Harmonic Series • Arbitrary Octave Divisions • Analogue Bass • Stereo Tape Delay
Sacred Geometry Microtonal Lab
Explore continuous overtone geometries across any custom division ($N = 2 \dots 64$), shape an analogue bass synthesizer directly under the graph, groove with a 1-lane 4/4 drum sequencer, and sculpt cascading echoes with stereo tape delay.
Want the same harmony engine in your own code? Get a free API key.
Deep restorative meditation, REM trance, somatic neural synchronization.
Microtonal Acoustics & Sacred Geometry
The Freedom to Divide the Acoustic Octave
Beyond the 12-TET Paradigm
Western music settled on 12 divisions because $2^{7/12} \approx 1.4983$, which is tantalizingly close to the pure Pythagorean fifth of $3/2 = 1.5000$. But 12-TET is only one coordinate in an infinite universe of pitch systems.
By dialing the octave into custom divisions ($N$), you can experience historic and exotic acoustic realms: 19-EDO provides virtually pure major thirds; 22-EDO unlocks the microtonal shruti system of Indian classical rāgas; 31-EDO mirrors Christiaan Huygens' 17th-century equal meantone; and 53-EDO resolves the Pythagorean comma to within 0.07 cents.
Integer Harmonics vs. Equal Divisions
When you choose Integer Harmonics ($N \to 2N$), the interval ladder is formed by standing wave physics: $f_k = f_0 \times \frac{N + k}{N}$. At $N = 16$, you access the pure overtone ladder with no frequency beating.
When you choose Equal Division ($N$-EDO), the octave is mathematically partitioned logarithmically: $f_k = f_0 \times 2^{k/N}$, allowing transpositional symmetry. THIRI unifies both models, calculating ground-truth frequencies in Hz so generative AI agents and musicians can produce microtonal works with mathematical rigor.