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)