Harmonic Series Calculator

This app calculates the frequencies of partials in a harmonic or subharmonic series, with the ability to stretch or compress the series. Results are generated as a tab-delimited list, ready for pasting into Excel or Google Sheets, or can be downloaded as a MusicXML file for importing into MuseScore, Dorico or Sibelius.

Frequencies are calculated using the following formula: $f_{n}=f_{0}(s(n-1)+1)^{x}+\alpha$, where $f_{0}$ is the fundamental frequency, $s$ is the Scaling (stretch) Factor, $n$ is the partial number, $x$ is the Exponent and $\alpha$ is the Frequency Addition constant. If the ‘Subharmonics’ checkbox is ticked, however, then frequencies are calculated as: $f_{n}=\frac{f_{0}}{(s(n-1)+1)^{x}}-\alpha$

How to use

1. Either select a note name and octave, or enter a fundamental frequency directly into the ‘Fundamental Frequency’ box.
2. Set any desired ‘harmonic stretching’ parameters, or leave as the default.
3. Enter the number of partials you wish to generate (default is 16)
4. Click ‘Calculate’ to generate tab-delimited output, music notation and spectrum.
5. Once generated, click ‘Play Frequencies’ to hear the harmonic series as sine tones, or click ‘Download MusicXML’ to export out to a MusicXML file.