This track is an example of a simple twelve bar backing track accompanying 3-note block harmony written in free Just Intonation (JI) with added sliding chords.

For example, one transition used is between a major triad 1st inversion (5 6 8) to a major triad root position (4 5 6), with 1 and then 2 different intermediate chords on the 1st and 2nd repetitions respectively:

1 intermediate chord on 1st repetition:
16   14   12
12   11   10
10    9     8

2 intermediate chords on 2nd repetition:
24   22   20   18
18   17   16   15
15   14   13   12

You could call these types of transition a ‘linear step’ since the frequencies of each note in the harmony undergo linear steps from the starting point to the end point. They are otonal, operating on the upper harmonics (the set of whole-number N, as opposed to utonal which operate on 1/N).

These types of transitions give access to higher prime numbers such as 11, 13, 17 in the examples above. In Just Intonation, hearing the higher prime numbers is the coolest thing of all and I fully anticipate this being as interesting and widespread a hobby as trainspotting or stamp collecting in the decades ahead. Imagine listening to all the prime numbers between 1 and 500! The sheer joy!! No doubt this type of thing will have a high frequency in the future.

If prime numbers wasn’t enough, some chords undergo continuous linear slides instead of linear steps. In the track icon, it is a screenshot of the spectrogram of this track, and a linear step looks like a ladder, but a linear slide looks like a slope of constant gradient. The great thing about a linear slide is that at any rational point during the slide, the notes are in a whole number ratio, but that ratio is changing constantly. So I guess it counts as some kind of extension of Just Intonation.

May your musical listening frequently slide into Just Intonation :) 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 the Twelve Bar Blues with 3-note harmony using linear steps and slides in Just Intonation

Colorado, Alaska and currently Central Coast California, US

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 

Example of the Twelve Bar Blues with 3-note harmony using linear steps and slides in Just Intonation

David Ryan