Phone sensors → body oscillators → music → entrainment → body. The founding circle.
YOUR PHONE ALREADY KNOWS
That $800 rectangle in your pocket has two motion sensors sampling 60 times per second. When it’s against your chest, it can feel you breathe. When you walk, it can estimate your heart rate from your cadence. When you tilt it, it can tell whether you’re paying attention or zoning out.
No Apple Watch needed. No chest strap. No special hardware. Your body is already broadcasting its rhythms. The phone is already listening. Nobody thought to connect the two.
THE LOOP
Your body oscillates. The phone reads it. Software turns those oscillations into music. The music pulls your body toward better coupling. Better coupling makes better music. Better music pulls harder.
The body tunes the instrument. The instrument tunes the body. That’s not a slogan. That’s the actual architecture.
WHAT ACTUALLY WORKS
Breathing detection: This is the best channel. Phone on your chest, it picks up each breath cycle as a tiny acceleration swing. Accurate to plus or minus one breath per minute. Degrades in your pocket. Dies on a table.
Walking cadence: When you walk, acceleration peaks at 1.5–3 Hz. Your heart rate tracks your walking tempo within about 10%. Not a heart monitor. A proxy that works during locomotion.
Posture as attention: The least physiological channel. Upright and stable = engaged. Slouched = checked out. It maps to attention, not cognition. But attention is what the instrument needs.
WHAT DOESN’T WORK
The phone can’t reach your gut, liver, pancreas, or immune system. Those oscillators are too slow and too internal. It only sees the fast group: heart, brain, breath. But that’s the group music can entrain anyway. We measure the oscillators we can change.
Also: a person lying down reading intently will register as “disengaged.” The proxy assumes you’re standing or walking. That’s the use case.
THE 4:1 TARGET
The sweet spot is 4 heartbeats per breath. That’s the natural ratio where heart and lungs couple most efficiently — respiratory sinus arrhythmia. So the instrument figures out your current breathing rate, calculates what tempo would push your heart rate toward 4:1, and plays at that tempo.
You breathe at 16 per minute. Target heart rate: 64 BPM. Music plays at 64 BPM. Heart rate drifts toward tempo (Bernardi 2006, published in Circulation). The ratio tightens. Coupling strengthens. Music gets simpler. The loop tightens.
THE FOUNDING CIRCLE
“What makes music good?” Coupled oscillators. The body IS coupled oscillators. Phone sensors read the body. The instrument makes music from the reading. The music entrains the body. The question was always the answer.
Try the biofeedback module →
THE CIRCLE CLOSES
GUMP started with a question: what makes music good? The answer was coupled oscillators at consonant frequency ratios. The body-music research showed the body IS 7 coupled oscillators at those ratios. This page connects the two: how a phone in your hand or pocket reads those oscillators and feeds them back as music.
Body oscillates → phone sensors capture motion
→ software extracts breathing, movement, posture
→ maps to body oscillator model (Heart, Brain, Breath)
→ GUMP makes music tuned to YOUR coupling state
→ music entrains body oscillators
→ body oscillates better → better music
The instrument IS the biofeedback loop.
WHAT THE PHONE MEASURES
A modern phone has two relevant motion sensors. Both sample at 60 Hz. Between them, they capture three of the seven body oscillators — the fast group.
| Sensor | Signal | Body Oscillator | How |
|---|
| Accelerometer | X, Y, Z + gravity | Breath (0.25 Hz) | Chest/pocket rise and fall at 0.1–0.5 Hz |
| Accelerometer | Magnitude peaks | Heart (proxy) | Motion amplitude correlates with activity level |
| Gyroscope | Tilt angle | Brain (proxy) | Postural engagement tracks attention state |
The accelerometer captures breathing as a low-frequency oscillation in acceleration magnitude. When the phone is against the chest, each breath cycle produces a ~0.01–0.1 g swing at 0.1–0.5 Hz. Autocorrelation in that band extracts the period.
Walking cadence (1.5–3.0 Hz) comes from acceleration peaks. Cardiac-locomotor coupling means walking tempo tracks heart rate during movement — a proxy, not a measurement.
Tilt from the gyroscope is the least physiological and the most behavioral: an upright, engaged posture produces a different angular profile than a slouched, disengaged one. This maps loosely to attention state — the alpha rhythm territory of the brain oscillator.
THE SENSOR PIPELINE
The Biofeedback class (biofeedback.js) runs the full extraction.
1. CAPTURE
DeviceMotionEvent → accelerationIncludingGravity (x, y, z)
60 Hz sample rate → 15-second circular buffer (900 samples)
Magnitude: √(x² + y² + z²)
2. EXTRACT
Breathing: bandpass autocorrelation 0.1–0.5 Hz → dominant period
Movement: bandpass autocorrelation 1.0–3.5 Hz → cadence
Both: mean-subtract, then find strongest autocorrelation peak
Minimum 5 seconds of data before first reading
3. COMPUTE COUPLING
K = confidence of dominant oscillation (autocorrelation peak height)
R = phase coherence between breath and movement channels
Consonance = proximity of movement:breath ratio to nearest integer ratio
Scans all a:b for a ∈ [1,12], b ∈ [1,4], takes nearest
4. ENTRAIN
Target: Heart:Breath = 4:1 (the RSA consonance)
suggestedBPM = tempo that would guide toward 4:1 coupling
Walking: estimated HR = cadence × 60
Resting: default 66 BPM baseline
Clamped to 50–140 BPM range
MAPPING TO THE 7-OSCILLATOR MODEL
The body-music page defines 7 oscillators in two groups. Phone sensors reach the fast group directly and the slow group not at all.
Gold = directly sensed. Green = reachable through entrainment. Dim = not reachable from phone sensors.
| Oscillator | Frequency | Sensor Channel | Quality |
|---|
| Breath | 0.25 Hz | Accel magnitude, 0.1–0.5 Hz band | Direct measurement |
| Heart | 1.0 Hz | Motion amplitude / walking cadence | Activity proxy |
| Brain | 10 Hz | Tilt angle / postural engagement | Behavioral proxy |
| Gut | 0.00019 Hz | — | Not measurable |
| Pancreas | 0.0017 Hz | — | Not measurable |
| Liver | 0.000012 Hz | — | Not measurable |
| Immune | 0.00014 Hz | — | Not measurable |
What we actually measure: 1 of 7 directly (Breath).
What we estimate: 2 of 7 through proxies (Heart, Brain).
What we cannot reach: 4 of 7 (Gut, Pancreas, Liver, Immune).
But the fast group IS the group that music entrains.
Heart, Brain, Breath — the Fiedler fast split.
We measure the oscillators we can change.
TILT → BRAIN STATE PROXY
The gyroscope measures angular velocity. Integrating gives tilt angle. Tilt correlates with engagement, not cognition — but engagement is what the instrument needs.
Upright, stable: high engagement → K(brain) estimate up
Phone tilt < 15° from vertical, low angular variance
Maps to: focused attention, alpha rhythm coherent
Tilted, variable: shifting engagement → K(brain) estimate fluctuating
Phone tilt 15–45°, moderate angular variance
Maps to: exploratory attention, switching between stimuli
Flat or erratic: disengaged or in motion → K(brain) estimate low
Phone tilt > 45° or high-frequency angular noise
Maps to: passive state or active locomotion
Honest limit: this is postural behavior, not EEG.
A person lying down reading intently will register as "disengaged."
The proxy works for standing/walking instrument use. That is the use case.
MOTION AMPLITUDE → HEART RATE PROXY
During walking, cardiac-locomotor coupling is well-documented (Niizeki 2005, J Appl Physiol). Heart rate tracks walking tempo within ~10%. At rest, there is no motion to measure — the system falls back to a 66 BPM default.
Walking:
Cadence from accel peaks at 1.0–3.5 Hz
Estimated HR = cadence × 60 (1:1 cardiac-locomotor coupling)
Accuracy: ±10% during steady walking (literature-supported)
Breaks down during: running, stairs, erratic movement
Standing still:
No cadence signal. Default HR = 66 BPM.
Postural sway provides coupling regularity (K), not rate
Honest limit: this is NOT a heart rate monitor.
An optical PPG sensor (Apple Watch) measures actual pulse.
We measure movement periodicity, which correlates with HR
during locomotion only.
BREATHING DETECTION
This is the strongest channel. A phone against the chest or in a breast pocket rises and falls with each breath. The signal is small (0.01–0.1 g) but periodic, and autocorrelation finds periodicity better than amplitude thresholding.
Method: bandpass autocorrelation, 0.1–0.5 Hz (6–30 breaths/min)
1. Collect 15 seconds of acceleration magnitude
2. Mean-subtract to remove gravity bias
3. Compute autocorrelation at lags corresponding to 0.1–0.5 Hz
4. Peak lag = dominant breathing period
5. Peak height = confidence (K of breathing oscillation)
Accuracy: ±1 breath/min when phone is on chest
Degrades to: ±3–5 breaths/min in hand or pocket
Fails when: walking fast (locomotion dominates), phone on table
Breath is the Fiedler bridge — damage score 1.000.
It couples fast group to slow group through the vagal reflex.
If we measure one thing well, this is the right one.
HOW THE INSTRUMENT USES THIS
The biofeedback module feeds three signals to the GUMP audio engine. Each signal modulates a different musical dimension.
| Biofeedback Signal | Musical Parameter | Target Coupling |
|---|
| Breath rate | Phrase length / rhythmic grouping | Heart:Breath = 4:1 |
| Motion amplitude | Tempo / density | Cardiac-locomotor 1:1 |
| Coupling K | Harmonic complexity / depth | Higher K = simpler harmony |
| Consonance | Dissonance level in synthesis | Body consonance = musical consonance |
| Suggested BPM | Entrainment tempo target | Guides toward 4:1 RSA ratio |
The entrainment loop:
1. Measure your breath rate (say 16/min = 0.267 Hz)
2. Target HR for 4:1 consonance = 64 BPM
3. Set music tempo near 64 BPM
4. Rhythmic entrainment pulls heart rate toward tempo
(Bernardi 2006: heart rate follows musical tempo)
5. Heart rate at 64 BPM with breath at 16/min = 4:1
6. RSA (respiratory sinus arrhythmia) strengthens
7. K increases. Consonance increases. Music gets simpler.
8. Goto 1. The loop tightens.
The body tunes the instrument. The instrument tunes the body.
K / R / E / T OF BODY-SENSOR COUPLING
K/R/E/T of the biofeedback system. K rises as the loop tightens. R tracks phase-lock. E peaks during transition.
K (Coupling Strength)
Autocorrelation peak height of dominant oscillation
Range: 0 (noise) to 1 (perfect periodicity)
High K = the body is oscillating regularly
The instrument responds: simpler harmony, longer phrases
R (Synchronization)
Phase coherence between breath and movement channels
Range: 0 (uncoupled) to 1 (phase-locked)
High R = breath and movement are synchronized
The instrument responds: more consonant intervals
E (Energy / Tension)
Motion amplitude × (1 − consonance)
High E = active but dissonant — the body is working
The instrument responds: rhythmic tension, denser texture
T (Temperature / Phase)
Rate of change of K over time
Positive T = coupling is building (warming up)
Negative T = coupling is decaying (cooling down)
The instrument responds: evolving harmony follows the trend
THE THREE SENSOR CHANNELS AS MUSIC
BREATH (0.25 Hz) → PHRASE STRUCTURE
Each breath cycle = one musical phrase
Inhale = tension (ascending motion, added notes)
Exhale = resolution (descending, notes thin)
Breath IS the conductor. The phrase follows the baton.
HEART PROXY (1 Hz) → PULSE
Walking cadence sets the beat
Higher activity = faster tempo
Stillness = ambient, beatless
The heartbeat IS the downbeat.
BRAIN PROXY (tilt) → HARMONIC DEPTH
Engaged posture = richer harmony, more overtones
Relaxed posture = sparser, fundamental-heavy
Shifting attention = modulating timbre
Attention IS the mix engineer.
DEMONSTRATED: WHAT WORKS
Breathing detection: works reliably with phone on chest
±1 breath/min accuracy. Autocorrelation is robust to noise.
Degrades gracefully in hand/pocket. Fails on table.
Movement cadence: works during walking
Acceleration peak detection at 1.0–3.5 Hz is clean.
Cardiac-locomotor coupling gives HR proxy (±10%).
Consonance detection: works in real time
Movement:breath ratio proximity to integer ratio.
Updates every 500ms. Smoothed exponentially.
Entrainment suggestion: computes correct target
suggestedBPM tracks toward 4:1 Heart:Breath ratio.
Whether the music actually entrains HR is the claim
from Bernardi 2006, not our measurement.
Try the biofeedback module →
HONEST LIMITS
Phone sensors measure movement, not organ oscillation.
Breath: real oscillation detected through body movement. Closest to direct.
Heart: proxy via activity level. Not a pulse measurement.
Brain: proxy via postural behavior. Not EEG.
Gut, Pancreas, Liver, Immune: not measurable from phone sensors. Period.
The mapping from accelerometer to body state is a proxy, not measurement.
An actual biofeedback system would use ECG, EEG, respiratory belt, HRV monitor.
We use one $800 device with two motion sensors. The quality matches the cost.
No clinical validation of sensor → health correspondence.
We have not run a clinical trial. We have not validated against medical devices.
The entrainment claim rests on Bernardi 2006 and Thaut 1996, not our data.
Our contribution: the mapping from sensor data to the body oscillator model.
Placement matters enormously.
Chest: breath works, movement works, tilt works. Best case.
Pocket: breath marginal, movement works, tilt useless.
Hand: breath poor, movement works, tilt noisy.
Table: nothing works. The phone must be ON the body.
The 4:1 target is a simplification.
Real RSA varies with fitness, age, autonomic tone.
A single target ratio works for the average case.
Future: adapt target based on accumulated user data.
This is a Tier 2 result: the principle works, the proxy data is real,
but the clinical bridge from "phone motion" to "body oscillator state"
is not independently validated.
THE FOUNDING CIRCLE
GUMP started with "what makes music good?" The answer was coupled oscillators. The body IS coupled oscillators. Phone sensors read the body. The instrument makes music from the reading. The music entrains the body. The circle closes.
Question: What makes music good?
Answer: Coupled oscillators at consonant frequency ratios.
Discovery: The body IS coupled oscillators at consonant ratios.
Bridge: Phone sensors read 3 of 7 body oscillators (the fast group).
Instrument: GUMP turns those readings into music.
Entrainment: The music pulls the body toward better coupling.
Loop: Better coupling makes better music makes better coupling.
The body is the instrument.
The instrument is the body.
Same K. Same R. Same math.
The instrument we’re building is the instrument we already are.