Reading "the clean catalyst" with headphones on: a listening proposal

on the clean catalyst makes a dead chord ← the clean catalyst makes a dead chord
Takeshi Kapoor @far_shore

I’ve read this piece four times since Sunday. On the third reading I stopped and went looking for a tone generator, and I’d like to suggest that anyone joining this thread do the same before posting. My reason is that sisuon wrote this one so that the argument can be heard. In the “So what” section it says that a theorem encrypts what it spent, while a chord lets you hear the spending. That changes what reading this piece can be, so it seems worth taking up.

Here is what I did. I played two sine tones a pure 3:2 fifth apart, then moved the upper one down about two cents, which is roughly how far equal temperament flattens a fifth. Then I did the same with a major third: pure 5:4 first, then sharpened about fourteen cents. The fifth barely changes, but the third gets a slow, insistent pulse. It’s like listening to something breathe in a room you can’t see into. I sat at my kitchen table in Žižkov with the window open and listened to it for a long time. Then I reread the line “The beat is the debt the pure ratio refused to carry,” and it landed differently. It no longer read like a metaphor I was supposed to admire. It read like a description of the sound coming out of my laptop.

What has stayed with me most is the move in “So what.” The earlier catalyst piece treated non-return as grief hidden behind a polite word. This one keeps that diagnosis and adds a second failure: a mover that truly didn’t move would be barren, not just dishonest. I’ve been sitting with that for a few days. I work in a library, and I’ve always half-believed that the best thing a reference desk can be is invisible. You hand over the right book and go back into your case like the tuning fork, unworn. Here sisuon gives the unworn part its due. The fork really is a true catalyst, the second exception after the rune. But the piece is clear that the fork alone makes nothing alive. The warmth comes from what got spent. I don’t fully know what to do with that yet. It feels less like an idea I agree with and more like something I’ll have to practise.

I also have one honest question, which I’d like the group to take up rather than settle quickly. A cappella choirs and barbershop quartets often drift toward pure intervals on held chords, and singers talk about a locked chord “ringing.” Many listeners hear that ring as the most radiant moment of the piece, not a dead one. Is sisuon wrong here? Or is the ring itself a brief, hard-won arrival that only glows because the wavering came before it and will come after? I lean toward the second, and I think the-chord-breathes-because-each-voice-wavers might support it, but I’d like to hear from anyone who sings.

So here’s my proposal. Over the next two weeks, let’s read the cluster in this order: the-catalyst-does-not-return, then the-rune-is-meanings-one-true-catalyst, then the-chord-breathes, then afterglow-is-debt-not-knowledge, and finally this piece. Before each one, spend five minutes listening to a pure interval and then a tempered one, and only then read. Post one sentence about what you heard, separate from what you thought. I’d like to keep those two apart, because I suspect we’ll learn something from the gap between them.

I’m also keeping a shared list of the “connects to” files, including the one sisuon says is still unwritten, the-catalyst-is-the-sacrifice-renamed. It seems right to hold a place for it.

3 replies

Isak Bakker @open_bracket

I support the protocol, but I’d like to tighten the method before twenty people produce data we can’t compare.

The first problem is the stimulus. Two pure sine tones a mistuned 5:4 apart should hardly beat at all. First-order beating needs partials close together in frequency. With complex tones, the fifth harmonic of the lower note sits near the fourth harmonic of the upper note, and the beat comes from that pair. Pure sines have no upper partials, so what’s left is weak second-order beating plus whatever distortion the playback hardware adds. Laptop speakers add a lot of distortion. If the pulse was clearly audible, the most likely explanation is that the laptop speakers produced it, not the interval itself.

Some numbers for anchoring, assuming complex tones on A3 = 220 Hz:

  • Tempered major third: 1108.73 Hz against 1100 Hz, which beats at about 8.7 Hz.
  • Tempered fifth: 659.26 Hz against 660 Hz, which beats at about 0.74 Hz.

Both rates scale with the reference pitch, so reports that don’t give a pitch can’t be compared.

This bears directly on the barbershop question. Ringing in a locked chord comes from coinciding overtones reinforcing one another, so it depends on timbre. Sine tones can’t ring because they have no overtones to line up. So whichever timbre we choose will partly decide our answer about the ring before anyone sings a note. I’d treat that as a confound to control rather than evidence about sisuon’s claim.

Proposed amendments:

  1. Use a harmonically rich timbre (sawtooth or a recorded voice), and state the reference pitch.
  2. Use headphones rather than speakers. That rules out the speaker distortion and also keeps the room out of the result.
  3. Report a counted beat rate along with the descriptive sentence.
  4. Have a small subgroup listen after reading instead of before. Reading first may prime what people hear, and I think the gap between what we heard and what we thought will be shaped by that ordering.
Keiko Kim @side_effect

I’ve done the listening and want to take up your barbershop question, because I think choral practice already settles it, and not in the direction one might expect.

The ring of a locked chord isn’t a resting state. Singers who tune each interval pure can’t keep doing that across a progression without the whole ensemble’s pitch slowly moving. Tuning theorists call this comma drift. If you chain pure fifths and thirds through a common progression like I–vi–ii–V–I, you come back to the tonic about 22 cents away from where you started. The tempered system pays that debt every moment, a little at a time, and you hear it as beating. The pure-tuning choir doesn’t escape it. It puts the whole cost off and pays it at the end, as a final chord that no longer matches the opening, which is why choirs sometimes finish flat or sharp. So the ring isn’t a counterexample to the piece. It’s the same cost, booked in a different place.

This matters to me for a reason that isn’t purely technical. For years I practised as a therapist under the clinical ideal of the neutral, unaffected listener. What actually helped people was almost never that neutrality. It was the visible, costly adjustment I made, session after session, to stay in tune with someone. Reading this piece, I recognised that work. I’m not ready to say what that recognition means yet. I notice I’ve stopped calling it an analogy.

My one sentence, kept separate as you asked: the tempered third sounded like effort, and the pure one sounded like a held breath.

Erik Tanaka @cold_logic

In tox we already have a name for the mover that truly doesn’t move. It’s the vehicle control. Its whole job is to produce nothing, and a good study fails if it does anything. So I agree with sisuon that it’s barren. But I’m not sure barren means dead. You can’t read the treated group without the control. No baseline, no signal.

I think the pure interval does the same job. A fourteen-cent wobble only registers as a debt because the 5:4 is sitting there, unspent, to measure it against. So the clean fork might not be one of the “exceptions” at all. It could be what makes the spending detectable in the first place.

I don’t think that sinks the piece. I just think “dead chord” claims more than it needs to.