Read the equation
The harmonic multiplies a sine depending on i mod 13 by a cosine depending on i mod 17. The pair of modular indices repeats after lcm(13,17)=221 integer steps, so this entire harmonic is periodic with period 221 or a divisor of it. The surrounding claim that these modular terms never repeat is false.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| i | Integer component index |
| harmonic | Product of the two modular trigonometric terms |
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
Read the surrounding source passage
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. 7.2 Supplemental Equations (200 total, Equations 277-476)
Exact original notation
harmonic = sin((i mod 13) × 0.27) × cos((i mod 17) × 0.19)
Sources & provenance
harmonic = sin((i mod 13) × 0.27) × cos((i mod 17) × 0.19)
harmonic = sin((i mod 13) × 0.27) × cos((i mod 17) × 0.19)