Canon #91, Birdsong

My latest canon takes inspiration from birdsong. It’s my first canon that refers to a sound-world outside itself, and at over six minutes, it’s also my longest canon so far. It’s able to be long because it’s not a single continuous canon but rather a montage of over twenty-five canonic episodes, each one attempting to capture something that I’ve heard in the universe of bird vocalizations. Each episode is a strict inversion canon, where the follower moves in the opposite direction from leader, and most episodes are what I might call “rapid-fire” canons where the follower enters very quickly after the leader. The piece doesn’t have an plot per se, but among the canons I’ve written, it’s the one that might be the most suggestive or accommodating of a plot. It was particularly fun to write, and I’m particularly excited to share it:

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Thank You, 2020!

There is no question that 2020 was a wretched year for so many people who fell ill with COVID, or lost a loved one to the disease, or lost their livelihood because of it, or suffered from the isolation and loneliness brought on by physical distancing. It was a plague year, and there are many reasons to wish it good riddance. In solidarity with all those who suffered so greatly in 2020, I feel reluctant to say anything good about the year. But when I reflect on all the fears that overtook me in March, I see that none of them came to pass, so I’ve come to think of 2020 as a merciful year.

Back in March I expected that I’d get COVID sooner or later, and so would many of my friends and family members, and in the coming months I’d witness some of them die. I know that these fears of illness and death came true for many people in 2020, but for me they didn’t. As I listened to the news each morning with continuing alarm, hearing that cases were rising, rising, rising everywhere, such an explosion was not mirrored in my own social circle: I know one person who caught the disease and recovered; everyone else in my network stayed healthy in 2020. It’s not fair that some people have the resources to protect themselves from this disease while others do not. But while we should be upset at the social inequities that lead to disparate health outcomes, we can also feel a bit of gratitude that COVID turned out to be more preventable than we initially feared. Back in March it seemed that COVID was an inscrutable and invincible monster. Of course, there are people who took all possible precautions in 2020 and still caught COVID – and there are many whose living situation or occupation or economic circumstances made those precautions impossible. But on the whole, COVID turned out to be a disease that we can avoid by wearing masks and staying apart. That’s better than it seemed in the early days, when we were told that masks couldn’t protect us, and when there were fears that COVID could come in the mail, that we had to disinfect every item that came into our house, that we should shower after going outside, that maybe a neighbor could pass the disease to us through a crack in a shared wall, and so on.

Back in March it wasn’t clear that a vaccine for COVID could ever be developed, and if it could, the experts told us, we might have years to wait. But by the end of the year, several vaccine candidates had been proven effective. Remarkable!

Back in March there was talk of the medical system collapsing, and how care might need to be rationed. If you got sick, they said on the news, there might be no bed for you in the hospital, or no ventilator, or no expert to operate it. Though I didn’t need to see a doctor in those early months, I worried about what might happen if I lost a dental filling that had given me trouble before. Would the dentist see me? And if so, would I be risking my life by going to the office? A few months later, the situation looked very different: with the proper precautions in place, it seemed that routine medical and dental care could be practiced safely. In September, I went in for a regular cleaning without incident, awestruck by normality having my teeth cleaned just like in pre-COVID times. There’s no doubt that healthcare workers were stressed to the breaking point in 2020 and the system struggled with unprecedented challenges — it almost fell down — but the sort of catastrophic collapse that some predicted back in March did not come to pass.

Back in March, it was hard to find toilet paper anywhere in physical stores or online. I tried to order rice and it was sold out everywhere. Rice! I feared that this was just the beginning of what would be a widespread breakdown of global supply chains. In the coming months, I expected I’d have to adapt to a totally different life, one without all of the products and services I had come to take for granted. I’d get a taste of the scarcity that is the norm for so many around the globe. And I’m sure there were many “preppers” who thought their time in the sun had finally come. But while shortages of toilet paper and rice were reminders of our dependency on intricate, precarious, and arguably destructive economic systems, these shortages did not persist or expand in 2020. Toilet paper returned to the shelves in due time. Supermarkets remained open throughout. The status quo resumed.

Back in March, the stock market crashed. There were days when trading was halted on the New York Stock Exchange because prices were dropping too fast. Some of us who fear that the global economy is a house of cards jumped to the conclusion that perhaps it was finally crumbling down. Despite said fear, I had invested my life savings in the market and now I thought I’d see those savings evaporate. But several months later, the market came roaring back, proving either that it is totally disconnected from reality, or that in reality, people were still buying and selling things just as they always had.

Back in March, I feared that the 2020 presidential election in the US would solidify the country’s descent into kleptocracy, autocracy, science-rejection, climate-change-denial, nepotism, insanity, or however you want characterize it, but what happened instead is that we got a bit of a reprieve from that descent.

So when I think of it this way: COVID turned out to be more preventable than we thought, a vaccine came much more quickly than we thought, the medical system and economy turned out to be more resilient than we thought, and the US political system didn’t veer into outright autocracy, I have to conclude that most everything about 2020 came out much better than I expected it to.

So, thank you, 2020! While you were a challenging year for all, and a miserable year for many, you were also a merciful year, considering how much worse you might have been. You made us fear the worst on all fronts but you left us with hope.


Canon #90, Thorite

Announcing Canon #90, “Thorite.”

This piece is a sequel to Canon #89, “Thulite” — I chose the name “Thorite” simply because it’s another mineral beginning with “th.”

Like its predecessor, this piece uses the octatonic or diminished scale. The articulation is staccato, and the voices almost never coincide. Each voice speaks in the pauses and gaps left by the other voice. Sometimes these gaps are between phrases (creating a sense that the voices are “taking turns”) and other times they’re within a phrase (creating a sense that the voices are speaking over one another).

This framework (octatonic scale, staccato articulation, no shared hits) allows for a good amount of freedom in composition. I found that I didn’t need to micromanage the intervallic relationships between voices in the same way that’s necessary with other canons. There’s one exception. I tried to keep the voices from playing the same pitch in direct succession, because the sound of an octave (even if staggered) is distinct enough that the listener might expect it to have some special meaning; if no special meaning is found, the experience is slightly disappointing. Other than avoiding octaves, I could pretty much let the voices flow according to their own whims without having to plan their vertical relationship on a note-by-note basis. This meant that I felt comfortable writing the piece from beginning to end without going through my typical iterative outlining process.

One thing I loved about writing this piece is the way it all grew from the material in the first twelve bars. In writing those first twelve bars, I kept facing the challenge of inventing new material — pulling something out of thin air, so to speak — but once those few bars had been written, the rest of the work was about restating and recombining the opening material — finding new meaning in it — all the way to the end.

On a technical front, the leader is in the bass most (but not all) of the time, and there’s a one-bar lag between leader and follower. The piece is notated in 4/4. It stays mostly in the octatonic scale containing C#-D but occasionally visits the other two octatonic scales (the one containing B-C and the one containing C-C#). It starts with imitation at the major sixth above, but the interval of imitation shifts around throughout the piece.

A rough outline of the piece might go like this. First there’s about ten bars of “conversation” where various key phrases are introduced. The conversation gives way to a passage that I call the “drunken zigzag.” Here, the voices ascend in an up-down-up-down fashion that is highly patterned, but is made to sound chaotic through a jagged, unpredictable rhythm. After the drunken zigzag, there’s a bit more conversation that then leads into the first “stretto,” a passage where the same theme is layered on top of itself multiple times. It’s not exactly akin to a fugal stretto and one could argue that stretto isn’t the right word to use here, but it’s the best one I’ve got at the moment so I’m using it. Next we have a bit more conversation with echoes of themes from earlier conversations, and then we have a restatement of the drunken zigzag, this time with some doubling and a different interval of imitation between the voices. This second drunken zigzag then leads into a new stretto that’s based on the themes from the first two bars of the piece, rearranged so a phrase of the form AB now becomes BA. After this middle stretto we hear more conversation (again, with echoes of the previous ones) and this leads into another drunken zigzag that’s special because it’s at half the speed (e.g. the rhythmic values are doubled). Next there’s some connective material that has the purpose of launching us into the third and final stretto, which uses the same rhythmic structure as the first stretto, but now the theme is descending instead of ascending. This third stretto visits all three transpositions of the octatonic scale, and leads us back to the C#-D scale where the piece began. The piece concludes with a repeated statement of a now-familiar phrase, first introduced in the second bar of the piece, with the voices finally, conspicuously imitating each other at the octave.

I’ve tried to blog about each canon I write, but there’s always much more to say about the piece than I can hope to write down. Reaching my ninetieth canon feels like something of a milestone so I’m planning to try something new. I’ll make a video where I walk through the piece and try to share how it works. Stay tuned for that.


Canon #89, Thulite

Announcing Canon #89, “Thulite.”

Many of my canons pursue an orderly relationship between leader and follower. As much as I want a canon to be interesting and provocative – a goal which sometimes results in musical complexity – I still want the canon’s structure to be clear. It’s not sufficient that the follower echoes the leader; this echoing must also be apparent to the ear. There’s a certain classic sound of contrapuntal imitation that I’m usually going for, regardless of whether the musical language is antique or modern. The leader announces a melody and we hear the follower reproduce it in a way that seems preordained, inexorable, “right” – like the voice of God. The leader sets an expectation and the follower fulfills it.

In writing my latest canon, “Thulite,” I wanted to try for a different aesthetic. I wondered if I could write a canon where the follower didn’t seem to be imitating the leader – where the two voices actually seemed to be antagonizing or contradicting each other – even if in fact, the follower was copying the leader exactly. Perhaps if the leader behaved in a more erratic, jagged, and unpredictable way than I usually seek, the follower too would sound unpredictable, as if it were doing its own thing altogether, even if that “thing” had been heard once before. Perhaps if the voices occasionally became entangled, the leader/follower relationship itself would be obscured.

To achieve this goal of a canon that doesn’t sound canonic, I put aside my typical writing process where I start with a skeletal outline and add detail in a series of iterations. Instead I composed the piece “on the fly,” one measure after another, without knowing anything about what might come next. The piece became a series of brief episodes, some of them having the jerky, erratic quality that I had been going for, and others having more of the classic imitative sound. The piece goes back and forth between chaotic and structured. But even in the latter case, the voices still seem to tug against each other with accents that don’t line up nicely.

The piece reminds me of the jerky, sudden, shifting movements of a cat-and-mouse game.

When I sat down to write, I intended to generate new material from beginning to end, but then I found a way to reuse some of what I had already written. One section from the early in the piece is repeated near the end with the same rhythmic structure but different melodic contours. And then, at the conclusion, we hear the material from the very beginning of the piece repeated in a different “key.” I put the word “key” in quotes because the piece is not conventionally tonal. Most of the material is in the B-C half-whole diminished scale (or octatonic scale). We hear enough material in this scale that its sound becomes familiar – a kind of tonal comfort zone – even though there is no specific center. In the middle of the piece, the leader remains in the established B-C half-whole diminished scale while the follower shakes things up, transposing material to the two other half-whole diminished scales (the A-sharp-B one and the C-D-flat one). As the piece approaches the conclusion it settles back into the pure B-C diminished scale, but then, in a surprise, the final passage is stated with both voices in the foreign C-D-flat diminished scale.

Importantly, the voices never play on the same beat, though they come as close as a 32nd-note away. I wanted the rhythms to seem whimsical and less ordered than my typical style, but I tried to achieve this without anything fancy like changing meters, complex polyrhythms, metric modulation, or the like. The score is notated in 4/4 and looks quite conventional. The imitation is strict: the follower copies the leaders intervals and rhythms exactly.

Some of the challenges in this piece were 1) keeping a sense of variety within the selected tonal material of the half-whole diminished scale, 2) maintaining a sense of gestural discord between the voices and avoiding the classic sound of imitation, 3) disrupting the beat while maintaining enough of sense of meter that the music can be heard as tugging against something, 4) creating episode-to-episode transitions that sound natural on the one hand but unexpected on the other.

My typical writing process usually leaves me with a result that seems final and unchangeable, but Thulite, written in an atypical way for me, opened so many possibilities, and could have gone in so many directions, that I feel the piece is only one of many possible manifestations of the intentions at play. Usually it feels right to name a piece after a gemstone or mineral, but with Thulite, for the first time, I wondered if I should change my naming scheme and use a more descriptive title. To keep things simple, I decided to stick with stones for now. My next steps will be to write a few more canons that explore the stylistic ideas that Thulite brought into focus for me.

Photography, Seasons

Fall 2020

Fall leaves can look like fire. Here, I see a ring of fire circling a negative space. When we look into that space we see nothing but a blur of still-green leaves above:

These leaves, rustling in the wind, all the same shade of red, look to me almost edible, like ornamental candy wafers:

The branches and stems here call my attention to all the work that had to be done in spring and summer to bring moisture and nutrients to so many leaves, then young, now orange and resplendent and soon to fall away:

This image recreates for me a bit of the swirling sensation that I experience when, in a forest, I notice that even the things I thought were still are moving:

Taking a closer look at a cluster of leaves glowing in the sun, we find there’s still some green to be seen and remembered as it cedes the stage to brown:

Sometimes a photograph that seems a mistake turns out to be more than that. Here, motion blur combined with shallow depth of field creates a composition that looks chaotic, but for me the diagonal stems give it structure and the smaller leaves in the background that are clearly in focus anchor this image as a photograph. A photograph that reminds me of an expressionist canvas:

In this image I don’t see any one leaf that’s particularly remarkable. The leaf that’s most clearly in focus is also shaded, so we aren’t able to enjoy its full visual potential. But this image teaches me that a composition doesn’t need to contain a “star” to be effective. The shallow depth of field makes the background seem like a watercolor and I like how everything hangs from those two stems at the top:

Here is an enchanted forest. The original version of this image was pale and badly overexposed, and nothing is quite in focus, so I considered discarding it. I find that trying to salvage a flawed image is usually a waste of time; better to go out and take another. But there are exceptions. My efforts to vivify this image in post-processing resulted in a product that represents — pretty darn well — what I think I actually saw. Just the other week, my mother told me that one of my grandmother’s first jobs in the 1930s was colorizing black and white photos. I wonder what my grandmother might have done with the original version of this image, which was nearly black and white, and how much the end product might have resembled what you see here:

My eye is drawn to fall leaves that glow in the sun. Sometimes I have to remind myself to look at those beautiful leaves that don’t happen to be illuminated at the moment:

Of course, I’ll always be a sucker for sunlight, whether it’s lighting up a thousand leaves or just one:

The images here were taken October 17th and 18th in Hopkinton and Berlin, Massachusetts, though I feel like I’ve been collecting them — maybe just the idea of them — for much longer. Dear viewer, thank you for joining me on my Fall journey this crazy year, 2020!



On Writing

It’s almost tautological to say that you can make something better by removing the bad or unnecessary parts. When we apply this advice to writing it means crossing things out with a red pen, or pressing the delete key, hoping that we’ve properly identified the pieces of text that aren’t essential to the whole. I used to try to improve my writing by combing over each sentence in search of “needless words” to remove. I came to realize that apparently needless words can serve a purpose that’s easy to overlook: they can improve the rhythm and pacing of a sentence and can contribute to subtle changes in inflection. I also came to realize that if my goal is to use the reader’s attention well, it’s more valuable to cut out entire paragraphs, pages, or chapters that are unnecessary than it is to worry about individual words. So how can a writer go for the really big prize, eliminating whole paragraphs, pages, and chapters as opposed to a few words here and there? Every piece of writing is different but there are common causes of bloat. I’ll venture to say that the biggest cause of bloat is anxiety – specifically, the writer’s anxiety manifested on the page. Basically, if you can cut the anxiety out of your writing you can make it shorter by, I don’t know, thirty, fifty, ninety percent without sacrificing your message.

When one sits down to write, it’s common to feel a swirl of emotions, and many of these are negative. Writing is hard! The thing you want to discuss might be very complicated. You might not even be sure what you want to say or fully convinced of the point you hope to make. Perhaps you’ve missed something important? You might not feel worthy of writing about your chosen topic, considering that you don’t have credentials X, Y, and Z. Perhaps your point is very serious and you worry that you won’t do it justice. Any time you write something, you expose yourself to criticism. People might misunderstand you. They might question you. They might think you’re naive or stupid. They might think your message is obvious, or that it’s unoriginal, or that you’re wasting their time, or that you haven’t done your homework, or that you’re an imposter.

You want to guard against imagined criticism and ridicule, so you start hedging, making disclaimers, trying to anticipate and preemptively respond to all possible lines of attack. You talk about how dauntingly complex it is to broach this particular topic. You move to establish your authority on the topic while also making sure that no one could accuse you of inflating your credentials. You move to defend your position while also making clear that you’ve considered all other sides of the matter and that you’re aware that nothing can be known for sure. Writing becomes an adversarial project where your goal is to score some points without losing more than you’ve gained. Writing becomes more about you than it is about subject at hand. You think you’re writing about your topic but really you’re manifesting your own personal anxiety with the topic as a vehicle.

If you can eliminate the anxiety, and the gunk it creates in your writing, you’ll be left with something that really shines… or maybe something that doesn’t shine… but you won’t know until you try. Imagine the reader likes you, respects you, trusts you, and is ready to understand your point. Imagine you’re a good writer and you have unfettered access to the truth. Now tell it as simply and vividly as you can. That’s your mission.

What I’m saying here is the product of my own quest as a writer and the insights I’ve gained from one remarkable book: Clear and simple as the truth by Francis-Noël Thomas and Mark Turner.

I’ll give an example from my own recent experience. Over the past four years, I’ve done a lot of thinking about how America has gotten so polarized and I’ve wanted to summarize my observations in an essay. But I’m not a social scientist, I don’t have a degree that’s applicable to this topic, and I haven’t done any formal research. I’m just a guy who’s spent some time reading, watching, and thinking. I could have started my essay by making disclaimers and explaining why the reader should still take me – a layperson, an average citizen – seriously as a commentator on the nation’s affairs. But I realized that no reader stands to benefit from my justification for why I should be taken seriously. That justification contributes nothing of value to their lives or their knowledge. If they’ve stumbled upon my essay, they’re ready to spend a few seconds or minutes trying to ascertain my point and decide if it’s interesting enough to pursue, so I better make the point efficiently and let them judge it for themselves. The more I hedge and defend and qualify what I’m saying, the harder that’s going to be for them. Expressing my own doubts about what I’m saying doesn’t help the reader either. It’s better that I speak with full confidence and let them decide if I’m right or wrong.

I make one particular assertion in my Polarization essay: I say that people tend to ascribe good intentions to those who share their gut reactions and bad intentions to those who don’t. This is something I happen to believe. Of course I’m aware that it’s the kind of claim that researchers in psychology and sociology might study and write papers about and gather data to support or refute. Because I respect expertise, I feel that I should either find references to support this claim or let the reader know that it’s just a hunch that I can’t support in any formal way. Maybe I encountered the claim sometime in the past and forgot the source — I had better look it up. If I were writing a paper for a college class I’d indeed have to do that. But an academic mindset is actually my enemy when it comes to writing effective personal essays. If I get quickly to saying what I really think, without the justification, the hedging, the pugilistic citations, the defenses, the reader will sooner be able to make their own judgement, and guess what… so will I! If I manage to get my point down on paper without the gunk of self-defense and reified anxiety, I’ll be able to discover what I actually think and then I’ll be able to decide whether I really believe it. Cut the fear, keep the meat. In this way, the goal of “Writing to learn,” named by William Zinsser, might come to fruition.



What causes polarization in society?

If this seems like an intractably complex question, let’s approach it by asking why polarization surprises us in the first place. Since it’s easier to stoke enmity than empathy, easier to start a war than to end one, why shouldn’t polarization be the norm? Why shouldn’t all societies be divided all the time?

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Language, Society

Don’t lead with lies, even quoted ones

To anyone in the media who might ever read this, I beg you to stop spreading propaganda through your well-meaning but counterproductive efforts at “fact checking.”

When a politician releases propaganda, they want the propaganda to spread. They’re hoping for people to repeat it as often as possible. They’re trying to exploit the illusory truth effect — the way familiarity breeds belief.

Whether the propaganda is repeated approvingly or disapprovingly doesn’t matter. As long as the repetition – the transmission – occurs, the goal is achieved. If you, as a member of the media, repeat the propaganda and then explain why it’s false, you’ve still repeated it and served the goal of the politician who wanted precisely that to happen. This applies especially to the genre of fact checking.

When you fact-check a statement by a politician, you often do it in two steps. First, you recite the statement: “Politician X said ‘Pigs can fly.’” Second, you address the veracity of the statement: “There is no evidence that pigs can fly.”

It matters what you lead with.

Leading with a falsehood – even a quoted one – is a terrible approach because it gives the falsehood the spotlight. Wouldn’t it be great if pigs could fly? You should give the truth the spotlight instead. The truth is at a disadvantage because it’s less titillating than the lie. Pigs are earthbound – how boring! If your goal is to promote the truth, you need to work extra-hard to compensate for its inherent disadvantage. Showcase the truth by introducing it first. Explain why it matters. Only then, once the truth has been firmly established, quote the lie. Then repeat the truth. “Pigs definitely can’t fly. But Politician X claimed today that they can. But we know they certainly can’t.”

After this “truth sandwich” has been presented – truth-lie-truth – you should then examine the motivations behind the lie. “Given that pigs can’t fly, why would a politician want citizens to believe the falsehood that pigs can fly? What is at stake?”

Realize that your audience consists of some people who trust you more than they trust Politician X, and some people who trust Politician X more than they trust you. If an audience member is in that first category – if they’re already suspicious of Politician X – then your fact-checking probably doesn’t tell them anything they didn’t already assume. You’re only asking them to dedicate more of their mental energy to considering a falsehood that they’ve already rightly dismissed. But if an audience member loves Politician X, they’re going to cling to what Politician X said. When you quote Politician X they’re going to concentrate on the quote itself, ignoring the analysis that you offer next. They’ll forget your quibbling assertion that Politician X’s statement is false because what you’re saying isn’t as exciting and they don’t really trust you to begin with.

The only way to make fact-checking effective as a tool for promoting the truth is to make it about the truth. The truth is the story. The truth is the main character. The truth gets the spotlight. The propaganda – the false statements that are being fact-checked – should be given a minor role. They should only be allowed an appearance after the truth has had its initial say. And once the propaganda gets its turn, the truth should get another turn, the final say.

When I started writing this post, I assumed I was developing the material on my own. Indeed, fact-checking has been a pet peeve of mine for some time and I had written about it back in 2016. But when I searched for the term “truth sandwich,” I came across an NPR article from 2018 citing the linguist George Lakoff. I vaguely remembered reading it back then. I must have internalized the idea and forgotten the source — not unlike someone who remembers a claim they heard during a “fact check” session and then forgets the fact-checking part. So… the “truth sandwich” idea isn’t mine – the credit goes to Lakoff. Back in 2018, Lakoff’s proposal got a few mentions. A few members of the media discussed it and published articles on it. I fear that two years later, the lesson has not been widely learned and propaganda maintains the upper hand, happily co-opting the efforts of those who attempt to fact-check it out of existence. So I will do what I can to promote Lakoff’s truth sandwich. I hope you will too.


Only Twelve Notes

How is it possible that all of music… uh… make that all of Western music… uh… make that much of Western music is formed from only twelve notes? How is it possible that some of the greatest music takes flight with fewer than twelve notes — only seven, or only five? This is a question that often occurs to people taking their very first steps in learning about music theory. If you knew absolutely nothing about the technical side of music, but you only knew of the infinite variety of musical experience – the way music can make you feel ecstatic and depressed and every shade in between, the way music can keep you entertained for hours on end – you might be shocked to learn that all of these diverse and brilliant riches are constructed from at most twelve elements. It seems unbelievable that you’d never get bored of those same twelve elements repeated over and over. But then you get used to the idea. As you learn more about music theory, you may feel that you understand how it all works, but the question “Only twelve?” might still cross your mind from time to time. I myself was thinking about it the other day and imagining how I might respond to a beginning student who insisted that there simply must be more than twelve notes. I imagined several responses I’d give the student, and I’ll record them here.

The first response is a cheeky one: asking more questions. So you’re surprised that there are only twelve notes? Then how is it possible that everything we taste is built from five basic flavor sensations: bitter, salty, sweet, sour, and umami? How is it possible that everything we see is based on three primary colors: red, blue, yellow? How is it possible that all of Shakespeare, no, all of English literature – everything we’ve ever read or written, and everything we will ever read or write – is formed from 26 letters and some punctuation marks? How is it possible that all of the content we’ve ever seen on the Internet – every video, every news article, every comment, every social media post – is represented using only two elements: ones and zeroes?

The second response is to dispute the premise. Yes, Western music has twelve named note but each named note may occur in many different ranges. The note A0 at the bottom of the piano’s range is a very different sonic experience from A7 near the top of its range, but they are both called A. A piano actually has 88 keys, not 12, and each of those 88 sounds different. If someone endeavors to sing the note A at 440hz, their voice may wobble slightly, or they may deliberately employ vibrato, in which case we hear a range of frequencies hovering around the 440hz mark. And in fact, a piano can be tuned in different ways – equal temperament is only one option. The use of twelve named notes is a simplification that conceals a much wider variety of sonic material that music can and does exploit. Music has cymbal crashes and washboard scratches and whispered words and other sounds that don’t have a specific pitch. And there is some Western microtonal music that uses 19 named notes, or 22, or 48….

A third response is to point out that twelve notes actually give rise to a very wide variety of permutations and combinations, which each have their own distinctive qualities. Lets say I want to make a sound combining four of the twelve named notes, and I want to pick one note to be the lowest, another (possibly the same) note to go above it, a third note to go above that, and finally a fourth note to go on top. I can do this in 12^4 = 20736 different ways. Now what if I want to create sequences of note combinations? The possibilities explode.

A fourth response is that notes can be delivered in an infinite variety of ways. A note can be loud or soft. It can be long or short. It can be played by a piccolo or a tuba or a guitar… or an entire ensemble. You can attack a note directly or you can slide up to it, or down to it. On each instrument there are countless articulations. There may be only one named note A, but that A can take countless forms.

A fifth response, perhaps the most interesting to me, is that notes can give different meanings to each other and can renew themselves in our perception. A sequence of notes can put a listener in a certain state of mind, and that state of mind then determines how the listener hears further notes in the sequence. If I play the note C a few times, it may come to sound familiar to you. If I play a C chord, followed by a G7 chord, followed by a C chord again, then the note C will sound like “home.” Even though you may have heard the F# chord millions of times in your life before, the F# chord would sound strange and unexpected if you heard it at this particular moment. Your perception of a note or a chord is not governed as much by your history of hearing it over your lifetime as it is by the context that’s been created by the notes and chords you’ve heard just moments ago. If I had played a different chord sequence – F# followed by C#7 and then F# again – it would be the note F# that you’d experience as “home” while the note C and its chord would sound alien and unexpected.

Music uses gesture and pattern to make certain notes and chords sound familiar while others sound foreign. Once a perceptual frame is established, music can shift it around, making the now-foreign sound familiar and the now-familiar sound foreign. In this way, you can listen to a four-hour concert that uses only twelve named notes, never getting bored with any of those twelve, because the context in which you’re hearing those notes – and thus the meaning those notes acquire – is constantly changing. A C that you hear at the beginning of the concert may not sound the same to you, may not mean the same thing to you, as a C that you hear in the middle or at the end. That C and in fact all of the twelve named notes are only vessels that assume different meanings and affects according to the infinite variety of contexts that they create for each other and the infinite variety of moods or perceptual frames that they put us in. Music uses notes to give meaning to other notes, and as the music continues, the meanings change. While the meaning of C can change over the course of a concert, it can also change from one moment to the next: C might serve as the root or anchor of the chord you’re hearing now — it might be a stable note in this instant — but it might become the tension-giving seventh of the chord you’ll hear next.

A sixth response is that we don’t only hear notes — and the melodies and harmonies they create — when we listen to music. We hear rhythm too, of course. (Another question: How is it possible that most of the rhythms in Western music are made from whole notes, half notes, quarter notes, sixteenth notes, thirty-second notes and their dotted and triplet varieties?) Beyond that, we hear texture. We hear performers, we hear composers, we hear the people the music is about, or the people it’s for; we hear something of the history of when it was written or performed; we hear the memory of when we heard it first or heard it last; we hear the way we feel right now as it relates to the sounds that confront us. We may be something of a different person each time we listen, and listen again, to the same piece. There’s that.