Octaves, odd harmonics, and why RootEQ uses primes instead of a 12-note scale

RootEQ does not snap bands to equal temperament. It does not know that you are in F# minor. Each root has a prime index: 2, 3, 5, 7, 11, 13, 17, 19, 23, or 29. Grid frequency number i is f0 × prime^(i+1). That formula is the whole grid.

Prime 2 — the octave lattice

This is the default, and it should be. A 110 Hz root grows 220, 440, 880, 1760… You are walking the same pitch class upward. Use it when you want a note to stay the same note while you trade weight for air: dip the root, lift an octave, leave the rest. Sub bass, sine-like synths, and round vocals live here.

Prime 3 — the odd, hollow, “boxy” lane

A 110 Hz root at prime 3 grows 330, 990, 2970… That is the neighborhood where square-ish timbres, cheap guitar cabs, and “honk” like to stack. If a snare’s ringing note is a third above something else in the chorus, you will hear it faster as a 3× than as a free bell you placed from a cheat sheet.

Prime 5 and the rest

Prime 5 jumps even harder: 5×, 25×. Useful when a nasal vocal or a buzzy saw needs a specific bristly partial attended to, and the octaves are innocent. Higher primes get sparse quickly — 11× of a 100 Hz root is already 1.1 kHz, then 12.1 kHz. They are not a full harmonic series. They are a thin series. That is a feature when you want to touch related frequencies without painting a dense chord of bells.

If you need every integer harmonic (2, 3, 4, 5, 6…), RootEQ is not a one-click “additive series” generator. You plant additional roots, or you branch a grid tone into a new root and grow a different prime from there. That is more work than a dedicated harmonic enhancer, and more precise, because each node still has its own gain and Q.

Do not expect it to quantize to a piano. If the singer is 18 cents sharp, the root should be 18 cents sharp too. You place it by ear or against the analyzer, not by music theory class.