Talk:Meantone family: Difference between revisions

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:: It wasn't originally my question, but let me try rephrasing it: Why is the POTE generator for it specified as being so close to 7\12 when 12edo is way out of the range for which Sharptone is optimal (unless you need it for pitch-bending the 7/4 up on a standard 12edo fretted instrument), and 5edo is the crossover point between Dominant and Sharptone, and Sharptone would give the most just 7/4 or 8/7 with a fifth somewhat sharp of the diatonic range of Meantone temperament? [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:49, 10 July 2025 (UTC)

::: Classical (5-limit) meantone clearly makes no sense beyond 3\5. Dominant doesn't make much sense beyond 10\17. I described the range of dominant as 7\12 to 10\17 in the Arhcytas clan page, which I hope you like. Unfortunately 10\17 isn't a natural boundary for meantone extensions, so maybe we'll keep 7\12 to 3\5 for dominant as we discuss it in this article. As for sharptone, the only 7-odd-limit monotone range of it is the singleton of 3\5, right? So that's the case for tuning it to 3\5. Our conventional optimization methods are least squares, which also make sense, but they obviously don't take those constraints into account. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:21, 11 July 2025 (UTC)

:::: . . . Which leaves me wishing that the name Sharptone hadn't been taken for what is really an exotemperament extension of Meantone, so that it could have been used for something more fitting as a counterpart to Flattone, like the strong extension that gives the patent 7th harmonic for 55edo, 67edo, and 122edo (to which I gave the placeholder name Mildtone inn [[Talk:Meantone]]). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:28, 11 July 2025 (UTC)

::::: I propose that the 7-limit temperament tempering out 21/20 and 28/27 be called ''trienmean'' in this case. I originally wanted to call it ''trientone'', but that conflicts with an already-existing term. [[User:2^67-1|2^67-1]] ([[User talk:2^67-1|talk]]) 09:00, 11 July 2025 (UTC)

:::::: I agree that sharptone really should be renamed (I presume it mainly exists in order to be detempered into scales, so shouldn't just be deleted). But "trienmean" sounds too much like "trimean" or some other kind of extension that splits meantone into three (lithium, mothra, ...). -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 13:17, 11 July 2025 (UTC)

::::::: How about Oneirotone? Because once you get past 5edo, [[5L 3s]] (the Oneirotonic scale, of which 5edo has the collapsed version) becomes valid. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:16, 11 July 2025 (UTC)

:::::::: I don't think sharptone should be renamed. There is not a strong reason to do so. Also, re-using old names isn't a great idea in the first place, so pls don't take this as a pathway to re-use the name ''sharptone'' for something else. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:38, 12 July 2025 (UTC)

::::::::: I'll agree on not reusing the old name, but I believe Sharptone shouldn't have taken that name in the first place. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:08, 13 July 2025 (UTC)

:::::::::: It may not be perfect but it's not inappropriate either, so we'll keep it unless there's a strong reason for renaming. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:23, 13 July 2025 (UTC)

: Put my vote in for that question as well. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:20, 10 July 2025 (UTC)

:: All I can think is that, sharp of 5edo, the M6 becomes sharp of the m7, and they cross over at 960 cents. [[User:Jerdle|Jerdle]] ([[User talk:Jerdle|talk]]) 09:50, 10 July 2025 (UTC)

== Request to remove impractical 17- and 19-limit extensions ==

I request removing "meantoid", "meridetoid", "meanploid", "meanenneadecoid", and "vincenzoid".

"Meanpoid" should be renamed to something else or straight-up made canonical.

Undecimal meantone is best tuned a little sharp of 31edo, with 31edo and 12edo as boundaries of diamond monotone, so 12 as a val makes a little more sense than 19e for the purpose of edo join here. Compare meanpop, which is 12e & 19, and 19 makes a little more sense than 12e, as meanpop is best tuned flat of 31edo. Now consider the 13-limit extension, called tridecimal meantone. This is a questionable extension, but to be fair at least the three vals supporting it (12f, 19e, 31) make sense for the purpose of edo join, and 31 actually makes some musical sense in the 13-limit. Unfortunately this locks 31edo in as the only useful tuning, as the prime 11 can't be flatter and the prime 13 can't be sharper. Therefore, any extension of this should be supported by 31 (not 31gh), be it simple or complex.

Besides tridecimal meantone we have meridetone, the 12f & 31f temp. 43 is the tuning here that plays the role of 31 in tridecimal meantone. For the same reason, any extension of this should be supported by 43 (not 43gh).

Meanpop works better with these extensions as tridecimal meanpop is a more flexible temp than tridecimal meantone. It has valid tunings between 19 and 31, and both 19 & 31 and 31 & 50 make sense in the 19-limit. These correspond to what we call "meanpoppic" and "meanpoid" currently.

Meanplop is centered around 19, similar to 31 to tridecimal meantone, and it should only be about 19 (not 19gh). Same for meanenneadecal and vincenzo.

[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:57, 22 August 2025 (UTC)

: Yes please! – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 18:08, 22 August 2025 (UTC)

: My thoughts on the matter, copied from the XA discord:

: > flattone -> hypnotone -> vincenzo (current 13-limit flattone)

: > sept meantone -> meanpop -> meanpop -> meantonic (current 19-limit meanpoppic)

: > sept meantone -> huygens -> grosstone -> huygens (current 19-limit grosstone)

: > or

: > sept meantone -> huygens -> grosstone -> roulette

: > sept meantone -> huygens -> grosstone -> mediantone

: > sept meantone -> huygens -> meridetone -> huygens (current 19-limit sauveuric)

: covers all subranges between 26edo and 12edo with 6 extension pathways. Note that the roulette (31 & 74) and mediantone (74 & 43) extensions to grosstone are very complex ''and not currently documented on the page''.

: I believe furthermore that 11-limit "meanenneadecal" should be renamed to "vincenzo" (which there is already precedent for, with 2.9.5.7.11 leantone referred to as "every other step of '''vincenzo'''"), and that tridecimal meantone should be decanonicalized (also that 11-limit huygens should be called huygens and not "undecimal meantone"). I don't believe any pathways extending from either flattone or septimal meantone to the 19-limit, other than these 8, are worth preserving. The rationale for preserving vincenzo and tridecimal huygens is that these are the best 19edo-specific and 31edo-specific extensions. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 06:33, 24 August 2025 (UTC)

::

:: '''Meantone extensions'''

::* to 7

::** "septimal meantone" (+10); sharp of 19edo

::** "flattone" (-9); flat of 19edo

::* to 11

::** "hypnotone" (+6); flat of 19edo

::** "meanpop" (-13); sharp of 19edo & flat of 31edo

::** "huygens" (+18); sharp of 31edo

::* to 13

::** "vincenzo" (-4); flat of 19edo

::** "meanpop" (+15); sharp of 19edo & flat of 31edo

::** "grosstone" (-16); sharp of 31edo & flat of 43edo

::** "meridetone" (+27); sharp of 43edo

::* to 17 & 19 (note all equate 19/17 to 2 gens)

::** "meantonic" (+26); sharp of 19edo & flat of 31edo

::** "huygens" (-5); sharp of 31edo & flat of 12edo

::** "roulette" (-36); sharp of 31edo & flat of 74edo

::** "mediantone" (+38); sharp of 74edo & flat of 43edo

:: For further reference, I included here a chart of the different meantone extensions, also transcluded from Discord, referring to individual mappings of each prime by name. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 06:43, 24 August 2025 (UTC)

::: What about meantone tunings that neither septimal meantone nor flattone nor dominant produce patent vals for, within the range otherwise covered by septimal meantone? Examples are [[55edo]] and 67edo at the less flat end and [[69edo]] and [[88edo]] at the more flat end. (I posted about both sets earlier on this Talk page.) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:41, 24 August 2025 (UTC)

:::: I have no problem with the 7-limit version of it. The higher-limit extensions may need further investigations. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:05, 24 August 2025 (UTC)

::: Looks like your names are determined on the mapping of the last primes, which I'm not getting the point of. The mapping of 7 is the more distinguishing feature of these temps and that's like the whole point of putting them into a temp family.

::: > huygens -> grosstone -> huygens

::: > huygens -> meridetone -> huygens

::: Alternating the names ''huygens'' and ''grosstone''/''meridetone'' sounds like a bad idea. 19-limit grosstone seems good enough to be canon to me, tho 19-limit meridetone is debatable (see below).

::: > tridecimal meantone should be decanonicalized

::: Agreed. I also observed grosstone is actually more of a counterpart of 13-limit meanpop, as both temper out 144/143 and have more flexible tunings. However, I'll have to dig some old archive to see how it came out as it is. I remember someone called one of the 13-limit extensions ''meaningless'' (literally), which may be a name worth of a revival.

::: > 11-limit "meanenneadecal" should be renamed to "vincenzo" (which there is already precedent for, with 2.9.5.7.11 leantone referred to as "every other step of '''vincenzo'''")

::: I'm not sure. 13-limit meanenneadecal is 12f & 19. 13-limit vincenzo is 12 & 19. Both only have 13-odd-limit diamond monotone at 19. Same for meanplop, 12e & 19. It's not obvious to me (and to a random user) that 12 & 19 would be a more natural extension than either 12f & 19 or 12e & 19. On the Hemimean clan page, leantone used to be described as every other step of meanenneadecal, only changed to vincenzo by Recentlymaterialized early this year for reasons unexplained.

::: > I don't believe any pathways extending from either flattone or septimal meantone to the 19-limit, other than these 8, are worth preserving.

::: The 19-limit extensions of meridetone aren't worth preserving if the 19-limit extensions of tridecimal meantone are removed and vice versa. Meridetone isn't sharp of 43edo. It's exactly 43edo, same as tridecimal meantone to 31edo, unless 13-odd-limit diamond monotone isn't an issue to you, in which case tridecimal meantone can be sharper than 31edo too.

::: Rejecting meanplop also needs further discussion if you believe meanenneadecal and/or vincenzo can be preserved.

::: > roulette & mediantone

::: Roulette and mediantone are 2.9.5.7 and since a temp can't be a weak extension of itself, these names can't be used unchanged here.

::: Last, on Discord, you wrote: "['meanpoid'] is the meanpop extension that continues all the way to 19edo, but I think the meantone extension most suited for really being 19edo-specific is vincenzo anyway; meanpoppic should be canonical."

::: "Meanpoid" ranges from 19 to 31. "Meanpoppic" ranges from 50 to 31 and are highly complex. I'm not getting why you believe meanpoppic is a better extension. It just looks way less practical as an extension.

::: So at present I'd act on the cautious side and only agree to decanonicalize tridecimal meantone.

::: Finally, you didn't mention dominant. I think, as a first step, undecimal dominant should be decanonicalized for the reason I put in the article.

::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:05, 24 August 2025 (UTC)

:::: > Looks like your names are determined on the mapping of the last primes, which I'm not getting the point of. The mapping of 7 is the more distinguishing feature of these temps and that's like the whole point of putting them into a temp family.

:::: Nowhere did I say that I had any proposals for renaming the 19-limit temperaments themselves. I named the individual mappings to the higher primes; those are not temperament names.

:::: > meanenneadecal vs vincenzo

:::: I think the logic behind vincenzo is essentially to use the septimal meantone mapping of 7 and flattone mappings for 11 and 13, and I think that's a pretty reasonable way to construct an 11-limit temp and a 13-limit temp. For the same reasons, I think meanplop, using the overcomplicated meanpop mapping of 11, for the sake of essentially no gain in being supported by edos other than 19, is worse than vincenzo which uses the flattone mapping of 11.

:::: > meanpoid vs meanpoppic

:::: Meanpoid doesn't work "from 19 to 31", it works ''in'' 19 and 31 exclusively. I think of 50edo as the standard meanpop edo, and the extension supported by 50edo is meanpoppic. As Lucius observed, there is a range between 19edo and 50edo. That range does not support septimal meantone. "19 & 31" as an edojoin is worth preserving, I suppose, though. That makes sense as an argument to keep meanpoid.

:::: > meridetone

:::: Meridetone ''is'' the counterpart of grosstone across 43edo, but its join is 43 & 55de. Again, as Lucius said, sharp of 43edo is outside the septimal meantone range. So I'd concede a point here, though I still think that sauveuric is the best meridetone extension. Note however that 19-limit meridetonic follows what I've called the "mediantone" extension to 17 and 19; however that extension is specifically 74 & 43 (supported by 117d), and due to its sheer complexity should serve nowhere else other than grosstone. I'd suggest "meridian" as a name for this 19-limit grosstone extension.

:::: For further elaboration on grosstone extensions: ⟨0 1 4 10 18 -16 -5 -3] (31 & 43) is the current canonical 19-limit grosstone. However it is not supported by the optimal grosstone edos (74, 105, and 117d). My suggestion above was the inclusion of two alternate 19-limit extensions, based on 19-limit didacus extensions, that are quite complex but supported by 74edo. These are ⟨0 1 4 10 18 -16 38 40] (74 & 43) "meridian" and ⟨0 1 4 10 18 -16 -36 -34] (31 & 74) "name TBD". However, due to their complexity and lack of coverage of the whole 31-to-43 range, I suggest neither of these should be canonical. Either 31 & 43 should remain canonical, or none of these three should be. In the latter case we could call 31 & 43 "grosstonian" and 31 & 74 "grosstonic", or something along those lines.

:::: > The 19-limit extensions of meridetone aren't worth preserving if the 19-limit extensions of tridecimal meantone are removed

:::: I think all the temps that remain here should be 19-limit. If we keep 13-limit huygens around, we should keep 19-limit huygens around.

:::: > Finally, you didn't mention dominant.

:::: 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 91: / Line 91: @@
 :: It wasn't originally my question, but let me try rephrasing it:  Why is the POTE generator for it specified as being so close to 7\12 when 12edo is way out of the range for which Sharptone is optimal (unless you need it for pitch-bending the 7/4 up on a standard 12edo fretted instrument), and 5edo is the crossover point between Dominant and Sharptone, and Sharptone would give the most just 7/4 or 8/7 with a fifth somewhat sharp of the diatonic range of Meantone temperament?  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:49, 10 July 2025 (UTC)
+::: Classical (5-limit) meantone clearly makes no sense beyond 3\5. Dominant doesn't make much sense beyond 10\17. I described the range of dominant as 7\12 to 10\17 in the Arhcytas clan page, which I hope you like. Unfortunately 10\17 isn't a natural boundary for meantone extensions, so maybe we'll keep 7\12 to 3\5 for dominant as we discuss it in this article. As for sharptone, the only 7-odd-limit monotone range of it is the singleton of 3\5, right? So that's the case for tuning it to 3\5. Our conventional optimization methods are least squares, which also make sense, but they obviously don't take those constraints into account. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:21, 11 July 2025 (UTC)
+:::: . . . Which leaves me wishing that the name Sharptone hadn't been taken for what is really an exotemperament extension of Meantone, so that it could have been used for something more fitting as a counterpart to Flattone, like the strong extension that gives the patent 7th harmonic for 55edo, 67edo, and 122edo (to which I gave the placeholder name Mildtone inn [[Talk:Meantone]]).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:28, 11 July 2025 (UTC)
+::::: I propose that the 7-limit temperament tempering out 21/20 and 28/27 be called ''trienmean'' in this case. I originally wanted to call it ''trientone'', but that conflicts with an already-existing term. [[User:2^67-1|2^67-1]] ([[User talk:2^67-1|talk]]) 09:00, 11 July 2025 (UTC)
+:::::: I agree that sharptone really should be renamed (I presume it mainly exists in order to be detempered into scales, so shouldn't just be deleted). But "trienmean" sounds too much like "trimean" or some other kind of extension that splits meantone into three (lithium, mothra, ...). -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 13:17, 11 July 2025 (UTC)
+::::::: How about Oneirotone?  Because once you get past 5edo, [[5L&nbsp;3s]] (the Oneirotonic scale, of which 5edo has the collapsed version) becomes valid.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:16, 11 July 2025 (UTC)
+:::::::: I don't think sharptone should be renamed. There is not a strong reason to do so. Also, re-using old names isn't a great idea in the first place, so pls don't take this as a pathway to re-use the name ''sharptone'' for something else. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:38, 12 July 2025 (UTC)
+::::::::: I'll agree on not reusing the old name, but I believe Sharptone shouldn't have taken that name in the first place.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:08, 13 July 2025 (UTC)
+:::::::::: It may not be perfect but it's not inappropriate either, so we'll keep it unless there's a strong reason for renaming. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:23, 13 July 2025 (UTC)
 : Put my vote in for that question as well.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:20, 10 July 2025 (UTC)
 :: All I can think is that, sharp of 5edo, the M6 becomes sharp of the m7, and they cross over at 960 cents. [[User:Jerdle|Jerdle]] ([[User talk:Jerdle|talk]]) 09:50, 10 July 2025 (UTC)
+== Request to remove impractical 17- and 19-limit extensions ==
+I request removing "meantoid", "meridetoid", "meanploid", "meanenneadecoid", and "vincenzoid".
+"Meanpoid" should be renamed to something else or straight-up made canonical.
+Undecimal meantone is best tuned a little sharp of 31edo, with 31edo and 12edo as boundaries of diamond monotone, so 12 as a val makes a little more sense than 19e for the purpose of edo join here. Compare meanpop, which is 12e & 19, and 19 makes a little more sense than 12e, as meanpop is best tuned flat of 31edo. Now consider the 13-limit extension, called tridecimal meantone. This is a questionable extension, but to be fair at least the three vals supporting it (12f, 19e, 31) make sense for the purpose of edo join, and 31 actually makes some musical sense in the 13-limit. Unfortunately this locks 31edo in as the only useful tuning, as the prime 11 can't be flatter and the prime 13 can't be sharper. Therefore, any extension of this should be supported by 31 (not 31gh), be it simple or complex.
+Besides tridecimal meantone we have meridetone, the 12f & 31f temp. 43 is the tuning here that plays the role of 31 in tridecimal meantone. For the same reason, any extension of this should be supported by 43 (not 43gh).
+Meanpop works better with these extensions as tridecimal meanpop is a more flexible temp than tridecimal meantone. It has valid tunings between 19 and 31, and both 19 & 31 and 31 & 50 make sense in the 19-limit. These correspond to what we call "meanpoppic" and "meanpoid" currently.
+Meanplop is centered around 19, similar to 31 to tridecimal meantone, and it should only be about 19 (not 19gh). Same for meanenneadecal and vincenzo.
+[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:57, 22 August 2025 (UTC)
+: Yes please! – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 18:08, 22 August 2025 (UTC)
+: My thoughts on the matter, copied from the XA discord:
+: > flattone -> hypnotone -> vincenzo (current 13-limit flattone)
+: > sept meantone -> meanpop -> meanpop -> meantonic (current 19-limit meanpoppic)
+: > sept meantone -> huygens -> grosstone -> huygens (current 19-limit grosstone)
+: > or
+: > sept meantone -> huygens -> grosstone -> roulette
+: > sept meantone -> huygens -> grosstone -> mediantone
+: > sept meantone -> huygens -> meridetone -> huygens (current 19-limit sauveuric)
+: covers all subranges between 26edo and 12edo with 6 extension pathways. Note that the roulette (31 & 74) and mediantone (74 & 43) extensions to grosstone are very complex ''and not currently documented on the page''.
+: I believe furthermore that 11-limit "meanenneadecal" should be renamed to "vincenzo" (which there is already precedent for, with 2.9.5.7.11 leantone referred to as "every other step of '''vincenzo'''"), and that tridecimal meantone should be decanonicalized (also that 11-limit huygens should be called huygens and not "undecimal meantone"). I don't believe any pathways extending from either flattone or septimal meantone to the 19-limit, other than these 8, are worth preserving. The rationale for preserving vincenzo and tridecimal huygens is that these are the best 19edo-specific and 31edo-specific extensions. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 06:33, 24 August 2025 (UTC)
+::
+:: '''Meantone extensions'''
+::* to 7
+::** "septimal meantone" (+10); sharp of 19edo
+::** "flattone" (-9); flat of 19edo
+::* to 11
+::** "hypnotone" (+6); flat of 19edo
+::** "meanpop" (-13); sharp of 19edo & flat of 31edo
+::** "huygens" (+18); sharp of 31edo
+::* to 13
+::** "vincenzo" (-4); flat of 19edo
+::** "meanpop" (+15); sharp of 19edo & flat of 31edo
+::** "grosstone" (-16); sharp of 31edo & flat of 43edo
+::** "meridetone" (+27); sharp of 43edo
+::* to 17 & 19 (note all equate 19/17 to 2 gens)
+::** "meantonic" (+26); sharp of 19edo & flat of 31edo
+::** "huygens" (-5); sharp of 31edo & flat of 12edo
+::** "roulette" (-36); sharp of 31edo & flat of 74edo
+::** "mediantone" (+38); sharp of 74edo & flat of 43edo
+:: For further reference, I included here a chart of the different meantone extensions, also transcluded from Discord, referring to individual mappings of each prime by name. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 06:43, 24 August 2025 (UTC)
+::: What about meantone tunings that neither septimal meantone nor flattone nor dominant produce patent vals for, within the range otherwise covered by septimal meantone?  Examples are [[55edo]] and 67edo at the less flat end and [[69edo]] and [[88edo]] at the more flat end.  (I posted about both sets earlier on this Talk page.)  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:41, 24 August 2025 (UTC)
+:::: I have no problem with the 7-limit version of it. The higher-limit extensions may need further investigations. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:05, 24 August 2025 (UTC)
+::: Looks like your names are determined on the mapping of the last primes, which I'm not getting the point of. The mapping of 7 is the more distinguishing feature of these temps and that's like the whole point of putting them into a temp family.
+::: > huygens -> grosstone -> huygens
+::: > huygens -> meridetone -> huygens
+::: Alternating the names ''huygens'' and ''grosstone''/''meridetone'' sounds like a bad idea. 19-limit grosstone seems good enough to be canon to me, tho 19-limit meridetone is debatable (see below).
+::: > tridecimal meantone should be decanonicalized
+::: Agreed. I also observed grosstone is actually more of a counterpart of 13-limit meanpop, as both temper out 144/143 and have more flexible tunings. However, I'll have to dig some old archive to see how it came out as it is. I remember someone called one of the 13-limit extensions ''meaningless'' (literally), which may be a name worth of a revival.
+::: > 11-limit "meanenneadecal" should be renamed to "vincenzo" (which there is already precedent for, with 2.9.5.7.11 leantone referred to as "every other step of '''vincenzo'''")
+::: I'm not sure. 13-limit meanenneadecal is 12f & 19. 13-limit vincenzo is 12 & 19. Both only have 13-odd-limit diamond monotone at 19. Same for meanplop, 12e & 19. It's not obvious to me (and to a random user) that 12 & 19 would be a more natural extension than either 12f & 19 or 12e & 19. On the Hemimean clan page, leantone used to be described as every other step of meanenneadecal, only changed to vincenzo by Recentlymaterialized early this year for reasons unexplained.
+::: > I don't believe any pathways extending from either flattone or septimal meantone to the 19-limit, other than these 8, are worth preserving.
+::: The 19-limit extensions of meridetone aren't worth preserving if the 19-limit extensions of tridecimal meantone are removed and vice versa. Meridetone isn't sharp of 43edo. It's exactly 43edo, same as tridecimal meantone to 31edo, unless 13-odd-limit diamond monotone isn't an issue to you, in which case tridecimal meantone can be sharper than 31edo too.
+::: Rejecting meanplop also needs further discussion if you believe meanenneadecal and/or vincenzo can be preserved.
+::: > roulette & mediantone
+::: Roulette and mediantone are 2.9.5.7 and since a temp can't be a weak extension of itself, these names can't be used unchanged here.
+::: Last, on Discord, you wrote: "['meanpoid'] is the meanpop extension that continues all the way to 19edo, but I think the meantone extension most suited for really being 19edo-specific is vincenzo anyway; meanpoppic should be canonical."
+::: "Meanpoid" ranges from 19 to 31. "Meanpoppic" ranges from 50 to 31 and are highly complex. I'm not getting why you believe meanpoppic is a better extension. It just looks way less practical as an extension.
+::: So at present I'd act on the cautious side and only agree to decanonicalize tridecimal meantone.
+::: Finally, you didn't mention dominant. I think, as a first step, undecimal dominant should be decanonicalized for the reason I put in the article.
+::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:05, 24 August 2025 (UTC)
+:::: > Looks like your names are determined on the mapping of the last primes, which I'm not getting the point of. The mapping of 7 is the more distinguishing feature of these temps and that's like the whole point of putting them into a temp family.
+:::: Nowhere did I say that I had any proposals for renaming the 19-limit temperaments themselves. I named the individual mappings to the higher primes; those are not temperament names.
+:::: > meanenneadecal vs vincenzo
+:::: I think the logic behind vincenzo is essentially to use the septimal meantone mapping of 7 and flattone mappings for 11 and 13, and I think that's a pretty reasonable way to construct an 11-limit temp and a 13-limit temp. For the same reasons, I think meanplop, using the overcomplicated meanpop mapping of 11, for the sake of essentially no gain in being supported by edos other than 19, is worse than vincenzo which uses the flattone mapping of 11.
+:::: > meanpoid vs meanpoppic
+:::: Meanpoid doesn't work "from 19 to 31", it works ''in'' 19 and 31 exclusively. I think of 50edo as the standard meanpop edo, and the extension supported by 50edo is meanpoppic. As Lucius observed, there is a range between 19edo and 50edo. That range does not support septimal meantone. "19 & 31" as an edojoin is worth preserving, I suppose, though. That makes sense as an argument to keep meanpoid.
+:::: > meridetone
+:::: Meridetone ''is'' the counterpart of grosstone across 43edo, but its join is 43 & 55de. Again, as Lucius said, sharp of 43edo is outside the septimal meantone range. So I'd concede a point here, though I still think that sauveuric is the best meridetone extension. Note however that 19-limit meridetonic follows what I've called the "mediantone" extension to 17 and 19; however that extension is specifically 74 & 43 (supported by 117d), and due to its sheer complexity should serve nowhere else other than grosstone. I'd suggest "meridian" as a name for this 19-limit grosstone extension.
+:::: For further elaboration on grosstone extensions: ⟨0 1 4 10 18 -16 -5 -3] (31 & 43) is the current canonical 19-limit grosstone. However it is not supported by the optimal grosstone edos (74, 105, and 117d). My suggestion above was the inclusion of two alternate 19-limit extensions, based on 19-limit didacus extensions, that are quite complex but supported by 74edo. These are ⟨0 1 4 10 18 -16 38 40] (74 & 43) "meridian" and ⟨0 1 4 10 18 -16 -36 -34] (31 & 74) "name TBD". However, due to their complexity and lack of coverage of the whole 31-to-43 range, I suggest neither of these should be canonical. Either 31 & 43 should remain canonical, or none of these three should be. In the latter case we could call 31 & 43 "grosstonian" and 31 & 74 "grosstonic", or something along those lines.
+:::: > The 19-limit extensions of meridetone aren't worth preserving if the 19-limit extensions of tridecimal meantone are removed
+:::: I think all the temps that remain here should be 19-limit. If we keep 13-limit huygens around, we should keep 19-limit huygens around.
+:::: > Finally, you didn't mention dominant.
+:::: 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)