Talk:Meantone

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Hypopental EDO's

I've added an article for "hyperpent" a.k.a. hyperpental edo's and it's antithesis, "hypopent," or hyperpental edo's to cover classifications of different equal divisions of the octave that temper the fifth either sharp or flat, descriptively, rather than as a matter of intent or purpose.

I'm not sure if this is virtually redundant with "meantone" and "superpyth", but, if it is, I'd be happy to delete those articles or merge any useful information here.

--Bozu (talk) 15:42, 9 July 2020 (UTC)

Definitely not redundant, but I remember seeing these concepts somewhere, in different terms. FloraC (talk) 13:25, 13 July 2020 (UTC)

Interesting. If you come across it again, please update. --Bozu (talk) 14:59, 13 July 2020 (UTC)

Mothra as a 7-limit extension

Seems that Mothra should be included under the 7-limit extensions of Meantone. After all, it IS included in meantone family, even if it doesn't get the organizational prominence of the standard Septimal Meantone and other competitors. Since it includes meantones with a fifth divisible by 3 all the way from 5EDO to 21cEDO, while the other 7-limit extensions are either more restricted in range (standard Septimal Meantone, Flattone, Dominant) or apply to only a very few equal temperaments in their range (Sharptone), it seems that Mothra should get more attention. Lucius Chiaraviglio (talk) 05:34, 1 August 2024 (UTC)

I think this article should mostly focus on septimal meantone and briefly cover other strong extensions (tho each septimal extension deserves its own article). Weak extensions aren't as closely connected to the original temp as strong extensions. I'd expect the discussion on weak extensions to be addressed in meantone family. FloraC (talk) 09:01, 2 August 2024 (UTC)

Shouldn't Mothra be considered a strong extension given its range of coverage? (I could see Cloudy as a weak 7-limit extension since it has a limited useful range.) Or am I misunderstanding what divides strong extensions from weak extensions? Lucius Chiaraviglio (talk) 14:57, 6 August 2024 (UTC)

There's indeed a misunderstanding. The exact meaning of a strong extension is an extension that doesn't split the period and generators. FloraC (talk) 15:23, 6 August 2024 (UTC)

“Meantone” ≠ “Septimal meantone”

I've noticed that in various parts of the wiki, “meantone” is sometimes used without qualification to refer to both conventional 5-limit meantone, which would include tunings across the spectrum, such as 12edo, 19edo, 31edo, 43edo, 50edo, and so on‌; and to septimal meantone, which is rather poorly tuned compared to the 5-limit in most of those (31edo and quarter-comma meantone being the exceptions).

In some cases, this is a mere abuse of terminology, intended to convey some observation about quarter-comma meantone in particular in a succinct way. However, in other cases it is a bait and switch: “meantone” is first introduced as a historical basis of music theory, and then it is claimed that in “meantone” some chord is an essentially tempered chord, but on closer inspection it turns out that the two occurrences of “meantone” actually refer to different things (5-limit meantone and septimal meantone respectively).

To avoid this kind of ambiguity, I suggest that wiki pages should consistently use the phrase “septimal meantone”, rather than just “meantone”, when referring to concepts that require the septimal extension, including chords of septimal meantone, and should use “meantone” on its own only when referring to the conventional 5-limit form.

--Bcmills (talk) 05:48, 24 August 2024 (UTC)

See Temperament naming for the basics of how temps are named. In most tuning between 11\19 and 7\12 of meantone, you get septimal intervals for free, which is why septimal meantone inherits the name. Historically, septimal intervals were known no later than Helmholz and Ellis (1875), tho they didn't use them to analyse meantone. But that's already one and a half centuries. It doesn't do any benefit to stop there when we can apply the knowledge of septimal intervals to reveal what meantone is actually up to.

The most important corollary of accepting meantone as a 7-limit temp is just that: introducing a number of essentially tempered chords, and to realize most if not all chords in common practice were 9-odd-limit concords, either essentially tempered or essentially just. While many consider 9-odd-limit as concordance and thus will rule out discordance in the analysis of common practice music, septimal intervals and the related essentially tempered chords are still more complex, and contextually later, than say 5-limit triads, so that treating them as discordance is still possible. Since they are basically free to be laid on or taken out, the distinction of classical and septimal meantone seems practically pointless. I can only see the need of it in very technical contexts such as tuning optimization. FloraC (talk) 08:32, 24 August 2024 (UTC)

It may be true that “you get septimal intervals for free” in the RTT mapping, but in many common tunings of meantone the septimal intervals aren't actually tuned well enough to have concordant septimal intervals: pretending that they're always there is “revealing what meantone could be up to if tuned a specific way”, not what it “is actually up to” as performed. Assuming that a piece composed in or influenced by meantone will be tuned in a way that supports a septimal interpretation is too much of a stretch — especially considering how much of the common-practice era applied meantone logic to well-tempered scales, which tend to optimize for better 5-limit intervals.

The septimal bait-and-switch pushes a deeply ahistorical interpretation in order to further the idea that ~every common chord should be interpreted as consonant. It's fine to present that idea as a possibility where it applies, but it shouldn't be taken as a given — especially when that obscures alternatives that don't require ahistorical assumptions.

--Bcmills (talk) 12:59, 24 August 2024 (UTC)

Whether a specific meantone tuning is good enough for septimal intervals is a subjective matter. The interest in septimal intervals is idiomatic from the last century (including the early days of the community such as A meantone tuning with six 7-limit tetrads) thanks to musicians like Harry Partch, and most would agree 11\19 to 7\12 is a reasonable assessment of meantone's range, in which septimal meantone rules. I don't think there's pretention involved in interpreting augmented and diminished intervals as septimal since it's there in any chromatic keyboard. If historical analysis didn't recognize their byproduct presence then it was seriously out of date, and we are here to set them straight since we develop temp theories. Moreoever you can't be 100% sure that literally everyone of common practice was ignorant about septimal intervals to say they're "ahistorical". A quick skim of the archive showed Mozart was suspected to have used them as a means of expression (TUNING digest 1370: Meantone).

Septimal meantone isn't the only evidence that common practice music was mostly concordant (note: I distinguish consonance and concordance and hope you do too; otherwise your summary of the idea would be inaccurate). It's in the existence of meantone in the first place: to eliminate the wolf fourths and fifths. FloraC (talk) 15:04, 24 August 2024 (UTC)