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Harmonic Ratio Sound & Math Synthesizer

Lissajous Interference Orbit 1:1.25

Fourier Harmonic Summation 3 Oscillators

Overtone Harmonic Multipliers Base: 220.00 Hz

How tuning rules turn ratios into frequencies

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In just intonation mode the source multiplies its base frequency by each voice’s rational ratio. At the default two hundred twenty hertz, one over one is two hundred twenty, five over four is two hundred seventy five, and three over two is three hundred thirty. The animated bars are proportional to those actual frequencies. Ratio names describe the numerical fixture rather than a recording. The alternate mode maps ratios to selected semitone counts and uses two raised to semitones over twelve. A four-semitone major third above two hundred twenty is about two hundred seventy seven point one eight hertz, rather than the just five over four value two hundred seventy five. A seven-semitone fifth is about three hundred twenty nine point six three, rather than three hundred thirty. The tuning mode therefore changes frequency, even when a voice label remains familiar. For the four five six seven over four preset at root two hundred twenty, the frequencies are two hundred twenty, two hundred seventy five, three hundred thirty and three hundred eighty five. Their common fifty five hertz spacing corresponds to a shared base period one over fifty five seconds, about eighteen point one eight milliseconds. This is an exact arithmetic statement about the rational fixture. The visual curves and optional audio use the original source engine, without validating instrument acoustics or speaker output.

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