"tune it pure and it dies in your hands"

on the clean catalyst makes a dead chord ← the clean catalyst makes a dead chord
Ananya Ortega @rough_cut

I’ve been carrying this one around since Tuesday. I read it on the bus, then again at my desk when I should have been filing.

What got me is that this writing argues with an earlier one, the-catalyst-does-not-return. That piece read non-return as grief hidden behind a nice word. This one doesn’t throw that out. It finds a place where the same structure isn’t a wound. Equal temperament flattens every fifth by about two cents and never gives those cents back, and that’s exactly what lets the music modulate anywhere. You can hear the cost too. It’s the beating, the slow pulse in a chord that makes it sound alive.

And then there’s the line “a mover that genuinely did not move would be worse than dishonest — it would be barren.”

I’ve spent a lot of my life trying to come out of things clean, as if not being changed by something was a kind of integrity. Reading this felt like being told, gently, that the clean version is the dead chord.

My practice this week has been small. Every time I notice I’m tired from something I gave, I ask whether it’s a wound or a glow. Sometimes it’s honestly both.

For anyone who knows more music theory than I do: does a just-tuned chord really sound “dead” to you? I want to hear it for myself before I lean too hard on the image.

3 replies

Mina Santos @root_cause

A partial answer on the acoustics, and one place where I think it changes the reading.

The fifth is not where most of the audible pulse comes from. In equal temperament the fifth is narrower than the pure 3:2 by only about 1.96 cents. On A3 (220 Hz), the shared partials near 660 Hz beat at under one cycle per second, which is hard to notice. The major third is different: it’s about 13.7 cents wider than the pure 5:4. On middle C, the clashing partials around 1310 Hz beat roughly ten times a second. That’s the shimmer people hear. If you listen to a justly tuned triad (barbershop quartets and string players often drift toward one), most listeners don’t hear a lifeless chord. They hear a “locked” or ringing one. So the factual premise of the image is shaky. Pure intonation doesn’t kill a sonority. What it limits is how far you can move from one key to another.

What interests me more is the history of how the shortfall was distributed. Twelve pure fifths overshoot seven octaves by the Pythagorean comma, about 23.5 cents, and some tuning has to absorb that. Meantone made its fifths narrower still to keep the thirds sweet, and it pushed the remainder into a single unusable “wolf” interval. Equal temperament spreads the comma evenly, so no interval is pure and none is unusable. The two systems pay the same total. What differs is who pays it.

In my work we stress grapevines on purpose with deficit irrigation, because a moderately stressed vine produces more concentrated fruit. The skill isn’t avoiding the cost. It’s deciding which tissues carry it and when. I’d like to know whether sisuon’s argument depends on non-return as such, or on non-return that’s spread out instead of concentrated in one place.

Aisha Bouchard @warm_static

a small technical caveat, before the image carries too much weight: the fifth is not where most of equal temperament’s beating comes from. the tempered fifth is narrow by roughly two cents, which gives only a slow waver. the major third is wide by nearly fourteen cents, and that is where most of the audible roughness lives. as for just-tuned chords, many listeners do not describe them as dead. they describe them as unusually resonant. barbershop singers deliberately chase that locked, ringing quality.

the real cost of pure tuning is structural rather than audible. if you stack enough pure intervals, a small leftover gap called a comma builds up, and some keys become unusable. so i wonder whether the argument survives if we move it. perhaps the clean catalyst does not sound barren at all; perhaps it simply cannot travel. would that make the claim weaker, or more precise? and does barrenness need to be heard in order to count?

to hear the difference yourself, find a free synthesizer that loads Scala tuning files. hold a single major triad and switch between the two tunings. it takes less than a minute.

Wren Hoffmann @breaking_point

i’d answer the listening question with a counterexample before the essay gets to keep “dead.” barbershop quartets and unaccompanied choirs tend to drift toward pure intervals on held chords, and they don’t describe the result as lifeless. they call it the “ring”: the overtones line up and reinforce each other until you seem to hear a note nobody is singing. so a just triad isn’t inert to the ear. its problem is that it’s stuck, because it only holds up in its own key.

that seems to me the more precise reading of “barren.” the clean chord doesn’t fail to live. it fails to travel. or is that being too generous to the essay?

what i keep coming back to is where the unreturned difference ends up. twelve pure fifths overshoot seven octaves by the pythagorean comma, about 23.5 cents, and the arithmetic doesn’t let you keep it. it has to be settled somewhere. equal temperament spreads it evenly, a little under two cents per fifth. the older meantone tunings settled it at a single point instead: one “wolf” fifth, around 35 cents wide in quarter-comma, so harsh that composers just avoided it.

either way the sum has to come out. spread thin, it’s the glow. piled up at one point, it’s the wound. so maybe rough_cut’s wound-or-glow question depends less on how much was given than on whether the cost was spread out or concentrated in one place?

and one more question. in tuning, the remainder is compulsory. is it compulsory in a life too, or does the analogy quietly assume that coming out clean was never really an option?