Talk:Varieties of equal temperament
This is not a forum for general discussion of the subject of the article.
- Add new text under old text.
- New to Wikipedia? Welcome! Learn to edit; get help.
- Assume good faith
- Be polite and avoid personal attacks
- Be welcoming to newcomers
- Seek dispute resolution if needed
It is of interest to the following WikiProjects:
Archives
This page has archives.Topics inactive for 365 days are automatically archived 1 or more at a time by ClueBot III if there are more than 8.
There a reference to Boiles 1969 in the Equal temperament#7-tone equal temperament section, which I've just rescued the cite for (Boiles, J. (1969). "Terpehua though-song", Ethnomusicology, 13, 42-47). This comes second hand from "Burns, Edward M. (1999). 'Intervals, Scales, and Tuning', The Psychology of Music", but I can't find anything that matches from Ethnomusicology. The listing for Ethnomusicology from 1969 lists a different paper in those page numbers, there is Tepehua Thought-Song: A Case of Semantic Signaling by Charles L. Boilés in 1967 but I lack the subject knowledge to determine if this is what Burns was actually referring to.
Could someone with such knowledge verify the details and what exactly not should be referenced to? I could have missed something or Burns could have made a mistake. -- LCU ActivelyDisinterested «@» °∆t° 16:15, 25 January 2024 (UTC) Reply
"Other instruments, such as some wind, keyboard, and fretted instruments, often only approximate equal temperament, where technical limitations prevent exact tunings."
Now I'm not a wind player (I'm a violinist) but I don't think this is true of wind instruments in general and I'm not convinced it's true of most fretted instruments either, except in a theoretical way where we assume the player hasn't mastered the ability to play with good intonation. I think it's only true of the default pitches the instrument theoretically produces.
For example, a flute player adjusts intonation by changing the angle at which they blow across the air hole, and the pitch of a guitar note changes according to how close to the fret a finger is and how firmly pressed down.
It's true that the instrument design often implies something different from equal temperament or from just intonation, but other than keyboard instruments and fixed-pitch percussion I think "technical limitations prevent exact tunings" is untrue in virtually all cases. You either learn the techniques for playing in tune, or don't get invited to play. Playing in an ensemble requires monitoring and adjusting your pitch all the time, in order to precisely match the other players. Musiconeologist (talk) 00:20, 31 January 2025 (UTC) Reply
- @Musiconeologist: Utterly valid point, and also rather irrelevant in an article about equal temperaments. The supporting reference also didn't really support it: it's entirely about fret-placement on fretted instruments, and the nearest it got to the subject was a comment that finger-pressure around the fret makes a simplistic theory fail. It didn't mention wind or keyboard instruments at all. I have therefore removed this section. Elemimele (talk) 17:04, 17 June 2026 (UTC) Reply
From the 'Europe' subsection:
"In the end, 12-tone equal temperament won out. This allowed ... atonal music such as that written with the 12-tone technique or serialism, and jazz (at least its piano component) to develop and flourish."
This claim does not belong in an encyclopedia article unless it is weakened, qualified, or supported with citations. Evaluating it requires speculating about fairly wild counterfactuals. Couldn't well-tempered atonal music similar to 12-tone serialism have flourished (to the extent that 12edo serialism 'flourished')? Couldn't piano jazz have flourished if some shallow well temperament was ubiquitous? ~2025-33969-28 (talk) 23:06, 15 November 2025 (UTC) Reply
Can someone with technical knowledge about Wikipedia's internal link structure look into this?
Several other articles on Wikipedia have links to a Regular Temperament page, but following those links brings you here to the Equal Temperament page.
Searching Wikipedia for "Regular Temperament" finds no page with that name. However, searching Wikipedia for pages that contain "regular temperament" gets the following message from Wikipedia.
There is a page named "Regular Temperament" on Wikipedia
And the text quoted in that message is a link. However, following that link still brings you here to the "Equal Temperament" page.
Maybe the Regular Temperament page still exists but has been mistakingly redirected here.
It should not be redirected here, because Regular Temperament and Equal Temperament are on different logical levels. Regular Temperament is the more inclusive term. Equal Temperament and Moment Of Symmetry (MOS) are special cases of Regular Temperament.
The Regular Temperament page needs to be restored so it can continue to be separately edited.
~2026-34537-05 (talk) 13:37, 15 June 2026 (UTC) Reply
- You can see the history of it here.Trumpetrep (talk) 23:53, 15 June 2026 (UTC) Reply
- I see. Thanks.
- That's unfortunate. I think it would have been better, and maybe it can still be done, to redirect it to a page that says something like this.
- The Regular Temperament page was deleted after n years of complaints about poor quality. You can read the archived deletion discussion here.
- That would prevent future readers being redirected with no explanation of why to an article that doesn't mention regular temperament and potentially misleads them into thinking regular temperament means equal temperament. It would also make available to those readers the valuable citations and links added to the deletion discussion that probably represent more research labor and information content than the original article.
- If you had not linked the discussion, I would never have never known it existed, let alone read the added info. ~2026-34537-05 (talk) 01:10, 17 June 2026 (UTC) Reply
- Can you take a moment to create a user name? That would be helpful.
- It's hard to follow what you are saying. The deleted article was a disservice to readers. It was largely original research.
- It's unclear what you would like to happen. If there's information that you feel should be in the encyclopedia, by all means add it. Trumpetrep (talk) 02:12, 17 June 2026 (UTC) Reply
- The argument is that it is a different topic, and that a new version with proper sourcing be created. You can go to WP:RFD if you believe that the current target is wrong. –LaundryPizza03 (d c̄) 17:44, 17 June 2026 (UTC) Reply
- Thanks for the link to the Redirects For Discussion area. It's very complicated there. It looks like to nominate the existing redirect (from Regular Temperament to Equal Temperament) to be discussed so that it can point somewhere else instead (to Musical Temperament), I would have to first have to edit the redirect page itself to put a special tag at the top. I don't even know how to find a redirect page, since it's normally invisible. It says there's an automated tool but it can only be used by confirmed users, which means I would first have to make 10 edits to existing English Wikipedia pages in order to automatically become a confirmed user. Even then, I think it would only be raw nominated, and I'm not sure where I would then describe the issue and the suggested fix. Wikipedia internal workings are complicated, which is why I initially asked if someone experienced would help. Could you? ~2026-34537-05 (talk) 19:40, 17 June 2026 (UTC) Reply
- I don't want to create an account. I'm just saying the current redirect is confusing to post-deletion readers like myself. What I would like to happen is for Regular Temperament to redirect to Musical Temperament instead of Equal Temperament, since all regular temperaments are musical temperaments but not all regular temperaments are equal temperaments, and because the Musical Temperament page at least mentions regular temperaments in its body. ~2026-34537-05 (talk) 19:21, 17 June 2026 (UTC) Reply
- Done. Thanks for explaining.
- I think the redirect to equal temperament was because it was the article that's in better shape. The Musical temperament article is more of a hash and needs a lot of work. Trumpetrep (talk) 19:52, 17 June 2026 (UTC) Reply
- Cool. I see the change. Hopefully, Musical Temperament will improve over time. ~2026-34537-05 (talk) 20:29, 17 June 2026 (UTC) Reply
- The articles about tuning are in generally poor condition. Recently, there's been a fair amount of effort to improve them. If there's anything you can do to help, it would be welcome! Comments like the ones you made here are certainly a form of help. They can prod editors to make improvements. Trumpetrep (talk) 23:06, 17 June 2026 (UTC) Reply
- Wikipedia:No original research/Noticeboard should bring people experienced with OR to the topic area. –LaundryPizza03 (d c̄) 19:51, 18 June 2026 (UTC) Reply
- The articles about tuning are in generally poor condition. Recently, there's been a fair amount of effort to improve them. If there's anything you can do to help, it would be welcome! Comments like the ones you made here are certainly a form of help. They can prod editors to make improvements. Trumpetrep (talk) 23:06, 17 June 2026 (UTC) Reply
- Cool. I see the change. Hopefully, Musical Temperament will improve over time. ~2026-34537-05 (talk) 20:29, 17 June 2026 (UTC) Reply
- The argument is that it is a different topic, and that a new version with proper sourcing be created. You can go to WP:RFD if you believe that the current target is wrong. –LaundryPizza03 (d c̄) 17:44, 17 June 2026 (UTC) Reply
Wikipedia policy specifies, "Article titles are based on how reliable English-language sources refer to the article's subject." A more accurate title for this article is "Varieties of equal temperament", which is why it was moved.
Since many of these varieties have articles of their own, I would recommend trimming this article considerably. It has become a kind of info dump for random facts and original research. Trumpetrep (talk) 03:01, 16 June 2026 (UTC) Reply
- @Trumpetrep: Sorry, you will need evidence that equal temperament is mostly specifically used for the 12-tone scale. –LaundryPizza03 (d c̄) 03:15, 16 June 2026 (UTC) Reply
- See below. This move was long overdue.
- What this article is really focused on are all the varieties of equal temperament. There's an argument that Wikipedia should have such an article. But what Wikipedia shouldn't have is an article that appropriates a widely used term for its title and then bewilders the general reader, which is our audience. "Equal temperament" should be an article about the standard tuning system. A farrago about all the other theoretical equal temperaments should be clearly labeled as such.
- In my view, Wikipedia would be a better resource if this page were deleted and its contents dealt with succinctly as a codicil of the primary article. But since Wikipedia is infinite, this page certainly can exist, just not in its currently deficient form. Trumpetrep (talk) 04:43, 16 June 2026 (UTC) Reply
- The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.
The result of the move request was: not moved. (closed by non-admin page mover) {{GearsDatapacks |talk |contribs |in solidarity }} 18:52, 28 June 2026 (UTC) Reply
- Varieties of equal temperament → Equal temperament
- Equal temperament → 12 equal temperament 12 equal temperament
– Moved without discussion. The mover claimed that the term equal temperament is specifically used for the 12-tone scale, but they provided no evidence for this. –LaundryPizza03 (d c̄) 03:18, 16 June 2026 (UTC) Reply
- Oppose. Wikipedia policy clearly states that article titles should reflect how reliable sources refer to the subject. There has been no claim that "equal temperament is specifically used for the 12-tone scale". Instead, there has been a move suggested by User:Elemimele back in March which points readers to the most commonly understood meaning of the term "equal temperament".
- It's odd that sources would be needed beyond what is already in the Equal temperament article which document this usage. Nevertheless:
- Barbour, J. Murray. Tuning and Temperament: A Historical Survey . Dover Publications, 2004. x.
- "Equal Temperament — The division of the octave into an equal number of parts, specifically into 12 semitones, each of which has the ratio of {\textstyle {\sqrt[{12}]{2}}}."
- Barnes, John. "Bach's Keyboard Temperament: Internal Evidence from the Well-Tempered Clavier." Early Music, vol. 7, no. 2, 1979. 236.
- "Keyboard composers of the present day usually write for equal temperament..."
- Cochrane, Lalage. "equal temperament." The Oxford Companion to Music. Oxford University Press, 2011.
- "A system of tuning the scale whereby the octave is divided into 12 equal semitones."
- Fuller-Maitland, John Alexander, and Wodehouse, Adela H.. A Dictionary of Music and Musicians (A.D. 1450-1880) by Eminent Writers, English and Foreign: With Illustrations and Woodcuts . Macmillan and Company, 1889. 71.
- "...in equal temperament, each Fifth ought to be made flat by one-twelfth of this Comma; but it is extremely difficult to accomplish this practically, and the error is always found to be greater in some Fifths than in others. If the theoretic conditions which the name 'equal temperament' implies, could be realised in the tuning of instruments, the Octave would be equally divided into twelve Semitones, six Tones, or three Major Thirds."
- Lindley, Mark. "Equal temperament." Grove Music Online, 2001. Oxford University Press.
- "Equal temperament is now widely regarded as the normal tuning of the Western, 12-note chromatic scale."
- Norden, N. Lindsay. "A New Theory of Untempered Music: A Few Important Features with Special Reference to 'A Cappella' Music." The Musical Quarterly, vol. 22, no. 2, 1936. 217.
- "MOST STUDENTS graduating from music schools, and many older musicians of experience, believe that all the music they hear is based on an octave divided into the twelve tones represented by the corresponding black and white keys of the piano keyboard. It is not strange that they should think so, for the piano is used in much of the ear-training and dictation given to students, and all the theory they learn is based upon the temperament of the piano, in which every tone is more or less out of tune. All present-day theory-books have been written with equal temperament in mind..."
- The Oxford Handbook of Critical Concepts in Music Theory. Oxford University Press, 2019. 20.
- "equal temperament was adopted by piano manufacturers en masse: it didn't take any extraordinary aptitude or training for tuners to get proficient at it, which spelled savings for employers...Equal temperament became the official house style of Broadwood's trend-setting outfit in the 1840s, just as the Victorian piano boom was getting into full swing, and just as the need to maximize productivity under conditions of more vigorous competition would have been felt more keenly, and would have sharply incentivized the streamlining and normalization of tuning operations."
- Slonimsky, Nicholas. Baker's Dictionary of Music . Edited by Richard Kassel. Schirmer Reference, New York, NY, 1997.
- "A precise logarithmic division of the octave into a predetermined number of tones. The scale based on 12 equal semitones (called 12-equal temperament) lies at the foundation of Western music since the mid-18th century."
- "Temperament", The New Harvard Dictionary of Music . Edited by Don Randel. Belknap Press of Harvard University Press, 1986. 837.
- "In the 20th century, a temperament with 12-part equal distribution has pre-dominated."
- "Tempered Tuning", Musical Opinion and Music Trade Review, Vol. 45, No. 534. March 1922. United Kingdom, n.p, 1921. 537.
- "Equal Temperament denotes the division of the octave into twelve semitones tuned to frequencies which result from the multiplication of each by the 12th root of 2, which is 1'05916."
- It seems that the editor proposing a counterintuitive move would be the one who needs to document that the meaning of "equal temperament" is anything but the commonly understood one. Trumpetrep (talk) 04:43, 16 June 2026 (UTC) Reply
- I would Oppose moving, for the reasons I gave before. To the vast majority of Western musicians "equal temperament" is always 12-ET, and 12-ET is referred to simply as "equal temperament". While I appreciate this will potentially irritate microtonalists and those with non-Western musical interests, we have to go with the commonly-used terminology (that's Wikipedia policy). The current titles deal with the dilemma quite well. They don't hide the existence of non-12-ET equal temperaments, but nor do they distort musical history by implying that 12-ET grew up in a family of equal temperaments where the octave is divided into n equal intervals with n = whatever you want. Western 12-ET was just another way to resolve the problem of fitting fifths (or thirds) into octaves and dealing with the mis-fit. The equal temperament article is therefore going to have to discuss its relationship to non-equal temperaments rather than how it fits into the scheme of all the other non-12 equal temperaments - which are better partitioned off into a "varieties" article, which can deal with microtonal music and non-Western traditions properly. Elemimele (talk) 09:55, 16 June 2026 (UTC) Reply
- see PianoDan below: yes, to clarify, I am supporting "Equal temperament" as the title of the article on 12ET, and "Varieties of equal temperament" (or similar) for the article on the whole range of different ETs. I don't really care about the redirect; the few people who go looking for 12ET by that name might actually be microtonalists interested in the varieties article. Maybe a hat-note or see-also in the "Equal temperament" article, clarifying that non-12-ETs are elsewhere, would sort them out? Elemimele (talk) 16:52, 16 June 2026 (UTC) Reply
- Oppose (I think - see comments) "Equal Temperament" is universally understood to refer to the primary system in use in Western music today, particularly in English language sources. On the other hand "12 Equal Temperament" is a term that you almost never encounter outside of highly specialized literature. Per WP:COMMONNAME, this appears to be an open and shut case. At the time of this writing, it appears the titles are assigned according to this rubric. ("ET" -> article on main system, "VET" -> article on variants, "12ET" -> redirect to ET.) My only hesitation is that I'm a bit confused by the move history, to the point that I'm uncertain whether "oppose" or "support" reflects the status quo. To be clear - I am in favor of the allocation of titles I have described, and I BELIEVE that means I am in opposition to a move. (User:PianoDan) — Preceding undated comment added 14:57, 16 June 2026 (UTC) Reply
- You & Elemimele are correct. The proposal is to move the articles to different locations from their current ones. The "Equal temperament" article now follows the Wikipedia policy on common names and is about the subject as it is commonly understood (see above). "Varieties of equal temperament" is about various tunings in addition to the 12-note chromatic standard.
- There are two proposed moves:
- 1. To move the "Equal temperament" article to "12 equal temperament".
- 2. To move the "Varieties of equal temperament" article to "Equal temperament".
- This dual move would return the articles to their previous names. Those names were not in accordance with Wikipedia policy. Per the suggestion of Elemimele, I changed them to be in compliance. LaundryPizza03's suggestion to move them back is a welcome opportunity for other editors to weigh in on the snafu. Trumpetrep (talk) 19:39, 16 June 2026 (UTC) Reply
- Oppose per COMMONNAME.SarekOfVulcan (talk) 17:57, 24 June 2026 (UTC) Reply
Trumpetrep (talk ·contribs ) removed an image from the read that is unreadable and presented similar information as an image later in the article, but that one includes only 12-TET. It was a chart comparing various equal temperaments and just intonations. I think we should build a new diagram (or a table) in vertical format. –LaundryPizza03 (d c̄) 05:57, 18 June 2026 (UTC) Reply
The image was:
–LaundryPizza03 (d c̄) 06:06, 18 June 2026 (UTC) Reply
- This is the duplicative image which is cited in the source of Just Plain Bill's unwieldy chart. It includes many more divisions than 12.
- Why is it Wikipedia's job to diagram all this out for the general reader? Does it make the article more comprehensible?
- I'd argue that it does not. Certainly, we shouldn't have multiple charts conveying similar information. There's no end to the way this information can be visualized. We should keep articles as clear as possible and direct people towards sources where they can learn more if they are interested. Trumpetrep (talk) 11:20, 18 June 2026 (UTC) Reply
- Then large part of the second half of Varieties of equal temperament#Twelve-tone equal temperament will need to be removed. –LaundryPizza03 (d c̄) 18:09, 18 June 2026 (UTC) Reply
- You're preaching to the choir on that one. I've long suggested this entire article should be deleted. Trumpetrep (talk) 18:16, 18 June 2026 (UTC) Reply
- Okay, but which parts? –LaundryPizza03 (d c̄) 19:43, 18 June 2026 (UTC) Reply
- Which parts of the entire page should be deleted? Trumpetrep (talk) 19:46, 18 June 2026 (UTC) Reply
- If you think so, go to WP:AFD. –LaundryPizza03 (d c̄) 19:52, 18 June 2026 (UTC) Reply
- One thing at a time. It's been encouraging to see you scraping out a lot of the cruft in this article. This whole subject area is overrun and in need of some serious attention. Trumpetrep (talk) 21:20, 18 June 2026 (UTC) Reply
- Okay. In this case, I'd say that we move the table to the article and delete everything else. Porbably better than the figure accompnying it. –LaundryPizza03 (d c̄) 23:29, 18 June 2026 (UTC) Reply
- One thing at a time. It's been encouraging to see you scraping out a lot of the cruft in this article. This whole subject area is overrun and in need of some serious attention. Trumpetrep (talk) 21:20, 18 June 2026 (UTC) Reply
- If you think so, go to WP:AFD. –LaundryPizza03 (d c̄) 19:52, 18 June 2026 (UTC) Reply
- Which parts of the entire page should be deleted? Trumpetrep (talk) 19:46, 18 June 2026 (UTC) Reply
- Okay, but which parts? –LaundryPizza03 (d c̄) 19:43, 18 June 2026 (UTC) Reply
- You're preaching to the choir on that one. I've long suggested this entire article should be deleted. Trumpetrep (talk) 18:16, 18 June 2026 (UTC) Reply
- Then large part of the second half of Varieties of equal temperament#Twelve-tone equal temperament will need to be removed. –LaundryPizza03 (d c̄) 18:09, 18 June 2026 (UTC) Reply
References
- ↑ Sethares (2005), fig. 4.6, p. 58 harvp error: no target: CITEREFSethares2005 (help)
Notes
- ↑ Sethares (2005) harvp error: no target: CITEREFSethares2005 (help) compares several equal temperaments in a graph with axes reversed from the axes in the first comparison of equal temperaments, and identical axes of the second.[1]
This could be worded better:
- Wendy Carlos created three unusual equal temperaments which divided the octave asymmetrically. She dubbed these scales alpha, beta, and gamma. Each approximates different just intervals.
They "divide the octave asymmetrically" in the sense that they ignore the octave. All three are designed to approximate the fifth, major third and minor third. —Antonissimo (talk) 07:41, 18 June 2026 (UTC) Reply
- They weren't designed to approximate intervals. That was a happy accident she described multiple times. Moreover, the article about these scales is where people can learn more about them. Trumpetrep (talk) 11:10, 18 June 2026 (UTC) Reply
- Now I see at that someone else optimized them to fit those three intervals. Okay. I still think that divided the octave asymmetrically suggests some scheme such as this: make the fifth (or some other interval) exact, divide the lower part of the octave into equal fractions of the fifth, and divide the upper part into equal fractions of the fourth. Why mention the octave at all? —Antonissimo (talk) 00:36, 19 June 2026 (UTC) Reply
- We had a very similar conversation at the page for these scales. Ignoring the octave was her starting point. She decided to focus on the peaks of consonance at smaller steps than the traditional scale and let the octave fall where it may. It's all in the article. Since there is an article about these scales, it doesn't seem necessary to go into much further detail in what is essentially a glorified list of varieties of equal temperament. Trumpetrep (talk) 03:52, 19 June 2026 (UTC) Reply
- Now I see at that someone else optimized them to fit those three intervals. Okay. I still think that divided the octave asymmetrically suggests some scheme such as this: make the fifth (or some other interval) exact, divide the lower part of the octave into equal fractions of the fifth, and divide the upper part into equal fractions of the fourth. Why mention the octave at all? —Antonissimo (talk) 00:36, 19 June 2026 (UTC) Reply