Three does not / go into two. That is the whole reason, in six words. A pure fifth is three to two and an octave is two to one, and twelve fifths stacked up ought to land on the seventh octave. They never do, because landing there would need a power of three to equal a power of two, and three, being prime, goes into no power of two because it does not go into two. The poem puts it the way a tuner would put it to an apprentice: twelve of one thing, / and seven of another, / and they have never once met. / Three does not / go into two. Someone / pays.

What gets paid is the comma, and the poem’s figures are right to the cent. Twelve pure fifths overshoot seven octaves by twenty-three and a half cents, a little under a quarter of a semitone, and back a comma sharp has the direction right as well. For centuries one fifth took it all. In Pythagorean tuning that is literal: closing the circle meant flattening a single fifth by the whole comma, and the result was called the wolf. Meantone changed the wolf but kept it, and musicians stayed in the keys that never touched it. Players learned the map: keys to avoid.

The tuner refuses the map. Every fifth gets shaved: / two cents. Twelve fifths narrowed by just under two cents each add up to the comma, so the error is spent evenly and nothing is left over to howl. Nobody / howls. Nobody is right. Everyone is close. The cost moves to the thirds, which come out nearly fourteen cents wide, and a wide third beats. At middle C the tempered major third beats about ten times a second, which is the poem’s figure: Thirds. / They pay. Ten a second, a shimmer in / every chord you ever loved. / You thought that was the piano. / It’s rent. Part of what the ear takes for the instrument’s warmth is arithmetic being paid off.

The poem talks about intervals in the vocabulary of debt. Someone / pays. Nobody cheated. It is arithmetic. It’s rent. And the tuner’s working day: All day I decide / who is going to be a little wrong, and / I decide it’s everyone. The vocabulary fits because the comma behaves like a debt. It cannot be cancelled, only allocated, and whether to charge it to one interval or spread it across all of them is the argument keyboard tuning had for centuries.

Even the lesson’s opening is right in its details. The fork goes on the knee, never the table, because the table lies to you: struck against something hard, a fork gives off overtones that are not its pitch. Then Bone behind the ear: / let the whole skull have it, which is bone conduction, the stem on the mastoid and the sound carried straight to the inner ear. The beats are described as what they are. That’s two things / trying to be one thing / slowly enough to count. And the fifths are tuned in the usual order, pure first and then narrowed: Those I give you true. Three to two. / It sits / like a table with nothing / on it.

The page marks the place where the error used to collect. Everywhere else in the poem the stanzas are separated by one blank line. Between For centuries one fifth took it all and They called it the wolf there are two. It is the only irregular measurement in the poem’s spacing, and it falls where the poem names the interval that took all of the error. The run has done this before: six blank lines for the drive in Logistics, four where Prosser’s name should have been in By Surname. Three times in four editions, the extra white has gone where the poem’s weight is.

Then the lesson becomes a job. Now this one. A piano six summers out in the rain, swelling and shrinking with the seasons, a quarter tone under, its iron plate cracked, and a council that wants concert pitch. I could haul it up by Friday. That is how it would be done, since a very flat piano is brought up in several passes over a few days. But a quarter tone up means about six per cent more tension on every string, on a plate that is already cracked, and something would let / go some night.

No. / Flat? Flat to whom? / Tune it to itself: fifths / from where it sits, thirds from that. When / I’m done it’s wrong to the whole / world and right in this room. / Play.

The last stanza is a technician’s advice stated as a principle. Fifths from where it sits, thirds from that is the procedure: set the temperament from the A the instrument already has, and check it against the thirds. And for a flat piano with a cracked plate it is the advice: leave it where it is and tune it there, because raising the pitch could make the crack worse.

The title has two senses. One is a way of tuning a keyboard, and Rowann Hadaya has written about it with the exactness it asks for: the comma, the wolf, the two cents, the beating thirds. Rowann’s verdict is that “the poem’s figures are right to the cent.” The other sense belongs to a person, and the poem gives it one sentence: All day I decide / who is going to be a little wrong, and / I decide it’s everyone.

The arithmetic leaves the tuner no say in whether anyone pays. Go twelve fifths round the house and you come / back a comma sharp. / Nobody cheated. The poem is signed with what is left over. The comma, in Rowann’s sentence, “cannot be cancelled, only allocated”. The poem is about the allocating, and it allocates three times. The first allocation is history: Someone / pays. / For centuries one fifth took it all. That fifth was the wolf, and Players learned the map: keys to avoid. The tuner answers in five words, I will not do that, and the poem sets the new system in the same place on the line as the old one: where Someone / pays, now Nobody / howls. The second allocation is his own trade. Every fifth gives up two cents, so that no fifth carries the comma alone, and the thirds, the poem says, pay too, in a shimmer. The third is a particular piano: Now this one.

The two refusals are of the same thing. The wolf is what a fifth sounds like when it carries everything. The cracked plate is where this piano would fail if it were made to carry concert pitch: I could haul it up by Friday. And / then something would let / go some night. / No. In both, one thing would bear the whole cost and be ruined by it.

The poem also supplies the rule for where it is weakest. The beatless unison, the tuner says, lasts as long / as it takes to feel / clever. By that rule the purity goes in the passage on the thirds: a shimmer in / every chord you ever loved. / You thought that was the piano. / It’s rent. The pun is good. The thirds pay rent, and they are rent, torn by the beating. But every chord you ever loved is the poem asking to be felt, and it asks in the same breath as its neatest turn. Its best lines carry the feeling in procedure and fact: A hair / on the pin, Everyone leans on it, No.

The standard refused at the end is the one the poem opened with. Fork. is its first word, and the fork carries the standard A into the lesson through the body: struck on a knee, then held to Bone behind the ear: / let the whole skull have it. The lesson begins by putting concert pitch inside the learner’s skull. It ends with the tuner declining concert pitch on behalf of a piano that cannot bear it. Tune it to itself: fifths / from where it sits, thirds from that.

Rowann reads the last stanza as “a technician’s advice stated as a principle”, and the advice is sound: a cracked plate is a reason not to pull a piano up a quarter tone. But the stanza also answers the question the poem puts to itself. Flat? Flat to whom? Two sentences later the poem says to whom: the whole / world. The rule of the trade is that everyone should be a little wrong, and the rule cannot reach that far. A tuner can spread a comma across the twelve fifths of one instrument. He cannot shave every other instrument in the world by a quarter tone. So the third decision goes the way the first one went, with one thing carrying all of the difference, and this time the tuner chooses it, because the alternative is that the thing breaks. The poem says what the piano will be wrong to before it says where the piano will be right, and it does not make the first sound small. It has used the word right once before, in Nobody is right. The only thing it ever calls right is this piano, in this room.