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").