For the longest time I've considered myself computer illiterate. Not in the sense that the term has conventionally been used (e.g., for grannies just learning how to use the mouse), but rather in the sense that the term must be used in a computer-saturated society, one in which the bar for literacy has been raised. Maybe it's optimistic to say this, but I think that “computer illiteracy” these days implies ignorance of programming and other higher level tasks, rather than a total unfamiliarity with the operation of a computer.
In an attempt to remedy my own illiteracy I recently started working through a couple of the courses at Codecademy, which is kind of like a Duolingo for computer languages. Specifically I've done about a third of the JavaScript course, and I've used what I've learned so far to build a random twelve-tone row generator. It is of course little more than a number scrambler (the digits 0–11)—and I'm absolutely sure that its code is inelegant, that there are more efficient ways (to which I'm currently ignorant) of coding its task (I'm thinking particularly of my having to input code for each note, which I doubt is really necessary)—but still it's kind of a cool little thing that some may find useful. In the future I hope to code some tools of more uniquely musical utility (maybe to uncover contrapuntal possibilities between pitch-class sets). Anyway, click the button below to generate a random twelve-tone row:
2/16: After sharing this post with the good people at r/MusicTheory, Reddit's music theory community, a couple users suggested some more efficient ways of generating a random twelve-tone row. Check out what they have to say, and thanks to u/kilimanjaroxyz and u/BinaryBullet for their suggestions! The latter also realized his code in relation to another *.js file that allows you to hear your row. Check it out on Plunker.
Here is [my original] code if anyone is interested:
function randomRowGenerator() {
confirm("Please click OK to generate a random twelve-tone row.");
var randomRow = [100,101,102,103,104,105,106,107,108,109,110,111];
for (y = 0; y < 12; y++) {
while(randomRow[y] > 99) {
x = Math.random()
//0//
var noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 0) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x <= 0.083)) {
randomRow[y] = 0
}
//1//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 1) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.083) && (x <= 0.166)) {
randomRow[y] = 1
}
//2//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 2) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.166) && (x <= 0.249)) {
randomRow[y] = 2
}
//3//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 3) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.249) && (x <= 0.332)) {
randomRow[y] = 3
}
//4//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 4) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.332) && (x <= 0.415)) {
randomRow[y] = 4
}
//5//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 5) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.415) && (x <= 0.499)) {
randomRow[y] = 5
}
//6//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 6) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.499) && (x <= 0.582)) {
randomRow[y] = 6
}
//7//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 7) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.582) && (x <= 0.665)) {
randomRow[y] = 7
}
//8//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 8) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.665) && (x <= 0.748)) {
randomRow[y] = 8
}
//9//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 9) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.748) && (x <= 0.831)) {
randomRow[y] = 9
}
//10//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 10) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.831) && (x <= 0.914)) {
randomRow[y] = 10
}
//11//
noteCount = 0
for (i = 0; i < y; i++) {
if (randomRow[i] == 11) {
noteCount = (noteCount + 1)
}
}
if ((noteCount == 0) && (x > 0.914)) {
randomRow[y] = 11
}
}
}
alert("Your random twelve-tone row (in integer notation) is: " + randomRow);
}
Saturday, February 15, 2014
Saturday, February 1, 2014
George Tremblay's “Definitive Cycle”
Recently, on a whim, I checked out George Tremblay's book The Definitive Cycle of the Twelve Tone Row (1974) from the library. If you don't know Tremblay (1911–82), who I only knew by name before reading this book, he was a Canadian composer who studied with Schoenberg after the latter's move to the U.S.[1] In this case the apple didn't fall far from the tree and Wikipedia says that in 1965 Tremblay founded the School for the Discovery and Advancement of New Serial Techniques. Indeed, such a school is perhaps the only place one might find the above text in active circulation.
The Definitive Cycle is a bit quaint, which is part of what attracted me to it in the first place.[2] One thing that dates the book straightaway is the foreword by one “E.H.H.,” which begins: “Between these covers lies the most innovative concept in the theory of dodecaphonic music.” We don't really make claims like that anymore (at least in print). Moreover, the table of contents lists such sections as “The Chorale” and “The Fugue,” which are difficult to imagine as having anything to do with dodecaphonic innovation (one could of course imagine such innovation being applied to these, but if such sections must be included they might be more appropriately placed at a lower position in the argumentative hierarchy).
The “definitive cycle” of the title (both mine and Tremblay's) is “an array of twenty-four sets of twelve rows each” that is generated by two basic algorithms, one which generates the rows within a set and one which generates from these rows the first row of the next set. Though it's problematic to speak of a true starting point or ‘mother’ row in this scheme, Tremblay conceives of the cycle as having been “developed from one row: the chromatic row,” which serves as the first row of the first set.[3]
The second row is derived by applying an algorithm to the first, namely by alternating the pitches of the first row's two hexachords, beginning with H2, such that the following row emerges: <6,0,7,1,8,2 || 9,3,10,4,11,5>. This is a pretty simple procedure, and it seems unlikely that we would have to dig up an obscure text by an obscure composer to see it written about. Nevertheless, the only concept I've come across in my limited exposure to post-tonal theory that resonates somewhat with Tremblay's process is that of the cross-partition.
A cross-partition is defined by Brian Alegant, its original theorizer, as “a two-dimensional configuration of pitch classes whose columns are realized as chords, and whose rows are differentiated from one another by registral, timbral, or other means.”[4] Right away it's clear that aspects of this definition are irrelevant to Tremblay's algorithm, which is abstract and implies nothing about how its input or output rows are realized. Moreover, along those same lines, a cross-partition is a way of deploying a row, not a way of transforming one row into another (though so-called “slot-machine” transformations of a cross-partition are possible). Nevertheless, what does seem relevant is the idea of a one-dimensional row reconceived in two dimensions. As one can see in Alegant's (or Wikipedia's) article there are a limited number of ways to configure a cross-partition (6x2,4x3,3x4,2x6). Of these, the 6x2 configuration best illustrates what Tremblay is up to, particularly as represented in the following matrix (for the sake of formatting, T = 10 and E = 11):
Note that these matrix elements represent order numbers (i.e., positions within the row) of the input row, not pitch classes (though in this case [i.e., the case of Set 1, Row 1] these are the same). Basically, the two hexachords are set up as the partitional harmonic units (in the above order, or one that preserves its adjacencies), and then the output row is generated by tracing the cross-partitional strands left-to-right and top-to-bottom (the directions would change of course if the hexachords were swapped or the vertical order was reversed). This is admittedly a kind of trivial application of the cross-partition concept, but as I've said it's the only post-tonal concept I'm familiar with in terms of which Tremblay's process can be described (their essential point of contact is a shared reliance on the interpolatory reconfiguration of a row).
Anyway, however you want to understand what Tremblay is doing, the way each set of his definitive cycle is spun out is by recursively applying the above algorithm to each new output row, until you end up back where you started. If you do this starting with the ‘ascending’ chromatic row, the following set of twelve rows is what you end up with:
— Set 1
Each set consists of six unique rows and their retrogrades. In Set 1—given that its starting point is the ne plus ultra of chromatic symmetry, the chromatic scale—it shouldn't be surprising that these rows are highly systematic. Particularly cool is Row 4, which demonstrates a triadic progression that completes an aggregate in the most efficient manner possible (i.e., in four chords). Having completed the set—as cross-partitioning Row 12 will simply yield Row 1—the first row of the next set is constructed in terms of the initial pitches of each of Set 1's rows in order (this is the second of the two algorithms I mentioned at the beginning of my post). So Set 2, Row 1 is <0,6,9,4,8,10,11,5,2,7,3,1>. This of course provides the starting point for the spinning out of the other eleven rows of the set, at which point the third set can be constructed, etc. etc. etc. until you have twenty-four sets of twelve rows each.
So what is the advantage or appeal of the definitive cycle in relation to the conventional paradigm of P-I-R-RI relationships? I think Tremblay would say that the cycle's selling point is its systematic unification—according to a pair of recursive principles—of a large variety of rows. Recursive networks such as the definitive cycle (or the circle of fifths for that matter) are useful to the composer because all that is needed to create colorful and coherent music is a mastery of the basic recursive algorithm (e.g., the dominant-tonic relationship in tonal music). If one were to develop through experience a facility in effecting the two basic modulations in Tremblay's system, one could coherently link any of the cycle's 288 rows. By contrast, a conventional twelve-tone matrix, according to the elusive E.H.H., is based upon a set of simple “devices” applied to a single row. He claims that “in [Tremblay's] cycle, the retrograde is created by logic and order rather than as a device” and that it contains “no inversion, no retrograde inversion, and no transposition.”[6] I don't think the standard P-I-R-RI paradigm is as substantially different from Tremblay's cycle as E.H.H. claims (i.e., they're both just row networks based on different principles of transformation), but the latter certainly allows for a much greater deal of pitch variety, which may be attractive to composers.
2/2: Just to clarify, the differences between Tremblay's cycle and a standard twelve-tone matrix are not trivial. The greater pitch variety of the former is mostly a function of its continual transformation of the intervallic content of its rows, whereas a standard matrix preserves its rows' shared intervallic identity (i.e., it makes explicit all the ways in which a certain series of intervals can be expressed). Nevertheless, my point is that I don't buy—as E.H.H. claims—that Tremblay's transformations are distinguished from the P-I-R-RI paradigm by their “logic and order.” I think that any hierarchical privileging of Tremblay's algorithms over the conventional “devices,” or vice versa, is ultimately based on nothing more substantial than “This relationship strikes me as more meaningful than that one.” They're both just transformative approaches to twelve-tone rows. Even if one says “Yeah, but P-I-R-RI preserve intervallic identity, so they're a fundamentally different thing than Tremblay's system,” this argument depends on the assumption that interval content is a strong basis for row identity (which is itself dependent upon the historical hegemony of P-I-R-RI). One could imagine, perhaps, an alternate history in which Schoenberg's big innovation was the definitive cycle, and generations of theorists and composers grew up feeling that chromatic scales and whole-tone scales were closely related much in the way that P0 and I6 of a row seem to be related from our actual perspectives. One counterargument for this dehierarchization is that the familiar twelve-tone operations in fact have a longer history in tonal music, and also that they relate rows in a way that's easier to render audible than the definitive cycle. Still though, I think the preference for one over the other is more a matter of taste than a question of “logic and order.”
[1] Incidentally, a more famous Canadian musician also died in 1982, Glenn Gould.
[2] I have a bit of a fetish for out-of-date books. Whenever I buy collections of poems, myths, etc. I go for older editions because their introductions are usually more entertaining.
[3] I say it's problematic to identify a fundamental row because the cycle is … well, cyclical; if you stick to the algorithms you eventually end up back where you started. The definitive cycle, in other words, could be generated from the first row of any of its twenty-four sets, or even from any of its 288 rows if we conceive of rows themselves as edgeless and cyclical (i.e., as directional series of adjacent pitches that theoretically loop) and of the boundaries between the sets as arbitrary divisions. Thus, to describe (as Tremblay does) “the entire fund of material” in the cycle as deriving from the chromatic row (as an ordered set, which Tremblay seems to imply) is arbitrary, a bit like describing Europe as the West and Asia as the East.
[4] Brian Alegant, “Cross-Partitions as Harmony and Voice Leading in Twelve-Tone Music,” Music Theory Spectrum 23, no. 1 (Spring 2001), 1. Alegant actually credits Donald Martino (“The Source Set and its Aggregate Formations”) with first exploring two-dimensional representations of linear sets.
[5] What I mean is that the color-coating is a bit haphazard and is intended only to facilitate the visual parsing out of the relevant subsets (i.e., one shouldn't assume that everything blue in this article, for instance, is related somehow). Within rows I will sometimes use more colors to avoid confusion (e.g., the fourth row splits into blue-green vs. red-orange to indicate minor vs. major triads in the respective hexachords).
[6] These “devices” are sometimes present incidentally, but not systematically.
The Definitive Cycle is a bit quaint, which is part of what attracted me to it in the first place.[2] One thing that dates the book straightaway is the foreword by one “E.H.H.,” which begins: “Between these covers lies the most innovative concept in the theory of dodecaphonic music.” We don't really make claims like that anymore (at least in print). Moreover, the table of contents lists such sections as “The Chorale” and “The Fugue,” which are difficult to imagine as having anything to do with dodecaphonic innovation (one could of course imagine such innovation being applied to these, but if such sections must be included they might be more appropriately placed at a lower position in the argumentative hierarchy).
The “definitive cycle” of the title (both mine and Tremblay's) is “an array of twenty-four sets of twelve rows each” that is generated by two basic algorithms, one which generates the rows within a set and one which generates from these rows the first row of the next set. Though it's problematic to speak of a true starting point or ‘mother’ row in this scheme, Tremblay conceives of the cycle as having been “developed from one row: the chromatic row,” which serves as the first row of the first set.[3]
(‘Ascending’) Chromatic Row:
<0,1,2,3,4,5 || 6,7,8,9,10,11>
The second row is derived by applying an algorithm to the first, namely by alternating the pitches of the first row's two hexachords, beginning with H2, such that the following row emerges: <6,0,7,1,8,2 || 9,3,10,4,11,5>. This is a pretty simple procedure, and it seems unlikely that we would have to dig up an obscure text by an obscure composer to see it written about. Nevertheless, the only concept I've come across in my limited exposure to post-tonal theory that resonates somewhat with Tremblay's process is that of the cross-partition.
A cross-partition is defined by Brian Alegant, its original theorizer, as “a two-dimensional configuration of pitch classes whose columns are realized as chords, and whose rows are differentiated from one another by registral, timbral, or other means.”[4] Right away it's clear that aspects of this definition are irrelevant to Tremblay's algorithm, which is abstract and implies nothing about how its input or output rows are realized. Moreover, along those same lines, a cross-partition is a way of deploying a row, not a way of transforming one row into another (though so-called “slot-machine” transformations of a cross-partition are possible). Nevertheless, what does seem relevant is the idea of a one-dimensional row reconceived in two dimensions. As one can see in Alegant's (or Wikipedia's) article there are a limited number of ways to configure a cross-partition (6x2,4x3,3x4,2x6). Of these, the 6x2 configuration best illustrates what Tremblay is up to, particularly as represented in the following matrix (for the sake of formatting, T = 10 and E = 11):
6-0
7-1
8-2
9-3
T-4
E-5
7-1
8-2
9-3
T-4
E-5
Note that these matrix elements represent order numbers (i.e., positions within the row) of the input row, not pitch classes (though in this case [i.e., the case of Set 1, Row 1] these are the same). Basically, the two hexachords are set up as the partitional harmonic units (in the above order, or one that preserves its adjacencies), and then the output row is generated by tracing the cross-partitional strands left-to-right and top-to-bottom (the directions would change of course if the hexachords were swapped or the vertical order was reversed). This is admittedly a kind of trivial application of the cross-partition concept, but as I've said it's the only post-tonal concept I'm familiar with in terms of which Tremblay's process can be described (their essential point of contact is a shared reliance on the interpolatory reconfiguration of a row).
Anyway, however you want to understand what Tremblay is doing, the way each set of his definitive cycle is spun out is by recursively applying the above algorithm to each new output row, until you end up back where you started. If you do this starting with the ‘ascending’ chromatic row, the following set of twelve rows is what you end up with:
— Set 1
- 0,1,2,3,4,5 || 6,7,8,9,10,11 (chromatic scale)
- 6,0,7,1,8,2 || 9,3,10,4,11,5 (alternating tritones)
- 9,6,3,0,10,7 || 4,1,11,8,5,2 (discrete tetrachords = fully dim. 7th chords)
- 4,9,1,6,11,3 || 8,0,5,10,2,7 (discrete trichords = maj./min. triads, namely AM–BM–Fm–Gm; also, H2 the same in Sets 9 and 17)
- 8,4,0,9,5,1 || 10,6,2,11,7,3 (discrete trichords = aug. triads)
- 10,8,6,4,2,0 || 11,9,7,5,3,1 (the two whole tone scales; H1=WT-0, H2=WT-1)
- R of 1
- R of 2
- R of 3
- R of 4
- R of 5
- R of 6
Each set consists of six unique rows and their retrogrades. In Set 1—given that its starting point is the ne plus ultra of chromatic symmetry, the chromatic scale—it shouldn't be surprising that these rows are highly systematic. Particularly cool is Row 4, which demonstrates a triadic progression that completes an aggregate in the most efficient manner possible (i.e., in four chords). Having completed the set—as cross-partitioning Row 12 will simply yield Row 1—the first row of the next set is constructed in terms of the initial pitches of each of Set 1's rows in order (this is the second of the two algorithms I mentioned at the beginning of my post). So Set 2, Row 1 is <0,6,9,4,8,10,11,5,2,7,3,1>. This of course provides the starting point for the spinning out of the other eleven rows of the set, at which point the third set can be constructed, etc. etc. etc. until you have twenty-four sets of twelve rows each.
So what is the advantage or appeal of the definitive cycle in relation to the conventional paradigm of P-I-R-RI relationships? I think Tremblay would say that the cycle's selling point is its systematic unification—according to a pair of recursive principles—of a large variety of rows. Recursive networks such as the definitive cycle (or the circle of fifths for that matter) are useful to the composer because all that is needed to create colorful and coherent music is a mastery of the basic recursive algorithm (e.g., the dominant-tonic relationship in tonal music). If one were to develop through experience a facility in effecting the two basic modulations in Tremblay's system, one could coherently link any of the cycle's 288 rows. By contrast, a conventional twelve-tone matrix, according to the elusive E.H.H., is based upon a set of simple “devices” applied to a single row. He claims that “in [Tremblay's] cycle, the retrograde is created by logic and order rather than as a device” and that it contains “no inversion, no retrograde inversion, and no transposition.”[6] I don't think the standard P-I-R-RI paradigm is as substantially different from Tremblay's cycle as E.H.H. claims (i.e., they're both just row networks based on different principles of transformation), but the latter certainly allows for a much greater deal of pitch variety, which may be attractive to composers.
2/2: Just to clarify, the differences between Tremblay's cycle and a standard twelve-tone matrix are not trivial. The greater pitch variety of the former is mostly a function of its continual transformation of the intervallic content of its rows, whereas a standard matrix preserves its rows' shared intervallic identity (i.e., it makes explicit all the ways in which a certain series of intervals can be expressed). Nevertheless, my point is that I don't buy—as E.H.H. claims—that Tremblay's transformations are distinguished from the P-I-R-RI paradigm by their “logic and order.” I think that any hierarchical privileging of Tremblay's algorithms over the conventional “devices,” or vice versa, is ultimately based on nothing more substantial than “This relationship strikes me as more meaningful than that one.” They're both just transformative approaches to twelve-tone rows. Even if one says “Yeah, but P-I-R-RI preserve intervallic identity, so they're a fundamentally different thing than Tremblay's system,” this argument depends on the assumption that interval content is a strong basis for row identity (which is itself dependent upon the historical hegemony of P-I-R-RI). One could imagine, perhaps, an alternate history in which Schoenberg's big innovation was the definitive cycle, and generations of theorists and composers grew up feeling that chromatic scales and whole-tone scales were closely related much in the way that P0 and I6 of a row seem to be related from our actual perspectives. One counterargument for this dehierarchization is that the familiar twelve-tone operations in fact have a longer history in tonal music, and also that they relate rows in a way that's easier to render audible than the definitive cycle. Still though, I think the preference for one over the other is more a matter of taste than a question of “logic and order.”
***
[1] Incidentally, a more famous Canadian musician also died in 1982, Glenn Gould.
[2] I have a bit of a fetish for out-of-date books. Whenever I buy collections of poems, myths, etc. I go for older editions because their introductions are usually more entertaining.
[3] I say it's problematic to identify a fundamental row because the cycle is … well, cyclical; if you stick to the algorithms you eventually end up back where you started. The definitive cycle, in other words, could be generated from the first row of any of its twenty-four sets, or even from any of its 288 rows if we conceive of rows themselves as edgeless and cyclical (i.e., as directional series of adjacent pitches that theoretically loop) and of the boundaries between the sets as arbitrary divisions. Thus, to describe (as Tremblay does) “the entire fund of material” in the cycle as deriving from the chromatic row (as an ordered set, which Tremblay seems to imply) is arbitrary, a bit like describing Europe as the West and Asia as the East.
[4] Brian Alegant, “Cross-Partitions as Harmony and Voice Leading in Twelve-Tone Music,” Music Theory Spectrum 23, no. 1 (Spring 2001), 1. Alegant actually credits Donald Martino (“The Source Set and its Aggregate Formations”) with first exploring two-dimensional representations of linear sets.
[5] What I mean is that the color-coating is a bit haphazard and is intended only to facilitate the visual parsing out of the relevant subsets (i.e., one shouldn't assume that everything blue in this article, for instance, is related somehow). Within rows I will sometimes use more colors to avoid confusion (e.g., the fourth row splits into blue-green vs. red-orange to indicate minor vs. major triads in the respective hexachords).
[6] These “devices” are sometimes present incidentally, but not systematically.
Saturday, January 18, 2014
Analyzing a Katy Perry Melody
So my trip back from visiting with the folks this Christmas was a hell of a Winterreise. Owing to the winter storm, I was—like many people—subject to flight cancellations and layover-sabotaging delays, even finding myself marooned in Washington D.C. for a night (though a woman I overheard in the customer service line had been stranded for days). Anyway, the last leg of my trip was traversed via late-night shuttle bus, which is where I came across the Katy Perry song I'd like to discuss briefly today. In ordinary circumstances I probably wouldn't have taken much notice of this song. I've thought since her first album that Katy Perry is one of the better mainstream pop musicians out there (though I didn't like any of the singles from her 2010 album), but generally speaking I'm not enamored of her music. That said, when “Dark Horse” (2013) came on the radio I was in the midst of a musical crisis.
The first song the station played used what Boston Globe columnist Marc Hirsh has dubbed the “Sensitive Female Chord Progression,” or I–V–vi–IV and its permutations (henceforth, “SFCP”).[1] Now, pretty much everyone knows how ubiquitous this chord progression is in current popular music—and I know it's driven many to their wit's end—but except for brief excursions to the grocery store I'm pretty well insulated from the radio and popular music generally, so I wasn't too irritated. In fact, I took it as an opportunity to reflect on the phenomenon of stock melodic and harmonic patterns generally, from the familiar “doo-wop progression” (cf. “Stand By Me,” “Earth Angel”) to older specimens like the passamezzo antico and the folia. I was amused when the next song also used the SFCP; my musico-historical narrative was literally playing out in front of me. When the song after that also used the SFCP I found myself slightly more irritated than amused, and very quickly it became apparent that the station's playlist was cascading into an avalanche of harmonic sentimentality.
When they trotted out “Dark Horse” I thought it was going to be the coup de grâce. The song opens with the progression G♭M–D♭M–B♭m–A♭M, which—while not the SFCP—is nonetheless a close relative (just exchange B♭m and A♭M), and depends for its effect on the same sort of major-minor ambiguity (or more properly, major-Aeolian ambiguity).
Yet, despite the inherent ambiguity of this progression, the layering of a B♭m ostinato (D♭–[C–]B♭–F) in another voice clearly settles the matter of major and minor in favor of the latter. As such we should interpret the progression as VI–III–i–VII in B♭ minor rather than IV–I–vi–V in D♭ major. This isn't really that interesting, and at this point in the song I still felt like a victim of some musical equivalent of Chinese water torture (each cycle of chords like another drop on the forehead). By the end of the first verse, however, I was sold.
In terms of instrumental texture the verse is very sparse, comprising only a tonic pedal (B♭) in the bass, a rhythmically augmented variant of the B♭m ostinato, and various percussive sound effects (e.g., hand claps). Most of the interest lies in the vocal line, which is more elegant than Top 40 typically delivers. This melody is constructed modularly out of two fundamental phrases, which I have transcribed and labeled as A and B (along with the ostinato in the upper voice):
Furthermore, the following is the structure that Perry erects out of these two modules:[2]
Note that vertical bars indicate barlines and en dashes indicate the continuation of a phrase over the barline (i.e., since A and B are both two measures long, they spill over into the measure after the one in which they are first indicated). “A-2” refers to the second, one-measure motive in A, which in practice is varied slightly when it's stuttered.[3] If we think in two-measure chunks we could reduce the above diagram down to A–A'–B–A', which of course is a tried-and-true design (it's the heart of sonata form). In this formal progression (both here and conventionally) the A material serves a normative function, while the B material serves as a point of contrast or digression. What I'll do now is characterize A and B in turn to demonstrate the ways in which they contrast (and connect).
Okay, looking at A first we can see that it is little more than an expansion of B♭ minor. The vocal line comprises—quite literally in the recording—two distinct motives: (1) an upper pentatonic neighbor on F, the dominant (i.e., SD4–5–4); and (2) an accented passing tone to the mediant (i.e., E♭–D♭), which then ‘steps’ down pentatonically to the tonic B♭. Taken together these motives outline the fifth B♭3–F4, which is harmonized by the ostinato. Overall we could characterize A as both pentatonic and scalar in its orientation (it proceeds completely by scalar step and implies no polyphony).
Turning our attention now to B, which follows after eight bars of A, we observe a striking contrast of melodic character. What was in A a stepwise pentatonic melody with static harmony becomes in B a diatonic compound melody with dynamic harmony.[4] The first measure of B unfolds B♭–A♮ over a sustained F, implying (in this case) a i–V progression from the first beat to the second. In the second measure the lower unfolded line moves E♭–F, suggesting predominant-to-dominant motion (in fact when the upper line in the unfolding is provided explicitly as a vocal harmony in the second verse [~1:36], the harmony is iio6 [if we disregard the bass pedal]). Moreover, in terms of range B complements A by covering the octave's remaining fourth, F4–B♭4. Overall we could characterize B as diatonic and chordal in its orientation (it implies multiple lines moving by diatonic steps). B is, in other words, functionally tonal, proceeding as i–V–iio6–V (mostly in spite of the ostinato and of course the bass pedal).
Thus, the verse melody as a whole could be described as a dialectic between two paradigms of pitch organization, melodically-oriented pentatonicism and harmonically-oriented diatonicism, of which—for mostly formal reasons (A–A'–B–A')—the former registers as normative while the latter registers as deviant. Indeed, in relation to A, the leading tone and harmonic dynamism of B sound strikingly exotic, and I think that this contrast between the phrases is the most affective local manifestation of the “witch-y, spell-y kind of black magic-y” vibe that Perry claims to have been going for.
Yet, in addition to characterizing this contrast, it's also worth taking a look at how the competing paradigms of A and B are mediated. One strategy we have already noted is that of relating the phrases as complementary portions of the octave B♭3–4, particularly as lower fifth and upper fourth. This division of the octave into species of fourth and fifth has precedents in ancient theory and practice, and is a classic basis for structuring a melody.[5] A more subtle connection between the A and B phrases is one of rhythmic symmetry. As one can see in my transcription, the second measure of A and the first measure of B feature the same rhythm in reverse order (4–4–88–4 || 4–88–4–4). Moreover, the first measure of A and the second measure of B both contrast with their subsequent and previous measures respectively by stressing longer durations. This is of course not a literal symmetry, and even the exact symmetry of the ‘inner’ measures is misleading in that the first beat of A-2 is continuously varied throughout the song. Nevertheless, in a broad sense there is a feeling of A as long–short (…88–4 ||) and B as short (|| 4–88…)–long.[6]
The most elegant negotiation between the two phrases is somewhat abstract. In short, Perry connects A and B such that there are smooth ‘modulations’ between their respective pitch paradigms. To observe this, let us consider the progression from A to B and back again. First, A traces a complete B♭ minor pentatonic scale, opening with the upper neighbor figure SD4–5–4 and then descending SD(4–)3–2–1. All of this motion is by scalar step. It's worth noting that a feature of the minor pentatonic scale is that the fourths above SD1 and SD4 are of the same quality, m3 + M2 (e.g., B♭–D♭–E♭ and F–A♭–B♭). This relationship is emphasized somewhat in A in terms of the similar emphasis given to B♭–D♭ and F–A♭. But it plays a more important role in the ‘modulation’ to the functional tonality of B. The lead-in to B is a stuttering of A-2, which consists of the fourth over B♭ stuttered a couple times (E♭–D♭–B♭, or SD3–2–1). The first measure of B—in a manner that is supported by the rhythmic symmetry noted above—picks up this thread of melodic thought by outlining the upper fourth (F–A♭–B♭), but with the substitution of A♮ for A♭. The effect of this is—as we have seen in discussing B as a compound melody—is to obliterate the sense of the pitches as adjacent scale degrees in a pentatonic scheme, and instead cast them as members of a diatonic fourth, from which G♭/♮ is missing (i.e., F–A♮ is now a skip rather than a scalar step). Thus, by way of chromatic inflection the first measure of B reinterprets in a contrasting pitch paradigm the second measure of A. The return to the pentatonicism of A is also effected with some subtlety. Upon hearing the F–A♭–F that opens A, we can't help but hear this as a continuation of the two unfolded lines of B. That is, it registers initially not as SD4–5–4 in B♭ minor pentatonic, but as part of the lines B♭–A♮–A♭ (upper) and F–E♭–F (lower). By the time B♭ is reached at the end of the phrase though, it's clear that we're back in pentatonic territory, and that the F–A♭ dyad was functioning as something of a paradigmatic pivot. Overall, in moving between the phrases Perry highlights intervallic relationships that mean one thing in A and another in B.
There's probably some stuff to be said about the other parts of the song, but the verse melody is where I think the real art is in “Dark Horse.” One broad point that I'd like to bring up relates to the fact that the chorus revisits the SFCP-like chord progression of the introduction (or, considered the other way, the introduction was a foreshadowing of the chorus). While the verse is virtually monophonic (in that the instrumental texture scarcely achieves a more than drone-like significance) and harmonically static (B is harmonically dynamic, but only in brief contrast to the normative and pentatonic A), the chorus is homophonic, with a vocal line supported by explicit chord changes throughout. Thus, the contrast between static pentatonicism and functionally tonal (and dynamic) diatonicism that exists within the verse also exists at the higher hierarchical level of verse and chorus. Within the chorus we may also find this sort of fractalesque self-similarity, in that the progression VI–III–i–VI—as a cousin of the SFCP—is characterized by an ambiguity between functional tonality (when heard in the major) and pentatonic thinking (particularly in the root motion D♭–A♭–B♭).
Ultimately I think that the real appeal of this song is that it actively engages the pentatonic-tonal dialectic that sits at the heart of American popular music, rather than just passively accepting it. In this respect “Dark Horse” has an almost Mozartean quality. Sadly, after this song was over, it was back to the Salieris.
[1] Hirsh justifies the term, which at first glance may seem misogynistic, by claiming that he first noticed it being used in 1998 by “Lilith Fair types baring their souls for all to see” (which I guess could itself be taken as misogynistic, but whatever; it seems to be the only term in circulation).
[2] I'm not really sure who to credit as the “composer” of “Dark Horse” since Wikipedia lists multiple writers, but the impression I get from an MTV article on the song is that Perry and a friend wrote everything that I will be discussing. For this reason I'll just refer to Perry as the composer.
[3] Note that the phrases as transcribed—including A-2—are often varied superficially to suit the text. Also note that in the actual song the dotted half-note F in the A phrase in fact droops down to E♭ within the first measure, but I didn't transcribe this because it seemed to me more an expressive gesture than part of the melodic content in a Platonic sense.
[4] I'm using “diatonic” here to mean the seven-note diatonic scale, not more broadly in the sense of anything that can be derived from that scale.
[5] The Wikipedia article on “octave species” provides a pretty good crash course. I'm no expert on ancient music theory but there is an old tradition of dividing the octave into species of fourth (diatesseron) and fifth (diapente). Indeed, the species of fourth and fifth are the constructive modules in terms of which the eight “ecclesiastical” modes were (originally, I think) conceived, a lower fifth and upper fourth forming an authentic mode and a lower fourth and upper fifth forming a plagal mode. This way of thinking about the octave is reflected in practice as far back as the Seikilos epitaph, which spans an E octave, stressing mostly the upper fifth A–E and cadencing with the lower fourth E–A. A less ancient example may be observed in the opening line of Victoria's motet “O magnum mysterium” (c. 1570): lower fifth (“O magnum mysterium”), upper fourth (“et admirabile sacra[men]–”), lower fifth (“–mentum”).
[6] One could also hear a degree of symmetry within A: [88–4]+[sustain] | [sustain]+[88–4]. The pitches only heighten this hearing in that the 88–4's both emphasize minor thirds over the structural pitches F and B♭. Note that this interpretation hinges on the perception of the quarter E♭'s as equivalent on some level to a sustained pitch.
The first song the station played used what Boston Globe columnist Marc Hirsh has dubbed the “Sensitive Female Chord Progression,” or I–V–vi–IV and its permutations (henceforth, “SFCP”).[1] Now, pretty much everyone knows how ubiquitous this chord progression is in current popular music—and I know it's driven many to their wit's end—but except for brief excursions to the grocery store I'm pretty well insulated from the radio and popular music generally, so I wasn't too irritated. In fact, I took it as an opportunity to reflect on the phenomenon of stock melodic and harmonic patterns generally, from the familiar “doo-wop progression” (cf. “Stand By Me,” “Earth Angel”) to older specimens like the passamezzo antico and the folia. I was amused when the next song also used the SFCP; my musico-historical narrative was literally playing out in front of me. When the song after that also used the SFCP I found myself slightly more irritated than amused, and very quickly it became apparent that the station's playlist was cascading into an avalanche of harmonic sentimentality.
When they trotted out “Dark Horse” I thought it was going to be the coup de grâce. The song opens with the progression G♭M–D♭M–B♭m–A♭M, which—while not the SFCP—is nonetheless a close relative (just exchange B♭m and A♭M), and depends for its effect on the same sort of major-minor ambiguity (or more properly, major-Aeolian ambiguity).
Yet, despite the inherent ambiguity of this progression, the layering of a B♭m ostinato (D♭–[C–]B♭–F) in another voice clearly settles the matter of major and minor in favor of the latter. As such we should interpret the progression as VI–III–i–VII in B♭ minor rather than IV–I–vi–V in D♭ major. This isn't really that interesting, and at this point in the song I still felt like a victim of some musical equivalent of Chinese water torture (each cycle of chords like another drop on the forehead). By the end of the first verse, however, I was sold.
In terms of instrumental texture the verse is very sparse, comprising only a tonic pedal (B♭) in the bass, a rhythmically augmented variant of the B♭m ostinato, and various percussive sound effects (e.g., hand claps). Most of the interest lies in the vocal line, which is more elegant than Top 40 typically delivers. This melody is constructed modularly out of two fundamental phrases, which I have transcribed and labeled as A and B (along with the ostinato in the upper voice):
 |
| Katy Perry feat. Juicy J, “Dark Horse,” verse phrases. |
Furthermore, the following is the structure that Perry erects out of these two modules:[2]
|| A | – | A | – | A | – | A-2 | A-2 | B | – | B | – | A | – | A-2 | A-2' ||
Note that vertical bars indicate barlines and en dashes indicate the continuation of a phrase over the barline (i.e., since A and B are both two measures long, they spill over into the measure after the one in which they are first indicated). “A-2” refers to the second, one-measure motive in A, which in practice is varied slightly when it's stuttered.[3] If we think in two-measure chunks we could reduce the above diagram down to A–A'–B–A', which of course is a tried-and-true design (it's the heart of sonata form). In this formal progression (both here and conventionally) the A material serves a normative function, while the B material serves as a point of contrast or digression. What I'll do now is characterize A and B in turn to demonstrate the ways in which they contrast (and connect).
Okay, looking at A first we can see that it is little more than an expansion of B♭ minor. The vocal line comprises—quite literally in the recording—two distinct motives: (1) an upper pentatonic neighbor on F, the dominant (i.e., SD4–5–4); and (2) an accented passing tone to the mediant (i.e., E♭–D♭), which then ‘steps’ down pentatonically to the tonic B♭. Taken together these motives outline the fifth B♭3–F4, which is harmonized by the ostinato. Overall we could characterize A as both pentatonic and scalar in its orientation (it proceeds completely by scalar step and implies no polyphony).
Turning our attention now to B, which follows after eight bars of A, we observe a striking contrast of melodic character. What was in A a stepwise pentatonic melody with static harmony becomes in B a diatonic compound melody with dynamic harmony.[4] The first measure of B unfolds B♭–A♮ over a sustained F, implying (in this case) a i–V progression from the first beat to the second. In the second measure the lower unfolded line moves E♭–F, suggesting predominant-to-dominant motion (in fact when the upper line in the unfolding is provided explicitly as a vocal harmony in the second verse [~1:36], the harmony is iio6 [if we disregard the bass pedal]). Moreover, in terms of range B complements A by covering the octave's remaining fourth, F4–B♭4. Overall we could characterize B as diatonic and chordal in its orientation (it implies multiple lines moving by diatonic steps). B is, in other words, functionally tonal, proceeding as i–V–iio6–V (mostly in spite of the ostinato and of course the bass pedal).
Thus, the verse melody as a whole could be described as a dialectic between two paradigms of pitch organization, melodically-oriented pentatonicism and harmonically-oriented diatonicism, of which—for mostly formal reasons (A–A'–B–A')—the former registers as normative while the latter registers as deviant. Indeed, in relation to A, the leading tone and harmonic dynamism of B sound strikingly exotic, and I think that this contrast between the phrases is the most affective local manifestation of the “witch-y, spell-y kind of black magic-y” vibe that Perry claims to have been going for.
Yet, in addition to characterizing this contrast, it's also worth taking a look at how the competing paradigms of A and B are mediated. One strategy we have already noted is that of relating the phrases as complementary portions of the octave B♭3–4, particularly as lower fifth and upper fourth. This division of the octave into species of fourth and fifth has precedents in ancient theory and practice, and is a classic basis for structuring a melody.[5] A more subtle connection between the A and B phrases is one of rhythmic symmetry. As one can see in my transcription, the second measure of A and the first measure of B feature the same rhythm in reverse order (4–4–88–4 || 4–88–4–4). Moreover, the first measure of A and the second measure of B both contrast with their subsequent and previous measures respectively by stressing longer durations. This is of course not a literal symmetry, and even the exact symmetry of the ‘inner’ measures is misleading in that the first beat of A-2 is continuously varied throughout the song. Nevertheless, in a broad sense there is a feeling of A as long–short (…88–4 ||) and B as short (|| 4–88…)–long.[6]
The most elegant negotiation between the two phrases is somewhat abstract. In short, Perry connects A and B such that there are smooth ‘modulations’ between their respective pitch paradigms. To observe this, let us consider the progression from A to B and back again. First, A traces a complete B♭ minor pentatonic scale, opening with the upper neighbor figure SD4–5–4 and then descending SD(4–)3–2–1. All of this motion is by scalar step. It's worth noting that a feature of the minor pentatonic scale is that the fourths above SD1 and SD4 are of the same quality, m3 + M2 (e.g., B♭–D♭–E♭ and F–A♭–B♭). This relationship is emphasized somewhat in A in terms of the similar emphasis given to B♭–D♭ and F–A♭. But it plays a more important role in the ‘modulation’ to the functional tonality of B. The lead-in to B is a stuttering of A-2, which consists of the fourth over B♭ stuttered a couple times (E♭–D♭–B♭, or SD3–2–1). The first measure of B—in a manner that is supported by the rhythmic symmetry noted above—picks up this thread of melodic thought by outlining the upper fourth (F–A♭–B♭), but with the substitution of A♮ for A♭. The effect of this is—as we have seen in discussing B as a compound melody—is to obliterate the sense of the pitches as adjacent scale degrees in a pentatonic scheme, and instead cast them as members of a diatonic fourth, from which G♭/♮ is missing (i.e., F–A♮ is now a skip rather than a scalar step). Thus, by way of chromatic inflection the first measure of B reinterprets in a contrasting pitch paradigm the second measure of A. The return to the pentatonicism of A is also effected with some subtlety. Upon hearing the F–A♭–F that opens A, we can't help but hear this as a continuation of the two unfolded lines of B. That is, it registers initially not as SD4–5–4 in B♭ minor pentatonic, but as part of the lines B♭–A♮–A♭ (upper) and F–E♭–F (lower). By the time B♭ is reached at the end of the phrase though, it's clear that we're back in pentatonic territory, and that the F–A♭ dyad was functioning as something of a paradigmatic pivot. Overall, in moving between the phrases Perry highlights intervallic relationships that mean one thing in A and another in B.
There's probably some stuff to be said about the other parts of the song, but the verse melody is where I think the real art is in “Dark Horse.” One broad point that I'd like to bring up relates to the fact that the chorus revisits the SFCP-like chord progression of the introduction (or, considered the other way, the introduction was a foreshadowing of the chorus). While the verse is virtually monophonic (in that the instrumental texture scarcely achieves a more than drone-like significance) and harmonically static (B is harmonically dynamic, but only in brief contrast to the normative and pentatonic A), the chorus is homophonic, with a vocal line supported by explicit chord changes throughout. Thus, the contrast between static pentatonicism and functionally tonal (and dynamic) diatonicism that exists within the verse also exists at the higher hierarchical level of verse and chorus. Within the chorus we may also find this sort of fractalesque self-similarity, in that the progression VI–III–i–VI—as a cousin of the SFCP—is characterized by an ambiguity between functional tonality (when heard in the major) and pentatonic thinking (particularly in the root motion D♭–A♭–B♭).
Ultimately I think that the real appeal of this song is that it actively engages the pentatonic-tonal dialectic that sits at the heart of American popular music, rather than just passively accepting it. In this respect “Dark Horse” has an almost Mozartean quality. Sadly, after this song was over, it was back to the Salieris.
***
[1] Hirsh justifies the term, which at first glance may seem misogynistic, by claiming that he first noticed it being used in 1998 by “Lilith Fair types baring their souls for all to see” (which I guess could itself be taken as misogynistic, but whatever; it seems to be the only term in circulation).
[2] I'm not really sure who to credit as the “composer” of “Dark Horse” since Wikipedia lists multiple writers, but the impression I get from an MTV article on the song is that Perry and a friend wrote everything that I will be discussing. For this reason I'll just refer to Perry as the composer.
[3] Note that the phrases as transcribed—including A-2—are often varied superficially to suit the text. Also note that in the actual song the dotted half-note F in the A phrase in fact droops down to E♭ within the first measure, but I didn't transcribe this because it seemed to me more an expressive gesture than part of the melodic content in a Platonic sense.
[4] I'm using “diatonic” here to mean the seven-note diatonic scale, not more broadly in the sense of anything that can be derived from that scale.
[5] The Wikipedia article on “octave species” provides a pretty good crash course. I'm no expert on ancient music theory but there is an old tradition of dividing the octave into species of fourth (diatesseron) and fifth (diapente). Indeed, the species of fourth and fifth are the constructive modules in terms of which the eight “ecclesiastical” modes were (originally, I think) conceived, a lower fifth and upper fourth forming an authentic mode and a lower fourth and upper fifth forming a plagal mode. This way of thinking about the octave is reflected in practice as far back as the Seikilos epitaph, which spans an E octave, stressing mostly the upper fifth A–E and cadencing with the lower fourth E–A. A less ancient example may be observed in the opening line of Victoria's motet “O magnum mysterium” (c. 1570): lower fifth (“O magnum mysterium”), upper fourth (“et admirabile sacra[men]–”), lower fifth (“–mentum”).
[6] One could also hear a degree of symmetry within A: [88–4]+[sustain] | [sustain]+[88–4]. The pitches only heighten this hearing in that the 88–4's both emphasize minor thirds over the structural pitches F and B♭. Note that this interpretation hinges on the perception of the quarter E♭'s as equivalent on some level to a sustained pitch.
Tuesday, December 24, 2013
Urvergessen?
Hello. Instead of greeting you with the “so I made a blog” spiel that has become a convention of the genre, I'll clarify the title Urvergessen for any non-Wagnerians out there. Urvergessen is a German neologism coined by Richard Wagner in Act III of Tristan und Isolde (1859). The meaning of the word is somewhat enigmatic, being as it is a combination of the prefix Ur-—which means “ancient,” “primal,” “primeval,” “original” (as in Urtext), etc.—and the verb vergessen—which means “to forget” or “unlearn.” Eric Chafe, in The Tragic and the Ecstatic, translates it as “primal forgetfulness” (229), but there are as many translations as there are translators.
In any case, Tristan sings this peculiar word in the course of his dialogue with Kurvenal in Scene 1 of Act III.[1] Having been mortally wounded at the end of the previous act, Tristan is awoken by the shepherd's “alte Weise” in Kareol and is greeted by Kurvenal's optimistic forecast of their future there. Yet Kurvenal's words fall on deaf ears, as Tristan can only think of the hereafter. The latter launches into a quasi-soliloquy that describes what sounds to modern ears like a near-death experience: “Ich war, wo ich von je gewesen, wohin auf je ich geh': im weiten Reich der Weltennacht” (“I was where I had been before I was and where I am destined to go, in the wide realm of the night of the world”).[2] Paradoxically, all one knows in this Weltennacht is “göttlich ew'ges Urvergessen” (“primal forgetfulness, divine and eternal”), a kind of not-knowing.
Wagner's fascination with this sort of wisdom in un-wisdom stemmed of course from his exposure to Schopenhauer, who believed that the essence of reality (the Will) is more accessible via the routes of un-reason (like music) than those of reason. In death, Schopenhauer thought, the Will's veil is pulled back and man is liberated from his corporal limitations. Thus we can understand the ambivalence inherent in Tristan's “Todeswonne-Grauen” (“terror of death's bliss”), an ambivalence rooted in the conflict between the human instinct for survival and the spiritual desire for meta-human enlightenment. More than anywhere else in the libretto, it is in this mystical, near-death reminiscence that the opera's philosophical foundation comes into focus.
As one might expect, the music that sets and accompanies these lines serves to highlight their dramatic importance. Not long into his solo, Tristan reaches the key of F minor, which has been the anchor point of the act so far (Kurvenal's optimism has been marked by major key excursions, particularly to F major). Yet by “Ich war, wo ich von je gewesen…” (see above), which is sung to a melody associated with the Weltennacht, Tristan has moved to A♭ minor. Over a dominant pedal he sings “göttlich ew'ges,” paraphrasing the Desire motive à la the Act III prelude.[3] Yet Tristan's climactic “Urvergessen!” (at 228/4/4 in the Schirmer vocal score) provides a jolt, both textually and musically:
Chafe hears in these measures “a paradoxical statement matched by perhaps the most mysterious enharmonic relationship in the opera” (318). The latter refers to his analysis of the unexpected D major as an enharmonic E♭♭ major (245). I'm more inclined to take the D major at face value and instead analyze 228/4/3's D♭ as an enharmonic C♯ (i.e., as some bastardized augmented-sixth chord leading to the dominant of G).[4] In some sense this interpretation can be reconciled with the Desire music that follows, which half-cadences in A, C, and E via the Tristan chord, which is itself a kind of bastardized French augmented-sixth. Taken together, these four tonics—A, C, E, and G—constitute what Robert Bailey refers to as the A/C “double-tonic complex,” or the grouping of two tonalities a minor third apart into a kind of meta-tonality, such that “either [tonic] can serve as the local representative of the tonic complex” (121–22).[5] Though he identifies A minor-seventh as the “harmonic embodiment" of the A/C complex (given its superimposition of A minor and C major), in fact the keys of A and C are of indeterminate quality in Bailey's scheme (“we are now dealing with the ‘chromatic’ mode of A and the ‘chromatic’ mode of C”). He identifies the A/C complex as an important factor in the large-scale organization of the Tristan “Prelude" and Act I, but is it also a factor here? I dunno; but however you want to analyze it, what one expects on the downbeat of 228/4/4 is E♭ major (or E♭ dominant-seventh), not D major.
Yet, despite the resonance of this foreign harmony with the bizarre notion of an Urvergessen, in some sense it is the melodic character of 228/4/4–5 that most reflects the text. There is really nothing more primordial sounding in a tonal context than the “arpeggiation" of an open fifth. Indeed, with its dotted rhythms this passage calls to mind the creatio ex nihilo of Beethoven's Ninth. The character of this “Urvergessen!” motive is mildly foreshadowed in the earlier line “im weiten Reich der Weltennacht,” (from 228/3/1) particularly in its final A♭4–D♭5–D♭4, but the former is much more austere, owing to its greater directness (i.e., fourth–fifth rather than fourth–octave). Though bare octaves are in a sense more “primal" than bare fifths, they don't really register as such because of the principle of octave equivalence, according to which the octave is not an interval at all (at least in pitch-class space). By contrast, the bare fifth—in a tonal context—implies a reduction of the triad to its skeleton, to its primary orienting interval. This effect is only heightened by Tristan's mature Wagnerian harmony, in terms of which an open fifth implies a stripping away of not only the third, but possibly also the seventh and the ninth.
There is certainly more to be said about this wonderful moment in what is probably my favorite opera, but for now the above will have to suffice. In summary, the shock that comes with Tristan's “Urvergessen!” is threefold: the D-major triad marks a disruption of the harmonic flow; Tristan's traversal of a fifth-split octave marks a stark departure from the default melodic idiom; and the word Urvergessen itself—in its novelty and paradoxical usage—marks a break from rational, human thought. Through this truly musico-logical rupture, Wagner allows us a glimpse of the Weltennacht, where the shackles of body and mind are dissolved in the Will.
[1] This dialogue parallels that of Brangäne and Isolde in Act I, Scene 3.
[2] My German is very bad. This translation is taken from RWagner.net, though I can't trace its provenance any further than that.
[3] The Desire motive is the one that opens the entire opera (the rising chromatic tetrachord G♯–B, with its characteristic rhythm). The Desire music, by contrast, is the first seventeen measures of the opera.
[4] … and by extension I would analyze the C♭ as a B♮ and possibly the F as an E♯ (though maybe that's a little pedantic).
[5] “An Analytical Study of the Sketches and Drafts," from Bailey's 1985 edition of the Prelude and Transfiguration from Tristan und Isolde.
In any case, Tristan sings this peculiar word in the course of his dialogue with Kurvenal in Scene 1 of Act III.[1] Having been mortally wounded at the end of the previous act, Tristan is awoken by the shepherd's “alte Weise” in Kareol and is greeted by Kurvenal's optimistic forecast of their future there. Yet Kurvenal's words fall on deaf ears, as Tristan can only think of the hereafter. The latter launches into a quasi-soliloquy that describes what sounds to modern ears like a near-death experience: “Ich war, wo ich von je gewesen, wohin auf je ich geh': im weiten Reich der Weltennacht” (“I was where I had been before I was and where I am destined to go, in the wide realm of the night of the world”).[2] Paradoxically, all one knows in this Weltennacht is “göttlich ew'ges Urvergessen” (“primal forgetfulness, divine and eternal”), a kind of not-knowing.
Wagner's fascination with this sort of wisdom in un-wisdom stemmed of course from his exposure to Schopenhauer, who believed that the essence of reality (the Will) is more accessible via the routes of un-reason (like music) than those of reason. In death, Schopenhauer thought, the Will's veil is pulled back and man is liberated from his corporal limitations. Thus we can understand the ambivalence inherent in Tristan's “Todeswonne-Grauen” (“terror of death's bliss”), an ambivalence rooted in the conflict between the human instinct for survival and the spiritual desire for meta-human enlightenment. More than anywhere else in the libretto, it is in this mystical, near-death reminiscence that the opera's philosophical foundation comes into focus.
As one might expect, the music that sets and accompanies these lines serves to highlight their dramatic importance. Not long into his solo, Tristan reaches the key of F minor, which has been the anchor point of the act so far (Kurvenal's optimism has been marked by major key excursions, particularly to F major). Yet by “Ich war, wo ich von je gewesen…” (see above), which is sung to a melody associated with the Weltennacht, Tristan has moved to A♭ minor. Over a dominant pedal he sings “göttlich ew'ges,” paraphrasing the Desire motive à la the Act III prelude.[3] Yet Tristan's climactic “Urvergessen!” (at 228/4/4 in the Schirmer vocal score) provides a jolt, both textually and musically:
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| Richard Wagner, Tristan und Isolde, Act III, Scene 1, 228/4/1–5. |
(~0:20:45)
Chafe hears in these measures “a paradoxical statement matched by perhaps the most mysterious enharmonic relationship in the opera” (318). The latter refers to his analysis of the unexpected D major as an enharmonic E♭♭ major (245). I'm more inclined to take the D major at face value and instead analyze 228/4/3's D♭ as an enharmonic C♯ (i.e., as some bastardized augmented-sixth chord leading to the dominant of G).[4] In some sense this interpretation can be reconciled with the Desire music that follows, which half-cadences in A, C, and E via the Tristan chord, which is itself a kind of bastardized French augmented-sixth. Taken together, these four tonics—A, C, E, and G—constitute what Robert Bailey refers to as the A/C “double-tonic complex,” or the grouping of two tonalities a minor third apart into a kind of meta-tonality, such that “either [tonic] can serve as the local representative of the tonic complex” (121–22).[5] Though he identifies A minor-seventh as the “harmonic embodiment" of the A/C complex (given its superimposition of A minor and C major), in fact the keys of A and C are of indeterminate quality in Bailey's scheme (“we are now dealing with the ‘chromatic’ mode of A and the ‘chromatic’ mode of C”). He identifies the A/C complex as an important factor in the large-scale organization of the Tristan “Prelude" and Act I, but is it also a factor here? I dunno; but however you want to analyze it, what one expects on the downbeat of 228/4/4 is E♭ major (or E♭ dominant-seventh), not D major.
Yet, despite the resonance of this foreign harmony with the bizarre notion of an Urvergessen, in some sense it is the melodic character of 228/4/4–5 that most reflects the text. There is really nothing more primordial sounding in a tonal context than the “arpeggiation" of an open fifth. Indeed, with its dotted rhythms this passage calls to mind the creatio ex nihilo of Beethoven's Ninth. The character of this “Urvergessen!” motive is mildly foreshadowed in the earlier line “im weiten Reich der Weltennacht,” (from 228/3/1) particularly in its final A♭4–D♭5–D♭4, but the former is much more austere, owing to its greater directness (i.e., fourth–fifth rather than fourth–octave). Though bare octaves are in a sense more “primal" than bare fifths, they don't really register as such because of the principle of octave equivalence, according to which the octave is not an interval at all (at least in pitch-class space). By contrast, the bare fifth—in a tonal context—implies a reduction of the triad to its skeleton, to its primary orienting interval. This effect is only heightened by Tristan's mature Wagnerian harmony, in terms of which an open fifth implies a stripping away of not only the third, but possibly also the seventh and the ninth.
There is certainly more to be said about this wonderful moment in what is probably my favorite opera, but for now the above will have to suffice. In summary, the shock that comes with Tristan's “Urvergessen!” is threefold: the D-major triad marks a disruption of the harmonic flow; Tristan's traversal of a fifth-split octave marks a stark departure from the default melodic idiom; and the word Urvergessen itself—in its novelty and paradoxical usage—marks a break from rational, human thought. Through this truly musico-logical rupture, Wagner allows us a glimpse of the Weltennacht, where the shackles of body and mind are dissolved in the Will.
Merry Christmas.
[1] This dialogue parallels that of Brangäne and Isolde in Act I, Scene 3.
[2] My German is very bad. This translation is taken from RWagner.net, though I can't trace its provenance any further than that.
[3] The Desire motive is the one that opens the entire opera (the rising chromatic tetrachord G♯–B, with its characteristic rhythm). The Desire music, by contrast, is the first seventeen measures of the opera.
[4] … and by extension I would analyze the C♭ as a B♮ and possibly the F as an E♯ (though maybe that's a little pedantic).
[5] “An Analytical Study of the Sketches and Drafts," from Bailey's 1985 edition of the Prelude and Transfiguration from Tristan und Isolde.
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