# Research notes

How each Sacred Audio instrument is modelled, what it is checked against, and why.

## Shards

### Where do the tones come from?

Each stone sounds the note of the chakra it is linked with in crystal practice, from root on C up to crown on B, on the suite's reference pitch. Its overtones come from its crystal system: quartz-family stones use 1 : 2.76 : 5.40 : 8.93, close to the partials of a struck bowl; cubic stones such as pyrite and fluorite sit near the harmonic series, 1 : 2 : 3 : 4.16; glass and carbon (obsidian, moldavite, tektite, shungite) are inharmonic, 1 : 1.73 : 3.1 : 5.2, with a short strike of noise.

Ring time is the Mohs hardness times 0.9 seconds, so selenite (2) fades in under two seconds and quartz (7) rings for more than six. These are our design rules for each stone, not measurements of a physical crystal.

### How does placement change the sound?

Every stone adds up what its neighbours give: shimmer, glow and vibration, weighted by distance and falling to nothing at about the radius of the altar. Amplifying stones multiply what a stone receives; grounding stones calm its vibration.

The result sets each stone's level, its two-octave shimmer partial, its tremolo rate and depth, and how much of it goes to the shimmer delay and the halo reverb. The altar you see and the sound you hear use the same rule.

### How light is it?

Every build renders all 29 ready-made grids with two held notes, a struck stone and the drone, and checks the level and the CPU. The busiest grid uses about 7 % of one core at 48 kHz on the build Mac. Levels sit around -19 LUFS, so it does not come in loud.

## King's Chamber

### Is it a convolution reverb?

No. Four engines share one model of the room: exact image-source early reflections up to the 8th order (about 500 paths in the first 100 ms), a bank of about 300 room modes below 190 Hz, the coffer's own cavity (an open-top quarter-wave near 98 Hz) with a granite resonance near 117 Hz, and a 16-line feedback delay network for the tail.

Each mode's level depends on where the source and the listener stand. That is why moving the listener changes the low end so much, and why a convolution reverb, frozen at one position, could not do this.

### Where do the dimensions come from?

From Flinders Petrie's survey: 10.47 × 5.234 × 5.80 m, a double square with a √5 diagonal. The coffer is 2.276 × 0.978 × 1.049 m outside. Nobody knows where the coffer first stood: Petrie found no setting-out marks and signs it had been moved. So you choose: Petrie's position, two later proposals, or centred.

### How do you know it sounds right?

We measure it on every build. At the centre of the room the decay (RT60) is 4.0, 3.9 and 3.0 seconds at 125 Hz, 1 kHz and 4 kHz, close to the roughly 4 seconds reported for the real chamber. Lying in the coffer, 2.3 s at 125 Hz. The decay knob set to 30 s measures 31.0 s. Every other sacred room lands within 25 % of its published decay, and the worst peak before the limiter is −0.3 dBFS.

### What are its limits?

The published acoustic figures for the chamber are thin and partly second-hand (Danley, Reid, Audio Ease). Our next step is to fit the model to measured impulse responses. The binaural output uses time and level differences between the ears, not HRTF. The chanting voices share the main source's mode pattern; giving each its own would cost about 16 times the CPU.

### Why mono bass, a duck and a limiter?

So it works in a mix. Below 120 Hz the tail is mono and anything under 30 Hz is cut, the Duck clears room for the kick, and a look-ahead limiter at −0.5 dBFS keeps 30-second tails safe. The 432 and 528 Hz keys are played as 108 and 132 Hz with two upper octaves, so 432 and 528 sound exactly.

## Divine Spatializer

### How does it place sound in 3D?

With a parametric binaural model: a time difference between the ears of up to about 0.66 ms, a head shadow that darkens the far ear down to about 1.7 kHz, a pinna notch that moves with height, a presence lift in front and a softer top behind, plus air absorption and a small room. It does not use measured HRTF data yet. HRTF and Ambisonics output are next on the roadmap.

### How are the routes built?

The Tree of Life is laid out in 3D with its 22 paths. On Metatron's Cube, each solid's orbit is a Hamiltonian cycle around the head, and "all 78 lines" is an Eulerian circuit that travels every line exactly once, found with Hierholzer's algorithm.

### How do you check it?

Tests on every build: Tiphareth on the Middle Pillar is centred to within 0.5 dB; Chesed reaches the right ear first and more than 1.4 times louder; Kether is brighter than Malkuth; motion never jumps more than 6 cm per step; and a binaural input keeps its two ears apart, so Binaura's beats pass straight through.

### Why does the Middle Pillar sound inside the head?

In our map Kether, Da'at, Tiphareth, Yesod and Malkuth lie along the listener's spine, so those spheres sound inside the body rather than around it. Where Kether and Da'at should sit exactly is still an open design question we keep listening to.

## Binaura

### How does Binaura make the beat?

Each ear gets a pure sine tone: the left at the carrier minus half the beat, the right at the carrier plus half. The brain hears the difference as a slow pulse. A 200 Hz carrier with a 10 Hz beat plays 195 Hz left and 205 Hz right. The beat glides between values on a smooth logarithmic curve.

### Why does a Gearbox journey never skip a band?

The order comes from the entrainment texts in our research library (Neuro Alchemy, Signal Protocol, Harmonic Alchemy): reach a band, settle, then move to the next one. Gearbox steps through every neighbouring band with a dwell time and a glide between them, and the test suite fails any journey that skips one.

The bands are Delta 0.5–3 Hz, Theta 4–7, Alpha 8–12, Beta 13–30 and Gamma above 30. The Schumann ladder is 7.83 Hz and its octaves; the Phi ladder divides a root tone (79.617, 117, 147 or 432 Hz) by φ until it lands in each band.

### How do you check it?

Every build renders every preset through the real plug-in. A 200 Hz carrier with a 10 Hz beat must measure 195 and 205 Hz to within 0.05 Hz. A ramp from 6 to 1.5 Hz over 60 seconds must pass 3.0 Hz at exactly 30 seconds. Every preset must peak at or below 0.9, and a journey that fades out must end in silence.

### Why does the mandala move so slowly?

Its motion is the beat divided down below 1 Hz, and it only brightens gently. We don't want a screen that flashes at brainwave rates, so it never does. For speakers or a room, the isochronic pulse carries the rhythm, because binaural beats need headphones.

## cymaheal

### Are the figures real physics?

cymaheal has two figure engines. The Classic engine, the one you see, draws the textbook figures: the classic cos·cos approximation for the square plate, membrane modes for the round plate, and breathing mandalas for water. They are stylised on purpose, because they read clearly at a glance and follow the music smoothly.

Under it we built a physical engine that solves free glass plates with Kirchhoff plate theory and an 80 mm water dish with the real capillary-gravity waves. We use it to check and tune the figures.

### What is the physics checked against?

The square plate, solved with the Rayleigh–Ritz method, reproduces the eigenvalues in Leissa's Vibration of Plates (NASA SP-160) exactly: 13.468, 19.596, 24.270, 34.801. The disc is within 0.3 %.

Against Chladni's own tone tables from 1787, all 31 square-plate tones land on the right mode, with a median error of 28 cents, and disc figures 22–66 have a median error of 31 cents. The best-fitting material is glass (Poisson ratio 0.22), which is what Chladni used. One question is still open: his figures 2–20 sit an octave and about 60 cents away from the rest, probably a second plate or a slip in transcription.

### How does it follow the melody instead of the kick?

Since version 2.9.5 the spectrum is weighted the way the ear hears it (A-weighting), and only clearly pitched peaks, at least 9 dB above their surroundings, steer the plate. Kick thumps and hi-hat noise are ignored. On a test mix of kick, rolling bass, lead and hats, the plate follows the lead note by note: 440, 523, 659, 587 Hz, four different figures.

### Where do the 1,266 library records come from?

Every record carries its source title and link: Chladni 1787 and 1817, Wheatstone 1833, Faraday 1831, Hans Jenny, Alexander Lauterwasser, Margaret Watts Hughes, CymaScope and more. Each is labelled as measured or as tradition. Claims such as Rife frequencies are kept as history, not as fact.

## Harmonia Mundi (coming soon)

### Where do the tunings come from?

Three systems: the Pythagorean tradition with C = 256 Hz, the intervals of Kepler's Harmonices Mundi, Book V (1619), and Hans Cousto's The Cosmic Octave (1978), where each planet's orbit is raised by octaves into hearing: Saturn at 147.85 Hz, the Moon at 210.42 Hz.

### How are the voices made?

Each planet is additive: 24 partials and a halo of 6 more, sung through formant filters for its Greek vowel. The orbit periods are real, scaled down: Saturn 10,759 days, the Moon 27.32 days.

### How does it know the planetary hour?

From the standard sunrise equation for your location, accurate to a minute or two, with the hours in Chaldean order. It's tested for Tampere and for polar night on Svalbard.

## Veil (coming soon)

### How is Veil built?

A lip buzz locked to the bore's first resonance, with voice and breath added, rings through eight modal resonators per channel. Their ratios and damping come from the wood or material you choose. Two vowel formants and a gentle saturation follow; the saturation is what makes the hummed difference tones.

The note follows the length: f = c / (4 · L · k), with k = 0.72 for a flared bore. 1.45 m plays E2, about 82 Hz.

### How was it voiced?

Against two real didgeridoo recordings: harmonic-to-noise around 5 dB, odd harmonics about 19 dB over the even ones, band energy within a few dB, and a natural pitch wobble of 12 to 20 cents.

## Lingua Sacra (coming soon)

### Where do the scales come from?

The Nippur modes are the seven-note modes reconstructed from Old Babylonian lyre-tuning texts, alongside an Ur pentatonic and a Hurrian hexatonic. Sanskrit brings ragas and thaats, Hebrew the Jewish prayer modes (shteygers), and Arabic the maqamat.

### What about quarter tones?

Lingua Sacra plays in 12-tone equal temperament. Maqamat with quarter tones, such as Rast, Saba and Bayati, use their standard 12-tone approximations, so everything stays in tune with the rest of your track.

### How does a word become a melody?

Gematria, Abjad, Katapayadi or Babylonian sexagesimal give each letter a number, and the numbers become steps in the scale. שלום (shalom), for example, is 376.

### Where does the groove come from?

The seals pulse where their lines truly cross. A pentagram's crossings divide each edge in the golden ratio, so the pulses fall long, short, long. The sound engine is a plucked Karplus-Strong string with six sympathetic strings, a six-mode body, jawari buzz and a reed.

## Platonic Solids (coming soon)

### How does geometry become sound?

Every vertex of the turning solid is a voice. Its depth sets the delay time, left and right set the pan, height sets the pitch, and facing you sets the level. When you morph between solids with different numbers of corners, the nearest vertices are matched and voices split or merge.

### What are the sources?

Plato's Timaeus (53c–57d): fire, air and water share the same triangle and turn into one another; earth only settles, so morphing out of earth is slowed. Kepler's Mysterium Cosmographicum (1596): the five solids nested as shells, 50 voices. Pythagorean C = 256 tuning, Cousto's Cosmic Octave, and the 24-gon prime wheel with its eight prime spokes.

### What did you leave out?

We found no sourced chart that links Solfeggio tones to the solids, so we don't ship one.

## Apex (coming soon)

### How is the rise made?

A beat repeat locked to the grid: the slices halve in length as the pitch climbs, while a high-pass drain, a low-pass, a trance gate and a widen-then-mono move with it. After the drop, the shot and a Doppler-falling beam play.

### Why does it sound clean?

Four-point Hermite reads, 3 ms equal-power crossfades, filters built so sweeps don't zipper, and 8 ms fades in and out. When Apex is idle, the output equals the input sample for sample.

### Where do the numbers come from?

The Kukulkan beam adds one odd harmonic per step, from sine towards square, up to 91, the steps of El Castillo. The Gematria gate is 441, the value of אמת (truth), written in binary as 110111001.

## Conjurer (coming soon)

### How does it arrange?

A rule engine built from psytrance co-production rules: drain, silence or slam into a drop; bring the bass back first in the rebuild; change the groove by taking things away; a K-B-B-B sub roll between about 39 and 58 Hz.

### How does it read a reference track?

It finds the tempo from the kick onsets, the downbeat from changes every 8 bars, and the sections from the energy below 110 Hz and between 110 and 250 Hz.

### Does it change my sound?

It only moves faders, pans and sends. No EQ, compressor or filter is ever added, and it uses your own Live presets.