Talk:Magic family

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New temperament - not sure if it exists

Warlock: tempers out 16807/16384 and 3125/3072. It is exceptionally well-tuned in 60edo. Jerdle (talk) 01:45, 29 July 2020 (UTC)

Just curious, who named this temperament? May I find one and name it too? FloraC (talk) 06:01, 29 July 2020 (UTC)

I named it after looking for interesting commas.Jerdle (talk)

Can I ask what the generator for this is? --CritDeathX (talk) 15:35, 29 July 2020 (UTC)

T8/7 (240¢) and T5/4 (~380¢). The 100¢ generator is probably 256/245.Jerdle (talk)

I ran it thru the temperament finder and my own code. This is the 25 & 35 temperament. Commas: 3125/3072, 16803/16384. Map: [<5 10 12 14|, <0 -5 -1 0|]. Wedgie: <<25 5 0 -50 -70 -13||. POTE generator: 100.1869. Badness: 0.287. Fits high badness temperament :) FloraC (talk) 18:28, 29 July 2020 (UTC)

Surprised by that. Using 60edo values, 7/4 is 960¢ (pretty accurate), 5/4 is 380¢ (still accurate, better than augmented), and 3/2 is 700¢ (pretty accurate). Jerdle (talk

No wonder it fits 60edo so well. After tempering out 245/243 to allow the generator to represent 256/243, not just 256/245, it becomes 60edo.

Maybe we'll log this anyway. FloraC (talk) 10:51, 30 July 2021 (UTC)

17- and 19-limit extensions

1. 17-limit magical is less accurate than 13-limit, so the current name which alters the root a little seems fine. The 19-limit extension needs to be decanonicalized. It's similar magnitudes of error and badness to "magica", Graham complexity 33 vs 34, so there's no reason to set one as canon and leave the other out. I propose simply magicus for this extension.
2. "Magia" looks a bit worse than magical, and its 19-limit extension isn't quite solid. If we took the -15-step mapping for prime 19, it would be supported by 60edo, which is a real magic tuning we wanna consider. However, it would increase the Graham complexity to 50, and since 19gh isn't a great val to begin with, I think this branch may be left as it is for now.
3. Sorcery is the 19 + 22 = 41f temp, so its mapping for 17 which utilizes 41f rather than 41fg is dumb. We should prolly just clip it after the 13-limit.
4. 19-limit necromancy is somewhat questionable. In fact, necromancy branches into 41 & 63, 41 & 104 and 63 & 104 in the 17-limit, similar to grosstone's 31 & 43, 31 & 74, and 43 & 74. In the 19-limit there's a single mapping that lines up 41, 63, and 104, which is the +26-step one, but this mapping blends less well with the -23-step mapping for prime 13, which somewhat favors the -15-step mapping for prime 19. Therefore, the current "19-limit necromancy" is the right choice only if you prioritize simplicity over accuracy, but since the very point of necromancy is the higher accuracy than magic, this extension feels really awkward in its role.
5. Telepathy is the 19e + 22 = 41ef temp. 13-limit telepathy doesn't even have a 13-odd-limit monotone tuning, so it's a big stretch already. I have no idea how it could be extended to the 19-limit. I think we should just clip it after the 13-limit.
6. Intuition is similar to sorcery. We should prolly just clip it after the 13-limit.
7. Witchcraft is similar to necromancy, but in this case I think at least the 17-limit makes more sense.
8. I have absolutely no idea about horcrux from the 13-limit onwards.
9. Darkstone seems useless. Brightstone's 11- and 13-limit extensions look wrong to me. To be clear, these two extensions aren't proper counterparts of each other: brightstone is muggles' counterpart, with magic comfortably sitting in the middle and muggles and brightstone covering the outer regions. So if muggles is 16 & 19, then surely brightstone should be 22f & 25e.

FloraC (talk) 19:49, 25 September 2025 (UTC)

Summary of changes

Based on the review above, the following changes have been made.

1. Decanonicalized 19-limit magical. Renamed it to magicus.
2. Removed sorcery, telepathy, intuition from the 17-limit onwards.
3. Removed necromancy and witchcraft for the 19-limit.
4. Replaced brightstone's 11- and 13-limit extension with 22f & 25e.

Remaining tasks

1. Devise names for the three 17-limit extensions of necromancy: 41 & 63, 41 & 104, and 63 & 104.
2. Determine what to do with horcrux and its extensions, as well as the names darkstone and brightstone.

FloraC (talk) 08:06, 22 October 2025 (UTC)