Blend the carrier and modular harmonic

Read the equation

The core value is an equal-weight sum of the carrier and harmonic components. With carrier bounded by two and harmonic by one in absolute magnitude, this formula is bounded by 1.5 in absolute magnitude, without an automatic [0,1] range. It defines a generated scalar component; the larger count comes from evaluating it at different indices.

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.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

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.

7.2 Supplemental Equations (200 total, Equations 277-476)

k1 = 2π/133 = 0.047124

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