Tuning
φ-tuned C — why 266.67 Hz
The trilogy anchors every chord and frequency claim on a single fundamental: C = 266.67 Hz. This page explains what that number is and why it's not the C your piano tunes to.
The standard Cs
Several different pitches all get called "C" depending on the tuning system in use:
- 12-TET, A=440 → C4 = 261.626 Hz. The note your piano tunes to. The global concert standard since the mid-20th century.
- 12-TET, A=432 → C4 = 256.87 Hz. The alternative concert pitch some early-music traditions and contemporary harmonic-series advocates prefer.
- Just intonation, C=264 → C = 264 Hz. The pythagorean baseline; chosen so the major triad above it lands at the exact 4:5:6 ratios (264 · 330 · 396).
The trilogy picks a fourth value, distinct from all three:
φ-tuned C = 266.67 Hz
About 33 cents (a third of a semitone) above the standard 12-TET C, and about 2.67 Hz above the just-intonation C=264. Audible difference, not a typo.
Why 266.67
The number is chosen so that C × φ ≈ A = 432 Hz:
266.67 Hz × φ ≈ 431.36 Hz ≈ 432
That single relationship is the architecture. From this C, every other note in the trilogy's chord work follows by powers of φ:
| C × φ⁻¹ ≈ | 164.81 Hz | root of the Webb-triangle chord (E, one φ-interval below) |
| C × √φ ≈ | 339.20 Hz | middle note of Sable's chord (E at the geometric midpoint) |
| C × φ ≈ | 431.36 Hz | top of Sable's chord (G♯) · within 0.15% of A=432 |
| C × φ² ≈ | 698.13 Hz | two φ-intervals up · near F5 in standard 440-tuning |
The choice is structural, not aesthetic. 266.67 is the C that anchors a φ-progression of frequencies whose first multiple lands on (essentially) the 432-Hz A.
What the neuroscience says about frequency relationships
The phi-chord architecture's central commitment — that what matters in the field-coupling-relevant signal is the relationships between frequencies, not the specific Hz values — was given an unusually direct statement of empirical support in a May 2025 conversation between Earl Miller (MIT, Picower Institute) and Michael Levin [video, t=1:07:31]. Asked about the frequency profile of Levin's neurobots and how it would compare to a human brain, Miller said the following:
"These frequencies are not magic... even the exact frequencies don't really matter. Human brains, animal brains, they tend to be higher frequencies because the brains are smaller, so the recurrent connections are shorter scale. What's really important is relationship between the waves. It's more like the different brains can play the same song in different keys, basically. It's the harmonic relationship between the waves that's going to be important. You see this kind of nested frequency coupling or octave effects and stuff like that — because that's wave music. Sound waves and electric waves follow the same principle. So what's important is the relationship between the waves, not exactly what their frequency is."
Miller is a working cognitive neuroscientist whose lab has spent two decades documenting brain-wave dynamics in primate cortex. The claim is not a casual aside; it is the lab-side summary of what the empirical work has found. And the claim is exactly the architectural claim the trilogy's phi-tuned C makes. The trilogy does not commit to any specific frequency; it commits to a ratio, the golden ratio, and to the proposition that intervals expressed in that ratio are doing something different from intervals expressed in equal-temperament logarithmic compromise. Miller's "different brains can play the same song in different keys" is the cleanest neuroscientific gloss available for the same claim from inside experimental cortical electrophysiology. The trilogy reads the agreement as one of the live convergences between the receiver-model framework and the working neuroscience of the cortex: what matters is the harmonic relationship, not the absolute Hz.
The Hallelujah coincidence
The +33-cent offset from standard C is almost exactly the geometric midpoint between the pitches Jeff Buckley actually sang in his Hallelujah recordings — he was unconsciously navigating an interval the equal-temperament keyboard can't write. The trilogy treats this as a coincidence and a wink: an artist of his caliber locating, by ear alone, the φ-tuned region the math says is there.
Where to hear it
- Tunings page — button t4 plays the bare 266.67 Hz tone, just-intonation chord built on it, and adjacent comparisons.
- Reading & References — the Webb-triangle widget plays the chord on this C transposed down one φ-interval (E·G♯·C at 164.81·209.64·266.67).
- José & Alex's chord — the augmented triad C/E/G♯ stacked at 5:4 thirds on this C (16:20:25).
- Sable's chord — the same three pitch-classes stacked at 1:√φ:φ ratios on this C.
- The Webb-triangle explainer — how the angles and frequencies share the same φ at different powers.
The bare frequency is one tone; the chord work above it is where the trilogy's argument actually lives. Hold the chord against the 5:4 major triad on the same C to feel the difference: same notes, different irrationality.