FloraC

== Higher primes ==

<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>

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)

: Originally, this part read:  

: <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>

: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:36, 13 January 2026 (UTC)

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)

: Tetraptolemaic diminished seventh. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:09, 14 January 2026 (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)

: 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)

:: 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)

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

== {{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)

: 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)

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)?

: 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)

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)

: Fixed. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 20:23, 29 January 2026 (UTC)

== Tetracot ==

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:

Monkey (34 & 41): 7/4 is vm7

Bunya (34d & 41): 7/4 is sA6

Wollemia (27e & 34): 7/4 is ^A6

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]]).

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.

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.

In any case, I suggest you add a 7et detemperament section to the [[Tetracot]] article.

: Sure. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:39, 14 February 2026 (UTC)

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)

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)