View source for Talk:5120/5103

== "Universal" name for 5120/5103 ==

I've noticed the conversation on the XA Discord about picking a name to replace "hemifamity comma". Suggestions I've seen include ''argent comma'' and ''pele comma''. I'm a bit biased towards ''aberschisma'' since I coined the name, but MidnightBlue pointed out that 6¢ is quite wide to be calling it a schisma, which I've also thought about. Maybe ''aberkleisma'' or even ''pentasept comma''?

: I'm not too invested into this comma, but will add my <strike>schisma</strike> 2c after seeing the Discord convo: ''pele comma'' and ''peleisma'' are fine with me, whereas I'm afraid ''argent comma'', while logical, may be confused with the [[argyria]] (which is more of an ''arg''ument for renaming the latter).

: On a side note, 5120/5103 does function like a kleisma for me, particularly because the ratio of the pental kleisma to it is the [[horwell comma]], which is among the staple commas in my 7-limit analysis of edos incl. 53. Because schismic x kleismic product words are among the best ways to make well-tempered 53-note scales, the pental kleisma is a chroma there, and when horwell tempered, it turns into 5120/5103 and is, among other roles, the scale-chroma between the 81/80 and 64/63 steps.

: Meanwhile, the ratio of 5120/5103 to the pental schisma is the [[garischisma]]. So for fans of the latter, which I'm not, it may act like a schisma instead, but that's less likely because the pental schisma flattens the fifth while the garischisma sharpens it, so if anything, the latter and 5120/5103 would be seen as 'negative schismas', which, btw, brings us to the concept of [[counterpyth]].

: Afaik, counterpyth has never been considered under this name without 5120/5103, whereas [[1216/1215]] works well together with other commas that stack slightly sharp fifths, such as the [[wilschisma]] and the [[symbiotic comma]], and the name ''Eratosthenes' comma'' is good, so I disagree with the assignment of the counterpyth family label to any temp with 1216/1215 in sintel's finder. I.e., to me, 5120/5103 is more related to counterpyth than 1216/1215 is. But I can't be sure of my judgment on this without FloraC's opinion. Either way, I don't mind ''counterpyth comma'' for 5120/5103, its 7-limit rank-3 then called counterpyth like its canonical extension to 2.3.5.7.19 already is. 

: --[[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 23:55, 1 June 2025 (UTC)

:: I'm all for ''argent comma''. The similarity with ''argyria'' isn't high enough to worry me. I'm against ''pele comma'' cuz that would set pele as canon which I don't think we should ever do. For the same reason I'd hesitate to call it ''counterpyth comma''. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:17, 2 June 2025 (UTC)

::: OK, then I settle on ''argent comma'' too. That matches my view of argent fifths as a distinct region that's roughly [65\111, 17\29] and sharp of the olympic / garischismic / symbiotic / wilschismic fifths region that's roughly [55\94, 65\111]. --[[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 18:38, 2 June 2025 (UTC)

:::: What about 41edo and 46edo? Those are both notable tunings that temper out the comma and have fifths that fall outside of your *argent* range. -- [[User:Tristanbay|Tristanbay]] ([[User talk:Tristanbay|talk]]) 00:35, 12 June 2025 (UTC)

::::: On my part I include 41edo within the argent range; and there's a case to be made that 46edo and 53edo, while notable, aren't truly representative of the intonation of tempering out 5120/5103. "Argent" strictly speaking refers not to a particular tuning range, anyhow, but to a specific tuning that sets the logarithmic ratio of the perfect fifth to the perfect fourth to be sqrt(2):1, for which one can define bands of tolerance around, but which very closely corresponds to the most accurate tunings that temper out this comma. Perhaps "argentisma" -> argentic, argentismic would be clearer, so as not to imply an RTT interpretation for the term "argent temperament" which is already in use. 

::::: Compare this to the intonation of counterpyth, which quite distinctly favors tunings of 3/2 far flatter than the optimum of tempering out 5120/5103 by itself: just 19/15 gives us roughly 1/16-comma hemifamity as opposed to just 15/14, 7/5, or 21/20 which provide 1/5, 1/6, and 1/7-comma tunings. For this reason, I oppose seeing counterpyth as a canonical extension to the 7-limit rank-3 {5120/5103} temperament. -- [[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 01:24, 12 June 2025 (UTC)

::::: I did think about making 24\41 the boundary instead, as rank-3 microtemps tend to have flatter fifths than that even if 152fg or 111 support them. My flat end of argent is surely not flatter than 24\41 and not sharper than 41\70. Between those are kwai fifths... that I may consider too damaged indeed on second thought, and so belonging to the "slightly exo" range codenamed argent. [[User:VIxen|VIxen]] ([[User talk:VIxen|talk]]) 20:23, 19 June 2025 (UTC)

:::: I prefer "Saruyo". It's the only name out of all these suggestions that directly indicates 5120/5103. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 09:19, 5 June 2025 (UTC)

: I have a dumb idea. Why not call it the *pell comma* after the Pell sequence of numbers, whose convergent ratio gives the approximate ratio between an octave and a perfect fourth for the optimal tuning of the temperament? [[User:Tristanbay|Tristanbay]] ([[User talk:Tristanbay|talk]]) 20:59, 18 September 2025 (UTC)

:: I think referencing the Pell sequence makes way more sense for a member of the family of commas going 50/49, 289/288, 1682/1681, 9801/9800, etc. The only relation of Pell numbers to 5120/5103 is the edo sequence, which seems rather secondary, as much as I'm a promoter of 239edo. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 22:42, 18 September 2025 (UTC)

: I propose the name "interkleisma", since 5120/5103 is the difference between 64/63 and 81/80 (the main formal commas for primes 5 and 7), and is around a kleisma in size.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 03:02, 13 February 2026 (UTC)

:: It's a half kleisma in 270edo (and 311edo if you consider other kleismata such as 1029/1024) tho. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:20, 13 February 2026 (UTC)

::: Your essay on the 13-limit JI space considers 5120/5103~352/351~847/845, 325/324~385/384, 364/363~441/440, 540/539~729/728, and 351/350 as kleismas. Even if it is a half-kleisma in 270edo, the comma is close enough to the rough interval region, and also no single edo should decide the name.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 16:58, 13 February 2026 (UTC)

:::: Oh wow, my bad. I'll change them to hemikleismata. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 21:39, 13 February 2026 (UTC)

Should we do a poll here? The name was basically pre-maturely changed according to a poll on XA Discord. Besides, we need to decide what to do with the temp's name. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:51, 22 January 2026 (UTC)

: If enough people want to, then I guess. I like the current name of this comma, and I was thinking of the associated full 7-limit temperament being "argentic" and the 2.3.7/5 subgroup one being "argic". [[User:Tristanbay|Tristanbay]] ([[User talk:Tristanbay|talk]]) 06:12, 27 January 2026 (UTC)

: Why not [[64/63|S8]]/[[81/80|S9]]? Are there many properties of this comma that aren't explained by it being ((8/7)/(9/8)) / ((9/8)/(10/9)) = (64/63) / (81/80) and hence ([[10/7]])/([[9/8]])<sup>3</sup>? --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 12:27, 16 February 2026 (UTC)

:: Because "ess eight over ess nine" is too many syllables. [[User:Tristanbay|Tristanbay]] ([[User talk:Tristanbay|talk]]) 05:34, 17 February 2026 (UTC)

: I'm fine calling it saruyoma, y'all sort this out. --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 10:04, 6 May 2026 (UTC)

=== Petition to officialize ''aberschisma'', and change ''hemifamity'' to ''aberschismic'' ===
At this point, ''aberschisma'' and ''aberschismic'' seem like the most widely liked and used names in xenharmonic communities. Thereby I request ''aberschisma'' be set as the permanent, main name for 5120/5103, and ''hemifamity'' be officially changed to ''aberschismic''. 

Please put your "yes" or "no" and signature below. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:56, 1 June 2026 (UTC)

# '''Yes'''. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:56, 1 June 2026 (UTC)
# Yes, sure, why not. --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 07:48, 1 June 2026 (UTC)
# '''Yes''', I'm only weakly towards that name, but it feels alright, if the community wants it. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 15:40, 1 June 2026 (UTC)
# '''Yes.''' [[User:Inthar|Inthar]] ([[User talk:Inthar|talk]]) 20:16, 1 June 2026 (UTC)
# '''Yes'''. "Argentic" should still refer to the 2.3.7/5 subgroup temperament, however, per the change I made. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 20:18, 1 June 2026 (UTC)
# '''Yes''', I find it a lot more usefully descriptive.  Hemififths and Amity are far from the main temperaments I associate with the comma, and Aberschismic comparatively describes quite well how I tend to use it (to equate 81/80~64/63 as a singular aberrisma) [[User:Unque|Unque]] ([[User talk:Unque|talk]]) 20:22, 1 June 2026 (UTC)
# '''Yes'''. [[User:DotuXil|dotuXil]] <span style="color:#f50c7d">(i like microtones)</span> 21:41, 1 June 2026 (UTC)
#'''Yes''', I'm ok with it in part since I was involved in coining the name [[User:Tristanbay|Tristanbay]] ([[User talk:Tristanbay|talk]]) 06:03, 3 June 2026 (UTC)

: I was under the impression that "argent" won out in the community? – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 12:30, 1 June 2026 (UTC)
:: In my opinion it's a bit too confusing with the logarithmic argent tuning, even though it is closely related. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 15:40, 1 June 2026 (UTC)
::: Seconded. --[[User:Lériendil|Lériendil]] ([[User talk:Lériendil|talk]]) 20:18, 1 June 2026 (UTC)