Keep the spacing. Change the ratios.
A silent arithmetic model of three ideal sinusoidal components. The reference rate stays at 200 Hz. No sound is generated, and the calculation does not predict what a listener will hear.
Choose an integer from 0 to 100 Hz. The original components are 400, 600, and 800 Hz.
| Component | Frequency | Ratio to 200 Hz |
|---|---|---|
| Low | 400 Hz | 2.000 |
| Middle | 600 Hz | 3.000 |
| High | 800 Hz | 4.000 |
Adjacent differences: 200 Hz and 200 Hz.
All three are integer harmonics of 200 Hz.
Exact common repetition rate: 200 Hz; repeat interval: 5.000 ms.
The common repetition rate is the greatest common divisor of these integer-hertz frequencies. After its repeat interval, every ideal component returns to its starting phase. That mathematical return is not a prediction of perceived pitch, nor evidence that the sound contains a spectral component at that rate.
Compare multiplication
Multiply the original frequencies by 1.1 instead: 440, 660, and 880 Hz. The differences become 220 Hz. Relative to 220 Hz, the ratios remain 2, 3, and 4. Adding a fixed amount and multiplying by a fixed factor preserve different relationships.