Talk:Sharpquart

Explanation of this temperament and why it's likely not worth inclusion on the wiki

You can find the commas from a mapping by treating a vector in the null space as a monzo. Type this into wolfram-alpha:

nullspace [[1, 1, 2], [0, 13, 7]]

and it gives you {(-19x, -7x, 13x): x is in the real numbers}.

Treating (-19, -7, 13) as a monzo, the corresponding comma is 2^-19 * 3^-7 * 5^13 = 1220703125/1146617856.

You can check that this is the comma that generates the temperament you described: enter the comma on sintel.pythonanywhere.com, and you will see that the mapping the website gives is the one you described. You can also see that this temperament is very high-badness, so it probably shouldn't be catalogued on the wiki.

The size of your generator is close to the size of the [Escapade] generator; Escapade is a much lower-badness temperament.

By the way, pretty much all the useful temperaments have already been catalogued, because we've searched through all of the lowest-badness temperaments already. (Badness is fast for a computer to calculate, which is why we can find a definitive list of the lowest-badness temperaments in order.)

-- User:Hkm (25 Mar 2025)