Beat Partner Frequency Three-Row Scan - Waves, Oscillations, and Resonance Step by Step

Three beat rows solve for the upper partner frequency that gives a desired beat against one fixed base note.

waves Against a 5 Hz base, beat targets 1 Hz, 2 Hz, and 3 Hz need upper partners 6 Hz, 7 Hz, and 8 Hz.

Example

Holding a base frequency fixed, the desired beat frequency sets the partner note. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Choose a partner frequency from the desired beat

Instead of only measuring the beat after two notes are chosen, this scan asks which upper partner frequency gives the desired beat against a fixed base.

f_{\text{partner}}=f_{\text{base}}+f_{\text{beat}}

One beat per second

A one hertz beat above the fixed base needs partner frequency 6 Hz.

f_{\text{partner}}=f_{\text{base}}+f_{\text{beat}}=5\ \text{Hz}+1\ \text{Hz}=6\ \text{Hz}

Two beats per second

A two hertz beat above the same base needs partner frequency 7 Hz.

f_{\text{partner}}=f_{\text{base}}+f_{\text{beat}}=5\ \text{Hz}+2\ \text{Hz}=7\ \text{Hz}

Three beats per second

A three hertz beat above the same base needs partner frequency 8 Hz.

f_{\text{partner}}=f_{\text{base}}+f_{\text{beat}}=5\ \text{Hz}+3\ \text{Hz}=8\ \text{Hz}

Beat target shifts the partner note

The base frequency stays fixed. Raising the desired beat raises the partner frequency by exactly the same amount.

\begin{array}{c|c|c}f_{\text{base}} & f_{\text{beat}} & f_{\text{partner}} \\ \hline 5\ \text{Hz} & 1\ \text{Hz} & 6\ \text{Hz} \\ 5\ \text{Hz} & 2\ \text{Hz} & 7\ \text{Hz} \\ 5\ \text{Hz} & 3\ \text{Hz} & 8\ \text{Hz}\end{array}