Talk:Tuning map

"Generator tuning map"

In the intro, it says a tuning map has one entry for each basis element (---> generator) of the temperament. This is also the best generalization of the concept of "formal primes" to a temperament, yet the page makes a distinction between tuning maps based on generators and on formal primes, for some reason, even though I'm pretty sure such a distinction is entirely meaningless.

Not sure what you are confused about here. Formal primes have little to do with this page.

– Sintel🎏 (talk) 19:34, 15 April 2025 (UTC)

Not sure why you said formal primes had little to do with this page. A formal prime is a JI subgroup basis element, whose tuning is given by each entry of the tuning map. What else could each entry of the tuning map represent? FloraC (talk) 20:57, 15 April 2025 (UTC)

The formal primes are said w.r.t. the JI subgroup. There's nothing to generalize. Magic's formal primes are 2, 3, 5, and 7. Magic's generators are ~2 and ~5/4. Perhaps you're confused by the terminology. Then let's say basis element of the JI subgroup, okay? FloraC (talk) 20:57, 15 April 2025 (UTC)

P.S. pls remember to sign your comment with ~~~~.

Misleading pseudoinverse

The use of the pseudoinverse here is kind of misleading since it is given:

[math]\displaystyle{ \begin{align} T &= GM\\ G &= TM^{+} \end{align} }[/math]

Which immediately leads to a contradiction if we substitute:

[math]\displaystyle{ T = GM = TM^{+}M \neq T }[/math]

since the pseudoinverse is only a right-inverse.

– Sintel🎏 (talk) 20:14, 15 April 2025 (UTC)