User talk:FloraC

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Meantone tuning spectrum additions?

My thoughts behind the additions I made to the tuning spectrum table (both removed and remaining):

1. Add clarification about syntonic comma vs other commas -- quite a number of commas appear in the table, but syntonic comma has its adjective stripped (as is traditional, so I didn't think it right to change that), which could be confusing to new people, especially if they have also seen another tuning spectrum table that has a different primary comma.
2. Fractions of Pythagorean comma appear often in this table, but the endpoints 7EDO and 5EDO have different 3-limit commas, so I thought it would be good to put those in there in the relevant lines.
3. 3/4-comma (especially) and 2/3 comma Meantone are very close to 7EDO.
4. Some of the EDOs in the table are there only by way of non-patent vals, but this was not explicit before.
5. 12EDO is almost exactly 1 Schisma Meantone; also, somebody (probably copy/paste error) had 12EDO notated as as "virtually 1/12 Pythagorean comma" and not "virtually 1/11 (syntonic) comma".
6. Since 5EDO is in the table (come to think of it, should it be there?), I thought the addition of some of the more prominent negative Meantone (not sure what it should be called) tunings would be in order, especially Ptolemismic which is very close to 5EDO.

For (especially) the first last, I now understand from your edit comment that non-Septimal-Meantone 7-limit and all 11-limit entries should go somewhere else. I did see the tuning table for Flattone, so maybe the entries close to 7EDO should go there? And maybe the Flattone EDOs currently in this table should also be moved there? But then flatter-than-flattone (Flattertone) doesn't have its own tuning spectrum table, and given that it is a sub-entry of the Meantone family article, I thought a new table would look kind of funny there. Similarly, Dominant doesn't have its own tuning spectrum table, and given that it is a sub-entry of the Meantone family article, I thought a new table would look kind of funny there. Not sure yet whether all negative Meantones like 17c should all go in a hypothetical Dominant tuning spectrum table, although 17c itself is Dominant. I DID see (although I must confess temporarily forgot about) the multiple tuning tables in Meantone vs Meanpop, so maybe the Ptolemismic tuning (11-limit) should go there? Although I'm not sure which of the tables it would fit into. Of these tables, only Tridecimal Meantone and Meanpop (but not Tridecimal Meanpop) have a negative meantone entry at all, and those are all only very slightly sharpened. Although at least if a new tuning spectrum table was needed in there, it wouldn't seem out of place. On the other hand, maybe such a hypothetical table should be somewhere else entirely, since undecimal negative Meantone (probably -- haven't done the math yet) would be neither Undecimal Meantone nor Meanpop?

Anyway, when I made my edits, I didn't realize that I was stepping on an organizational convention in making the edits I thought of above, so until I learn it better, I will revert back to proposing such potentially organization-altering changes in the Talk pages associated with the pages I am considering, and sorry for the trouble.

Lucius Chiaraviglio (talk) 18:03, 30 July 2024 (UTC)

Thank you for sharing your thoughts. I appreciate your professionality regarding editing the wiki.

1. Since you clarified this in the first entry, I think it's good now. The syntonic comma is also special cuz the article is about meantone. In other temps you shouldn't see fractions of the syntonic comma.
2. The fractional Pythagorean-comma tunings are senseless enough – I've never seen anyone looking for them, nor are they technically compatible with RTT. If I were bolder I'd remove all the Pythagorean-comma and septimal-comma tunings alike, but I'd better consult the community first. The actual problem is, there's no point adding those information of fractional limmas or fractional apotomes cuz there's no other fractions. Also every edo has such an association: for 19edo it's a 1/19-(19-comma) tuning; for 31edo it's a 1/31-(31-comma) tuning.
3. I don't think closeness to an edo warrants an entry. Why would someone look for those instead of grabbing the exact edo tuning?
4. I appreciate the specification of vals you added. Thank you.
5. Thank you for correcting it.
6. You have a point here. I think 5edo should have a place there cuz it's a relatively low-numbered edo that defines the edge of a tuning range (5-odd-limit diamond monotone), making it significant. Some higher edos tho really just clutters the space, esp. those in the flattone or dominant range. Pls note that extensions like flattertone and dominant will eventually get their own pages and own tuning spectra. I can make this quickly happen, if someone asks. But I don't think a simple split of the spectrum is the best solution. For one thing, all the extensions are meantone extensions and all the 5-limit eigeninterval tunings still apply. I think it's a question of which range to put the focus on. For meantone it's prolly best to maintain a higher precision in the meantone range, for flattone higher precision in the flattone range, etc.

FloraC (talk) 08:53, 31 July 2024 (UTC)

Sorry, just now saw this. (Xenharmonic Wiki used to notify me when somebody added something to a page that have "Watch" checked on, and now it mysteriously quit doing that -- this happening to you too?).

1. Seems to me that if a foreign comma produces a useful eigenmonzo or subset temperament (including part of a well-temperament), it might be worth mentioning.
2. Part of the same thought as above.
3. Part of the same thought as above -- why would someone look for a comma fraction that gets close to an EDO? Well, for starters, if they are making a well-tempered derivative of an EDO, they might want the exact comma fraction (even if a foreign comma) to get the exact eigenmonzo in the desired part of the well-tempered derivative, like quarter-comma or sixth-comma segments of some historical well-temperaments (and historical example of foreign comma: whole schisma in segment of Kirnberger temperament, and if I recall correctly also in somewhat later well-tempered relatives of 12EDO). So by analogy, whole-comma and 3/4-comma (and maybe even 2/3-comma) meantone might be useful for somebody making a well-tempered derivative of 7EDO (and 7WT does exist in world music, in the Republic of Georgia at least, although from what I read they make their well-tempered version differently from this example). Also, if a fractional-comma (even if foreign comma) meantone is very close to an EDO, a rendition of it with the same number of notes per octave can serve as a well-tempered version of an EDO in its own right: historically, 31 notes per octave quarter comma meantone as likely used on the Clavemusicum Omnitonum is close enough to 31EDO that the wolf fifth is tamed down to a dog fifth. Likewise with 12 notes per octave sixth-comma meantone (a more yappy dog, but at least you can play the whole gamut on a common non-extended Halberstadt keyboard). Also related to this: I keep thinking that the line for Pythagorean tuning should also show the alternate name 0-comma meantone, since shoehorning Pythagorean tuning into the 5-limit and higher is of actual musical interest (such as shown on the pages for Pythagorean augmented second and diminished fourth).
4. I think somebody else (or you?) adjusted the "d" warts on those, about which I wasn't sure of since I hadn't figured out that the table was supposed to be focused on septimal meantone rather than a grand unified meantone tuning table.
5. (Foreign comma schisma was eliminated -- but see above about Kirnberger temparment.)
6. No rush. I know how it is, already being up later than I should be doing this.

But now I'm thinking it might be good to have a grand unified table of fifths and flattened/sharpened-fifth-based temperaments and their member EDOs. An obvious starting point would be to copy and paste the meantone tuning spectrum, but the table would need to have columns added to designate temperament (since some of these would be non-meantone -- for starters, especially Superpyth and Mavila) and extensions; also equivalent extension names for other meantone-like temperaments. Would require some thought of how to have enough information while keeping it readable for those having non-humongous screens, though (especially when something appears on more than one temperament and/or extension).

Lucius Chiaraviglio (talk) 14:48, 6 August 2024 (UTC)

Closeness to an edostep is a property of a JI interval, so these things go to the interval's page. For example the page 50/33 has a section describing its proximity to 3\5. That should be enough for users looking for information on well temp design. It doesn't have to be in the meantone tuning spectrum.

Another problem is right in the "useful eigenmonzo". Eigenmonzo is an RTT concept, and some tunings aren't technically compatible with it. All the fractional Pythagorean-comma tunings aren't, so you gotta specify "as M2", "as m3" etc. which are pretty awkward. Same with the "full-schisma" tuning (the Kirnberger fifth is a d6; you're forcing it to be the P5). The actual tuning that tunes the Kirnberger fifth pure is the 1/11-comma tuning, which is even closer to 7\12. It's also extremely close to the 1/12-comma tuning which tunes the schisma itself pure. That aside, I don't think the Kirnberger fifth is ever actively looked for. It's more of an artifact of well temp design.

Speaking of well temp design, I think it has become an art in itself. God knows how many well temps have been invented in the world and so there's no point tryna document all the fifths ever used in them. If you just want a giant table of fifths there's a page for that: List of interesting fifths. It's a bit unmaintained. Maybe you can help cleaning it up.

FloraC (talk) 16:08, 6 August 2024 (UTC)

I've put an entry in the Talk for that. Lucius Chiaraviglio (talk) 05:28, 7 August 2024 (UTC)

I couldn't resist looking up some syntonic comma equivalents of the Georgian 7WT, reportedly most commonly alternating 4ED3/2 (step size 175.489¢) and 3ED4/3 (step size 166.015¢). You can get REAL CLOSE to these with alternating 2/3-comma meantone (9/8 flattened by 4/3 syntonic comma = 175.235¢) and 7/8-comma meantone (9/8 flattened by 7/4 syntonic comma = 166.274¢). So did the Georgia 7WT really arise as alternating 4ED3/2 and 3ED4/3, or did it come from alternating 2/3-comma meantone and 7/8-comma meantone and then inflating one or both very slightly to make the octave just (from 1190.8¢ to 1200.0¢)? Lucius Chiaraviglio (talk) 06:38, 7 August 2024 (UTC)

Are you sure these Georgian 7wt intervals are related to meantone at all? Is 5-limit harmony sought for in this tradition in the first place? FloraC (talk) 07:50, 7 August 2024 (UTC)

I can't be sure of it, but 7EDO (and thus 7WT) does fit on meantone, so it seems like too good a coincidence to pass up, at least for giving a decent look. Of course, 7EDO (and thus 7WT) is at a major nexus of temperaments (the syntonic-chromatic equivalence continuum), so meantone isn't the only possibility; it might be hard to find a record of what thinking went into the invention of Georgia 7WT in the first place. Lucius Chiaraviglio (talk) 15:13, 7 August 2024 (UTC)

Hmm, I'm not convinced. 7edo technically supports meantone, but it's a really poor tuning of it. 7-tone traditions around the world are almost never meantone. 5-tone, 7-tone, and 12-tone traditions are more likely related to the 3-limit/Pythagorean tuning, generated and equalized. FloraC (talk) 03:48, 8 August 2024 (UTC)

Fractional-octave temperament pages

I would like to add Template:Navbox fractional-octave as a footer at the very bottom of all fractional octave temperament pages. This would not replace Template:Fractional-octave navigation, but only exist alongside it.

The template is a joint effort of Ganaram Inukshuk, ArrowHead and myself, and as the name suggests uses the new standardised Template:Navbox.

Are you happy for me to go ahead and add it?

I would also like to remove “Category:Temperament collections” from all fractional octave temperament pages, because they are all already included in “Category:Fractional-octave temperaments” which is a subcategory of “Temperament collections”, so they don’t really need to be included twice and it’s neater and more organised them having their own subcategory (most other types of temperament collection have their own subcategory too).

Are you happy for me to go ahead and do that also?

--BudjarnLambeth (talk) 02:18, 4 December 2024 (UTC)

Happy for both. Go ahead. FloraC (talk) 07:00, 5 December 2024 (UTC)

Thank you, I appreciate your reply :) I will go ahead with those changes now. --BudjarnLambeth (talk) 07:14, 5 December 2024 (UTC)

Subsets and Supersets af AFDOs (Pages AFDO, 2afdo, 3afdo, …n-afdo)

Flora, you have put so much effort and time into maintaining and editing the AFDO pages - thank you for that. There is one aspect of these pages that I'm not sure I understood correctly, so I'll just address my question directly to you. It's about the terms subset and superset of an AFDO.

On the 2afdo page we read:
2afdo “is a superset of 1afdo (equivalent to 1edo) and a subset of 3afdo”.
Can 2afdo be a subset of 3afdo when no intervals are shared (except the octaves)?

Similarly, the 3afdo page explains...
3afdo “is a superset of 2afdo and a subset of 4afdo”,
but neither has any intervals in common with 3afdo (except octaves).

The AFDO page tells us that in general...
“All AFDOs are subsets of just intonation, and up to transposition, any AFDO is a superset of a smaller AFDO and a subset of a larger AFDO (i.e. n-afdo is a superset of (n - 1)-afdo and a subset of (n + 1)-afdo for any integer n > 1).”
As you may have noticed I’m not convinced that the example given is correct.

I've been playing around with overtone scales for a while now, in order to construct a prototype keyboard with dynamic intonation control. Personally I would summarize my experience with this project as follows:

• To create a superset of an n-afdo , I’d multiply n by a (preferably small) integer number including 2 (i.e. 9-afdo is a superset of 3-afdo).
• To create a subset of an n-afdo , I’d divide n by any of its prime factors

(i.e. 5-afdo and 3-afdo are both subsets of 15-afdo).

Your comment is very much appreciated – thanks for your time.
All the best --Holger Stoltenberg (talk) 11:35, 12 December 2024 (UTC)

You might be missing the fact that afdos are octave-repeating tunings and that octave-equivalent rotation is a thing. For edos it's the prime factor rule, since each edo only has one mode. For afdos, n-afdo has n distinct modes. So in the 2- and 3afdo example, 2afdo has two modes: 2:3:4 and 3:4:6. 3afdo has three modes: 3:4:5:6, 4:5:6:8, and 5:6:8:10. 3:4:5:6 is a superset of 3:4:6, so 3afdo is a superset of 2afdo. The same is true for any two distinct afdos and any two distinct ifdos. I hope that answers your question. FloraC (talk) 12:03, 12 December 2024 (UTC)

Thanks for your quick and detailed response. The examples you provided are very helpful, so I have got the idea. I'll have to dig a little deeper into the subject of octave repeating tunings and octave equivalent rotation.
Best --Holger Stoltenberg (talk) 16:31, 12 December 2024 (UTC)