Talk:Tuning ranges of regular temperaments

Def of nice range

I don't understand this: "we may define a tuning range by finding the convex hull in tuning space of the tunings with one eigenmonzo 2 (pure octaves tunings) and the rest [of what?] a set of r - 1 members [why doesn't it matter which r-1 members we choose?] of the p-odd limit tonality diamond, when this tuning [how is "this" tuning chosen?] is defined." Actual math notation and formatting procedures as lists would help, if nothing else. Inthar (talk) 12:38, 28 January 2021 (UTC)

Is "bump" acceptable here? :) Haha, if Inthar doesn't understand this either, then I am really concerned. Surely someone can explain? Maybe there's something on the old tuning lists... nope, I don't find anything. --Cmloegcmluin (talk) 17:59, 25 May 2021 (UTC)

Missing word?

In section #Other tuning ranges, I read at the end of the 3rd sentence: [...] participants can correctly identify that tunings intervals in the way prescribed by the mapping. I think that there is a word missing between tunings and intervals. --Xenwolf (talk) 19:51, 27 May 2021 (UTC)

Good catch. Actually, it was missing a possessive apostrophe. Try it now? --Cmloegcmluin (talk) 23:53, 27 May 2021 (UTC)

Open or closed?

In an email correspondence, Dave Keenan suggested that the diamond tuning ranges should be considered open ranges, that is, that their extrema should be excluded. For example — per the examples given on the page — for 5-limit meantone, 4/3 and (12/5)^(1/3) would not themselves be diamond tradeoff generators, and 2/5 and 3/7 would not themselves be diamond monotone generators. I think this seems reasonable, but I wouldn't add it to the page unless I was sure that historically the ranges hadn't been defined otherwise. Does anyone happen to know whether they've been explicitly stated to be open or closed ranges? --Cmloegcmluin (talk) 04:15, 21 January 2022 (UTC)

I'd like to hear Dave's reasons. FloraC (talk) 11:13, 21 January 2022 (UTC)

Honestly it doesn't matter, I'd like to make it consistent though. (My vote is for open) - Sintel (talk) 17:55, 21 January 2022 (UTC)

Dave didn't explicitly give reasons. But from the context, I believe his point is that to truly be a meantone tuning, there must be some compromise between the tunings of the just perfect fifth and major third, and if no compromise at all is made, then the tuning has no business being called a meantone. And that this sentiment might then be extended to other temperaments (with less explicitly instructive names than "meantone") regarding whichever JI intervals they're defined as making compromises between. I think this makes enough sense, myself.

It seems that no one is aware of the original authors specifying one way or another, though? So if we don't know what is "actually" the case about these tuning ranges' openness, for now, the best possibility might be to recognize that it's an unknown on the main page, and say that for now you may want to be specific as to whether you're using diamond tuning ranges in an open or closed sense, on a case by case basis. --Cmloegcmluin (talk) 20:10, 21 January 2022 (UTC)