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# Harmonic Series
- URL: https://www.smoothpebbles.org/harmonic-series/
- Published: 2024-06-10T00:00:00.000Z
- Updated: 2026-08-04T05:50:16.000Z
- Author: Richard Flanders

I plotted the harmonic series for a major triad, 3rd and 5th against the root. This is what a major chord looks like mathematically.

This is just plotting the sine waves for a major triad chord (root, 3rd, 5th). The 3rd is a ratio of 5/4\. The fifth is a ratio of 3/2\. If you plot the sine of these functions over time using a simple line graph it just looks like sine waves at those 3 frequencies. But if you use an XY graph, plotting the 3rd and 5th against the root, you get my picture. The Y axis is the root. The X axis is the 3rd and 5th. Note I lowered the 3rd and 5th amplitudes to see them more clearly.

I'm sure you already know what the graph is showing. A major 3rd means that its frequency makes 5 cycles for every 4 of the root. A major 5th means it makes 3 cycles for every 2 of the root. This is why they sound so good, because the waves converge at a fixed rate.

![](https://storage.ghost.io/c/fb/e7/fbe7045a-eafe-435c-a0b1-2a8711854853/content/images/2026/08/Harmonic-Series-2.jpg)