Talk:Meantone family

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Errors in edolists

The edolists are very flawed. How is 53edo a dominant meantone?! PiotrGrochowski (info, talk, contribs) 15:59, 10 October 2018 (UTC)

Typo in Septimal Meantone section?

In the Septimal Meantone section, it says that nine fifths are needed to reach the interval for 7, C ~ A#. I count ten fifths, and so does the Wikipedia article on Septimal Meantone Temperament.

Caption text

Note	Fifthspan
C	0
G	1
D	2
A	3
E	4
B	5
F#	6
C#	7
G#	8
D#	9
A#	10

Edit: And the table in the Meantone vs Meanpop page also says ten fifths for C - A#.
Are we missing something?
Lucius Chiaraviglio (talk) 02:51, 22 July 2024 (UTC)

It seems like an error indeed, good catch. --Fredg999 (talk) 04:59, 22 July 2024 (UTC)

I wonder if the error arose because whoever typed it was looking at the monzo [-17 9 0 1⟩ = 137781/131072 for the flattone comma (not sure if that is an official name), which maps 9 fifths (octave-reduced) to 8/7 as D♯ and thereby 9 fourths (octave-reduced) to 7/4 as B♭♭, and then they typed it into the septimal meantone description by mistake? (Unfortunately this comma doesn't currently have its own page as far as I can tell, although if it doesn't have an official name, not having its own page isn't surprising -- maybe also the problem for some of the other septimal extensions commas?) Lucius Chiaraviglio (talk) 20:10, 24 August 2024 (UTC)

Sharptone?

Still trying to figure out why sharptone exists as a septimal extension to meantone, when the only EDO it seems to really work for (that is, without a 'd' wart) is 5EDO, and then the other equal temperaments listed under it are 12d and 7d (the latter being way over on the flat end of the usable meantone tuning spectrum); meanwhile, Dominant also works for 5EDO, since B♭ is enharmonic to A in 5EDO. Seems like this name should have been saved for a more useful subset of the sharp approximate half of the meantone tuning spectrum. Lucius Chiaraviglio (talk) 12:04, 19 August 2024 (UTC)

Commas listed in Extensions?

Shouldn't the commas listed under Extensions also appear in the comma lists of the respective sub-temperaments listed later on? Lucius Chiaraviglio (talk) 22:08, 23 August 2024 (UTC)

Deletion of higher-limit Vincenzo

What's the reasoning behind doing this? Was it discussed with anyone else? If not, deleting one of the highest-limit temperaments on the whole wiki seems like a bad idea. Yourmusic Productions (talk) 18:47, 24 March 2025 (UTC)

Personally I feel like this page is getting a bit out of hand with how many ridiculous stuff is here. If you think those are useful feel free to revert my edit. – Sintel🎏 (talk) 20:03, 24 March 2025 (UTC)

Prime 47 in higher-limit Vincenzo is literally identified with 3/2. There is no point in including some harmony as high as 47 in a temperament if it is allowed to be tuned this far off. 47-limit Vincenzo would be useful if it actually reflected any high-limit structures. It does not. --Lériendil (talk) 20:12, 24 March 2025 (UTC)

"deleting one of the highest-limit temperaments on the whole wiki seems like a bad idea" this would be true if the temperament was even remotely reasonable. It's basically only useful for detempers, in which case, someone doing a detemper of one of those edos doesn't need this temperament to do it, because they will just detemper the edo. To put into perspective how useless it is, tempering out 25/24 (dicot) is much more fruitful for detempers, because it meaningfully describes certain JI scales that have 5/4 and 6/5 subtend the same number of scalesteps, such as a generator sequence. --Godtone (talk) 20:39, 24 March 2025 (UTC)

And yes, it was discussed with others; multiple people noticed it was a unusually ridiculous temperament that clearly served no practical musical purpose. --Godtone (talk) 20:45, 24 March 2025 (UTC)

Stuff above 19-limit deleted

Why delete stuff above the 19-limit (Latest revision as of 2025-03-24T09:25:25)? I wouldn't recommend putting in new stuff above the 19-limit (or in some cases 23-limit), but since somebody already did the work, why not keep it? Lucius Chiaraviglio (talk) 21:33, 24 March 2025 (UTC)

See discussion above. – Sintel🎏 (talk) 23:18, 24 March 2025 (UTC)

Okay, so it's specific to this particular higher-limit stuff not being useful, not that any higher-limit stuff should be cut out. Fair enough. And I didn't connect the name Vincenzo to the stuff that was deleted. Lucius Chiaraviglio (talk) 06:49, 25 March 2025 (UTC)

Yeah. We're currently proposing a more extensive streamlining of the septimal meantone strong extensions as well because many extensions include mappings of different primes with incompatible tuning tendencies. I don't believe this would be applied more generally; meantone extensions are a somewhat extreme case in terms of clutter, and doing this would help illuminate what actually useful extensions are there in different tuning subranges of meantone. But these extensions will continue to reach the 19-limit. --Lériendil (talk) 13:38, 26 March 2025 (UTC)

Fair enough. And while we're on the subject of streamlining, I would recommend a reorganization so that the main article starts with 5-limit Meantone (and its tuning spectrum table either reflects this or also includes the other major 7-limit extensions), and Septimal Meantone is moved to its own article like Flattone, Dominant, etc. (also getting its own tuning spectrum table if the tuning spectrum tables are not all merged). I can think of pros and cons for merged and separate tuning spectrum tables. But since past historical use of Meantone usually didn't pay much attention to septimal intervals, putting Septimal Meantone ahead of all of the others might not be the best way to organize things, given that modern use (which eventually will also be historical, and arguably already is for the early-to-mid 20th Century) has usage of Dominant being, um, dominant. Lucius Chiaraviglio (talk) 17:15, 26 March 2025 (UTC)

Replace 7-limit mohajira with 2.3.5.11

The page states that mohajira makes more sense as an 11-limit temperament than 7-limit. I personally didn't even know that mohajira had a canonical mapping of 7 at all.

Plus it would finally give 2.3.5.11 porcupine something to compare with!

-- VectorGraphics (talk) 09:52, 22 June 2025 (UTC)

The 2.3.5.11-subgroup restriction of mahajira is mohaha, which has been covered in rastmic clan. FloraC (talk) 09:57, 22 June 2025 (UTC)

Sharptone "well-tuned" sharp of 5edo?

How is sharptone relatively well-tuned sharp of 5edo when the POTE generator is so close to 7\12? Jerdle (talk) 09:50, 10 July 2025 (UTC)

There are better extension options available when tuned flat of 5edo. -- VectorGraphics (talk) 19:21, 10 July 2025 (UTC)

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? 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. 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). 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. 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, ...). -- 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. 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. 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. 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. FloraC (talk) 13:23, 13 July 2025 (UTC)

Put my vote in for that question as well. 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. 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.

FloraC (talk) 11:57, 22 August 2025 (UTC)

Yes please! – 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. --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. --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.) 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. 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.

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. --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.

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 (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. --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 this archive. FloraC (talk) 11:57, 26 August 2025 (UTC)

FloraC (talk) 10:55, 26 August 2025 (UTC)

(last updated by 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.

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 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. --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.

FloraC (talk) 09:52, 27 August 2025 (UTC)

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