User talk:Aura: Difference between revisions

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By the way, do you know if other media files are supported on this site the same way? These days, the most usable Web standard is Opus, and it provides the best combination of compression, quality, and latency. MP3 is not open source and generally is one of the worst standards ever designed. It was rendered obsolete more than a decade ago. It can be clearly seen in the Web video. (I don't mean some industries such as car audio, notorious with their media retards.) Anyway, I know who I can ask... — [[User:SAKryukov|SA]], ''Monday 2021 February 15, 18:16 UTC''

== Space Tour, Welcome to Dystopia, and 159edo ==

Hey Aura, I just listened to your two 159edo compositions, “Space Tour” and “Welcome to Dystopia”, and I thought you would like to hear some feedback. I think both of your compositions are incredible and I can’t imagine how long it must have taken you to detune everything by hand. I also have a few questions. First of all, what is the approximation of 159edo that you use and how is it different from 159edo itself? Second of all, how did you decide which EDOs “Space Tour” would mimic at different parts of the song? [[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 00:44, 19 February 2021 (UTC)

: The approximation of 159edo that I use differs from 159edo itself by fractions of a cent. The reason it's only an approximation is because I can only specify tuning to within two decimal places in MuseScore- the main program I use to compose and generate sound- as opposed to being able to straight-up divide the octave into 159 equal parts as would be required to have true 159edo. As for how I decided what EDOs to mimic, well, some were easy- like 12edo, 24edo and 53edo, while most of the others were inspired by the comments of others concerning said EDOs in the [[Table of edo impressions|Table of EDO impressions]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:25, 19 February 2021 (UTC)

:: Thanks for your reply. I think it's interesting that you feel the need to specify that you aren't writing in true 159edo just because MuseScore has a limitation to its retuning capabilities that most likely nobody will notice. I also write microtonal music in MuseScore, which means that my compositions are also tuned very slightly differently from true EDOs. Personally, I don't think that the slight discrepancies that come from the retuning limitations of various music making software and hardware have to be accounted for. In fact, I think it would be better for these discrepancies to be ignored if they are only a few hundredths of a cent wide, as is the case for your compositions. Do you have any additional thoughts on this matter? --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 03:10, 19 February 2021 (UTC)

::: It maybe true that these discrepancies won't be noticed by listeners, but the fact that I'm the one doing the tuning and cent-size look ups for various intervals means that I would feel as if I were being somewhat disingenuous to the more strict analysts who use computers for their analysis if I didn't add that disclaimer. I hope this makes some degree of sense. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:17, 19 February 2021 (UTC)

== MuseScore 159edo retuning plugin... ==

Hey Aura, I’ve been thinking about how a 159edo retuning plugin for MuseScore could be made, so I want to explain the main issue and offer 3 potential solutions. This block of text comes directly from the n-tet retuning plugin README. “A maximum of 3 arrows are allowed on each accidental, as MuseScore currently does not provide accidentals with more than 3 arrows. Due to these limitations, and with the help of quartertone accidentals, the plugin can only handle EDOs with a sharpness rating of up to 8.” The main problem here is that 159edo has a sharpness rating of 15 (one sharp equals 15 steps), meaning that there would have to be support for septuple up and septuple down accidentals in MuseScore for each note in 159edo to be accessible. (Assuming usage of ups and downs notation without lifts and drops). Here are my three solutions. The first solution is to come up with a notation system for 159edo using accidentals that can be found in MuseScore’s advanced palate. Then, a fork of euwbah’s n-tet retuning plugin would have to be made which could map all of the accidentals to edostep offsets. (Sharp equals 15 steps, triple up natural equals 3 steps, etc) The second solution is to use ups and downs notation from 53edo combined with “+” and “-“ symbols to indicate 1 step offsets for 159edo. For this to be effective, the plugins which raise and lower a note by one edostep (these plugins are included with the n-tet retuning plugin) would have to be modified to add and remove the “+” and “-“ symbols as necessary as well as changing the accidental and the pitch offset. The third solution is to use polychromatic notation for 53edo and to use the up and down arrow accidentals to access the notes in 159edo. Again, the pitch up and pitch down plugins would have to be modified. This time, these plugins would have to change the note head color as well as changing the accidental and the pitch offset. I would like to know which option you think is best for making 159edo compositions in MuseScore. In addition, since the programming language for MuseScore (Qt) is a bit too confusing for me to make anything meaningful in, you’ll have to ask FloraC to do the actual coding. I might be able to help a little bit, but not much. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 18:34, 19 February 2021 (UTC)

: Is it possible that there's a fourth solution? I mean, I already have a planned set of accidentals that seems to work, but they seem to need refining in terms of their design. In addition to the traditional natural, sharp, flat, double sharp and double-flat accidentals there are two new sets of quartertone accidentals, and an interesting set of tree-like arrows.

:[[File:Quarter-accidentals-narrow-rastmic-wide.png|300px]]

:# top line: narrow

:# middle line: rastmic (standard)

:# bottom line: wide

:The above image shows the new quartertone accidentals, while the image below shows the remainder of the new accidentals.

:[[File:Possible 159edo Accidentals.png|150px]]

:top row from left to right:

:# rastma wide

:# biyatisma wide

:# syntonic wide

:# syntonic + rastma wide

:# syntonic + byatisma wide

:# double syntonic wide

:bottom row from left to right:

:# rastma narrow

:# biyatisma narrow

:# syntonic narrow

:# syntonic + rastma narrow

:# syntonic + byatisma narrow

:# double syntonic narrow

:I hope the above accidentals make sense. I mean, I'm trying to make my approach to this whole thing as clean and straighforward as possible. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:45, 19 February 2021 (UTC)

:: It seems like you’re thinking of using custom accidentals with MuseScore. As far as I know, MuseScore has absolutely no support for importing custom accidentals, but I could be wrong. Even if MuseScore could support custom accidentals, I don’t think the custom accidentals could be utilized in a plugin because the plugin would have to be able to recognize these new accidentals with internal accidental codes. Since I know almost nothing about Qt, the programming language used to make plugins in MuseScore, you’ll have to double check with FloraC if your fourth solution is possible/feasible. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 20:05, 19 February 2021 (UTC)

::: At a certain point, I'm afraid custom accidentals are a must. That said, I am willing to wait and perfect this system first. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:09, 19 February 2021 (UTC)

:::: For now, while custom accidentals cannot be supported in MuseScore, wouldn't you rather have the detuning done automatically by a modified version of the n-tet retuning plugin rather than you having to input all the cent offsets yourself?

:::: [[File:Musescoremicrotonalaccidentals.png]]

:::: This image shows all of the microtonal accidentals currently in MuseScore. I'm sure at least some of them can temporarily suit your needs. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:08, 19 February 2021 (UTC)

::::: I'm willing to wait for MuseScore 4 for this considering that that version is currently in the works, in part because some of the accidentals that could otherwise be the most useful have been found to present legibility issues. However, I don't think it will hurt to at least get the ball rolling on this one. With that, do you have the time and or resources to help me finalize the designs of these custom accidentals of mine? Once that's done, we can talk to Euwbah and others about how to implement these in MuseScore 4. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:14, 19 February 2021 (UTC)

:::::: Well, I do have some time this weekend, but I wouldn’t say I have the resources to assist with making custom accidentals. I’m not an artist and I don’t have any kind of glyph editing programs or other art making programs. I can give feedback on your custom accidentals every now and then but I can’t help directly with the accidental making process. My main reason for asking you about this plugin is to give you a way of composing in 159edo without having to worry about retuning the notes manually. That’s why I think it would be better for you to have a temporary solution that doesn’t require any custom accidentals whatsoever. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:42, 19 February 2021 (UTC)

== New Comma ==

Hey Aura, can you give me your thoughts on the somewhat esoteric comma that I called the "Goldis" comma? I particularly would like to know if you have a better name for it and if you can think of higher limit extensions to the temperament. (The link to the page is on my user page) --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:58, 18 March 2021 (UTC)

== A potentially useful thing I came up with... ==

Hey Aura, I have another thing that I would like you to check out and give me your thoughts on. It might be more up your alley as it is based on Just Intonation. It's called the [[User:Userminusone/Averiant|Averiant]]. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 22:46, 25 July 2021 (UTC)

: I checked it out and I'm not sure what to make of it at the moment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:43, 26 July 2021 (UTC)

:: That's understandable. One thing I didn't mention, though, is that the Averiant could be useful for finding new commas. As an example, the comma 128/125 can be derived by taking the (1/3)averiant between 2/1 and 1/1 to get 5/4, and then equating 5/4 with 1/3 of an octave (or equivalently, equating 125/64 with an octave). 128/125 is quite a large comma but my point is that this approach could theoretically be used to find much smaller commas. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:31, 26 July 2021 (UTC)

::: I believe that, but how do you specifically narrow your commas down to those with low prime limit? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:11, 26 July 2021 (UTC)

:::: Sorry for the late reply, but to answer your question, one thing you could do is start with three simple ratios and find the averiantal percentage of the middle ratio relative to the two outer ratios, which you can then use to derive the comma. As an example, I could calculate the (1/1 - 5/4)averiantal percentage of 8/7, which is 3/5. To derive a comma from this, I would equate (8/7)^5 with (5/4)^3, resulting in the [[rainy comma]]. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 20:25, 1 August 2021 (UTC)

== Please remember to link new edo pages from the parent page ==

Please remember to add a link in the ''EDO'' page when you create new edo pages. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:08, 23 December 2022 (UTC)

== Where is Folly of a Drunk? ==

Where is it now? I love it very much! Can I listen to it and refer to friends?

I recently listened to all I found on your pages, like it.</br>

Thank you.</br>

—SA

: Hey! It's been a while since we last talked! I'll have to reestablish Folly of a Drunk on here, but I'm not in the position to do that right now. Besides, you might also want so hear Kite's arrangement. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:54, 15 July 2023 (UTC)

:: Thank you for your reply. I recently wrote to you on Youtube page “How Many Notes Are There? The Theory of Quarter Tones” (not very good one). I have a lot of new development, including Microtonal Fabric. It's too early to discuss now. But I must say that Microtonal Fabric is permanently used in Brainin School of Music for a pretty long time now. Brainin reported that little children master feeling micro tones wonderfully well and show unmatched level of musical intellect. Professional musicians usually fail to solve the problems well solved by those little students… --[[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]) 13 July 2023

:: Where is that Kite's arrangement? Yes, I would like to hear it. Will you give me a link? --[[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]) 13 July 2023

::: Here you go: https://youtu.be/fOZiX7f7t8Q?t=806 --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 00:15, 14 September 2023 (UTC)

:::: Thanks Fred. I was at work at the time I got SA's message. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:37, 14 September 2023 (UTC)

::::: Thank you, Fred! Thank you, Dawson! Great work! But I would like to access Aura's original audio variant as well. --[[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]) 13 July 2023

:::::: Okay, I've put Folly of a Drunk back onto my user page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:32, 22 September 2023 (UTC)

== Temperament(s) for Diatonicized Chromaticism? ==

I have been listening to the music of [[Ivan Wyschnegradsky]] (whose page needs expansion) and looking up how to put [[11L 2s]] scale that he called "Diatonicized Chromaticism" into one or more temperaments. My thoughts on this in part can be found at [[User:Lucius_Chiaraviglio/Musical_Mad_Science#Musical_Mad_Science_Musings_on_Diatonicized_Chromaticism|Musical Mad Science Musings on Diatonicized Chromaticism]] (although this needs updating and filling in. Searching for relevant intervals and commas has led me to [[The Nexus]] and to the conclusion that you would be the person to talk to about this. Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:14, 28 March 2025 (UTC)

: Sorry I didn't get to this sooner. Oddly enough, while I'm not terribly familiar with many aspects of this scale, I do know that 159edo supports it, with the large step at 13\159 and the small step at 8\159. It should be noted that 13\159 represents 128/121, while the small step represents 28/27- the latter is tempered together with 729/704 because the symbiotic comma is tempered out. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:36, 6 April 2025 (UTC)

:: Thanks -- I had also noticed that 159edo supports this scale, although I didn't track down what the steps temper to.

:: I took some time out from trying to figure out the temperament for 11L 2s to trying to figure out the temperament for the next higher analog of this scale to serve as a basic scale for a multiple of 12edo: [[17L 2s]], for which [[36edo]] implements the basic version of this scale. (I have made a start at this under what I linked above, on the same page.) I don't know whether Ivan Wyschnegradsky had this scale in mind when he was composing the few compositions he wrote in 36edo (I have yet to see a score for any of these compositions, and none of the YouTube videos of them are of the scrolling score type), but I was struck by how similar it sounded to his 24edo compositions (although with noticeably smaller steps), so I suspect that he might have had something of the sort in mind. (Unfortunately I haven't seen any of his writings about this, although one of the videos of his ''24 Preludes'' has a substantial excerpt about working with 11L 2s in 24edo, linked from my user sub-page that I linked above.)

:: Surprisingly, the going has been easier for 19L 2s than for 11L 2s, despite having had longer to work on figuring out a temperament for 11L 2s. So maybe figuring this out for 19L 2s will teach me how to do it for 11L 2s, although working with the 11th harmonic seems to be just inherently weird.

:: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:52, 6 April 2025 (UTC)

::: Yes, working with the 11/8 paramajor fourth is inherently weird- it takes either the 16/15 diatonic semitone or the 5/4 major third to set it up, and it really seems to like being a chord root in a 1/1-25/22-14/11-3/2 chord. Have you tried working with this stuff? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:29, 6 April 2025 (UTC)

:::: I haven't worked with it myself, but I am trying to gain an understanding. Obviously it isn't easy — Ivan Wyschnegradsky and a very few others figured it out, but only a very few others. But you gave me an idea of things to test, with the 1/1-25/22-14/11-3/2 chord. Although keep in mind that in 24edo (which Ivan Wyschnegradsky used most of the time, along with Alois Hába and a few compositions of Charles Ives), 14/11 maps down to the same as 5/4 (8\24) due to 24edo's badly flat 7th harmonic, while 25/22 maps not to the closest interval 9/8 as 4\24, but up to the same as 22/19 as 5\24, because its 5th harmonic is sharp (but not sharp enough for mapping as 25 instead of 5^2). But then again, I don't know whether Alois Hába or Charles Ives (ore much more recently, Scott Crothers) ever used 11L 2s as opposed to other ways of using 24edo; 11L 2s may be unique to Ivan Wyschnegradsky. Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:44, 6 April 2025 (UTC) Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:34, 7 April 2025 (UTC)

::::: Oddly enough, my experiments with how to handle the 11/8 paramajor fourth relative to the tonic have been largely carried out in 159edo, but I must say that even in 24edo, that 11/8 wants to go to either 3/2 relative to the tonic, or, to 4/3 relative to the tonic- at least in terms of chord roots. It should be noted that the 11/8 seems to literally bring in its own set of related accidentals relative to the key you're in- I've already hinted at 25/16 being dragged in, and the same is true with the 7/4, which, in this capacity, acts like an ultramajor sixth relative to the tonic. Naturally, the 33/32 will likely be dragged in as well, but what I didn't tell you is that 75/64 wants to rear its head in scalar motion on a tIV chord- the only two default scale degrees relative to the tonic that can be used with a tIV chord are the 5/4, and the 15/8. Otherwise, if you use an 11/8, it has to either be part of a 1/1-11/8-3/2 suspension on the tonic, or as part of a 1/1-5/4-3/2-55/32 built on the 8/5 relative to the tonic. There are other chords I know, such as the 1/1-11/8-15/8 built on the tonic, or the 1/1-11/8-7/4 built on the tonic, but these tend to be harder to set up and follow up properly. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:50, 7 April 2025 (UTC)

:::::: Keep in mind that 159edo is going to be a LOT different from the low to mid (and even upper-mid) double digits EDOs. You get literally a lot finer control over how your chords sound. Of course, the downside is that you need an instrument (or group thereof) that can play that many pitches (or you need to be REALLY GOOD on a continuous-pitch instrument). Another thing I noticed is that in 11L 2s it is hard to choose a mode that lets you hit common 5-limit intervals without going off-scale with accidentals. (I need to see how that plays out with 7-limit intervals in an EDO that supports the 7-limit better than 24edo, like 37edo or 59edo or 61edo, although I noticed that if you go all the way afield to 50edo or 46edo, this scale shoots itself in the foot by not mapping intervals of ANY mode to 3/2 or 4/3, which map differently than in 11L 2s EDOs closer to 24EDO in the tuning spectrum. Not sure yet, but I think 17L 2s operating in in the 2.3.7... subgroup may have less of that problem.) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:03, 7 April 2025 (UTC)

::::::: I know that 159edo is different to many of the smaller EDOs that you pointed out- there's a reason I chose to specialize in that particular tuning system. Furthermore I should mention that a 53edo-based instrument can have a few extra buttons added so that one may divide the step of 53edo into three- think the Neod, which is mentioned on the 159edo page. Of course, I think it pays to let people hear what 159edo is capable of by means of writing music for that tuning system in MuseScore Studio 4 or later and post the results to YouTube- that way, people might just be inspired to build the instruments necessary for live performance. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:26, 7 April 2025 (UTC)

::::::: On another note, I'm not sure how 11L 2s fares in 159edo in terms of what it can reach, and while it is important to note that 11L 2s can't often hit common 5-limit intervals in as of itself, I should think that detempered versions of that MOS, as well as the MOS itself, could still be useful in 159edo, as that will expand my capabilities. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:26, 7 April 2025 (UTC)

:::::::: I saw that Neod video a while back, although I should probably give it another go. I should look at 11L 2s in 159edo once I get back to working on a temperament (or probably clan of temperaments) for that scale. In an EDO that big, you might well want to add some strategic accidentals to the scale. And I have been impressed by a subset of works I have seen written in MuseScore 4 — the capabilities of MuseScore (including synthesizing instrument imitations that actually sound decent) seem to have greatly improved in the last few years. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:30, 7 April 2025 (UTC)

::::::::: Truth be told, some of the music linked on the 159edo page is mine, and I've also written music in MuseScore 3 as well as MuseScore Studio 4. Not only that, but I've codified a few musical tropes involving the 11/8 relative to the tonic. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:16, 8 April 2025 (UTC)

:::::::::: I'll have to check them out (actually listened to 1 already, but quite a while ago, before I started thinking much about this).

:::::::::: Meanwhile, I thought it would be useful to have a table of odd harmonics of the various EDOs supporting 17L 2s to make it easier to track stability of mapping, and I plan to do this for 11L 2s as well (which so far I had been doing this for by way of manual lookup of each EDO, which is time-consuming). Right now it is actually a collection of tables, because Template:Harmonics in equal doesn't have a way to string them together and doesn't have a way to set a uniform column width. Any idea how to fix this, other than manually creating a table with values copied from these? In the process of doing this, I have noticed an interesting comparison: 11L 2s has a very well-behaved 11th harmonic (it has to, since 11/8 and 16/11 is the generator pair), but doesn't seem to have well-behaved low harmonics; but in contrast, 17L 2s doesn't have a simple generator (23/16 is too flat by a few cents, and 13/9 is too sharp, and has multiple odd harmonics/subharmonics in it anyway), and the harmonics of the compound ratios that could be used as generators for it are NOT well-behaved, except that the 3rd harmonic is amazingly well-behaved, only flipping to a different mapping at 112edo and higher EDO values (and the 23rd harmonic would be well-behaved if only it wasn't flat of the actual generator — it would be an excellent generator for [[21L 2s]] or the soft end of [[2L 19s]]).

:::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:12, 8 April 2025 (UTC)

:::::::::: I finished doing the above for 11L 2s. Note that 11/8 (the dark generator, and thereby the bright generator 16/11) remains stable throughout the entire currently posted 11L 2s table &emdash; the worst relative error is -34.8%, at 127edo, so your favorite 159edo still easily fits in. Right now I strung out the odd harmonics to high values in case I need these for composite ratios, which seem likely to be needed for 17L 2s, but seem like they may not be needed for 11L 2s (but better leave them in for now until I am sure they are not needed). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:54, 9 April 2025 (UTC)

::::::::::: Wait, I thought that the large step of 11L 2s in 159edo was 13\159, not 11\159... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:10, 9 April 2025 (UTC)

:::::::::::: Good catch of typo -- fixed this. Also rechecked the rest, but didn't find any more. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:30, 10 April 2025 (UTC)

:::::::::::: Scrolling through these table groups, I started noticing interesting things, like how even though the 11th harmonic is the only one with stable mapping all the way through 11L 2s, some of the others have stable mapping in sections, like the 3rd harmonic has stable mapping in the middle section but is all over the place in both the hard and soft ends, but the 9th harmonic actually does okay in the hard end, as does the 17th harmonic (both of these get to be all over the place in the soft end), and the 5th and 13th harmonics have stable mapping in the soft end as long as the EDO values are not too large.

:::::::::::: In partial contrast, with 17L 2s, the harmonic/subharmonics of the generator have unstable mapping (because no simple ratio with a reasonable sized numerator and denominator fits into this zone), but the 3rd harmonic is nearly rock-solid (and 112b is a respectable if overly-complex quarter-comma meantone approximation), although presumably its mapping would break if I put in the rest of the right-most column of the MOS spectrum table. And there the 5th harmonic seems very much usable in the soft end of the scale tuning spectrum as long as the EDO sizes don't get too large (and even then, sometimes it is still okay), which looks to me like enabling a 2.3.5.23 meantone extension; it goes all over the place in the hard end, but there the 25th harmonic shines and is rock-solid as long as you don't go harder than 36edo (basic), and the 13th harmonic just barely misses being rock-solid in this zone (just barely breaks on 125edo, for which 125f would be not bad). Although those harmonics would also appear less solid if I included the rest of the MOS tuning spectrum.

:::::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:28, 10 April 2025 (UTC)

In reply to your previous comment, I should mention that I'd like to know where ~3/2 is relative to the 11L 2s of 159edo. I imagine it's rather far along the generator sequence. At the same time, I'm wondering what sorts of chords you can actually get from 11L 2s in 159edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:53, 10 April 2025 (UTC)

: This is further up on my page than the tables of odd harmonics: For the fifths in the basic 11L 2s (Wyschnegradsky) diatonicized chromatic scale (the version that 24edo yields), the 11/8-span of a patent fifth is a stack of 10 intervals of 11/8, octave-reduced. I haven't yet done this calculation for 159edo — it isn't too far off from basic, but it has small enough increments that attempting to use the same 11/8-span gives the b val fifth instead of the patent fifth. 00:07, 11 April 2025 (UTC)

: Did this for 159edo — the 16/11-span of 3/2 is 51. And it doesn't even work for the next EDO up or down from the last column of the tuning spectrum table of 11L 2s (135edo or 146edo, respectively) — the 3rd harmonic mapping is too unstable for EDO sizes that large in this region. Also, 51 is so many iterations of the generator that it goes well outside of the 11L 2s scale. Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:53, 11 April 2025 (UTC) Last Modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:52, 11 April 2025 (UTC)

:: Fascinating. I guess that means we need to look into chords with 94\159 fifths, which actually approximate 128/85 rather than 3/2. These chords clearly cannot be pure 5-limit either, but that's okay. Given that you mention 2.3.5.23 meantime, I'm now wondering if we can cobble together something for 11L 2s based on the ~128/85 archagall fifth. To start on this front, what are the modes of 11L 2s that contain ~128/85 in 159edo? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:40, 11 April 2025 (UTC)

::: I need to do the modes for 11L 2s with respect to coverage of standard diatonic intervals anyway, but that's going to take a bit of time, so stay tuned. The 128/85 b fifth is going to stick out like a sore thumb in the midst of the much more accurate other intervals that 159edo has, though, so maybe it would be better to try to come up with a decent MODMOS derived from 11L&nbsp2s for 159edo? In the meantime, I figured out which equal temperaments this might apply to, since they get their fifth from 51 stacked and octave-reduced 16/11 generators, leading up to 159edo: 37b, 61, 98, 159 (have not yet tried to extend beyond 159edo to see how far you can get before the fifth mapping breaks again). Note that for 61edo, 51 stacked and octave-reduced 16/11 generators gives the same note as 10 stacked and octave-reduced 11/8 generators. I also included 37b to show the small endpoint of the series (and if you really want to go weird, include 24b); judging by the pattern, the next member of the series would be 257 (not yet sure of wart, if any). Graham Breed's temperament finder lists some more members of the series without warts, going up into the thousands, but doesn't give the temperament a name beyond [https://x31eq.com/pyscript/rt.html?ets=159_98&limit=2_3_11 159 & 98], and I don't see 61edo listed in the Nexus, Nexus clan, or Nexus family, although 159edo comes up several times (maybe one of those temperaments would be better, although they probably go from the fifth to the 11/8 rather than the other way around, and would not necessarily support 11L 2s). Its enormous complexity is presumably the reason it never got a name; I don't know the specifics for computing badness, but I am going to stick my neck out and guess that this temperament would have huge badness despite its high accuracy.

::: As for 2.3.*.23, the 23rd harmonic mapping is pretty unstable in the zone of 11L 2s — it gets better mapping stability in 17L 2s, although this region has its generators sharp enough relative to 23/16 that larger EDO sizes often flip to the next flatter approximation, so the generator for that needs to be something between 23/16 and 13/9.

::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:21, 11 April 2025 (UTC)

::: The modes of 11L 2s that enable reaching 4/3 and/or 3/2 within-scale are not very many. If you want to get both, you have to use sLLLLLsLLLLLL (no other mode gets both). If you want to get 3/2 but can live without 4/3 (more common than the opposite), then you can also use LsLLLLLsLLLLL or sLLLLLLsLLLLL. If you use LLLLLLsLLLLLs or LLLLLsLLLLLLs or LLLLLsLLLLLsL you can get 4/3 but not 3/2. In EDOs with fine enough steps to distinguish 128/85(?) from 3/2, this instead gets you 128/85(?) (or 85/64(?) instead of 4/3). So if we want a MODMOS for 159edo that gets us back to 3/2 (and maybe 4/3) we need a second generator that gets tempered to be the same as 11/8 or 16/11 in the coarser EDOs supporting 11L 2s but distinguished in the finer ones. Not sure yet what that would be, and not sure yet whether 128/85 is the best slightly-inflated fifth substitute to use for this purpose. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:02, 12 April 2025 (UTC)

:::: Well, the ~128/85 fifth of 159edo is indeed useful in its own right as an imitation of the kind of thing you see in 22edo. Perhaps we can play to the strengths of that type of system where two ~128/85 intervals octave-reduced add up to ~17/15, and two instances of ~17/15 add up to ~9/7- yes, that is how 159edo works since both 22edo and 159edo support archagall temperament. Not only that but the ~128/85 interval is 159edo's best approximation of 17edo's fifth, so we could also shoot for 11L 2s harmonies that evoke the kind of stuff found in 17edo and it's multiples. The point is that if the ~11/8 and ~16/11 intervals count as ambisonances (basically, they're both consonances and dissonances at the same time) for our intents and purposes, as I know they do for mine, then we can afford to play with some of the less accurate intervals in our 11L 2s harmonies- assuming we play our cards right. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:28, 12 April 2025 (UTC)

::::: [[24576/24565#Mavka_a.k.a._archagallismic|Mavka a.k.a. archagallismic]] looks sort of like what we want, although that seems like more dimensions than we need, and I don't know how you would map that many dimensions onto any kind of keyboard, even before considering the size. (But maybe that could be trimmed down to a rank-3 temperament that is different from Archgallic, so as to get the 11/8 in there?) I see that its multiple generators include ~3, and it includes 150edo as a patent val, so you can get both 128/85 and 3/2. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:25, 12 April 2025 (UTC)

:::::: If I can map 159edo onto an isomorphic keyboard layout using [[tertiaschis]] temperament, albeit by squashing the hexagons, then we can work together to map a lower-dimensional temperament that relates to archagallic temperament. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:39, 12 April 2025 (UTC)

::::::: Tertiaschis looks interesting. Meanwhile, I determined that the Rastma (243/242) is NOT the right interval for differentiating 159edo from 61edo (lower on the series I noted above) — 159edo maps it correctly to 1 increment, but 61edo not only doesn't temper it out, but inflates it to 2 increments, while 98edo inverts it. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:16, 12 April 2025 (UTC)

::::::: Should have tried the Char comma/chroma ([[256/255]]) first. This is tempered out in 24edo, 37edo, 61edo, and 98edo, but correctly maps to 1 increment of 159edo; it is exactly the amount by which an archagall fifth exceeds a normal fifth. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:13, 13 April 2025 (UTC)

:::::::: Nice catch. Yeah, the char subchroma will prove useful to us. Come to think of it, however, the way that this interval plays with the intervals of 11L 2s reminds me of how the syntonic comma plays with the intervals of 5L 2s... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:30, 13 April 2025 (UTC)

::::::::: That's the idea. Although other parts of the 11L 2s tuning spectrum may need alternate syntonic comma/chroma analogs, just like some parts of the 5L 2s tuning spectrum are best served by 64/63 instead of 81/80. (And sorry about the typo in the [[256/255]] page.) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:12, 13 April 2025 (UTC)

::::::::: Checking in to let you know I didn't forget about this. In addition, I've been coming to the conclusion that while 17L 2s seems to fit with temperaments that proceed along at least part of the vertical axis of the corresponding tuning spectrum table, 11L 2s requires temperaments that proceed along the horizontal axis of the corresponding tuning spectrum table. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 01:49, 21 April 2025 (UTC)

::::::::: Also, 256/255 currently has an edit war going on about whether its names should include "char comma", from our point of view, "char comma" would have been nice for enabling "char chroma" in tuning systems that use it as an interval instead of tempering it out. I thought about putting this in the associated discussion page, but the edit war is going on with apparently no inclination to put any further discussion there (although plenty of old discussion about naming exists there).

::::::::: Separately, work on 17L 2s is looking like it might give me a decent 2.3.5.13.23 meantone extension (but still need to check 13th harmonic mapping stability to be sure).

::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:20, 21 April 2025 (UTC)

::::::::: For 17L 2s, had to go for a 2.3.5.23.53 meantone extension to get the soft half of the spectrum — the 13th harmonic mapping just wasn't stable enough. Now that I've got that done, I wonder if giving the very high harmonics another look might turn up something similar for 11L 2s? Bonus points if it works accurately enough to include an EDO as large as 159edo (for the 17L 2 meantone extension, 146edo was too big to fit without an accuracy-degrading 'c' wart as well as an 'i' wart). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:13, 22 April 2025 (UTC)

::::::::: On second thought, what turned out to be necessary for (at least the soft half of) 17L 2s might not help for 11L 2s, because the former didn't have a stable generator fraction within range, whereas the latter does &mbdash; hence the same extraordinary measures might not do much for it. But it can't hurt to check. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:28, 22 April 2025 (UTC)

:::::::::: Sorry about not responding for a while, I had stuff to do, but I was reading what you were saying, and I've been checking in on harmonies that you can get from instances of ~85/64 and ~128/85. It seems that in 159edo, starting on your ~17/16, you can build an approximation of a 1/1-25/22-128/85-320/187 suspension easily, and you can use this as an unexpected option for something resembling a Neapolitan chord. Not sure how this chord fits with 11L 2s however- it probably doesn't. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:24, 24 April 2025 (UTC)

::::::::::: 11L 2s won't include 25/22 (29\159, which is 3\159 too high) or 320/187 (123\159, which is also 3\159 too high — I just checked to make sure it maps correctly, although 200/117 is a lot more accurate). I was thinking maybe a MODMOS derived from 11L 2s would do it, but for that to work, one would have to be too high and the other too low. So it would have to be made with accidentals. Of course, 159edo has a load of other scales, so maybe one of these might do the job without accidentals. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:10, 24 April 2025 (UTC)

:::::::::::: I don't know if this is a good temperament for 11L 2s, but I stumbled upon [[Alphatricot_family#Tritricot|Tritricot]] while looking up stuff for temperamental generator of temperaments supporting 17L 2s: All listed *-limits of Tritricot list 159edo as their first optimal tuning. (And even if Tritricot isn't optimal for 11L 2s, it WILL work by hook or by crook, since all EDOs listed in the optimal tuning sequence are ≥159edo, and 159edo is already >143edo, which is the largest EDO that DOESN'T support 11L&nbsp2s, being to 11L 2s what 35edo is to 5L 2s. But I have yet to check whether you have to use some awful number of generators to get 11/8 or 16/11. Although at that high an EDO size, a MODmos based upon 11L 2s is likely to be better anyway, and for that you're going to want at least a secondary generator.) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:05, 28 April 2025 (UTC)

== Notability guidelines review ==

I drafted up a new proposal for the notability guidelines over at [[User:Sintel/Notability guidelines]].

You can use the talk page there to let us know what you think about them, especially in context of the discussion on the previous proposal wrt some of the pages you created.

Thank you! – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 23:46, 7 May 2025 (UTC)

: Note for future readers: this conversation moved to [[User talk:Sintel/Notability guidelines]] from this point. --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 02:41, 8 May 2025 (UTC)

@@ Line 257: / Line 257: @@
 By the way, do you know if other media files are supported on this site the same way? These days, the most usable Web standard is Opus, and it provides the best combination of compression, quality, and latency. MP3 is not open source and generally is one of the worst standards ever designed. It was rendered obsolete more than a decade ago. It can be clearly seen in the Web video. (I don't mean some industries such as car audio, notorious with their media retards.) Anyway, I know who I can ask... &mdash;&nbsp;[[User:SAKryukov|SA]],&nbsp;''Monday&nbsp;2021&nbsp;February&nbsp;15,&nbsp;18:16&nbsp;UTC''
+== Space Tour, Welcome to Dystopia, and 159edo ==
+Hey Aura, I just listened to your two 159edo compositions, “Space Tour” and “Welcome to Dystopia”, and I thought you would like to hear some feedback. I think both of your compositions are incredible and I can’t imagine how long it must have taken you to detune everything by hand. I also have a few questions. First of all, what is the approximation of 159edo that you use and how is it different from 159edo itself? Second of all, how did you decide which EDOs “Space Tour” would mimic at different parts of the song? [[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 00:44, 19 February 2021 (UTC)
+: The approximation of 159edo that I use differs from 159edo itself by fractions of a cent.  The reason it's only an approximation is because I can only specify tuning to within two decimal places in MuseScore- the main program I use to compose and generate sound- as opposed to being able to straight-up divide the octave into 159 equal parts as would be required to have true 159edo.  As for how I decided what EDOs to mimic, well, some were easy- like 12edo, 24edo and 53edo, while most of the others were inspired by the comments of others concerning said EDOs in the [[Table of edo impressions|Table of EDO impressions]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:25, 19 February 2021 (UTC)
+:: Thanks for your reply. I think it's interesting that you feel the need to specify that you aren't writing in true 159edo just because MuseScore has a limitation to its retuning capabilities that most likely nobody will notice. I also write microtonal music in MuseScore, which means that my compositions are also tuned very slightly differently from true EDOs. Personally, I don't think that the slight discrepancies that come from the retuning limitations of various music making software and hardware have to be accounted for. In fact, I think it would be better for these discrepancies to be ignored if they are only a few hundredths of a cent wide, as is the case for your compositions. Do you have any additional thoughts on this matter? --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 03:10, 19 February 2021 (UTC)
+::: It maybe true that these discrepancies won't be noticed by listeners, but the fact that I'm the one doing the tuning and cent-size look ups for various intervals means that I would feel as if I were being somewhat disingenuous to the more strict analysts who use computers for their analysis if I didn't add that disclaimer.  I hope this makes some degree of sense. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:17, 19 February 2021 (UTC)
+== MuseScore 159edo retuning plugin... ==
+Hey Aura, I’ve been thinking about how a 159edo retuning plugin for MuseScore could be made, so I want to explain the main issue and offer 3 potential solutions. This block of text comes directly from the n-tet retuning plugin README. “A maximum of 3 arrows are allowed on each accidental, as MuseScore currently does not provide accidentals with more than 3 arrows. Due to these limitations, and with the help of quartertone accidentals, the plugin can only handle EDOs with a sharpness rating of up to 8.” The main problem here is that 159edo has a sharpness rating of 15 (one sharp equals 15 steps), meaning that there would have to be support for septuple up and septuple down accidentals in MuseScore for each note in 159edo to be accessible. (Assuming usage of ups and downs notation without lifts and drops). Here are my three solutions. The first solution is to come up with a notation system for 159edo using accidentals that can be found in MuseScore’s advanced palate. Then, a fork of euwbah’s n-tet retuning plugin would have to be made which could map all of the accidentals to edostep offsets. (Sharp equals 15 steps, triple up natural equals 3 steps, etc) The second solution is to use ups and downs notation from 53edo combined with “+” and “-“ symbols to indicate 1 step offsets for 159edo. For this to be effective, the plugins which raise and lower a note by one edostep (these plugins are included with the n-tet retuning plugin) would have to be modified to add and remove the “+” and “-“ symbols as necessary as well as changing the accidental and the pitch offset. The third solution is to use polychromatic notation for 53edo and to use the up and down arrow accidentals to access the notes in 159edo. Again, the pitch up and pitch down plugins would have to be modified. This time, these plugins would have to change the note head color as well as changing the accidental and the pitch offset. I would like to know which option you think is best for making 159edo compositions in MuseScore. In addition, since the programming language for MuseScore (Qt) is a bit too confusing for me to make anything meaningful in, you’ll have to ask FloraC to do the actual coding. I might be able to help a little bit, but not much. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 18:34, 19 February 2021 (UTC)
+: Is it possible that there's a fourth solution?  I mean, I already have a planned set of accidentals that seems to work, but they seem to need refining in terms of their design.  In addition to the traditional natural, sharp, flat, double sharp and double-flat accidentals there are two new sets of quartertone accidentals, and an interesting set of tree-like arrows.
+:[[File:Quarter-accidentals-narrow-rastmic-wide.png|300px]]
+:# top line: narrow
+:# middle line: rastmic (standard)
+:# bottom line: wide
+:The above image shows the new quartertone accidentals, while the image below shows the remainder of the new accidentals.
+:[[File:Possible 159edo Accidentals.png|150px]]
+:top row from left to right:
+:# rastma wide
+:# biyatisma wide
+:# syntonic wide
+:# syntonic + rastma wide
+:# syntonic + byatisma wide
+:# double syntonic wide
+:bottom row from left to right:
+:# rastma narrow
+:# biyatisma narrow
+:# syntonic narrow
+:# syntonic + rastma narrow
+:# syntonic + byatisma narrow
+:# double syntonic narrow
+:I hope the above accidentals make sense.  I mean, I'm trying to make my approach to this whole thing as clean and straighforward as possible. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:45, 19 February 2021 (UTC)
+:: It seems like you’re thinking of using custom accidentals with MuseScore. As far as I know, MuseScore has absolutely no support for importing custom accidentals, but I could be wrong. Even if MuseScore could support custom accidentals, I don’t think the custom accidentals could be utilized in a plugin because the plugin would have to be able to recognize these new accidentals with internal accidental codes. Since I know almost nothing about Qt, the programming language used to make plugins in MuseScore, you’ll have to double check with FloraC if your fourth solution is possible/feasible. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 20:05, 19 February 2021 (UTC)
+::: At a certain point, I'm afraid custom accidentals are a must.  That said, I am willing to wait and perfect this system first. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:09, 19 February 2021 (UTC)
+:::: For now, while custom accidentals cannot be supported in MuseScore, wouldn't you rather have the detuning done automatically by a modified version of the n-tet retuning plugin rather than you having to input all the cent offsets yourself?
+:::: [[File:Musescoremicrotonalaccidentals.png]]
+:::: This image shows all of the microtonal accidentals currently in MuseScore. I'm sure at least some of them can temporarily suit your needs. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:08, 19 February 2021 (UTC)
+::::: I'm willing to wait for MuseScore 4 for this considering that that version is currently in the works, in part because some of the accidentals that could otherwise be the most useful have been found to present legibility issues.  However, I don't think it will hurt to at least get the ball rolling on this one.  With that, do you have the time and or resources to help me finalize the designs of these custom accidentals of mine?  Once that's done, we can talk to Euwbah and others about how to implement these in MuseScore 4. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:14, 19 February 2021 (UTC)
+:::::: Well, I do have some time this weekend, but I wouldn’t say I have the resources to assist with making custom accidentals. I’m not an artist and I don’t have any kind of glyph editing programs or other art making programs. I can give feedback on your custom accidentals every now and then but I can’t help directly with the accidental making process. My main reason for asking you about this plugin is to give you a way of composing in 159edo without having to worry about retuning the notes manually. That’s why I think it would be better for you to have a temporary solution that doesn’t require any custom accidentals whatsoever. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:42, 19 February 2021 (UTC)
+== New Comma ==
+Hey Aura, can you give me your thoughts on the somewhat esoteric comma that I called the "Goldis" comma? I particularly would like to know if you have a better name for it and if you can think of higher limit extensions to the temperament. (The link to the page is on my user page) --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:58, 18 March 2021 (UTC)
+== A potentially useful thing I came up with... ==
+Hey Aura, I have another thing that I would like you to check out and give me your thoughts on. It might be more up your alley as it is based on Just Intonation. It's called the [[User:Userminusone/Averiant|Averiant]]. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 22:46, 25 July 2021 (UTC)
+: I checked it out and I'm not sure what to make of it at the moment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:43, 26 July 2021 (UTC)
+:: That's understandable. One thing I didn't mention, though, is that the Averiant could be useful for finding new commas. As an example, the comma 128/125 can be derived by taking the (1/3)averiant between 2/1 and 1/1 to get 5/4, and then equating 5/4 with 1/3 of an octave (or equivalently, equating 125/64 with an octave). 128/125 is quite a large comma but my point is that this approach could theoretically be used to find much smaller commas. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:31, 26 July 2021 (UTC)
+::: I believe that, but how do you specifically narrow your commas down to those with low prime limit? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:11, 26 July 2021 (UTC)
+:::: Sorry for the late reply, but to answer your question, one thing you could do is start with three simple ratios and find the averiantal percentage of the middle ratio relative to the two outer ratios, which you can then use to derive the comma. As an example, I could calculate the (1/1 - 5/4)averiantal percentage of 8/7, which is 3/5. To derive a comma from this, I would equate (8/7)^5 with (5/4)^3, resulting in the [[rainy comma]]. --[[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 20:25, 1 August 2021 (UTC)
+== Please remember to link new edo pages from the parent page ==
+Please remember to add a link in the ''EDO'' page when you create new edo pages. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:08, 23 December 2022 (UTC)
+== Where is Folly of a Drunk?  ==
+Where is it now? I love it very much! Can I listen to it and refer to friends?
+I recently listened to all I found on your pages, like it.</br>
+Thank you.</br>
+—SA
+: Hey!  It's been a while since we last talked!  I'll have to reestablish Folly of a Drunk on here, but I'm not in the position to do that right now.  Besides, you might also want so hear Kite's arrangement. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:54, 15 July 2023 (UTC)
+:: Thank you for your reply. I recently wrote to you on Youtube page &ldquo;How Many Notes Are There? The Theory of Quarter Tones&rdquo; (not very good one). I have a lot of new development, including Microtonal Fabric. It's too early to discuss now. But I must say that Microtonal Fabric is permanently used in Brainin School of Music for a pretty long time now. Brainin reported that little children master feeling micro tones wonderfully well and show unmatched level of musical intellect. Professional musicians usually fail to solve the problems well solved by those little students&hellip; --[[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]) 13 July 2023
+:: Where is that Kite's arrangement? Yes, I would like to hear it. Will you give me a link? --[[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]) 13 July 2023
+::: Here you go: https://youtu.be/fOZiX7f7t8Q?t=806 --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 00:15, 14 September 2023 (UTC)
+:::: Thanks Fred.  I was at work at the time I got SA's message. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:37, 14 September 2023 (UTC)
+::::: Thank you, Fred! Thank you, Dawson! Great work! But I would like to access Aura's original audio variant as well. --[[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]) 13 July 2023
+:::::: Okay, I've put Folly of a Drunk back onto my user page. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:32, 22 September 2023 (UTC)
+== Temperament(s) for Diatonicized Chromaticism? ==
+I have been listening to the music of [[Ivan Wyschnegradsky]] (whose page needs expansion) and looking up how to put [[11L&nbsp;2s]] scale that he called "Diatonicized Chromaticism" into one or more temperaments.  My thoughts on this in part can be found at [[User:Lucius_Chiaraviglio/Musical_Mad_Science#Musical_Mad_Science_Musings_on_Diatonicized_Chromaticism|Musical Mad Science Musings on Diatonicized Chromaticism]] (although this needs updating and filling in.  Searching for relevant intervals and commas has led me to [[The Nexus]] and to the conclusion that you would be the person to talk to about this.  Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:14, 28 March 2025 (UTC)
+: Sorry I didn't get to this sooner.   Oddly enough, while I'm not terribly familiar with many aspects of this scale, I do know that 159edo supports it, with the large step at 13\159 and the small step at 8\159.  It should be noted that 13\159 represents 128/121, while the small step represents 28/27- the latter is tempered together with 729/704 because the symbiotic comma is tempered out. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:36, 6 April 2025 (UTC)
+:: Thanks -- I had also noticed that 159edo supports this scale, although I didn't track down what the steps temper to.
+:: I took some time out from trying to figure out the temperament for 11L&nbsp;2s to trying to figure out the temperament for the next higher analog of this scale to serve as a basic scale for a multiple of 12edo:  [[17L&nbsp;2s]], for which [[36edo]] implements the basic version of this scale.  (I have made a start at this under what I linked above, on the same page.)  I don't know whether Ivan Wyschnegradsky had this scale in mind when he was composing the few compositions he wrote in 36edo (I have yet to see a score for any of these compositions, and none of the YouTube videos of them are of the scrolling score type), but I was struck by how similar it sounded to his 24edo compositions (although with noticeably smaller steps), so I suspect that he might have had something of the sort in mind.  (Unfortunately I haven't seen any of his writings about this, although one of the videos of his ''24 Preludes'' has a substantial excerpt about working with 11L&nbsp;2s in 24edo, linked from my user sub-page that I linked above.)
+:: Surprisingly, the going has been easier for 19L&nbsp;2s than for 11L&nbsp;2s, despite having had longer to work on figuring out a temperament for 11L&nbsp;2s.  So maybe figuring this out for 19L&nbsp;2s will teach me how to do it for 11L&nbsp;2s, although working with the 11th harmonic seems to be just inherently weird.
+:: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:52, 6 April 2025 (UTC)
+::: Yes, working with the 11/8 paramajor fourth is inherently weird- it takes either the 16/15 diatonic semitone or the 5/4 major third to set it up, and it really seems to like being a chord root in a 1/1-25/22-14/11-3/2 chord.  Have you tried working with this stuff? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:29, 6 April 2025 (UTC)
+:::: I haven't worked with it myself, but I am trying to gain an understanding.  Obviously it isn't easy &mdash; Ivan Wyschnegradsky and a very few others figured it out, but only a very few others.  But you gave me an idea of things to test, with the 1/1-25/22-14/11-3/2 chord.  Although keep in mind that in 24edo (which Ivan Wyschnegradsky used most of the time, along with Alois Hába and a few compositions of Charles Ives), 14/11 maps down to the same as 5/4 (8\24) due to 24edo's badly flat 7th harmonic, while 25/22 maps not to the closest interval 9/8 as 4\24, but up to the same as 22/19 as 5\24, because its 5th harmonic is sharp (but not sharp enough for mapping as 25 instead of 5^2).  But then again, I don't know whether Alois Hába or Charles Ives (ore much more recently, Scott Crothers) ever used 11L&nbsp;2s as opposed to other ways of using 24edo; 11L&nbsp;2s may be unique to Ivan Wyschnegradsky.  Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:44, 6 April 2025 (UTC)  Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:34, 7 April 2025 (UTC)
+::::: Oddly enough, my experiments with how to handle the 11/8 paramajor fourth relative to the tonic have been largely carried out in 159edo, but I must say that even in 24edo, that 11/8 wants to go to either 3/2 relative to the tonic, or, to 4/3 relative to the tonic- at least in terms of chord roots.  It should be noted that the 11/8 seems to literally bring in its own set of related accidentals relative to the key you're in- I've already hinted at 25/16 being dragged in, and the same is true with the 7/4, which, in this capacity, acts like an ultramajor sixth relative to the tonic.  Naturally, the 33/32 will likely be dragged in as well, but what I didn't tell you is that 75/64 wants to rear its head in scalar motion on a tIV chord- the only two default scale degrees relative to the tonic that can be used with a tIV chord are the 5/4, and the 15/8.  Otherwise, if you use an 11/8, it has to either be part of a 1/1-11/8-3/2 suspension on the tonic, or as part of a 1/1-5/4-3/2-55/32 built on the 8/5 relative to the tonic.  There are other chords I know, such as the 1/1-11/8-15/8 built on the tonic, or the 1/1-11/8-7/4 built on the tonic, but these tend to be harder to set up and follow up properly. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:50, 7 April 2025 (UTC)
+:::::: Keep in mind that 159edo is going to be a LOT different from the low to mid (and even upper-mid) double digits EDOs.  You get literally a lot finer control over how your chords sound.  Of course, the downside is that you need an instrument (or group thereof) that can play that many pitches (or you need to be REALLY GOOD on a continuous-pitch instrument).  Another thing I noticed is that in 11L&nbsp;2s it is hard to choose a mode that lets you hit common 5-limit intervals without going off-scale with accidentals.  (I need to see how that plays out with 7-limit intervals in an EDO that supports the 7-limit better than 24edo, like 37edo or 59edo or 61edo, although I noticed that if you go all the way afield to 50edo or 46edo, this scale shoots itself in the foot by not mapping intervals of ANY mode to 3/2 or 4/3, which map differently than in 11L&nbsp;2s EDOs closer to 24EDO in the tuning spectrum.  Not sure yet, but I think 17L&nbsp;2s operating in in the 2.3.7... subgroup may have less of that problem.)  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:03, 7 April 2025 (UTC)
+::::::: I know that 159edo is different to many of the smaller EDOs that you pointed out- there's a reason I chose to specialize in that particular tuning system.  Furthermore I should mention that a 53edo-based instrument can have a few extra buttons added so that one may divide the step of 53edo into three- think the Neod, which is mentioned on the 159edo page.  Of course, I think it pays to let people hear what 159edo is capable of by means of writing music for that tuning system in MuseScore Studio 4 or later and post the results to YouTube- that way, people might just be inspired to build the instruments necessary for live performance. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:26, 7 April 2025 (UTC)
+::::::: On another note, I'm not sure how 11L 2s fares in 159edo in terms of what it can reach, and while it is important to note that 11L 2s can't often hit common 5-limit intervals in as of itself, I should think that detempered versions of that MOS, as well as the MOS itself, could still be useful in 159edo, as that will expand my capabilities. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:26, 7 April 2025 (UTC)
+:::::::: I saw that Neod video a while back, although I should probably give it another go.  I should look at 11L&nbsp;2s in 159edo once I get back to working on a temperament (or probably clan of temperaments) for that scale.  In an EDO that big, you might well want to add some strategic accidentals to the scale.  And I have been impressed by a subset of works I have seen written in MuseScore 4 &mdash; the capabilities of MuseScore (including synthesizing instrument imitations that actually sound decent) seem to have greatly improved in the last few years.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:30, 7 April 2025 (UTC)
+::::::::: Truth be told, some of the music linked on the 159edo page is mine, and I've also written music in MuseScore 3 as well as MuseScore Studio 4.  Not only that, but I've codified a few musical tropes involving the 11/8 relative to the tonic. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:16, 8 April 2025 (UTC)
+:::::::::: I'll have to check them out (actually listened to 1 already, but quite a while ago, before I started thinking much about this).
+:::::::::: Meanwhile, I thought it would be useful to have a table of odd harmonics of the various EDOs supporting 17L&nbsp;2s to make it easier to track stability of mapping, and I plan to do this for 11L&nbsp;2s as well (which so far I had been doing this for by way of manual lookup of each EDO, which is time-consuming).  Right now it is actually a collection of tables, because Template:Harmonics in equal doesn't have a way to string them together and doesn't have a way to set a uniform column width.  Any idea how to fix this, other than manually creating a table with values copied from these?  In the process of doing this, I have noticed an interesting comparison:  11L&nbsp;2s has a very well-behaved 11th harmonic (it has to, since 11/8 and 16/11 is the generator pair), but doesn't seem to have well-behaved low harmonics; but in contrast, 17L&nbsp;2s doesn't have a simple generator (23/16 is too flat by a few cents, and 13/9 is too sharp, and has multiple odd harmonics/subharmonics in it anyway), and the harmonics of the compound ratios that could be used as generators for it are NOT well-behaved, except that the 3rd harmonic is amazingly well-behaved, only flipping to a different mapping at 112edo and higher EDO values (and the 23rd harmonic would be well-behaved if only it wasn't flat of the actual generator &mdash; it would be an excellent generator for [[21L&nbsp;2s]] or the soft end of [[2L&nbsp;19s]]).
+:::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:12, 8 April 2025 (UTC)
+:::::::::: I finished doing the above for 11L&nbsp;2s.  Note that 11/8 (the dark generator, and thereby the bright generator 16/11) remains stable throughout the entire currently posted 11L&nbsp;2s table &emdash; the worst relative error is -34.8%, at 127edo, so your favorite 159edo still easily fits in.  Right now I strung out the odd harmonics to high values in case I need these for composite ratios, which seem likely to be needed for 17L&nbsp;2s, but seem like they may not be needed for 11L&nbsp;2s (but better leave them in for now until I am sure they are not needed).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:54, 9 April 2025 (UTC)
+::::::::::: Wait, I thought that the large step of 11L 2s in 159edo was 13\159, not 11\159... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:10, 9 April 2025 (UTC)
+:::::::::::: Good catch of typo -- fixed this.  Also rechecked the rest, but didn't find any more.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:30, 10 April 2025 (UTC)
+:::::::::::: Scrolling through these table groups, I started noticing interesting things, like how even though the 11th harmonic is the only one with stable mapping all the way through 11L&nbsp;2s, some of the others have stable mapping in sections, like the 3rd harmonic has stable mapping in the middle section but is all over the place in both the hard and soft ends, but the 9th harmonic actually does okay in the hard end, as does the 17th harmonic (both of these get to be all over the place in the soft end), and the 5th and 13th harmonics have stable mapping in the soft end as long as the EDO values are not too large.
+:::::::::::: In partial contrast, with 17L&nbsp;2s, the harmonic/subharmonics of the generator have unstable mapping (because no simple ratio with a reasonable sized numerator and denominator fits into this zone), but the 3rd harmonic is nearly rock-solid (and 112b is a respectable if overly-complex quarter-comma meantone approximation), although presumably its mapping would break if I put in the rest of the right-most column of the MOS spectrum table.  And there the 5th harmonic seems very much usable in the soft end of the scale tuning spectrum as long as the EDO sizes don't get too large (and even then, sometimes it is still okay), which looks to me like enabling a 2.3.5.23 meantone extension; it goes all over the place in the hard end, but there the 25th harmonic shines and is rock-solid as long as you don't go harder than 36edo (basic), and the 13th harmonic just barely misses being rock-solid in this zone (just barely breaks on 125edo, for which 125f would be not bad).  Although those harmonics would also appear less solid if I included the rest of the MOS tuning spectrum.
+:::::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:28, 10 April 2025 (UTC)
+In reply to your previous comment, I should mention that I'd like to know where ~3/2 is relative to the 11L 2s of 159edo. I imagine it's rather far along the generator sequence.  At the same time, I'm wondering what sorts of chords you can actually get from 11L 2s in 159edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:53, 10 April 2025 (UTC)
+: This is further up on my page than the tables of odd harmonics:  For the fifths in the basic 11L 2s (Wyschnegradsky) diatonicized chromatic scale (the version that 24edo yields), the 11/8-span of a patent fifth is a stack of 10 intervals of 11/8, octave-reduced.  I haven't yet done this calculation for 159edo &mdash; it isn't too far off from basic, but it has small enough increments that attempting to use the same 11/8-span gives the b val fifth instead of the patent fifth.  00:07, 11 April 2025 (UTC)
+: Did this for 159edo &mdash; the 16/11-span of 3/2 is 51.  And it doesn't even work for the next EDO up or down from the last column of the tuning spectrum table of 11L&nbsp;2s (135edo or 146edo, respectively) &mdash; the 3rd harmonic mapping is too unstable for EDO sizes that large in this region.  Also, 51 is so many iterations of the generator that it goes well outside of the 11L 2s scale.  Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:53, 11 April 2025 (UTC)  Last Modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:52, 11 April 2025 (UTC)
+:: Fascinating.  I guess that means we need to look into chords with 94\159 fifths, which actually approximate 128/85 rather than 3/2.  These chords clearly cannot be pure 5-limit either, but that's okay.  Given that you mention 2.3.5.23 meantime, I'm now wondering if we can cobble together something for 11L 2s based on the ~128/85 archagall fifth.  To start on this front, what are the modes of 11L 2s that contain ~128/85 in 159edo? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:40, 11 April 2025 (UTC)
+::: I need to do the modes for 11L&nbsp;2s with respect to coverage of standard diatonic intervals anyway, but that's going to take a bit of time, so stay tuned.  The 128/85 b fifth is going to stick out like a sore thumb in the midst of the much more accurate other intervals that 159edo has, though, so maybe it would be better to try to come up with a decent MODMOS derived from 11L&nbsp2s for 159edo?  In the meantime, I figured out which equal temperaments this might apply to, since they get their fifth from 51 stacked and octave-reduced 16/11 generators, leading up to 159edo:  37b, 61, 98, 159 (have not yet tried to extend beyond 159edo to see how far you can get before the fifth mapping breaks again).  Note that for 61edo, 51 stacked and octave-reduced 16/11 generators gives the same note as 10 stacked and octave-reduced 11/8 generators.  I also included 37b to show the small endpoint of the series (and if you really want to go weird, include 24b); judging by the pattern, the next member of the series would be 257 (not yet sure of wart, if any).  Graham Breed's temperament finder lists some more members of the series without warts, going up into the thousands, but doesn't give the temperament a name beyond [https://x31eq.com/pyscript/rt.html?ets=159_98&limit=2_3_11 159 & 98], and I don't see 61edo listed in the Nexus, Nexus clan, or Nexus family, although 159edo comes up several times (maybe one of those temperaments would be better, although they probably go from the fifth to the 11/8 rather than the other way around, and would not necessarily support 11L&nbsp;2s).  Its enormous complexity is presumably the reason it never got a name; I don't know the specifics for computing badness, but I am going to stick my neck out and guess that this temperament would have huge badness despite its high accuracy.
+::: As for 2.3.*.23, the 23rd harmonic mapping is pretty unstable in the zone of 11L&nbsp;2s &mdash; it gets better mapping stability in 17L&nbsp;2s, although this region has its generators sharp enough relative to 23/16 that larger EDO sizes often flip to the next flatter approximation, so the generator for that needs to be something between 23/16 and 13/9.
+::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:21, 11 April 2025 (UTC)
+::: The modes of 11L&nbsp;2s that enable reaching 4/3 and/or 3/2 within-scale are not very many.  If you want to get both, you have to use sLLLLLsLLLLLL (no other mode gets both).  If you want to get 3/2 but can live without 4/3 (more common than the opposite), then you can also use LsLLLLLsLLLLL or sLLLLLLsLLLLL.  If you use LLLLLLsLLLLLs or LLLLLsLLLLLLs or LLLLLsLLLLLsL you can get 4/3 but not 3/2.  In EDOs with fine enough steps to distinguish 128/85(?) from 3/2, this instead gets you 128/85(?) (or 85/64(?) instead of 4/3).  So if we want a MODMOS for 159edo that gets us back to 3/2 (and maybe 4/3) we need a second generator that gets tempered to be the same as 11/8 or 16/11 in the coarser EDOs supporting 11L&nbsp;2s but distinguished in the finer ones.  Not sure yet what that would be, and not sure yet whether 128/85 is the best slightly-inflated fifth substitute to use for this purpose.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:02, 12 April 2025 (UTC)
+:::: Well, the ~128/85 fifth of 159edo is indeed useful in its own right as an imitation of the kind of thing you see in 22edo.  Perhaps we can play to the strengths of that type of system where two ~128/85 intervals octave-reduced add up to ~17/15, and two instances of ~17/15 add up to ~9/7- yes, that is how 159edo works since both 22edo and 159edo support archagall temperament.  Not only that but the ~128/85 interval is 159edo's best approximation of 17edo's fifth, so we could also shoot for 11L 2s harmonies that evoke the kind of stuff found in 17edo and it's multiples.  The point is that if the ~11/8 and ~16/11 intervals count as ambisonances (basically, they're both consonances and dissonances at the same time) for our intents and purposes, as I know they do for mine, then we can afford to play with some of the less accurate intervals in our 11L 2s harmonies- assuming we play our cards right. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:28, 12 April 2025 (UTC)
+::::: [[24576/24565#Mavka_a.k.a._archagallismic|Mavka a.k.a. archagallismic]] looks sort of like what we want, although that seems like more dimensions than we need, and I don't know how you would map that many dimensions onto any kind of keyboard, even before considering the size.  (But maybe that could be trimmed down to a rank-3 temperament that is different from Archgallic, so as to get the 11/8 in there?)  I see that its multiple generators include ~3, and it includes 150edo as a patent val, so you can get both 128/85 and 3/2.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:25, 12 April 2025 (UTC)
+:::::: If I can map 159edo onto an isomorphic keyboard layout using [[tertiaschis]] temperament, albeit by squashing the hexagons, then we can work together to map a lower-dimensional temperament that relates to archagallic temperament. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:39, 12 April 2025 (UTC)
+::::::: Tertiaschis looks interesting.  Meanwhile, I determined that the Rastma (243/242) is NOT the right interval for differentiating 159edo from 61edo (lower on the series I noted above) &mdash; 159edo maps it correctly to 1 increment, but 61edo not only doesn't temper it out, but inflates it to 2 increments, while 98edo inverts it.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:16, 12 April 2025 (UTC)
+::::::: Should have tried the Char comma/chroma ([[256/255]]) first.  This is tempered out in 24edo, 37edo, 61edo, and 98edo, but correctly maps to 1 increment of 159edo; it is exactly the amount by which an archagall fifth exceeds a normal fifth.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:13, 13 April 2025 (UTC)
+:::::::: Nice catch.  Yeah, the char subchroma will prove useful to us.  Come to think of it, however, the way that this interval plays with the intervals of 11L 2s reminds me of how the syntonic comma plays with the intervals of 5L 2s... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:30, 13 April 2025 (UTC)
+::::::::: That's the idea.  Although other parts of the 11L&nbsp;2s tuning spectrum may need alternate syntonic comma/chroma analogs, just like some parts of the 5L&nbsp;2s tuning spectrum are best served by 64/63 instead of 81/80.  (And sorry about the typo in the [[256/255]] page.)  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:12, 13 April 2025 (UTC)
+::::::::: Checking in to let you know I didn't forget about this.  In addition, I've been coming to the conclusion that while 17L&nbsp;2s seems to fit with temperaments that proceed along at least part of the vertical axis of the corresponding tuning spectrum table, 11L&nbsp;2s requires temperaments that proceed along the horizontal axis of the corresponding tuning spectrum table.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 01:49, 21 April 2025 (UTC)
+::::::::: Also, 256/255 currently has an edit war going on about whether its names should include "char comma", from our point of view, "char comma" would have been nice for enabling "char chroma" in tuning systems that use it as an interval instead of tempering it out.  I thought about putting this in the associated discussion page, but the edit war is going on with apparently no inclination to put any further discussion there (although plenty of old discussion about naming exists there).
+::::::::: Separately, work on 17L&nbsp;2s is looking like it might give me a decent 2.3.5.13.23 meantone extension (but still need to check 13th harmonic mapping stability to be sure).
+::::::::: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:20, 21 April 2025 (UTC)
+::::::::: For 17L&nbsp;2s, had to go for a 2.3.5.23.53 meantone extension to get the soft half of the spectrum &mdash; the 13th harmonic mapping just wasn't stable enough.  Now that I've got that done, I wonder if giving the very high harmonics another look might turn up something similar for 11L&nbsp;2s?  Bonus points if it works accurately enough to include an EDO as large as 159edo (for the 17L&nbsp;2 meantone extension, 146edo was too big to fit without an accuracy-degrading 'c' wart as well as an 'i' wart).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:13, 22 April 2025 (UTC)
+::::::::: On second thought, what turned out to be necessary for (at least the soft half of) 17L&nbsp;2s might not help for 11L&nbsp;2s, because the former didn't have a stable generator fraction within range, whereas the latter does &mbdash; hence the same extraordinary measures might not do much for it.  But it can't hurt to check.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:28, 22 April 2025 (UTC)
+:::::::::: Sorry about not responding for a while, I had stuff to do, but I was reading what you were saying, and I've been checking in on harmonies that you can get from instances of ~85/64 and ~128/85.  It seems that in 159edo, starting on your ~17/16, you can build an approximation of a 1/1-25/22-128/85-320/187 suspension easily, and you can use this as an unexpected option for something resembling a Neapolitan chord.  Not sure how this chord fits with 11L 2s however- it probably doesn't. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:24, 24 April 2025 (UTC)
+::::::::::: 11L&nbsp;2s won't include 25/22 (29\159, which is 3\159 too high) or 320/187 (123\159, which is also 3\159 too high &mdash; I just checked to make sure it maps correctly, although 200/117 is a lot more accurate).  I was thinking maybe a MODMOS derived from 11L&nbsp;2s would do it, but for that to work, one would have to be too high and the other too low.  So it would have to be made with accidentals.  Of course, 159edo has a load of other scales, so maybe one of these might do the job without accidentals.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:10, 24 April 2025 (UTC)
+:::::::::::: I don't know if this is a good temperament for 11L&nbsp;2s, but I stumbled upon [[Alphatricot_family#Tritricot|Tritricot]] while looking up stuff for temperamental generator of temperaments supporting 17L&nbsp;2s:  All listed *-limits of Tritricot list 159edo as their first optimal tuning.  (And even if Tritricot isn't optimal for 11L&nbsp;2s, it WILL work by hook or by crook, since all EDOs listed in the optimal tuning sequence are ≥159edo, and 159edo is already >143edo, which is the largest EDO that DOESN'T support 11L&nbsp2s, being to 11L&nbsp;2s what 35edo is to 5L&nbsp;2s.  But I have yet to check whether you have to use some awful number of generators to get 11/8 or 16/11.  Although at that high an EDO size, a MODmos based upon 11L&nbsp;2s is likely to be better anyway, and for that you're going to want at least a secondary generator.)  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:05, 28 April 2025 (UTC)
+== Notability guidelines review ==
+I drafted up a new proposal for the notability guidelines over at [[User:Sintel/Notability guidelines]].
+You can use the talk page there to let us know what you think about them, especially in context of the discussion on the previous proposal wrt some of the pages you created.
+Thank you! – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 23:46, 7 May 2025 (UTC)
+: Note for future readers: this conversation moved to [[User talk:Sintel/Notability guidelines]] from this point. --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 02:41, 8 May 2025 (UTC)