Talk:Miracle extensions

I want to change other pages about extensions in the same way, so first i would like to figure out how to do this one well. Thoughts on my changes? Is this worth doing at all? Also, does it make sense to call 31 & 41 & 72 "rank-3 miracle"? Squib (talk) 18:38, 21 December 2025 (UTC)

I don't think it's more intuitive to introduce an extra generator and then temper it back than to look where a prime fits in the existing generator chain.

The name of 31 & 41 & 72 is mirage.

—FloraC (talk) 08:33, 22 December 2025 (UTC)

I agree that the most intuitive thing is to look where a prime fits in the existing generator chain, but except for prime 13 (and 19), that's not what this page currently does. 273/272 describes 17's relationship to 13, 300/299 describes 23's relationship to 13, and 392/391 describes 23's relationship to 17. Their position in the generator chain is different for each extension, even though the description applies to all of them. If we refer to these extensions first as extensions of mirage, then we are describing each prime's position in the genchain because 13 is a generator.

Essentially, I think that this page is fundamentally about mirage, even in its current state. It would be more intuitive to understand if it described miracle extensions accordingly. However, since I suspect I'm in the minority here, I'll move my changes to my userpage for now.

Squib (talk) 16:45, 18 January 2026 (UTC)

I disagree that this article is about mirage in its current state, as nowhere in the article is prime 13 taken as an independent generator. The position of the prime is specifically given in the interval chain for each extension, and the consequence of each choice is discussed in the opening section. As for the extensions to the 17-limit, 273/272 relates 17/13 to 21/16, so the position of 17 can be inferred once the position of 13 is decided, tho I guess it could use some explanation to make this fact clear. I haven't looked too closely at further extensions beyond the 17-limit to have a solid idea about them. —FloraC (talk) 17:07, 18 January 2026 (UTC)

Miracle is most naturally an 11-limit temperament. Revelation is miracle with an alternative mapping for 11 which is both more complex and less accurate. Although revelation is an extension of 7-limit miracle, this page should be about extensions of 11-limit miracle, just like magic extensions is about extensions of 7-limit (not 5-limit) magic. Because revelation doesn't fit with what the rest of this page is about, it should have its own page just like muggles has its own page. Squib (talk) 22:08, 18 January 2026 (UTC)