Error in Identification of Distinct Intervals

[r-b0]

Hello Mark,

I have creating and exploring new musical scales when I stumbled upon your blog post "https://www.pataphysical.info/a-new-musical-scale.html"

I believe there is an error in one of the examples on that page which I would like to bring to your attention. [or conversely my understanding will be rectified]

Within "a-new-musical-scale" a 16-degree scale is created from a sequence of 30 harmonics, referenced to the fourth harmonic. The scale is as follows, matching that posted in "a-new-musical-scale":

1/1, 17/16, 9/8, 19/16, 5/4, 21/16, 11/8, 23/16, 3/2, 25/16, 13/8, 27/16, 7/4, 29/16, 15/8, 2/1

Next, all distinct intervals within that scale are examined; herein is where I believe there is an error. Omitting unison to octave, the largest interval within that scale is from 17/16 to 2/1 = 32/17

Within the "large set of distinct intervals" posted in the "a-new-musical-scale" blog post, there are 13 additional intervals greater than 32/17.

Is this a mistake or am I misunderstanding how you went about calculating intervals in the 16-degree scale created from a sequence of 30 harmonics, referenced to the fourth harmonic?

Thank you for your time.

[MarkCWirt]

Hey, sorry for taking so long to get back to you -- hope this isn't spam by default because of it.

I needed to take some time off the internet, so I haven't really looked at this in a few years. But I was revisiting the project to bring it up-to-date with the new versions of SymPy (because I was getting ready to start another sympy-based project) and I came across you post.

I have to be honest with you -- I haven't looked at this for a while, so I'm going to have to think about what may be happening. If I had to guess, I think what may be happening is that the distinct intervals are being calculated before the intervals are being normalized. If that's the case it should be changed because, well, as you point our, it's confusing.

If it needs to be changed I'll cut a new release -- may be a good excuse to go all 1.0.

Thanks again, and again sorry that it's taken so long to respond. I'll ping you when I have looked at it (if you're at all still interested -- you probably aren't and I understand. I was pretty remiss).