Two-frequency carrier in the indexed component generator

Read the equation

The carrier adds sin(φt) to cos(τt). It is a deterministic sum of two oscillations, with amplitude bounded by two in absolute value. The exact frequency convention for τ belongs to this source version; claims about the independent modular harmonic’s periodicity do not follow from this carrier.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

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Original context

Each core equation uses golden ratio-modulated sinusoidal coupling:

t = i × 0.03125                                  // Time parameter

carrier = sin(t × φ) + cos(t × τ)              // φ-modulated carrier

harmonic = sin((i mod 13) × 0.27) × cos((i mod 17) × 0.19)

core[i] = 0.5 × carrier + 0.5 × harmonic        // Blend

The mod 13 and mod 17 create interference patterns that never exactly repeat.

carrier = sin(t × φ) + cos(t × τ)              // φ-modulated carrier