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)