Talk:Meantone family: Difference between revisions

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:::: I haven't looked into dominant extensions at all so I'll give myself no say in this. I feel dominant has way too many extensions for an exotemp (whose only reasonable tuning is 12edo, tbh) though. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 17:23, 24 August 2025 (UTC)

::::: > I named the individual mappings to the higher primes; those are not temperament names.

::::: That's new to me, and nice to hear. Thank you for clarifying.

::::: > meanenneadecal vs vincenzo

::::: In fact, 13-limit meanenneadecal has a (Sintel) TE complexity of 44.4. 13-limit vincenzo's TE complexity is 45.0. Moreover, the 13-odd-limit Graham complexities of 13-limit meanenneadecal and vincenzo are 15 and 14, respectively. In both cases the differences are insignificant. Meanplop is, however, significantly more complex, with a TE complexity of 69.5 and a 13-odd-limit Graham complexity of 23. So I think you have a good point on the inferiority of meanplop, but based on the figures above, I can only conclude 13-limit meanenneadecal remains very competitive. As for the combination of septimal meantone's 7 and flattone's 11 and 13, I'm afraid I don't think it inherently makes a temp nice.

::::: > meanpoid vs meanpoppic

::::: "Meanpoid" works from 19 to 31 perfectly fine, afaik. It's also extremely natural for meantone to map 17/16 to m2 and 19/16 to m3, even tho that implies conflating 17/16 with 19/18 and 18/17 with 20/19 as a result of tempering out 153/152 and 171/170. That said, I recognize that in flatter tunings, mapping 17/16 to m2 and 19/16 to m3 works less well as the diesis is larger than expected, so that's a case against the canonicity of "meanpoid". However, since 13-limit meanpop ranges from 19 to 31, and since you "think of 50edo as the standard meanpop edo", it would only make sense for this range to be divided into 19 & 50 and 50 & 31, neither being canon. Therefore, I think we should document three noncanonical temps: 19 & 50, 50 & 31, and 19 & 31. The situation is comparable to the grosstone range you analysed next, which I like and appreciate.

::::: > I think all the temps that remain here should be 19-limit.

::::: Yeah.

::::: > dominant

::::: Dominant's basic range is 12 & 17c, so I don't call it an exo. I think it at least makes sense to document 12 & 17c, "undecimal dominant" (pending decanonicalization), and 12e & 17c, "domination". 12 & 17ce "domineering" is very questionable from the 11-limit and doesn't deserve a 19-limit extension. It looks like it has the lowest badness in the 11-limit, so it's notable for that fact, which means the 11-limit is where it should just end. 12e & 17ce "arnold" is more funny: I heard it was the mapping corresponding to some Arnold's analysis on 12edo, but more obviously it's related to HEJI. Imo its 13-limit extension is "wrong", so I suggest it also end at the 11-limit.

::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 16:11, 25 August 2025 (UTC)

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 :::: I haven't looked into dominant extensions at all so I'll give myself no say in this. I feel dominant has way too many extensions for an exotemp (whose only reasonable tuning is 12edo, tbh) though. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 17:23, 24 August 2025 (UTC)
+::::: > I named the individual mappings to the higher primes; those are not temperament names.
+::::: That's new to me, and nice to hear. Thank you for clarifying.
+::::: > meanenneadecal vs vincenzo
+::::: In fact, 13-limit meanenneadecal has a (Sintel) TE complexity of 44.4. 13-limit vincenzo's TE complexity is 45.0. Moreover, the 13-odd-limit Graham complexities of 13-limit meanenneadecal and vincenzo are 15 and 14, respectively. In both cases the differences are insignificant. Meanplop is, however, significantly more complex, with a TE complexity of 69.5 and a 13-odd-limit Graham complexity of 23. So I think you have a good point on the inferiority of meanplop, but based on the figures above, I can only conclude 13-limit meanenneadecal remains very competitive. As for the combination of septimal meantone's 7 and flattone's 11 and 13, I'm afraid I don't think it inherently makes a temp nice.
+::::: > meanpoid vs meanpoppic
+::::: "Meanpoid" works from 19 to 31 perfectly fine, afaik. It's also extremely natural for meantone to map 17/16 to m2 and 19/16 to m3, even tho that implies conflating 17/16 with 19/18 and 18/17 with 20/19 as a result of tempering out 153/152 and 171/170. That said, I recognize that in flatter tunings, mapping 17/16 to m2 and 19/16 to m3 works less well as the diesis is larger than expected, so that's a case against the canonicity of "meanpoid". However, since 13-limit meanpop ranges from 19 to 31, and since you "think of 50edo as the standard meanpop edo", it would only make sense for this range to be divided into 19 & 50 and 50 & 31, neither being canon. Therefore, I think we should document three noncanonical temps: 19 & 50, 50 & 31, and 19 & 31. The situation is comparable to the grosstone range you analysed next, which I like and appreciate.
+::::: > I think all the temps that remain here should be 19-limit.
+::::: Yeah.
+::::: > dominant
+::::: Dominant's basic range is 12 & 17c, so I don't call it an exo. I think it at least makes sense to document 12 & 17c, "undecimal dominant" (pending decanonicalization), and 12e & 17c, "domination". 12 & 17ce "domineering" is very questionable from the 11-limit and doesn't deserve a 19-limit extension. It looks like it has the lowest badness in the 11-limit, so it's notable for that fact, which means the 11-limit is where it should just end. 12e & 17ce "arnold" is more funny: I heard it was the mapping corresponding to some Arnold's analysis on 12edo, but more obviously it's related to HEJI. Imo its 13-limit extension is "wrong", so I suggest it also end at the 11-limit.
+::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 16:11, 25 August 2025 (UTC)