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)

:::::: > 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.

:::::: That's something to consider (and indeed none of these is deserving of canonicity compared to the others), though as I said, 19 & 50 doesn't really work with the septimal meantone mapping of 7 ([[Talk:Meantone#Unlisted(?) strong 7-limit Meantone extension (maybe related to Catasyc or Laruquadbiyoti?)|per Lucius]]), so I don't believe it's worth adding 19 & 50 to the meanpop extensions. I think keeping 19 & 31 and 50 & 31 makes sense though.

:::::: > > meanenneadecal vs vincenzo

:::::: I suppose I'll concede to keeping both extensions in the 13-limit (though idk what the details of what either are in the 19-limit), though I'd still rather the 11-limit temperament be called "vincenzo" than "meanenneadecal".

:::::: > dominant

:::::: Fine with that proposal. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 16:42, 25 August 2025 (UTC)

::::::: > meanpop extensions

::::::: Septimal meantone covers the full range from 19 to 12, with 19edo being the turning point of prime 7's tuning; this is established in multiple places in the page. For example, we have five extensions in the overview section in which prime 7 alternates between a sixth and a seventh.

::::::: Lucius' extension is different not for its complexity but for mapping prime 7 to a fifth, which isn't really comparable with septimal meantone or flattone. You can always find more and more accurate mappings of the prime by mapping it to more and more remote steps, and altho some of them are reasonable, you can't take it for granted that they supersede part of the basic mappings' ranges, in this case the bottommost part of septimal meantone.

::::::: Therefore, I still think we ''can'' document 19 & 50, but I'm also totally fine with suspending it for the time being.

::::::: > meanenneadecal vs vincenzo

::::::: Since the data shows no clear advantage of vincenzo over meanenneadecal (badness-wise it's actually a little worse), I'm not for switching the root's name, but I'm fine with decanonicalizing 13-limit meanenneadecal by either changing the name of 13-limit meanenneadecal or changing the root's name to something different from both.

::::::: Btw, unfortunately, ''meaningless'' was grosstone's former name. See [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19166.html this archive]. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:57, 26 August 2025 (UTC)

::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:55, 26 August 2025 (UTC)

::::::: (last updated by [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:57, 26 August 2025 (UTC))

:::::::: > Lucius' extension is different not for its complexity but for mapping prime 7 to a fifth {. . .}

:::::::: For the record, the extension in question maps 7/4 to C-G𝄪𝄪(*) (fifthspan +29), so it is a way-augmented fifth, not just a fifth.

:::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 17:19, 26 August 2025 (UTC)

:::::::: That's acceptable overall. So to be clear, the extensions we seem to be in agreement on getting rid of would be: meantonic, meridetonic (make sauveuric the canonical 19-limit meridetone), meanplop, meanundec, and meanundeci (along with 13-limit extensions of domineering and arnold), and we'd want to document 31 & 74, 74 & 43, possibly 19 & 50, along with Lucius's extensions. That still leaves the question of nomenclature. I don't believe that "meantone" should be canonical beyond the 11-limit, since huygens and meanpop are about as good as each other. I *do* think that grosstone should be canonical with respect to huygens though, at least to the 13-limit. (I also don't really like the name "grosstone", honestly.)

:::::::: So one proposal would be to recycle "meantonic" for what's currently tridecimal meantone and 17-19-limit "huygens". Currently, the "meantonic" extension seems to be mentioned, outside of the "Meantone family" page and discussion directly pertaining, solely on the [[17/16 (Korean)|Korean article for 17/16]], so I don't think this proposal is very demanding. Then we can call grosstone, at least unto the 13-limit, "tridecimal huygens". I'm not sure whether I'd want canonicity to continue after that to the 19-limit, so we can keep "grosstone" as the name for 31 & 43 in the 17- and 19-limits.

:::::::: We also should maybe address hemimeantone, semimeantone, and bimeantone. I think the issue with most of these extensions is that they're best treated outside of the hierarchy of prime limits (trimean definitely is, since no-sevens superpine is more natural compared to either of its extensions to prime 7), but other than that I'm not sure of the redundancy of any of them. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 22:59, 26 August 2025 (UTC)

::::::::: Hmm, my only minor issue is 13-limit grosstone's canonicity w.r.t. 11-limit huygens. I have my own doubts here, and as I showed you in the archive, at least two ppl believed it was actually inferior to the current 13-limit meantone for one reason or another. Meanwhile, I do think the current 17- and 19-limit grosstone are good enough to be virtual canon w.r.t. 13-limit grosstone so I might call it ''grosstonic'' (cf. ''miraculous'' and ''miracle''). So these all point to not changing 13-limit grosstone itself. (Renaming it to something completely different is another topic.)

::::::::: I don't see a problem with hemimeantone, semimeantone, or bimeantone. They are 43 & 62, 62 & 74, and 38df & 50, respectively, which all look reasonable as they are. The 50 & 62 temp is even missing, which we may call semimeanpop. Trimean is 43 & 50 and superpine is 36 & 43. The 2.3.5.11.13 part are the same and 43edo is the turning point for primes 7, 17, and 19. I see that the 2.3.5.11.13-subgroup temp is already documented in the No-sevens subgroup temperaments page. Does that mean the 7-limit-based entries should be removed from this page? Idk.

::::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:52, 27 August 2025 (UTC)

::::::::: P.S. I propose ''fokkertone'' for current 13-limit meantone, in analog to ''meridetone''.

=== Summary of changes ===

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

# Decanonicalized tridecimal meantone. Renamed it to ''fokkertone''.

# Canonicalized 17- and 19-limit huygens w.r.t. tridecimal meantone, thus effectively also renaming it to ''fokkertone''. Removed meantonic, the other 17- and 19-limit extension of tridecimal meantone.

# Canonicalized 17- and 19-limit sauveric, thus effectively renaming it to ''meridetone''. Removed meridetonic, the other 17- and 19-limit extension of meridetone.

# Removed meanplop (12e & 19), the other 13-limit extension of 11-limit meanpop.

# Removed meanundec (12f & 19f), a 13-limit extension of 11-limit meanenneadecal.

# Removed meanundeci (12e & 19e), an 11-limit extension of septimal meantone.

# Removed domineering and arnold, two extensions of dominant, from the 13-limit onwards.

# Added mildtone (55 & 67) for the 7-limit.

# Add semimeanpop (50 & 62) up to the 19-limit.

=== Remaining tasks ===

# Devise names for the three 17- and 19-limit extensions of grosstone: 31 & 74, 43 & 74, and possibly 31 & 43.

[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:38, 22 October 2025 (UTC)

@@ Line 238: / Line 238: @@
 :::: 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)
+:::::: > 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.
+:::::: That's something to consider (and indeed none of these is deserving of canonicity compared to the others), though as I said, 19 & 50 doesn't really work with the septimal meantone mapping of 7 ([[Talk:Meantone#Unlisted(?) strong 7-limit Meantone extension (maybe related to Catasyc or Laruquadbiyoti?)|per Lucius]]), so I don't believe it's worth adding 19 & 50 to the meanpop extensions. I think keeping 19 & 31 and 50 & 31 makes sense though.
+:::::: > > meanenneadecal vs vincenzo
+:::::: I suppose I'll concede to keeping both extensions in the 13-limit (though idk what the details of what either are in the 19-limit), though I'd still rather the 11-limit temperament be called "vincenzo" than "meanenneadecal".
+:::::: > dominant
+:::::: Fine with that proposal. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 16:42, 25 August 2025 (UTC)
+::::::: > meanpop extensions
+::::::: Septimal meantone covers the full range from 19 to 12, with 19edo being the turning point of prime 7's tuning; this is established in multiple places in the page. For example, we have five extensions in the overview section in which prime 7 alternates between a sixth and a seventh.
+::::::: Lucius' extension is different not for its complexity but for mapping prime 7 to a fifth, which isn't really comparable with septimal meantone or flattone. You can always find more and more accurate mappings of the prime by mapping it to more and more remote steps, and altho some of them are reasonable, you can't take it for granted that they supersede part of the basic mappings' ranges, in this case the bottommost part of septimal meantone.
+::::::: Therefore, I still think we ''can'' document 19 & 50, but I'm also totally fine with suspending it for the time being.
+::::::: > meanenneadecal vs vincenzo
+::::::: Since the data shows no clear advantage of vincenzo over meanenneadecal (badness-wise it's actually a little worse), I'm not for switching the root's name, but I'm fine with decanonicalizing 13-limit meanenneadecal by either changing the name of 13-limit meanenneadecal or changing the root's name to something different from both.
+::::::: Btw, unfortunately, ''meaningless'' was grosstone's former name. See [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19166.html this archive]. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:57, 26 August 2025 (UTC)
+::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:55, 26 August 2025 (UTC)
+::::::: (last updated by [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:57, 26 August 2025 (UTC))
+:::::::: > Lucius' extension is different not for its complexity but for mapping prime 7 to a fifth {. . .}
+:::::::: For the record, the extension in question maps 7/4 to C-G𝄪𝄪(*) (fifthspan +29), so it is a way-augmented fifth, not just a fifth.
+:::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 17:19, 26 August 2025 (UTC)
+:::::::: That's acceptable overall. So to be clear, the extensions we seem to be in agreement on getting rid of would be: meantonic, meridetonic (make sauveuric the canonical 19-limit meridetone), meanplop, meanundec, and meanundeci (along with 13-limit extensions of domineering and arnold), and we'd want to document 31 & 74, 74 & 43, possibly 19 & 50, along with Lucius's extensions. That still leaves the question of nomenclature. I don't believe that "meantone" should be canonical beyond the 11-limit, since huygens and meanpop are about as good as each other. I *do* think that grosstone should be canonical with respect to huygens though, at least to the 13-limit. (I also don't really like the name "grosstone", honestly.)
+:::::::: So one proposal would be to recycle "meantonic" for what's currently tridecimal meantone and 17-19-limit "huygens". Currently, the "meantonic" extension seems to be mentioned, outside of the "Meantone family" page and discussion directly pertaining, solely on the [[17/16 (Korean)|Korean article for 17/16]], so I don't think this proposal is very demanding. Then we can call grosstone, at least unto the 13-limit, "tridecimal huygens". I'm not sure whether I'd want canonicity to continue after that to the 19-limit, so we can keep "grosstone" as the name for 31 & 43 in the 17- and 19-limits.
+:::::::: We also should maybe address hemimeantone, semimeantone, and bimeantone. I think the issue with most of these extensions is that they're best treated outside of the hierarchy of prime limits (trimean definitely is, since no-sevens superpine is more natural compared to either of its extensions to prime 7), but other than that I'm not sure of the redundancy of any of them. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 22:59, 26 August 2025 (UTC)
+::::::::: Hmm, my only minor issue is 13-limit grosstone's canonicity w.r.t. 11-limit huygens. I have my own doubts here, and as I showed you in the archive, at least two ppl believed it was actually inferior to the current 13-limit meantone for one reason or another. Meanwhile, I do think the current 17- and 19-limit grosstone are good enough to be virtual canon w.r.t. 13-limit grosstone so I might call it ''grosstonic'' (cf. ''miraculous'' and ''miracle''). So these all point to not changing 13-limit grosstone itself. (Renaming it to something completely different is another topic.)
+::::::::: I don't see a problem with hemimeantone, semimeantone, or bimeantone. They are 43 & 62, 62 & 74, and 38df & 50, respectively, which all look reasonable as they are. The 50 & 62 temp is even missing, which we may call semimeanpop. Trimean is 43 & 50 and superpine is 36 & 43. The 2.3.5.11.13 part are the same and 43edo is the turning point for primes 7, 17, and 19. I see that the 2.3.5.11.13-subgroup temp is already documented in the No-sevens subgroup temperaments page. Does that mean the 7-limit-based entries should be removed from this page? Idk.
+::::::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:52, 27 August 2025 (UTC)
+::::::::: P.S. I propose ''fokkertone'' for current 13-limit meantone, in analog to ''meridetone''.
+=== Summary of changes ===
+Based on the review above, the following changes have been made.
+# Decanonicalized tridecimal meantone. Renamed it to ''fokkertone''.
+# Canonicalized 17- and 19-limit huygens w.r.t. tridecimal meantone, thus effectively also renaming it to ''fokkertone''. Removed meantonic, the other 17- and 19-limit extension of tridecimal meantone.
+# Canonicalized 17- and 19-limit sauveric, thus effectively renaming it to ''meridetone''. Removed meridetonic, the other 17- and 19-limit extension of meridetone.
+# Removed meanplop (12e & 19), the other 13-limit extension of 11-limit meanpop.
+# Removed meanundec (12f & 19f), a 13-limit extension of 11-limit meanenneadecal.
+# Removed meanundeci (12e & 19e), an 11-limit extension of septimal meantone.
+# Removed domineering and arnold, two extensions of dominant, from the 13-limit onwards.
+# Added mildtone (55 & 67) for the 7-limit.
+# Add semimeanpop (50 & 62) up to the 19-limit.
+=== Remaining tasks ===
+# Devise names for the three 17- and 19-limit extensions of grosstone: 31 & 74, 43 & 74, and possibly 31 & 43.
+[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:38, 22 October 2025 (UTC)