Talk:CET

Concern about acronym

The acronym "ET" is also used in the community for "equal temperament", so it's confusing to also use it for "equal tuning" as is done here.

I wanted to know what the origin of using "cET" for "cent equal tuning" was. The earliest use of "cET" I could find in the Yahoo archives was here: https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_1.html (As an aside, this happens to be the oldest post in the entire archive.) So this was in 1995, but Gary Marrison did not unpack the acronym into "cent equal tuning"; his audience must have already known what he was talking about, or guessed from context. He does say there that the 88-cET tuning comes from Bill Sethares; I went to Tuning, Timbre, Spectrum, Scale (PDF link here: http://www.r-5.org/files/books/rx-music/tuning/William_A_Sethares-Tuning_Timbre_Spectrum_Scale-EN.pdf) and there I find Sethares crediting it back to Morrison! Strangely though, his bibliography points to "G. R. Morrison, “88 cent equal temperament,” Xenharmonikon 15 (1993)", yet this article does not exist; I went through my entire physical catalog of Xenharmonikon, volumes 1 through 18, and while I did see a ton of articles from Morrison and at least one from Sethares, I never saw any article titles mentioning 88-cET. Also, I realized that TTSS wasn't published until 1999 so this is after whatever discussion on the Mills Tuning list. So I'm afraid the origin of "cET" — both originator and originating date — are still unknown. But notice that the name of the article is "88 cent equal temperament" (my italics), not "88 cent equal tuning". And Sethares's glossary confirms this. Furthermore, there is no occurrence of "cent equal tuning" in the Yahoo archives, yet many occurrences of "cent equal temperament". So it appears that whoever and whenever "cET" was first introduced, it was introduced as a temperament, not a tuning.

Further evidence for this can be found in the history for the 88-cET page. From 2010, it was originally described as "88 cent equal temperament", and it wasn't until 2019 that Xenllium changed it from "temperament" to "tuning", without giving a description for their edit to explain their reasoning (revision here: https://en.xen.wiki/index.php?title=88cET&type=revision&diff=40220&oldid=1070). The 97.5-cET tuning page does not unpack the acronym, but the way it's written implies "tuning" rather than "temperament", but this page was not created until 2020, so its author (XenWolf) likely took their cue from Xenllium's revised version of 88-cET. The 65-cET and 125-cET pages — the two other examples of cET's on the wiki — don't unpack the acronym at all (these pages are from Andrew Heathwaite in 2011, and Chris Vaisvil in 2014, respectively, so it's worth noting that no one author is responsible for this situation).

Now, these aren't regular temperaments in the modern conventional sense, because they don't correspond to a linear mapping. But there's nothing wrong with calling them temperaments if their purpose is to approximate (or "temper") another pitch system, such as JI. That's all "equal temperament" meant originally before Gene Ward Smith's retconning via Wikipedia etc. in the early 2000's.

I found no examples in the Yahoo archives of ET standing for "equal tuning".

That all said, I did find many examples of "equal tuning" used to mean the same thing as "equal temperament", so perhaps this ambiguity is long ingrained and there's little to do about it.

For what it's worth, I would personally suggest naming these according to the naming system I developed recently with Paul Erlich and Billy Stiltner; under this naming system, these would be APS65¢, APS88¢, etc. where APS stands for "arithmetic pitch sequence". So, for example, if we were to add additional names to pages for the Carlos alpha, beta, and gamma systems, I would rather use APS77.965¢, APS63.833¢, and APS35.099¢, respectively, than 77.965cET, 63.833cET, and 35.099cET. It's too easy to confuse "cET" with "ET", or even "tET" as I sometimes see (where the "t" is for "tone"). --Cmloegcmluin (talk) ??:??, 23 October 2023 (UTC)

Many articles titled … equal temperament were changed to equal tuning some time ago. I believe it started with arithmetic sequences, and later these irrational constructs. I think the debate of equal tuning vs equal temperament in the contemporary context is equivalent to deciding which element is the inseparable essence of this thing: is it the concrete cent values, or is it the approximation relations (it doesn't need to be linear but still)? Currently most rank-1 entities here are described as tunings, such as edos, the only exception being Carlos "scales" (they are described as equal temperaments with standard tunings) and BP/13edt (they are separate articles).

I've personally long stopped using the acronym ET except in n-et, not to mention cET or tET. Heck, the cent and tone (steps actually) aren't even applied to the same object. cET means each step is of a number of cents whereas tET means each octave has a number of steps. So I agree APS-p or 1ed-p are superior terms here. However, I wouldn't say the same to the standard tunings of Carlos cuz that would cause loss of precision.

We should probably get @CompactStar involved (who I tagged on Discord). They recently moved 16/15 equal-step tuning to 1ed16/15. It's good time we discuss about this too. FloraC (talk) 05:32, 24 October 2023 (UTC)

Whoa, dang, I don't think it ever occurred to me before to think of sequences as 1-divisions! What a simple and interesting solution. Here's the full set of names in Paul's, Billy's, and my system now:

n-EFD-p	(n-)AFS-p	n-OD-p	(n-)OS-p
n-E(P)D-p	(n-)APS-p	n/a	(n-)AS-p
n-ELD-p	(n-)ALS-p	n-UD-p	(n-)US-p

So this insight from CompactStar shows me that we could eliminate the need for all of the sequences in this system (AFS, APS, ALS, OS, AS, US) by simply looking at them as 1-divisions of the appropriate type, like so, where n → 1:

n-EFD-p	1-EFD-p	n-OD-p	1-OD-p
n-E(P)D-p	1-E(P)D-p	n/a	1-AD-p
n-ELD-p	1-ELD-p	n-UD-p	1-UD-p

But we can actually do even better! That weirdness with the AD situation calls my attention to another fact: if it's 1-E{X}D-p, then the {X} doesn't matter, so everything may as well be simply E(P)D. The only reason to specify L or F would be to correspond with whatever format the p was given in; it doesn't actually affect the system. And as Flora recently showed me, while I myself intended for APS only to be given in cents, when I wrote up the wiki article, I ended up giving some of them in pitch, so there's some natural gravity to thinking this way. Also, AD didn't even exist before so it'd be awkward if this introduced it. So here's what that change looks like, where F → (P), L → (P), O → A, U → A, then A → E:

n-EFD-p	1-E(P)D-p	n-OD-p	1-E(P)D-p
n-E(P)D-p		n/a
n-ELD-p		n-UD-p

Now, thinking of 1 division of something is inherently awkward, so this isn't a strict win such that I'd deprecate all the existing sequence stuff. But I do like how 1-divisions leverage the n-division structure that people are already familiar with, and it doesn't conflict with the sequences at all, so I'm certainly not against CompactStar's approach here. I think there's room for both, but I'd just like to see what the community prefers, and if sequences go by the wayside, I understand and accept. --Cmloegcmluin (talk) 19:43, 24 October 2023 (UTC)

Well I forgot to write my response to this yet again. I advocate for the 1edx format at least for just x, since it is the notation that is already in common use for 1edo and 1edt (we don't call 1edo 2/1-equal step tuning) and is also the notation supported by Infobox ET. But I am not entirely sure about this for cETs, for 88cET for example it has to be 1ed88\1200, 1ed88 ¢ or even 150ed2048 (the latter is the most straightforward to me but it removes the reference to 88 cents, and no one composes in 88cET with 2048/1 as the period). I think those still may be beter than 88-cET though–I see 88cET (if T is temperament) as similar to saying 12-TET, it implies a temperament, but we need a different phrasure for the equivalent of saying 12edo where there is no temperament implied. And if 88cET has the T as tuning, then that brings up the issue of ET being commonly used to mean temperament that was mentioned earlier. CompactStar (talk) 08:05, 25 October 2023 (UTC)

I personally don't see issue with 1-ED88 ¢ or 1ed88 ¢ or however one wants to format it. So since we all seem to agree that the 88-cET form is problematic, I would advocate renaming that page either to 1ed88 ¢ or to APS88 ¢ (and the same would go for the other three cET pages). I do see your point that some users may wish to convey their use of the APSp/1-EDp structure as a temperament, but this seems less important than the issue of the lack of parallelism between cET and tET as Flora pointed out, especially since so many people don't seem to understand or at least care about the conceptual difference between an equal division and an equal temperament, and we could just come up with something better for that eventually if needed. --Cmloegcmluin (talk) 00:29, 27 October 2023 (UTC)

I agree. Just a minor correction: 1ed88¢ (no space) because I have not seen spaces on xedy format names (same for APS). CompactStar (talk) 01:04, 27 October 2023 (UTC)

Also correct me if I'm wrong, but wouldn't APS88¢ repeat arithmetically and thus be entirely different from 1ed88¢? For example the second step of APS88¢ would be 1+(2^88/1200-1)*2, which my calculator tells me is about 171 cents, in contrast to 1ed88¢'s 176 cents. CompactStar (talk) 01:07, 27 October 2023 (UTC)

Nevermind for ^ this, I think I've mistaken APS for AFS. CompactStar (talk) 01:08, 27 October 2023 (UTC)

It shouldn't matter whether it's APS, AFS, or ALS. As I described in more detail earlier (search on "But we can actually do even better"), when I showed that an A{X}S is equivalent to 1-E{X}D, then pointed out that if there's only one division, then they're all the exact same thing; how the resource is divided (by pitch, frequency, or length) is irrelevant if the period is only divided into one unit, or in other words is not divided. You just have to find how to express the period in terms of the "divided" resource. For example, the equivalent AFS for APS88¢ would be AFS(2^88/1200) ≈ AFS1.052. --Cmloegcmluin (talk) 01:43, 27 October 2023 (UTC)

Don't AFS, APS and ALS have different ways of repeating/equivalence beyond the period? CompactStar (talk) 02:09, 27 October 2023 (UTC)

Oh yeah, ugh. I just got really confused. Scratch all that. Sorry. --Cmloegcmluin (talk) 02:37, 27 October 2023 (UTC)

I've also just now scratched out the stuff I wrote in my earlier post, which was similarly misguided. --Cmloegcmluin (talk) 16:52, 27 October 2023 (UTC)

Okay, I agree with your (CompactStar's) decision not to rename the 88cET page, because as a search of the wiki for that name reveals, it apparently achieved fairly widespread use for some time. That said, I think we should avoid propagating the n-cET pattern further than that, and it seems we have agreement on that point. I think it would be appropriate to rename the existing pages using your 1ed approach. I could also add the APS name in the article body as an alternative name. And I would prefer for the pages (except for the historical 88cET page) to lose any reference to "cET".

As for this CET page itself, it could be renamed to "1ed" but that seems a bit awkward; instead, it seems totally reasonable to include this list of four tunings on the existing APS page in a new section called "List of APSs". This list could also include links to the Carlos Alpha, Beta, and Gamma scales. If we house the list on the APS page, though, we may want to consider for each of the four 1ed pages making the APS name the primary name (the first name on the page, and the name of the page itself), and the 1ed name the secondary name.

I have gone ahead and corrected the 88cET page with respect to the tuning vs temperament issue. I didn't do it for the 125cET page yet because this would be rendered moot if we remove all references to cET there. --Cmloegcmluin (talk) 19:53, 29 October 2023 (UTC)

Let me know if anyone has any issues with this plan. If I don't hear any concerns within a week, I'm happy to go ahead and take care of making the changes. --Cmloegcmluin (talk) 18:13, 30 October 2023 (UTC)

Hm. But probably we have more discussion to do. Because I see Flora mentioned that CompactStar moved "16/15 equal-step tuning" to "1ed16/15", but there are still many other pages like this:

• 8/7 equal-step tuning
• 15/14 equal-step tuning
• 18/17 equal-step tuning
• 21/20 equal-step tuning
• 25/24 equal-step tuning
• 33/32 equal step tuning
• 81/80 equal-step tuning

I think that might be all of them.

I notice that 15/14, 18/17, and 81/80 already have given the AS form as an alternative name.

The difference between AS and APS is that AS stands for "ambitonal sequence", not "arithmetic pitch sequence". It's the same thing, but rational.

I can see these going any of three ways: left how they are (with 16/15 returned to its previous state), everything changed to the 1ed format, or everything changed to the AS format. Whichever way we choose, I just want consistency.

So, if these were all renamed to AS, instead of joining the list of APS's I described above, they would go on an analogous list on the AS page. These two lists would link to each other with a "see also", though.

But I also see that we have pages like 2ed25/24 and 2ed5/4, whose presence seems to make the 1ed approach more appealing. So perhaps for these rational pages, which are more similar to equal divisions of the octave (the octave being rational), we would prefer the 1ed format? --Cmloegcmluin (talk) 18:31, 30 October 2023 (UTC)

Oh, if you ask me, I prefer the 1ed format for the near-universal acceptance of 1edo. FloraC (talk) 08:46, 1 November 2023 (UTC)

Fine by me. I can enact the above plan, then, except that I will make all of the primary names follow the 1ed format. --Cmloegcmluin (talk) 02:58, 2 November 2023 (UTC)

Okay, it has been done. Except that I can't actually delete this cET page myself, so I've only marked it for deletion. Also, I needed to make one additional update that I didn't describe above: Module:Harmonics in cet‎ needed to be updated to avoid the "cET" name (I didn't yet rename the template and module themselves; this seemed less important). Thank you to Flora for bringing the nature of the Carlos Alpha, Beta, and Gamma scales to my attention, namely that there are multiple tunings of each; by the way, I started a discussion on the Carlos Alpha page regarding those tunings. Well, please let me know if I missed anything, or if now that I've taken the step in this direction, if any further changes now seem clearly appropriate. Thanks. --Cmloegcmluin (talk) 20:12, 7 November 2023 (UTC)

I'd like to re-open this discussion. As I worked on a few "1ed" pages tonight, I found that many of them are not really justified to have their own dedicated page, and a merge is the best way to go, as they are often very closely related to other tunings which may be expressed more simply, such as an EDF (as that's the kind of feature that makes these nonoctave tunings notable and musically relevant in the first place), and it is better to explain on those pages what kind of fine-tuning may be considered beyond the general form of the tuning system. Nonetheless, for the few pages that might remain, especially those more widely known as being equal multiplications of a cent value and not as being something else, we still need to title their pages appropriately.

I've also taken the time to read the whole conversation above, and I'm surprised I didn't participate in it, I suppose I must have been busy at the time. Many of the arguments don't make sense to me.

Potential confusion between tuning and temperament? On the contrary, I find it convenient that the letter 'T' can stand for both tuning and temperament, since they are so often used interchangeably; after all, a temperament is a tuning that tempers, so it's just a matter of where you put your focus. Flora mentioned something along those lines, too. If that ever prevented anyone from making microtonal music, we should have noticed by now. Similarly, I don't get the issue with n-tET behaving as the inverse of x-cET, and that being potentially confusing. I don't think I've ever heard of someone confusing 88cET with 88tET, especially since the letters 'c' and 't' look rather different (both in lowercase and in uppercase). I think the letter 'c' conveys quite clearly the idea of cents, and when you know it's an equal temperament (or tuning!) based on 88 cents, if you know at least one other tuning, you know that doesn't imply 88 tones to the octave. And if you're worried that a single letter difference could be missed, in that case we'll need to fix a lot more things, because this certainly wouldn't be our first offender in that regard.

Another argument that doesn't resonate with me is the coherence with 1edo and 1edt. While these are not unusable tuning systems, they are certainly more of an exception than a standard model to follow. In most xenharmonists' minds, at least from what I can grasp (and from my intuition as a teacher), "1edo" belongs to the "edo" series, not to the "1ed" series. While it's possible to understand terms like "1ed88c", it's certainly not what I'd say out loud, for example. These kinds of considerations tend to be completely overlooked when discussed online by text only. Similarly, the existence of many sources using an "x-cET" form should not be erased from the wiki just because a few like-minded people thought it would be best to use a single standardized system. It's good to provide standardized options, but if it's not the most common one, then it shouldn't be used as a primary term. That's why we have pages like Bohlen-Pierce and Carlos Alpha, after all.

While the Xenharmonic Wiki doesn't always follow the same guidelines as Wikipedia, I generally take inspiration from their general rules when they make sense to apply here as well. In particular, their guidelines for article titles state that the most common name should take priority over the most accurate name; in particular, what most people are most likely to type in the search box is probably the title to choose. I'm certain that most people who land on "1ed88c" via the search box do so by searching "88cET", not "1ed88c, except a few nerds that spend too much time on the wiki like us. In general, we shouldn't take decisions based on "I like this" or "I don't like that". We, as editors, represent the xenharmonic community as a whole and attempt to describe our shared knowledge. Of course, we can add our bits of knowledge when we think we can contribute something more, but that shouldn't come with ignoring or erasing other people's contributions as if they were inferior.

Morrison and Sethares talked about "88-cent equal temperament". It was quickly abbreviated to "88cET" (variously with or without a hyphen, and with various capitalizations too). Several musicians adopted these terms. And so this is why I re-added "88cET" to the lead section of the corresponding page tonight, and similarly for a few others too. I am however waiting a bit before I rename the pages back to their previous "cET" form, because I don't want to act unilaterally, the same way I believe the change to "1ed" form could be perceived as unilateral, from the perspective of 3 people vs. the community. Wikis work based on a consensus, and obviously since you had a consensus of 3 people last time you discussed it, you proceeded, and I can't contest that. But I am going against the consensus now, and I hope we can reach a decision which makes the wiki more intuitive to navigate and read for a majority of users, not just a few math nerds already deep down the xen rabbit hole. --Fredg999 (talk) 06:49, 1 August 2025 (UTC)

Okay, I don't consider the ambiguity of ET a major issue. But I insist we should stick to equal-step tuning as the main name if we were to revert to that state.

Personally, I don't take issue with the likelihood of confusion between CET and TET, tho I can't speak for Douglas, who brought that up. My problem with using CET and TET is in their semantic inconsistency.

So far I can't see any of the names being more common than the others. It's plausible that ppl are more likely to search 88cet than 1ed88c in the searchbox, for the reasons outlined, but that is no replacement for real data, for which we should prolly get more ppl involved, start a poll in the server, etc.

FloraC (talk) 10:08, 3 August 2025 (UTC)

I don't think I've ever seen anyone use 1ed88c to describe the tuning of their music on any online platform or elsewhere. Have a look at the music sections of these equal cent tunings and try to convince me that the two forms are equally likely. --Fredg999 (talk) 12:13, 3 August 2025 (UTC)

The only works I see come from Carlo Serafini, Chris Vaisvil, and Mundoworld. Among those, Mundoworld's two pieces were released in 2021 and 24, which are perhaps the most relevant. The rest I'm not so sure of since they came out so early that this naming question couldn't have been brought to them. So that's the three composers, which imo is hardly indicative of anything. FloraC (talk) 13:09, 3 August 2025 (UTC)

Please look outside of the Xen Wiki if you're going to make that sort of argument. I can find several sources using cET terminology (mostly about 88cET), but the only search results I get for 1ed88c are hex color codes. People like Joseph Monzo, William Sethares, X. J. Scott, Gary Morrison (of course), etc., used that term way before the three composers you mentioned above. Isn't that proof already that CET is the most commonly used term? Some sources only mention 88cET specifically, but others clearly identify a general notation for CETs. --Fredg999 (talk) 20:17, 4 August 2025 (UTC)

That could be proof that CET was the most commonly used term. However, the AS/APS series of terms was only brought to the table in 2021, with several ppl involved, and this terminology discussion started in 2023, adding another lot of context. The point is your citations aren't indicative of what ppl choose today, for which my suggestion is to start a poll in the server (I might as well do that right now). FloraC (talk) 12:03, 5 August 2025 (UTC)

Poll result:

• 88cet: 10
• APS88c: 2
• 1ed88c: 2
• 150ed2048: 1

I respect this and acknowledge the commonness argument is indeed sound.

FloraC (talk) 11:31, 6 August 2025 (UTC)

Merge CET pages

I believe we should document related (stretched or compressed) tunings under the same article as we are doing with most edo pages. Also, the degree of precision in 88cET, for example, is arbitrary--why 88cET rather than 87.9 or 88.1--and the degree of precision cannot be consistent across similar articles, as precision up to the cent is too precise at very large step sizes and too imprecise at small ones. It is also more likely that the tuning is conceptualized as 8ED~3/2 or 41ED8 anyway, so I think calling the page 8ED3/2 or 41ED8 is superior to 88cET. More generally, I don't think the page title of any equal tuning should be XcET or APSXc. --hkm (talk) 18:17, 5 August 2025 (UTC)

By the logic of merging 88cet with 8edf or 41ed8, we would also need to merge Carlos Alpha with 9edf, Carlos Beta with 11edf, Carlos Gamma with 20edf, and BP with 13edt. FloraC (talk) 11:31, 6 August 2025 (UTC)

I think we should be careful when applying systematic thinking to merging and splitting discussions. Some tunings may be notable enough to justify having their own pages despite their similarity with other tunings. At the moment, I think it's safer to start with merging less commonly used tunings. Similar tunings should be mentioned on each page's lead section when they're not merged, and it's already the case most of the time. --Fredg999 (talk) 16:01, 6 August 2025 (UTC)