Motte, or now, with Gjerdingen and the masters of the Galant. Although the galant style, with its easily recognizeable body of schemata recommends itself well to such in-depth training, in a real way, it is all the same what repertoire is chosen, just so long as young musicians get the experience of a close encounter with a real music. *

Moreover, the Gjerdingen book is both scholarly and fun. I can't wait to try composing in sequences of Montes, Pontes, and Fontes, or Romanescas, Fenarolis, and Sol-Fa-Mi's. Get the book!

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* I don't have the fluency with the Galant that a longer study of the Gjerdingen would provide, but I have had the pleasure of singing and playing Central Javanese music, a repertoire in which schemata -- if I can borrow the term -- are shared by text, vocal melody, instrumental compsition, dance, and puppet movement. Amazing stuff.