Talk:Mercurial comma

Commas, commas, commas!

Hi there, Yourmusic! I saw that you had made a page for the comma 557122275/556583994, which is pretty neat! My only problem is that this seems to not be in the 19-limit; although 557122275 has 19^5 within it, the prime factorization for 556583994 is 2 × 3^3 × 1373 × 7507. If this was just a simple calculation problem, then I guess you should fix it up quick! --CritDeathX (talk) 13:44, 25 September 2020 (UTC)

It's fixed meanwhile (557122275/556583994 → 557122275/556583944). --Xenwolf (talk) 14:06, 25 September 2020 (UTC)

Ah, wonderful! Thanks for the help, Xenwolf! --CritDeathX (talk) 14:13, 25 September 2020 (UTC)

Yeah, looks like I slipped a digit when typing. Thanks for the fix. --User:Yourmusic_Productions 16:33, 25 September 2020 (UTC)

You are welcome. 🙂 But how to name it? (could there be other relevant pairs of ratios approximating the golden ratio - including corresponding commas)? --Xenwolf (talk) 14:15, 25 September 2020 (UTC)

The not particularly accurate 12edo equivalent one that uses the closest pure ratios to the semitone & tone would be (9/8^5 x 18/17^2)/2=4782969/4734976, which is 17.4591 cents Or [-14 14 0 0 0 -2⟩ The 19edo one would use 14/13 and 29/26 and come out flat but by a smaller amount, etc. Anyone who wants to crunch the math of all these up is welcome. --User:Yourmusic_Productions 17:25, 25 September 2020 (UTC)

Okay, how are y'all figuring this out? I'm asking because I'm wondering what it would be for 159edo... --Aura (talk) 17:47, 25 September 2020 (UTC)

Nevermind, It seems you can only do this for EDOs in the Golden Meantone series... --Aura (talk) 18:00, 25 September 2020 (UTC)

What about the Luster comma? That seems like a good name... --Aura (talk) 14:25, 25 September 2020 (UTC)

On that note, one could potentially call this comma the "lustrisma"... --Aura (talk) 14:28, 25 September 2020 (UTC)

How about a periodic table joke - as its very close to golden meantone, only sharpening the octave slightly to make the individual intervals purer, call this combination of pure 19/17's and 15/14's mercury meantone, and the comma by which the scale exceeds the octave the mercurial comma. That has a certain elegance to it, and just as importantly, isn't already taken. --User:Yourmusic_Productions 19:43, 25 September 2020 (UTC)

Nice idea, looks like an alchemistic approach to tuning. --Xenwolf (talk) 19:59, 25 September 2020 (UTC)

Cool. I'll get right on that. --Yourmusic Productions 20:05, 25 September 2020 (UTC)

For the record,
I deleted the page with the wrong name and
swapped redirection between 557122275/556583944 and Mercurial comma. --Xenwolf (talk) 13:44, 16 December 2020 (UTC)