Talk:Golden ratio
Phith root of phi
I've (temporarily) removed the material about the phith root of phi from this page. I noticed one little thing on this page and went to fix it, but then found myself sucked into a full audit of the thing, and my impression at this time is that this [math]\sqrt[\varphi]{\varphi}[/math] is currently too specific, too confusing, and too incomplete to keep on this page which is important and should be more of a short, clear summary type of page.
In particular, I think it needed to be pointed out that [math]\sqrt[\varphi]{\varphi}[/math] is used as an frequency multiplier, like acoustic phi, and yet its described in terms of the other phi, logarithmic phi, i.e. for sharing the property of generating golden scales.
However, the fact that logarithmic phi generates golden scales is not, and should not, be described on this page; that detail should be reserved for the logarithmic phi page. And so the next thought is: if [math]\sqrt[\varphi]{\varphi}[/math] remains on the wiki, then it would be on the logarithmic phi page.
But that might not be the final thought, though, because this interval might have some properties in common with acoustic phi, and in that case it would be confusing to host it only on one of the two phi pages. In that case, it should get its own dedicated page. Because at this time it's unclear to me whether [math]\sqrt[\varphi]{\varphi}[/math] has properties in common with acoustic phi, I didn't know where to put it, and so that's where I'm at now.
There's another question which seems open to me, of how taking the phi root works in general. I think both of these questions are important to be answered as part of qualifying this material for the wiki.
Another minor note: if/when any of this material does go back to the wiki, then MOS scales, Fibonacci numbers, and equave, which were not links before, should be.
--Cmloegcmluin (talk) 08:51, 1 July 2024 (UTC)
- Hello. You might want to include it on Phi to the phi.
- [math]\sqrt[\varphi]{\varphi} = \varphi^{1/\varphi} = \varphi^{\varphi - 1}[/math].
- [math]\varphi^{\varphi} = \varphi \cdot \varphi^{\varphi - 1}[/math] (Fibonacci recurrence on logarithmic space).
- This may also be called "phi to the phi". By style of [math]\Phi = \frac{1+\sqrt{5}}{2}[/math] and [math]\varphi = \frac{-1+\sqrt{5}}{2}[/math], [math]\varphi^{\varphi} = \varphi^{1/\Phi} = 1/(\Phi^{1/\Phi}) = 1/(\sqrt[\Phi]{\Phi})[/math].
- --Dummy index (talk) 14:02, 2 July 2024 (UTC)
- Oh, phith root of phi has a track record of being used in a song.(49edo #Approximation to irrational intervals, Star Nursery) More important than the phi to the phi --Dummy index (talk) 12:19, 4 July 2024 (UTC)