title: PUM Synthesizer — design proposal audience: builder + Sheela Rahman (Xosar) frame status: proposal v1; references existing scope3d prototype sources: pum_core (this repo) · scope3d/ (prior session, 32-step interpretation) · Bendall PART 15/17 · Sheela Rahman / Xosar interviews

PUM Synthesizer — design proposal

0. Frame

This is a proposal for a physical + software synthesizer whose entire architecture is generated from PUM. Every parameter (oscillator pitch, filter Q, modulation rate, envelope time, Lissajous figure aspect, cymatic plate diameter) is a PUM-derived rational, not a free-floating number.

The reference frame is Sheela Rahman / Xosar’s “coherent frequencies” approach: she treats PUM ratios as physical resonance addresses rather than musical aesthetics, and uses sound + cymatics + geometry as a single unified probe. The synthesizer below is built so any setting can be cited back to a PUM seed — there are no “magic numbers.”

The scope3d prototype in ~/claude/scope3d/ is already step 1: a 3D oscilloscope with a 32-knob voice bank driven by the 24 PUM rows, three render modes (Lissajous XYZ, Waterfall FFT, Cymatics Chladni). This proposal extends scope3d into a fuller instrument and sketches the hardware path.

1. The model in synth terms

2. Architecture (3 layers)

Layer 1 — Voice generators

Eight oscillators per voice, addressed by (cardinal × dimension) in the projection grid:

osc_index = cardinal_index * 4 + dimension_index   # 0..15

freq(osc) = MUSIC_C * (cardinal_value / (dim_fraction * 1000))
          = (800/3) * cardinal_value / (1000 * n * 10/9)
          = (240/n) * cardinal_value / 1000

Concretely (Hz):

After octave-folding into the audible band [27.5, 20000] Hz every cell becomes a usable musical pitch. The projection grid in pum_svg/projection_grid.svg is the voice patch panel.

Layer 2 — Modulation

Five modulators wired in parallel, each driven by a different PUM rate:

Quantizer: every modulator’s depth and rate snap to elements of the PUM rational lattice (so randomized = still lattice-valid).

Layer 3 — Spatial / output

Quadrature panning (Vajra-mirror): left-front (+), right-front (+), left-rear (−), right-rear (−). Pairs at 90° apart per the patent’s charge-source layout. Sum ≈ true zero at the centre (the Plasmoid singularity). Acoustic equivalent of a real Vajra: the listener stands at the zero point.

Lissajous XYZ render (already in scope3d): X = cardinal_a, Y = cardinal_b, Z = dimension_modulator. Rotating the projection through dim-fraction angles draws the four-quadrant rose as a 3D figure.

3. Patches that ship out of the box

Patch A — “Protium drone”

• 8 voices on freq(AETHER × 5D) = 25,920 Hz / 27 ≈ 960 Hz and octaves
• HYDROGEN_LFO modulating amp at 0.5184 Hz
• 3-4-5 triangle envelope: attack = 86.4 ms (3-side scaled), hold = 345.6 ms (4-side), release = 432 ms (5-side)
• Cymatic mode: visualises Chladni nodes for a circular plate at 960 Hz
• Use: root drone for any PUM piece. The hidden tempo is the precession rate.

Patch B — “Vajra basket-weave”

• 15 voice pairs (30 osc) on the 16-EDO scale (75 cents per step, from pum_tuning/pum_16sector.scl)
• Outer 15 phase-locked CW; inner 15 anti-phase CCW (opposite twists)
• 5:1 amplitude ratio outer:inner (volume-ratio identity)
• Quadrature panner active
• Use: texture pad for the central torus motion. The 5:1 imbalance creates a self-stabilising vortex in the stereo field.

Patch C — “Element resonator”

• One voice per noble gas at its V value scaled into audible range
• H = 32,400 / 16 = 2025 Hz
• He = 3,136 / 4 = 784 Hz
• Ne = 147,456 / 64 = 2304 Hz
• Ar = 82,944 / 32 = 2592 Hz (= GREAT_YEAR / 10)
• Kr = 19,600 / 16 = 1225 Hz
• Xe = 64 → 64 Hz (no octave shift)
• Rn = 1,225 → 1225 Hz (= Kr)
• Triggering each voice runs the right-triangle cascade as a glissando through the time-cascade decimals
• Use: play the periodic table directly. Bendall’s elemental V table becomes a custom tuning per element.

Patch D — “Sanskrit Time”

• 311,040 Hz divided 11.111 → 27,993.6 → fold into 27.99 Hz (rumble)
• Ring-mod against RFEU_RING (1,296 Hz)
• 16-sector Sequencer running at 22.5° per step at the Schwabe tempo (11.111-second loop)
• Use: slow-evolving textural piece keyed to the Aether→Matter conversion factor

4. Hardware build (Eurorack-compatible, ~$400 BOM)

Software-only path: build entirely in Reaper / Bitwig / VCV Rack with the .scl scales loaded from pum_tuning/.

5. Integration with the existing scope3d prototype

~/claude/scope3d/ already does the Lissajous + FFT + Chladni rendering. Concrete extensions to ship:

1. Load the new pum_core symbols as preset banks. The 58 catalogued symbols become 58 quick-recall presets, each a frequency × dimension address.
2. Map every patch (A-D above) to a button in the UI. Patches encode envelope + modulation + render mode in one click.
3. Hook the Hydrogen cascade as an automatic filter sweep — when a note is played, an 8-stage filter cascade with cutoff times [24, 60, 60, 60, 60, 60, 60, 24] (in subdivisions of the master clock) runs through the cascade values, ending at TIME or LIGHT. This makes the H story audible.
4. Cymatics export — render Chladni node patterns at each PUM cardinal frequency to PNG/SVG (this becomes the bridge to the materials section below).
5. Microtonal Scala load — drop in pum_dimension.scl and pum_16sector.scl from pum_tuning/. UI shows note → cents from C = 800/3 Hz.
6. ext-clock: accept a master clock tap and lock all PUM-derived rates to whole-number ratios of it. Lets the synth sync to a DAW or to Sheela’s existing performance setup.

6. Why this is more than a tuning system

A normal microtonal synth lets you load arbitrary scales. A PUM synth is constrained: every parameter must be derivable from {AETHER, SUN, TIME, MATTER, dim_fraction(n)} via {×, ÷, ±} on small rationals. That’s a strong constraint and it produces a recognisable sonic signature: sounds at PUM addresses rationally interlock with each other across all axes simultaneously (pitch ratio, envelope time, modulation rate, panning angle).

In Rahman’s framing this is what “coherent frequency” means — not a single Hz value but a whole geometry of relationships that are each others’ integer multiples in some basis. A PUM patch sounds like one thing, not eight overlaid things, because every component shares the basis.