Examples

Science

• Harmonicity Metrics Computation on MNE Epochs File
• Peaks extraction methods
  • Retrieving frequency information from simulated signals using the biotuner
  • Peaks functions (see the doc)
  • Fixed
  • FOOOF
  • Empirical Mode Decomposition
  • Harmonic recurrence
  • Endogeneous Inter-Modulation Components
  • Effect of noise on peaks detection
• Harmonicity metrics
  • Harmonic similarity
  • Inter-harmonic concordance
  • Euler Gradus Suavitatis
  • Sub-harmonic tension
• Matching biosignals to mathematical series
  • 1. Extract peaks and ratios from the EEG
  • 2. Which mathematical series is present?
  • 3. Across the whole montage
  • 4. Derive musical structures
  • 5. Creative views — where the (extended) peaks sit among the series
  • 6. Effect of order on matching
  • 7. Parameters to control
• From Spectral Peaks to Harmonic Spectrum Analysis
  • Relation between harmonicity and phase-coupling
• Resonance & Connectivity Cookbook
  • 1. Setup
  • 2. H-only spectrum (single signal)
  • 3. Full single-signal resonance R = H × PC
  • 4. Swapping harmonic kernels
  • 5. Coupling metrics — and the n:m convention rule
  • 6. Ratio kernels — binary (legacy) vs fraction (new)
  • 7. Combine rules — H × PC → R
  • 8. Surrogate-null normalization
  • 9. Cross-channel resonance — compute_cross_resonance
  • 10. Connectivity matrices on multi-channel data
  • 11. Reproducing legacy compute_global_harmonicity
  • Further reading
• Biotuner Paper Design and Implementation Examples
  • Figure 2. Comparative analysis of different metrics evaluated across frequency pairs from unison to octave.
  • Figure 3 (pairs). Correlation Matrix for sets of 2 peaks
  • Figure 3 (triplets). Correlation Matrix for sets of 3 peaks
  • Figure 4. Time-Resolved Harmonicity using instantaneous frequencies for three different types of signals
  • Figure 5. Identification of spectral chords using time-resolved harmonicity
  • Figure 6. Comparison of Normalized Dissonance and Harmonic Entropy Across Different Sets of Harmonics.
  • Figure 8. Visualization of Euclidean rhythms with varying maximal denominators
  • Figure 8. Harmonic Spectrum
• Biotuner Toolbox Paper Results Figures
  • Figure 6. Performance analysis of different peak extraction methods
  • Figure 7. Harmonicity on Simulated EEG
  • Figure 8. Subject-level T-statistics comparing wakefulness to different sleep stages
  • Figure 9a. Transitional Harmony in I-IV-V-I progression
  • Figure 9b. Smoothed transitional harmony for ecg simulated signals
  • Figure 9c. Distribution of transitional harmony values
  • Figure 10. Transitional harmony on simulated EEG
  • Figure 11. Harmonic Connectivity

Music

Tuning

• Constructing musical tunings with biosignals
  • Table of content
  • 1. Spectral peaks extraction
  • 2. Deriving tuning from peaks ratios
  • 3. Dissonance curve
  • 4. Harmonic entropy
  • 5. Classical tuning creation
  • 5.3. Scale from generator interval
  • 6. Scale reduction
  • 7. Scale from multiple time series
  • 8. Exporting scale in scala format
  • 9. Plotting consonance matrix for a specific scale
  • 10. Computing scale metrics
  • 11. Visualizing ratios with Lissajous curves
  • 12. Listening to scales
• Deriving spectral chords from biosignals
  • Spectral chords from spectral centroid
  • Spectral chords from instantaneous frequencies
  • Listening to spectral chords
  • Exporting spectral chords as MIDI files

Rhythm

• Constructing euclidian rhythms from biotunings
  • Deriving euclidian rhythms from a series of ratios
  • Finding consonant euclidian rhythms from a set of frequency ratios
  • Visualizing euclidean biorhythms

Coupling

• Phase-Amplitude Coupling
  • Deriving tunings from PAC information
  • Deriving euclidian rhythms from PAC information

Harmonic geometry

• Lissajous and harmonograph curves
  • Lissajous gallery — 2-D curves at different ratios
  • 3-D Lissajous knots
  • Pairwise grid and compound curves
  • Phase drift
  • Harmonograph examples
  • Effect of damping
• Chladni plates and spherical harmonics
  • Rectangular plate — pure modes
  • Circular plate (Bessel modes)
  • Polygonal plate (finite-difference)
  • From a chord input — chladni_from_input
  • Spherical harmonics — closed-surface eigenmodes
• Tuning circles, polygons, and cycloids
  • Star polygons
  • Times-table circles
  • Tuning circle
  • Rose curves
  • Epicycloid / hypocycloid
• Fractal layouts and generative L-systems
  • Stern-Brocot tree — chord-driven layouts
  • Continued-fraction rectangles
  • Farey sequence layouts
  • Subharmonic tree — chord-driven polar layout
  • Iterated-function system from a chord
  • L-system curves and recursive polygons
  • Self-similar tuning (nested ratio scaffolds)
• 3-D harmonic geometry
  • Harmonic knots — 3 coprime frequencies weave a closed curve
  • Lissajous tubes — extruded 3-D Lissajous curves
  • Harmonic surfaces — sphere, torus, cylinder
  • Harmonic point clouds
  • 3-D L-systems and recursive polyhedra
• Geometry metrics and chord transitions
  • Radar — six chords on a rectangular Chladni plate
  • Trajectory — recursive polygon along a chord morph
  • interpolate_chords — visualising the morph
  • fade_in_components — growing a chord by extension
  • blend_fields — pixel-space crossfade between two algorithms
• Chladni cymatics — chord-driven nodal patterns
  • 1. Lossless integer-ratio extraction
  • 2. The four mode schemes
  • 3. D4 symmetrisation — applied at the density stage
  • 4. pair_subset — keeping curves bold at any chord size
  • 5. Chord-fingerprint gallery — sand-grain rendering
  • 6. Painted rendering — perceptual cmap alternative
  • 7. max_mode — taming high-LCM chords
  • 8. Pipeline composition: RigidPlate → Granular
  • 9. Animation — chord-sequence morph
  • Recipe quick reference

Harmonic geometry — media (chord-driven response operators)

• The media subpackage: medium protocol, domains, pipelines
  • A single medium — respond(chord) returns a GeometryData
  • Domains — change the boundary, keep the chord
  • Pipelines — chain media
  • default_source — transport / morphogenetic media auto-wrap
• Eigenmode and wave-field media
  • Eigenmode — RigidPlate across three domains
  • Eigenmode — ClosedSurface on a sphere (chord-driven Y_lm modes)
  • Eigenmode — Elastic (anisotropy in the wave operator)
  • Eigenmode — PlasmaLattice (chord-tuned ion crystal)
  • Wave-field — Interference (five paradigms)
  • Wave-field — Acoustic (multi-source pressure field)
• Parametric and transport media
  • Faraday — chord-tuned cymatics patterns
  • Granular — sand-on-plate density across chords
  • Tracer — flow streamlines on a wave field
  • Streaming — acoustic-streaming velocity magnitude
• Morphogenetic media — pattern growth shaped by chords
  • Crystallization — snowflake-style chord growth
  • ReactionDiffusion — chord-driven Gray-Scott patterns

Bio-colour (deriving colour from a biosignal)

• biocolors — deriving colour from a biosignal
  • 1. Three entry points
  • 2. A palette from a signal’s spectrum
  • 3. Six ways to derive colour
  • 4. Temperament — the character of a palette
  • 5. Colouring a tuning
  • 6. The colour layer
  • 7. Auditing a palette

Bio-elements (biosignals, the periodic table, and materials)

• bioelements — from biosignals to the periodic table, and to materials
  • An element is a spectrum is a chord is a tuning
  • Matter is compositions of atoms
  • Composition is recursive: a cloud is water + air
  • The dictionary spans matter — a measured claim
  • A biosignal resonates with materials, not just atoms
  • Every material affords a palette — its flame colours
  • And a tuning, a chord, a form
  • The compositional hierarchy
  • Applied: a night of sleep, read as changing matter