I love to cook. My favorite part is chopping vegetables and inhaling their aroma as they sauté on the stove.
When I was younger, and when I want to try something new, I would follow recipes.
Often, though, I simply mix together and season what I have on hand.
I can do this because I’ve been cooking for more than a decade. So I know—
What the various ingredients taste like.
How to cook them using different methods.
How their flavors combine together.
Now I’m no expert chef or even some Andrew Rea-level home chef (though I’ll gladly binge with Babish any day).
But I have developed a baseline level of discernment: the capacity to judge well in the absence of a recipe, formula, or rubric.
Developing discernment is one of the highest aspirations for chefs.
Discernment liberates your imagination. It helps you know in your gut what will be the effect of your instinctive actions. It frees you to create in moment and instills a quiet, playful confidence.
For those same reasons, it’s also one of the highest aspirations for composers.
But composers often have to develop this discernment despite the theory and composition training they’ve received. Traditional composition pedagogy is filled with superstitions (see my mentor David Rakowski’s catalog of buttstix).
Imagine, if when you were learning how to cook, you had peers and mentors insisting on things like:
“Your recipe can’t be any good because it has tomatoes in it. Tomatoes are so cliché.”
“Your recipe is too similar to others to be any good.”
“You’re not a real chef until you put your own spin on broiling.”
“Your food doesn’t count because you made it in your home for yourself rather than at a fancy restaurant for paying customers.”
Such superstitions about cooking ingredients and methods rightly seem stupid.
Superstitions are the opposite of discernment.
But in music, suckers fall for that drivel all. the. time.
I would know. As a composer, I fell hard for it for almost a decade.
This is why I created the Wizarding School for Composers—to help other composers and aspiring composers develop real discernment.
With that discernment, my students work with greater fluency and joy all while having greater clarity on what actually moves the needle in making their music vivid, sophisticated, and magical.
As composers, we all know that ideas, technique, and process are inseparable:
Ideas are the specific musical gestures we imagine.
Technique is what we have internalized—physically, aurally, and theoretically—about music in general.
Process is how we use that technique to bring our ideas to life.
When these three align, composing is a joy.
When they’re not, it sucks. And, stuck, you struggle to string one note after the last.
That “what comes next?” frustration is the worst.
It makes you feel stupid and stressed.
You begin to think that you’ve forgotten how to compose—and, sometimes, wonder if you ever knew how to compose to begin with.
There are many ways out of this writer’s block, but which exit strategy to choose depends on which creative ditch—or, in other words, which maladaptive creative process—you’ve fallen into.
One such maladaptive strategy is the “right note” syndrome.
It happens whenever there’s a gap between what you hear in your head and what you comprehend about it.
Because of that gap, you can begin to obsess over a particular note, chord, or rhythm. You will play or listen to it over and over again, trying but never able to get it “right.”
This process is maladaptive because it doubles down on the idea/technique/process imbalance rather than relieving it.
The basic cause of “right note syndrome” is that you are applying your technique too narrowly.
The most important unit of music is the phrase, not any note-level event. When you fixate on details, you lose sight of both the technical and artistic contexts that could validate your choices.
The cure is, first, to refocus your attention on the phrase itself—not its details:
What is this phrase doing?
What is its mood?
How does the detail in question fit into the bigger picture of this phrase? Of the larger phrase group?
These questions will naturally inspire others about your artistic inspiration, too:
What is this phrase expressing?
What about that feeling, image, or idea must the music capture in this phrase? What can be given to a different phrase?
How does this phrase fit into the bigger picture of your influences and ideas?
Often, these questions are sufficient to get you unstuck.
Tonality is a musicological debate about style disguised as a theoretical debate about pitch organization.
Whether it's Schenker's arrogant, narrow nationalism or Tymoczko's generous, imaginative catholicism, the debate around what defines “tonality” is, at its core, a question of repertoire.
No one would argue that the music of Bach, Beethoven, or Brahms is not tonal. But what about William Byrd? Or Bull? Or, to go the other direction, Barber? Or Britten? To say nothing of Charlie Byrd or the Beatles?
Whether the music of these latter figures is tonal depends on who you ask. But whether it exhibits pitch organization is indisputable.
Hence, tonality is fundamentally a question about style, not pitch organization.
Style is a red herring for composers
Learning to distinguish “tonal” from “atonal,” “post-tonal,” “pre-tonal,” or “extended tonal” music carries about the same relevance as distinguishing between sub-genres of death metal. It’s not useless—but it doesn't describe really how the music works. It mostly just identifies its stylistic markers.
In other words, “tonality” is an elaborately justified label.
For composers who want to know how music works, such stylistic labels are a red herring. Style can tell you what combination of features will produce a particular “sound,” but they don’t actually show you how it works. As Charles Ives quipped, “What has sound got to do with music?”
Milton Babbitt affirmed Ives’s quip when he asserted, “Nothing gets old faster than a new sound.”
Lest you think this bias against “sound” is some avant-garde fetish: First, remember how much avant-garde composers focused on sonic innovation. Second, put Babbitt’s words in the mouth of any pop music agent or producer, and you’ll notice that they fit right at home there, too.
Like cars and smartphones, the value of unique “sounds” quickly depreciates.
Style tells you little about musical excellence. Instead, it is a proxy for cultural power and relevance. Again, this is not a useless consideration—but it is, at best, tangential to the question of pitch organization.
Musicians can organize pitch in a lot of ways
In truth, “tonality” comprises a detailed collection of pitch strategies that musicians have used in various combinations and emphases. Many of these strategies carry over into music that exists at the edges or beyond the boundaries of what scholars consider “tonal.”
Among other concepts and approaches, they include assumptions about
octave equivalence
tuning and enharmonic equivalence
structural hierarchies
distinctions between consonance and dissonance
the qualities, spellings, and inversions of different intervals and chords
the functional equivalence of chord inversions
harmonic consistency
harmonic syntax via scale-degree function or hypermetrical placement
harmonic and voice-leading schemata
the usage of different scales
the prevalence of stepwise motion generally in melodic lines and strongly in harmonic voice leading
melodic shape via step progressions, rhythmic permutations, or hypermetrical placement
melodic structure via rhythmic motives, pitch motives, and pitch contours
the harmonic implications of all melodic lines
the functional distinction between the bass line and upper voices
degrees of formal articulation indicated by coordinated of harmonic and melodic gestures (i.e., cadences and pitch centricity)
Despite being almost 20 items long, this list is hardly an exhaustive catalog of pitch organization concepts and approaches. What distinguishes different styles is how they remix these principles.
Some pieces use many of these strategies. Others use only a subset of them. Still other pieces use different pitch strategies entirely.
Though many pieces contain all of these strategies, no single piece can be said to exemplify all of them.
Focus on the effect and interaction of choices, not their labels: What does Debussy’s music do to create its unique states of being?
Focus on the effect, not the label
Furthermore, none of these strategies or their applications is intrinsically “excellent” or “superior.” But noticing them allows musicians to hone their discernment about how specific pieces create the musical effects they do.
For instance:
How can Debussy get away with writing parallel fifths?
How does Beethoven write an hour-long symphony that isn’t boring?
How does Rachel Portman write an hour-long soundtrack that isn’t boring?
Why does Byrd’s counterpoint feel different than Bach’s and different again from Bartók’s?
How does Mahler give you goosebumps?
How does John Coltrane create the luminous sheen in his solos?
These questions do tell you something about style—but when you go beyond merely labeling these features to describing their relationships to key moments in a specific piece, that’s when you really start to understand how music works.
That’s when you can discern not just why Debussy’s style is different than Clara Schumann’s (for instance), but what the music is doing to create its unique states of being.
Thus, the most pertinent analytical question for composers is not “What style is this piece and why?” or even “What specific choices did x composer make?” but “What is the effect of these choices?”
Last week, I posted some notes about the fourth movement of Ligeti’s Chamber Concerto. As I thought further about what I wanted to do musically in my Hub New Music piece, I thought of John Adams’s Phrygian Gates. What I hear common to both pieces is a harmonic wash—that is, both pieces saturate entire spans of a register using collections of seconds.
Adams’s piece interests me because his harmonic wash is modal rather than chromatic. Further, it (often) has a discernible pulse and is constructed from repeating, distinct melodic cells. (In contrast, Ligeti’s piece generally features rhythms that are presto possible and pitch sequences that are deliberately patternless, within each passage’s given constraints.)
So before I go further, here is Adams’s piece, for your listening pleasure:
General Observations
Because my analytical purpose is to gather ideas for my own composition, I will not examine the entire piece in depth. These, however, are some parameters worth noting:
Most of piece consists of steady eighth- and 16th-note surface rhythms that often create a sense of pulse but never of beat. Some passages feature a quarter-note pulse (e.g., m. 554 ff.). Adams also composes the central section, “A Series of Weights and Measures” (m. 640-808), using tied whole notes of notably uneven durations.
On a local level, Adams creates consistency be establishing “interference patterns” between the right and left hand. For instance, in bar 8, he juxtaposes a 3-note cell against a 2-note one. (The periodic unisons these particular cells create is not a bug; it creates a shimmer whose cause is just beyond the reach of most careful listeners.)
These cells tend to be little upward gestures. Or least, they begin with an upward gesture before a downward one (cf. bar 201 ff.). Thus, the contrast at bar 255 ff., with its clear downward microgestures, is notable (cf. bars 518 ff. and 954 ff.).
These cells often consist of one note per hand, but regularly contain as many as four. Generally, these chords remain static for the duration of the phrase, though there is at least one passage (bar 159 ff.) in which the pianist must undulate between dyads.
Adams beams each pattern separately, making it easy to divide the piece into separate phrases. In each phrase, Adams varies the length and pitch content of its constituent cells. Because individuals phrases often maintain a cell from their preceding phrase, because large sections of the piece maintain a steady pulse, and because Adams further instructs the performer that “no single pattern [should] ever dominate[ ] another,” it can be difficult to tell when one phrase ends and another begins. Thus, this separation into “phrases” by beaming is often more a courtesy to the performer than a distinction Adams intends the listener to hear.
Sometimes Adams introduces both cells at the start of the phrase (see observation no. 1 above). Other times, he elides the start of one cell with the ending of a previous cell, for instance, in bar 19:
From the start, Adams adds disruptive elements to most phrases. For instance, in the phrase that begins in bar 9, Adams disrupts the right hand’s 3-note cells with 2-note interjections (bracketed in red).
Sometimes Adams inserts these interjections between cells, as in the example above. Other times, they replace notes in existing cells. For instance, in bar 37, Adams sets up a new pattern, but in bar 37, he replaces the last note of the right hand’s cell with a foreign pitch (bracketed):
These interruptions and replacements have several effects:
By changing the alignment of a phrase’s cells, they change the resulting interference pattern.
They create notable landmarks, (1) because they occur only a handful of times, (2) because they happen at unpredictable intervals, and (3) because they consist of pitches that don’t belong to the prevailing pattern.
Adams, like Ligeti, uses voice leading to shape individual phrases into larger trajectories. For instance, the most formally significant melodic motion in bars 1-57 is the slow, stepwise descent of E4 to A3.
Like Ligeti, Adams, also sometimes uses gestures to create trajectories. For instance, in bars 85-113, Adams gradually adds pitches above the interrupting E5, creating an “expanding-density gesture.” After B5 comes in bar 96, the addition of a pitch in the subsequent phrase’s interrupting element is expected, though not necessarily the specific pitch and timing (E6 in bar 104).
A Lengthy Digression on Adams’s Use of Modes
In his program notes, Adams explains that “‘Gates,’ a term borrowed from electronics, are the moments when the modes abruptly and without warning shift.” On a local level, “mode” in Phrygian Gates, however, often means something more akin to “diatonic collection” than it does to “scale.” “Scale” describes well Vaughan Williams’s use of modes to create clear pitch hierarchies. In Debussy, too, though these hierarchies can be more ambiguous, they consistently operate on both local and formal levels. In contrast, because Adams composes his phrases out of static cells, voice leading only functions on a formal level in Phrygian Gates. In consequence to both its static cellular construction and its formal-only voice leading, the piece only weakly, if at all, creates the sense of pitch centricity necessary to cast its modal pitches into hierarchal relationships with one another.
Indeed, the opening 113 bars of the piece seem to deliberate obfuscate the pitch A as the “root” or “center” of the four-sharp diatonic collection. In fact, the piece sounds E-centric when it opens and C#-centric in bar 44. When the long-range voice leading finally arrives at A3 in 56, Adams creates further confusion by interjecting the extra-modal Bb.
Now, I wrote that “‘mode’ in Phrygian Gates . . .often means something more akin to ‘diatonic collection’” because there are some exceptions. The E phrygian section that begins in bar 236 does sound like E-phrygian, not simply the white-key diatonic collection, because Adams thoroughly grounds it on E1 and E2 in the bass (cf. the C# in bars 640-808). Contrast this with the B-lydian music that follows it (bar 266): as with the opening “A lydian” music, B does not project itself as the center of a pitch hierarchy. Instead, whatever pitch is in the bass generally sounds most important. Thus, B gains its pre-eminence only in bar 311.
In short, Phrygian Gates generally lacks pitch hierarchies. Its pitches generally attain prominence for registral and timing reasons rather than voice-leading ones. Perhaps surprisingly given their radically different harmonic colors, Phrygian Gates and the fourth movement of Ligeti’s concerto both share this harmonic feature. However, whereas Ligeti achieves this lack of pitch hierarchy by using the symmetrical chromatic scale, Adams achieves it by constructing his piece using repeating, static melodic cells.
Lastly, I should note in passing the formal design of Adams’s modal usage. Adams mentions in the program note that the piece is “a 22-minute tour of half of the cycle of keys” that switches between the Lydian and Phrygian modes in each key change. Other scholars have diagrammed this progression (e.g., p. 14 here, cf. p. 135 here) and even debated each section’s modal identities. These details don’t really matter to me. The big picture affirms this general compositional wisdom: pitch-centric compositions longer than 3-5 minutes generally require shifts in collection and centricity to keep the listener’s attention.
Takeaways
As with analyzing Ligeti’s piece, my purpose in analyzing Adams’s is to help me identify some potential composition exercises to better capture the sound I was imagining. So here are the ideas that I have:
I don’t think I want to compose my piece out of short, static cells. However, I could try composing it out of short, static phrases—like Michael Torke’s Yellow Pages (that’s a whole other analysis project). Like Adams, I can experiment with placing these phrases in counterpoint with each other. So, to begin with, here’s my task:
Write a variety of short, static phrases
These phrases should vary in
length
rhythm (unlike Adams’s which are at a steady rhythm)
overall pulse (e.g., is this phrase mostly a 16th-note gesture or an 8th-note one?)
pitch content — more specifically
mode/collection
subsets of that mode/collection
stepwise vs. arpeggiated motion
density — they can consist of up to 3 pitches (though probably in closed voicing to start)
Identify: Do single/simple-contour phrases work better than ones that seem like little melodies?
Having written these phrases, I will then experiment in combining them
Which ones sound good with each other? At which transpositions?
What different orderings can I create?
Next, how can I disrupt these phrases? What is the effect of different lengths of disruptions?
Again, by the time you read this, I’ll likely have already conducted these experiments.
This is not so much an analysis as it is the sketch or the start of one. Its goal is understand the compositional possibilities this movement suggests to me on a particular Tuesday afternoon.
While composing my latest piece for Hub New Music (with generous funding by the Barlow Endowment), I began to think of a recent experience I had, and this memory triggered a strong emotional and musical response. After composing out a sketch of this idea, I noticed that what I wrote and was imagining reminded me of the fourth movement of Ligeti’s Chamber Concerto. I don’t want blatantly to copy the movement, but I thought it prudent and useful to see what Ligeti does in it.
Here, for your listening pleasure, is that movement:
General Observations
First, some general observations:
A very fast surface rhythm prevails throughout, but because it’s not perfectly stable (having both linear and contrapuntal variations), the music does not sound metronomic.
Most of the piece is very quiet. Ligeti uses loud dynamics for formal purposes: to build to and from the climax* and to punctuate the coda. (On this idea of climax, see the heading entitled “Form” below.)
Though it sounds really busy, much of the counterpoint in this piece actually consists only of 2-4 voices.
Chromatic clusters feature prominently in the harmony—but when I say “harmony,” I don’t refer only to “vertical simultaneities.” For instance, I hear the opening clarinet duo more as an “arpeggiated” chromatic pentad (filling in and including all the chromatic notes of a P4) that gradually shifts upward from D3-G3 to E3-A3.
No one will claim that this movement is easy to play. However, for three reasons, Ligeti’s voice-leading choices do make it more gracious than not to play:
Though statistically the instruments are “arpeggiating” chromatic clusters of various sizes, Ligeti tends to avoid chromatic intervals unless he’s writing a fragment of the chromatic scale (3+ notes).’
In turn, much of this “arpeggiation” takes place within the span of a fifth or even smaller. Further, within this span, two-thirds of the voice-leading consists of stepwise motion. The remaining voice-leading consists mostly of thirds, with only the occasional fourth or fifth. In other words, though these lines are fast, they require little physical motion.
In situations when the arpeggiation spans wider than a fifth, Ligeti writes idiomatically for the instruments. For instance, the string writing in bar 43 ff. is accomplished by simple string crossing (of adjacent strings); fingering the exact pitches is otherwise just as economical as if Ligeti had written it all within the span of a fourth.
Ligeti uses chromatic clusters prominently but not exclusively. For instance, near the end of the piece, the chromatic lines begin to be voice-led (roughly) by perfect fifths (see note in bar 49). Likewise, the run in bar 7 starts as a chromatic cluster but widens into a Major 7th chord, and then a polytonal one in bar 8. The tonal reference of these sonorities is very weak, but the difference in harmonic content and voicing is clearly audible.
This is a good place to note that the distinction between “Pitch set” and “Pitch-class set” is very useful in this piece. “Pitch-class set” describes “all the pitches sounding irrespective of their octave.” In contrast, “pitch set” refers to the actual registers in which those pitches reside. The collection of pitches in bar 8 may all belong to the chromatic hexatonic pitch-class set (m2-m3-m2-m3-m2), but the pitch set of this collection is audibly arranged as a polychord (B-flat minor over D major). Now, in common-practice music, triads can be voiced, inverted, and doubled in myriad ways but still retain a clear relationship to their root-position chord. Not so in chromatic music: very few (if any) people will hear the Dmaj-Bbmin polychord as a revoicing of chromatic hexatonic collection.
Form
I hear the piece in four major sections. The closure of three of these (1st, 2nd, 4th) is defined a harmonic coalescence around a dyad or triad. The third major section comes to repose by reaching the registral extreme of the piano.
I
bar 1: two clarinets fill in a D3-G3 that gradually shifts up to E3-A3 and then thins out . . .
bar 5: coalescing on the E3-A3 dyad and ending in an upward run (bar 7) to
bar 8: coalesce on D major/B-flat minor polychord spanning D5-F6. The registral band narrows to . . .
bar 14: the E6-F6 trill, which voice-leads up to . . .
II
bar 15: F#, inaugurating a unison (+ 4 octaves) line between the piccolo and bass clarinet. This line is re-orchestrated/doubled in various chromatic pitch-class sets. It’s taken over by the piano as P5 (+ 4 octaves) at the end of bar 23.
bar 24: The horn (which entered on a sustain note in bar 22) leads off a melodic line (doubled by strings then winds). The surface rhythm of this line gradually accelerates as its register also increases. Meanwhile the piano (sempre fortissimo) also increases in density and register until . . .
III
bar 31: It is cut off by the double bass solo (with a subtle trombone sustain) that chromatically spans E1-A1. This band remains ≈P4/A4, changes color slightly (other instruments with these same pitches and rhythms that align on but not within notated beats) slowly transposes up . . .
bar 40: . . . to coalesce on C#2-G2 dyad with bass clarinet and cello
IV
bar 42: The violins, viola, and cello begin to arpeggiate chromatic lines roughly a fifth apart (and span roughly 2.5 octaves) that are moving upward at an unstable, unequal rate. In bar 45, the winds enter, sustaining pitches from the strings. In bar 46, the strings exchange similar for contrary motion until . . .
bar 49: the strings ultimately (albeit for only half a bar) arpeggiate a 6-octave span of fifths from Bb1 to F#6. They then move by contrary motion inward. Meanwhile, high winds resume their chattering over a span of about an octave that rises over two bars from the bass register into the soprano/alto one, then only above the treble staff (roughly mid bar 51).
bar 52: Meanwhile, the strings’ contrary motion leads to the cello and bass sustaining A3 and the violins and viola trilling A4/Bb4.
bar 53: The high wind chatter narrows around and then leaves only the oboe’s loooong forte D#6 (against the strings’ A/Bb).
Coda: Ligeti finishes by arpeggiating 3-4 chromatic clusters (depending on how you want to count them) in the winds and keyboards: two loud gestures followed by a few quiet ones.
To sum up, here is my simplified, not-at-all-to-scale, graphical-sketch-on-a-post-it-note (the relative height of the lines represents pitch):
A quick post-it note sketch of the form of the fourth movement of Ligeti’s Chamber Concerto.
I asterisked the word climax when I mentioned it in the previous heading. I’m not definitively prepared to say that the loud part at the end of section II is the movement’s climax. It is definitely “the loudest part in the middle of the piece,” so in that sense, it is climactic. However, section IV leads also somewhere just as rich (the widest and fullest texture of the whole piece) and noteworthy (the loooong, loud oboe note).
Lacking the time to examine the particulars closely enough to build a solid case one way or the other, I will point out that the build to fortissimo in section II does create a reference point to which the end of section IV/start of the coda responds. In other words, just as the formal parallelisms between the four sections help demarcate them as sections, the parallels between the ending of sections II and IV are formally significant. That is, what happens at the end of section II helps the end of the piece sound like the end of the piece.
Takeaways I Will Use Immediately
Though some of these general and formal observations will be useful for me in writing my piece for Hub New Music, my most immediate takeaways have to do with deliberate use of register and density. Here are some compositional exercises and experiments I’m going to try as a result of studying this piece:
Identify narrow registral bands (less than, say, 1.5 octaves). Sketch some ideas specific to that register and its associated tone colors. (Karalyn Schubring has a cool piano piece that does this.)
Imagine these passages:
using different collections
in different registers
at different dynamics
with different doublings/parallel motion
What different gestures can I create, more than static bands?
These, in combination with increasing/decreasing voices? Changing doublings?
How long must one of these gestures be so that it doesn’t sound like a melody but as something larger? (I imagine the answer exists in relation to (1) the size of the collection I’m trying to express, (2) the number of voices expressing that collection, and (3) the rate at which the whole collection can be presented.)
Of what different idioms can I take advantage for the various instruments that will make my music easier for them to play?
Developing these initial experiments and having some clear reference points for them was my purpose for analyzing that movement by Ligeti. By the time you read this blog post, I will have already conducted many of these experiments.
At the start of the year, I began working in earnest on the flute and harp piece I wrote for Luke Blackburn’s EcoMusic concert. Due to the COVID-19 pandemic is no longer happening this week, but that postponement does allow for a special opportunity! See below for more details.
During the idea-gathering phase, besides reading all about butterflies and toying with some musical metaphors about them, I also perused the flute and harp literature for ideas.
After surveying a bunch of harp music, something just clicked. I realized something I hadn’t noticed before about writing for harp: Unlike in piano writing, harp parts rarely feature fleshed out inner voices.
In fact, of the two dozen or so pieces I looked at today, I saw barely any inner voice writing that went beyond voice leading between chords. Take Britten’s Suite for Harp. Or Saariaho’s Tocar. Or Pierné’s Impromptu-Caprice. Or Tüür’s Prints. Stylistically, these pieces are all over the map. But they all lack any substantive inner-voice writing. Colin Matthew’s Little Suite has maybe a dozen bars of an independent middle voice, but also mostly aligns with this trend.
The harp: not an inner voice instrument.
Looking now over nkoda’s “Essential Harp” collection of scores:
The Scarlatti sonatas have some — but mostly not
Ditto the Handel B-flat concerto
Glinka’s Mozart Variations are entirely devoid of it
Ginastera’s Harp Concerto has some mildly independent inner voice writing — but only in the second movement
Jolivet’s Prelude again only has some mildly independent writing
. . . and so it goes. Now, I’m sure there are plenty of harp players out there who can point me to their secret stash of pieces with rich inner voices. But from what I can tell, such writing is just not idiomatic for the harp.
What seems to be most common is textures of 1 or 2 layers. In fact, some of the most common textures seem to be (1) 2 notes in one hand and one note in the other, (2) one note per hand, or even (3) one note at a time.
These textures may be embellished (unsurprisingly) with all manner of arpeggiation, figuration, and doubling/planing. They may sometimes even feature block chords with smooth voice leading — but this still counts as doing one thing.
So I wrote my flute and harp piece accordingly. Here’s a draft of the first movement:
The ink erosion in this chant manuscript is an example of inherent vice.
“Inherent vice,” says Wikipedia, “is the tendency in physical objects to deteriorate because of the fundamental instability of the components of which they are made, as opposed to deterioration caused by external forces.”
As a property of physical objects, this is why certain papers and films last longer than others. It also is why materials deteriorate the way they do.
But what interests me about inherent vice are its potential musical analogies. Here a few examples of how inherent vice can be recreated in music.
Fred Rzewski: Les Moutons de Panurge
Rzewski makes it easy for performers to get lost, and in the score, he explicitly directs the performers that “if you get lost, stay lost. Do not try to find your way back into the fold.” The analogy to inherent vice is pretty clear: the piece will fall apart. What’s fascinating though is how Rzewski repurposes this as a virtue. Thus, the title feels to me like a humorous reference to Isaiah 53:6: “All we like sheep have gone astray.” (To my ears, there is no obvious reference to Handel’s setting in Rzewski’s piece, other than a general, wandering melodic contour.)
Alvin Lucier: I Am Sitting in a Room
As with Rzewski’s piece, the inherent vice of Lucier’s musical-acoustic scenario is the desired outcome. Here, the vice comes not from confusing the musicians, but from harnessing the result of rerecording the same speech, repeatedly, which gradually washes out the speakers voice and reveals the acoustic resonance of the room in which it is performed. The overall process and result feels like a metaphor for merging with the universe and reminds me of the Buddhist doctrine of anattā.
Michael Gordon: Gotham, Part III
The third part of Michael Gordon’s Gotham undergoes a similar process, albeit composed out and for orchestra. I find fascinating the different textures that he teases out of having the violins initial line unravel. Inasmuch as the process is composed out, rather than a result of the score’s execution, I wouldn’t consider the vice here to be as “inherent” as Rzewski’s or Lucier’s pieces. It’s more like “predestinated vice”: the composer decided the piece would gradually fall apart, so he ensured that it happens.
Every orchestration textbook will tell you that the lower limit of the violin (scordatura aside), is a G3 (G below middle C).
But even with a normally tuned violin, composers don’t always obey that limit. Here are two examples (plus a bonus one in viola) that show why a composer might write beyond that written limit.
To Preserve a Melodic Line
In Richard Strauss’s Sinfonia Domestica he writes (at reh. 74) this:
As Ernest Toch points out in The Shaping Forces of Music, “It is the pitch-line, its curve or curves, its shape, its profile, its ascensions and descensions which determine the character, the gesture of the melody. . . . Richard Strauss, in his ‘Sinfonia domestica’, draws the last consequence of this consideration by entrusting the violins with a note which is even below the range of the instrument and therefore cannot be produced. The passage is reinforced by the violas and horns and its sounding is thus assured. It would be intolerable, even to the composer’s eye to replace the low f# with its higher octave. He wants the line at least to be understood — playable or not” (67).
If I were writing that passage today, I might parenthesize the note to make it clear to the players that I don’t expect them to play it. Regardless, this is a valid, albeit rare, reason to write below the range of an instrument.
To Preserve the Tonal Meaning
A far more common reason to write below the written limit is to clarify the tonal meaning of a pitch. In this case, composers aren’t actually writing an unplayable note; they’re simply spelling it in an unusual manner.
For example, in the first movement of Borodin’s String Quartet no. 2 (bar 55), Borodin writes:
Likewise, in the second movement of his Serenade for Strings, Dvorak writes a low B for the viola (bar 4):
In both cases, the composer is harnessing the notation to tell the performers something about the pitch relationships. Just last week, a fellow evensong choir member of mine identified a similar case in this tenor line in Elgar’s “Great is the Lord”:
“Why did Elgar just not write this as a G?” he asked.
In each of these three cases, the composers wanted the performers to know that these pitches did not have a chromatic relationship, but rather a diatonic one. In other words, they wanted the performers to know that the note they were playing (or singing) was acting as a leading tone to the note that followed it. In an earlier blog post, I referred to this as “structural chromaticism”: “these notes merely represent the overthrow of one diatonic collection (say, CDEFGAB) by a different diatonic collection (say, C#DEF#GAB).”
In the examples above, Borodin and Elgar both write F-double sharp to tonicize G-sharp, and Dvorak writes B-sharp to tonicize C-sharp. Now, you may note that, whereas C-sharp minor is the key of Dvorak’s entire phrase, neither Elgar or Borodin ever establish a key of G-sharp. That difference is immaterial. In tonal music, pitch functions can last as briefly as a single interval. The entire scale never has to be present, nor must the music match the prevailing key signature.
So if these tonicizations are so brief, why do these composers write them with these “strange” spellings? Why write a low F-double sharp for violin or a low B-sharp for viola? Simply put, because the diatonic spelling helps performers understand the musical meaning better than the chromatic one. In each of these three cases, the “simpler” chromatic spelling (G to G-sharp or C to C-sharp) would obscure the diatonic relationships that Borodin, Dvorak, and Elgar want us to hear.
Classical dissonance begins with a consonant preparation, continues to the dissonance in question, and finishes with a consonant resolution. Wikipedia says as much.
But as I was falling asleep I started wondering about the topology of suspensions — which suspensions work in which situation. There are three basic suspensions: 9-8, 7-6, and 4-3. In the chart below, I listed all the possibilities of preparation-dissonance-resolution in a somewhat scrambled order:
It turns out the topology of suspensions is somewhat bent. That is to say, not every bass interval is equally represented among each of the suspension categories:
Upward and downward seconds are capable of supporting any kind of suspension.
Fifths/fourths can support 9-8 suspensions either upward or downward, but the 4-3 suspension only works with ascending fifths/descending fourths, and the 7-6 suspension only works with descending fifths/ascending fourths.
Thirds are least capable of supporting suspensions. The direction of the third mandates the suspension type. The ascending third can support a 4-3 suspension. The descending third can support a 7-6 suspension.
I’m sure there’s some math to explain the asymmetrical distribution of bass intervals, but for 11:30 on a Thursday night, I’m going to leave this observation stand as is.
I love the opening swirl of violins in “Jupiter” from Gustav Holst’s The Planets. Who doesn’t?
Take a moment and listen to it:
It’s thrilling!
But what really gets me going as a composer are the details of its composition. This passage is extraordinarily elegant.
Here’s the excerpt from the score:
What makes this passage so elegant?
Motive: The texture is composed of a single, three-note motive: a minor third followed by a major second. Holst presents this motive in two transpositions (starting on E and A) in two octaves (E4/A4 and E5/A5). Elegance is how the passage is composed of such a limited set of materials.
Disposition: Though we hear the first two bars as a two-octave, upward run, it’s actually Holst introducing each transposition separately. The fact that the motive spans only a fourth makes it extraordinarily easy to play on the violin. Elegance is how Holst distributes the pitches in this easy-to-play manner to generate a larger effect.
Rhythm vs. Meter (I): Holst casts his three-sixteenth-note motive into four-sixteenth-note beats. Each entrance initially seems like a four-sixteenth-note motive, but the ensuing music dispels that notion. Instead, we soon hear that Holst has set up a 4 against 3 polyrhythm. That is, the rhythmic placement of the motive relative to the meter keeps shifting in a 4:3 ratio. Elegance is how this simple tension creates excitement and energy.
Rhythm vs. Meter (II): Though the motivic relationship to the meter forms a kind of polyrhythm, the rhythmic relationship of each transposition relative to the others remains constant. For instance, the E4 transposition always sounds A-E-G while the E5 transposition sounds E-G-A. Because each instance of the motive is the same 3 sixteenth-notes long, this 1:1 duration ratio ensures that they remain in the same micro-canonic relationship with each other. Elegance is how Holst composes the texture canonically rather than micromanaging the details.
Orchestration: Coupling instruments in octaves is one of the foundations of common-practice orchestration. Holst does it constantly in The Planets. This passage can also be read as a kind of octave doubling: the canon with entrances on E and A in bar 1 is repeated an octave above in bar 2. The resulting texture’s polyrhythmic and pentatonic wash reinforce the impression that this relationship is an octave doubling of two lines rather than Holst wanting you to hear the four individual lines. The rocking strings that open Thomas Adès’s Tevot fill a similar purpose. As individual lines, they have direction, but as a composite texture, they create a grainy wash rather than discernible counterpoint. Elegance is taking a simple, common idea and presenting it in a fresh, becoming way.
As a composer, I love such elegance in other’s music and I strive for in my own. These kinds of musical ideas captivate me, because they create the kind of shimmering, ambiguous tension like light through a gemstone or waves reflected on the bottom of a pool. They represent one kind of musical depth: patterns whose components can be heard but which do not resolve into an unambiguous impression. The tension that remains creates a space where the soul can live.
