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FloraC

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== Creating new EDO pages ==
== Higher primes ==
Hi FloraC,  
A while back I made an edit on [[181edo]], saying it has less than 30% error on most prime harmonics up to 137. You removed this info, giving the edit summary "don't bombard the readers with random prime numbers. 30% unsigned error isn't even special." There is a similar section on the page for [[43edo]], which goes as follows:
I wanted to let you know that I was just filling in some gaps in EDO pages temporarily, I plan to expand the pages at some point in the future. [[User:MisterShafXen|MisterShafXen]] ([[User talk:MisterShafXen|talk]]) 15:10, 8 January 2025 (UTC)


: I'm not sure of the benefits of filling in the gaps. There are infinitely many gaps. My advice is to only create a page when you have stuff to expand. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:46, 8 January 2025 (UTC)
<blockquote>Although not [[consistent]], 43edo performs quite well in very high prime limits. It has unambiguous mappings for all prime harmonics up to ''113'' (after which the demands on its pitch resolution finally become too great), with the sole exceptions of 23, 71, 89, and 103, making a great [[#Ringer 43|Ringer scale]].</blockquote>


== En dashes vs. em dashes ==
Here, prime 41 with 37.5% relative error is considered "unambiguous". Four missing primes in the 113-limit isn't really too special with this rather relaxed bound. You may want to do something about this section, though maybe more can be kept as 43edo is smaller than 181.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 22:52, 12 January 2026 (UTC)
Hi, can you point out on which article I replaced en dashes with em dashes where they were interchangeable? Was it on [[3L 4s]]? Because if that's the page you were referring to, on that page I replaced some hyphen-minuses with minus signs, not en dashes with em dashes. Note that minus signs and em/en dashes can be hard to distinguish from each other in the source editor. [[User:ArrowHead294|<math>\overrightarrow{\,\,\scriptsize\text{ArrowHead294}\,\,\,}</math>]] [[User talk:ArrowHead294|(speak to me)]] 15:59, 25 February 2025 (UTC)


: I replied in your user talk page. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:49, 26 February 2025 (UTC)
: Originally, this part read:  


== What exactly are the reasons for keeping "Pythagorean" but not allowing names for higher-limit trivial temps? ==
: <blockquote>Although not consistent, it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to 64 [61], with the sole exceptions of 23 and, perhaps, 41. </blockquote>
I personally find defining trivial temps useful as the families defined by them determine what temperaments "flatten" larger subgroups down to the trivial temperament's subgroup.


: First of all, the name of the trivial temps in all limits is ''JI''.  
: Then some editor was being crazy about it cuz ''four'' exceptions are no ''sole'' exceptions. But I don't think I'm gonna remove that entirely. Rather, I'm moving it to a higher-limit JI subsection of the approximation to JI section to hopefully declutter the theory section.  


: ''Pythagorean tuning'' is kept becuz it has history and becuz Pythagoras was known to haved worked with the 3-limit. Also, ''Pythagorean tuning'' isn't called ''pythagorean temperament''. The latter should generally be avoided cuz it can be confused with compton, the temp that tempers out the Pythagorean comma. Another example is ''Alpharabian tuning'', which was lately added cuz al-Farabi was known to have worked with undecimal intervals.
: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:36, 13 January 2026 (UTC)


: Now, given ''Alpharabian tuning'' has been added, it would seem okay to add something like ''Classical tuning''. After all, Classical music tempers 5-limit intervals, which give rise to the name ''classical intervals'', so it's related. However, "Classical tuning" has a big problem: it can be used to contrast meantone, the temperament that tempers classical intervals and that is actually used by Classical music. Iow which of JI and meantone is more Classical? It's meantone. Therefore, ''Classical tuning'' isn't a proper alias for JI.
== 2187/1250 ==
I’m planning to draft a page for 2187/1250 in my userspace since it’s a 5-limit ratio closely approximating 7/4, but I think I should name it something. Something like 5-limit harmonic-esque seventh or something referencing the ragismic temperament since it’s 4375/4374 below 7/4. Do you have any name suggestions? <span style="display: inline-block;transform: rotate(15deg);background:#E1EBF2;font-family:Verdana;text-shadow: 3px 3px 4px #0008;">[[User:Hotcrystal0|hotcrysta]][[User talk: Hotcrystal0|l0]]</span> 19:12, 14 January 2026 (UTC)


: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:04, 21 April 2025 (UTC)
: Tetraptolemaic diminished seventh. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:09, 14 January 2026 (UTC)


== On declaring Zeta peaks ==
== Generator counts ==
Hello Flora, regarding some of the changes I submitted on some EDO pages like the 217EDO or 311EDO page, and more generally, why not declare these big zeta EDOs to be such in the ET infobox, or in the case of 311EDO, why not expand the visible limit to 41? I feel like that'd be important information about these EDOs that would otherwise be left out to the average reader. --Eufalesio[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 10:56, 11 September 2025 (UTC)
I'm planning to start another chord page draft at [[User:Overthink/Chords of pajara]] (not yet created as of the time this is written). The issue is that it's not as simple to give a chord by generator counts, as there's a half-octave period in pajara. The page [[Unidec/Chords]] uses a val, but it is quite messy. I propose the following solution: The half-octave is taken as the period, and the generator is a perfect fifth. Intervals reachable by stacking fifths are just written with a number; for example, 1&ndash;3/2&ndash;12/7 would be "0&ndash;1&ndash;3". An interval that requires stacking fifths from the half-octave would be written with "T" (for tritone) before the number of fifths stacked; for example, 1&ndash;6/5&ndash;3/2 would be written as "0&ndash;T3&ndash;1". Maybe it would be better to give an "R" (for root) before intervals reachable by stacking fifths, so that 1&ndash;6/5&ndash;3/2 would be "R0&ndash;T3&ndash;R1", which is more readable. I'm also not too sure if the fifth should be the generator or the semitone instead.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:28, 20 January 2026 (UTC)


: The community decided that zeta should not be displayed in the infobox some time ago, with some saying they don't care it being displayed in large edos. However, until a line is drawn somewhere, in which case it can be automated, I'm just gonna keep this feature out for consistency's sake.  
: I have to say I'm influenced by hkm's usage of an apostrophe to denote an offset by a period, so in that scheme, 1–6/5–3/2 can be written as "0–'3–1". I feel it looks fairly clean, not too intrusive, at least for temps with a semi-octave period. I think the generator should be taken as the fifth, not the semitone, cuz it's easier to think of the temp as two chains of fifths offset by a semi-octave. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:29, 20 January 2026 (UTC)


: For the harmonics table, the default number of columns is usually good and extra columns should be added in a separate, collapsed table. Overwidth tables break the page layout on some devices.
:: Hm... Maybe placing the apostrophe ''after'' the number is more readable. This way 1–6/5–3/2 will become "0–3'–1", and the number coming first is more readable, plus it will be read as "3 prime" which fits better with math notation.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 21:39, 20 January 2026 (UTC)


: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:18, 11 September 2025 (UTC)
::: Good point. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:49, 21 January 2026 (UTC)


== On temperament degeneracy ==
== {{monzo| -37 0 0 0 0 10}} ==
Does there exist a page for the {{monzo| -37 0 0 0 0 10 }} comma, or the difference between 10 13/8s and 7 octaves? <span style="display: inline-block;transform: rotate(15deg);background:#E1EBF2;font-family:Verdana;text-shadow: 3px 3px 4px #0008;">[[User:Hotcrystal0|hotcrysta]][[User talk: Hotcrystal0|l0]]</span> 16:24, 20 January 2026 (UTC)


Hello Flora, regarding the changes in concept I submitted to Bixby and Archon, why aren't they not degenerate?
: As you can see in ''Small comma'' page, the comma was named the ''valerisma'', and no articles exist for it. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 16:28, 20 January 2026 (UTC)


For Bixby, if you temper out 4/3, it results in ~3/2 being mapped to an octave. If you temper 3/2 instead, 4/3 is 1 octave. If you temper 3/1 instead, then all 3's become unisons. In all of these cases, you are effectively destroying prime 3 and forcing it to be equal to some number of octaves, however as many as you like, so it matters little what you temper. Same with Archon destroying prime 5.
== Odd prime sum limit notability ==
I noticed that you removed the mentions of odd prime sum limit records I made from a couple of edo pages. Is it too arbitrary of a metric for prime approximation to be mentioned on these pages? If so, how is it different in this regard from Pepper ambiguity (still mentioned on the 270edo page)?


It would be the same thing as tempering out 17/16, tempering an octave-reduced harmonic to the nearest octave would be effectively removing it from the system assuming pure octaves. It should follow that the simplest subgroup of this temperament, 2.17, it is equivalent to the 2-limit, and can only be represented by 1edo; you get no real sonic benefit from just using octaves.
: I do take issue with Pepper ambiguity specifically when the intervals involve inconsistency, but as the information have been there for a long time I don't feel like removing them. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:46, 29 January 2026 (UTC)
: <small>P.S. pls remember to sign your comment with <code><nowiki>~~~~</nowiki></code>. </small>


Running tuning optimizations on those is possible, but the data you get is wild because the optimizer is trying to make up for the fact that a prime would be mapped to pure octaves.
== EDO impressions ==
In your EDO impressions for 36edo you mentioned adding “third tones”, even though the correct term here would be “sixth tones”. Can you fix that? <span style="display: inline-block;transform: rotate(15deg);background:#E1EBF2;font-family:Verdana;text-shadow: 3px 3px 4px #0008;">[[User:Hotcrystal0|hotcrysta]][[User talk: Hotcrystal0|l0]]</span> 18:16, 29 January 2026 (UTC)


Antitonic wouldn't be a degenerate temperament because while 9/8 is a wild thing to be called a comma, it can be represented ''at least'' in 2edo and 4edo, and you get the tiniest semblance of 3/2... truly a troll temperament.
: Fixed. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:23, 29 January 2026 (UTC)


I would call degenerate any temperament that can only represented by patent val by 1edN, or worse by 0edo (which of course is trivial). --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 12:30, 31 December 2025 (UTC)
== Tetracot ==


: The octave can be tempered.  
On the page [[Tetracot extensions]], you suggested splitting it into four pages: [[Monkey]], [[Bunya]], [[Modus]], and [[Wollemia]]. Tetracot splits the [[2187/2048|apotome]] into four comma steps. It maps 5/4 to the vM3, 11/8 to the sA4, and 13/8 to the n6. The main tetracot edos are [[27edo]] (27e val for prime 11), [[34edo]], and [[41edo]]. These extensions differ is the mapping of prime 7:


: Bixby isn't the same as the 2.5 subgroup. 2.3.5 is reduced to 2.5 only if you temper out 3/1. In bixby ~2/1 can be bent towards ~3/2 just as ~3/2 can be bent towards ~2/1. For the same reason archon isn't the same as the 2.3 subgroup.
Monkey (34 & 41): 7/4 is vm7


: Tempering out 17/16 easily makes sense by detuning each octave 25 cents wide to get a 17/1 that's only about 5 cents narrow.
Bunya (34d & 41): 7/4 is sA6


: Even tho these temps are still wild, they are not as wild as you think, and certainly not degenerate cuz degeneracy means actually removing a dimension, like tempering out a literal harmonic and not just selectively an octave-reduced harmonic.
Modus (27e & 34d): 7/4 is m7


: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:12, 31 December 2025 (UTC)
Wollemia (27e & 34): 7/4 is ^A6


:: Degeneracy is normally understood to be limiting behavior; the case of degeneracy being a removal of a dimension is specific to linear algebra, according to the broader mathematical definition, these temperaments can still be considered degenerate cases, hear me out:
I've noticed that in 27edo the pythagorean thirds are quite clearly supermajor/subminor, and the 5-limit thirds are quite far from each other, with [[5/4]] being the same 400{{c}} major third as in 12edo, and [[6/5]] being slightly flat at 311.{{Overline|1}}{{c}}. 34edo makes 5/4 and 6/5 both about equally sharp, and the pythagorean thirds are mapped as in 17edo. 41edo maps the pythagorean thirds close to just, but the 5-limit thirds are slightly closer to neutral as a result. In any case, intervals of 11 and 13 are mapped to neutral intervals. The way I tend to think of tetracot is as a tertian structure (like [[keemic]]).


:: Assuming 1edo is a trivial temperament of the 2-limit:
Monkey and modus map 7/4 to a 7th (they are supported by the 7edo patent val). The tertian structures of 27edo and 41edo are quite clearly different, while 34edo is somewhat similar to both (though IMO closer to 27edo as 34d is better than patent 34). Here 34d&27 is modus, while 34&41 is monkey. They are quite clearly different, as modus sets the pythagorean thirds to septimal ones while pental thirds are halfway between the septimal thirds and neutral ones. Monkey, on the other hand, distinguishes the pythagorean thirds from pental and septimal ones, and sets them equidistant from pental and septimal thirds.


:: Let's think about the simplest case scenario: Going from the 3-limit, tempering out 4/3 to get a rank-1 temperament. This "rank-1 Bixby" can only be represented by patent val by 1edo, where each step is an (tempered) octave, and fifths are rounded to octaves, same with 5/4s and all other primes. Here, the structure has collapsed, since only the 2-limit is left and only the trivial temperament (1edo) can represent it.  
Bunya and wollemia, on the other hand, map 7/4 to a 6th (corresponding to the 7d val). Bunya (34d&41) maps 7/4 to a sA6, so that 28/27 is equated with 33/32 as an sA1, as in [[parapyth]]. This sets the pythagorean major third to [[14/11]], and 9/7 to an sd4 instead. Bunya also tempers out [[225/224]], so that 7/4 is equated with the [[225/128]] augmented 6th, which in tetracot is a vvA6&nbsp;=&nbsp;sA6. Wollemia (27e & 34), on the other hand, is quite strange. It tunes the fifth so that the pythagorean intervals are close to septimal intervals, but doesn't actually map them to septimal intervals. Instead, 28/27 is mapped to a ^1, so 9/7 is a v4, and 7/6 is a ^A2. Optimal tunings of wollemia are close to optimal tunings of modus, but doesn't temper out [[64/63]], instead equating septimal supermajor/subminor intervals to tridecimal ultramajor/inframinor intervals via tempering of [[91/90]]. In wollemia [[14/11]] is also mapped to the same interval as [[5/4]], and [[11/8]] the same interval as [[7/5]]. I'm not too sure of the significance of this yet, besides that both the 27e and 34 vals contain these equivalences.


:: Even in the 5-limit extension (Bixby proper), no other type of temperament collapses its structure so much that it is ''only'' representable by patent val by 1edo, not even Antitonic. Since the 3-structure has collapsed to the 2-limit and only the 2.5 subgroup makes sense, I believe that the only reasonable way to look at this, is to see it as a degenerate case.  
In any case, I suggest you add a 7et detemperament section to the [[Tetracot]] article.


:: In Antitonic, you can temper the period to get a bit closer to "fifths" and "octaves", but the structure has not collapsed. In fact, Antitonic is the first proper 3-limit temperament, it even demonstrates 3-2 telicity!
--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 23:45, 13 February 2026 (UTC)


:: I believe this is a useful case of degeneracy that should be used to categorize these limiting temperaments. I wouldn't deem them exotemperaments, no that's far too generous... just degenerate temperaments.
: Sure. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:39, 14 February 2026 (UTC)


:: --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 16:55, 31 December 2025 (UTC)
== About schismina ==
What's the deal with the schisminic temp? It is 2.3.5.7.13, there's no 11. Also, I would deem the differences I outlined are notable, because they show how many ''simple'' ratios of 35 have tiny differences with tridecimal equivalents and viceversa. Specially 8505/8192, whose pressence in Sagittal pretty much assumes that the schismina is either tempered out or fudged. It's that important of a schisma, we have to sell it as such! --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 17:05, 22 February 2026 (UTC)
 
: > What's the deal with the schisminic temp? It is 2.3.5.7.13, there's no 11.
 
: That's why ''schismina'' isn't a great name for the comma; there's no room to distinguish the minimal-prime-subgroup temp and the full-prime-limit temp according to our rules. I've proposed something else in ''Talk: 4096/4095''.
 
: > I would deem the differences I outlined are notable.
 
: I think there's a problem in how you present your ideas. If all you wanna discuss is the merge of intervals of 13 with intervals of 35, add that instead. A pair of ratios may serve as an example, but the entire point is in the context. The ratios alone which comprise three- or even four-digit ones aren't notable cuz no one uses them in music.
 
: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:33, 22 February 2026 (UTC)
 
== Thanks ==
Hello Flora, how are you today? I see you corrected some mistakes I unwittingly made when editing MOS pages, for example, when I called 2L 17s a MOS of Pycnic temperament and you took it out, noting that 2L 17s is actually tritonic temperament. So, I just wanted to say thank you, and I will double-check my edits in the future. [[User:MisterShafXen|MisterShafXen]] ([[User talk:MisterShafXen|talk]]) 17:28, 6 May 2026 (UTC)
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