Talk:Würschmidt diesis spiral progression

What is this

This page is linked from 31edo main article. It's unclear what the point of this is to me. Is a sprial progression a generic thing and the given progression is an example of it? Or is this exact progression called the spiral progression? I feel like it's not high enough importance to be linked from the 31edo page.

– Sintel🎏 (talk) 16:36, 30 May 2025 (UTC)

I think that spiral progression is a generic thing and this page lists a specific type of it. Other examples of spiral progressions show up in, for instance, 159edo using 5\159 as the interval in question. Suffice to say that spiral progressions are a specific type of progression that enables you to modulate downwards or upwards by an interval that's approximately equal to one third of a ~16/15 interval, and 31edo just so happens to provide a decent example of it. Does this make sense? Regardless, this is a musical composition technique, so I would think it relevant. --Aura (talk) 04:40, 31 May 2025 (UTC)

After doing a little math to check myself, it seems I stand corrected. It now seems that spiral progressions only exist where the ~128/125 is tempered to one third of ~16/15 by means of the the comma 393216/390625 being tempered out. Sorry for my erroneous assumptions! --Aura (talk) 05:16, 31 May 2025 (UTC)

Just double checked my math again, and this type of spiral progression also works in 34edo, which also tempers out the wurschmidt comma. I'm starting to wonder if there are other types of spiral progression, however, seeing as it does in fact seem that spiral progressions in general are connected to ~16/15 being divided by three. Regardless, this page should probably be renamed "Wurschmidt spiral progression" because this type of spiral progression is one of the defining progressions of wurschmidt temperament. --Aura (talk) 05:41, 31 May 2025 (UTC)