This track is an example of where the melody in each bar alternately takes utonal and otonal values, that is, uses alternately subharmonics (of a very high note) and harmonics (of a very low note).

The bass and backing was devised first, using a repeating series of 12 chords which were alternately utonal and otonal.

After that, the melody was chosen from the subharmonic or harmonic spectrum for that chord in each bar.

Its in three parts - a melody, a 2 part harmony, then all 3 parts superimposed.

Harmony is supposed to be a bit tricky and captivatingly strange at times! Enjoy the 11ths, 13ths and 29ths - Dave

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See also:
- https://arxiv.org/a/ryan_d_1 (arXiv) for a list of my academic paper pre-prints, including my writing on music theory and Just Intonation
- http://orcid.org/0000-0002-4785-9766 (ORC ID) for my academic profile
- https://www.linkedin.com/in/davidryan59 for my LinkedIn profile

Example of alternating undertone and overtone melody and harmony

most of the music is straight from tiktok.  the other music is from a friend

I'm into Just Intonation (JI), which is using harmonics (or undertones) to generate music. Over time, my profile will fill up with wonderful and melodious New Harmony, fresh from the infinite vaults of the original and best source of harmony, Just Intonation.

I’ve written some papers on the music theory of Just Intonation. You can check them out via the arXiv link below. Topics include the mathematical analysis of harmony (in Just Intonation), and a notation system to cover all of Just Intonation.

Enjoy listening!

a little bit of everything  including  Christmas  music 

All my stuff is now free on bandcamp! https://ahornberg.bandcamp.com/

Example of alternating undertone and overtone melody and harmony

David Ryan