Talk:Meantone temperament

message: This is what was in the article before I edited. I don't really understand it, and what I do understand doesn't seem strictly relevant to meantone, so I'm moving it here. I've replaced it with a stubby entry for now, but I'll be expanding it in time. --Camembert
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Original article text follows
In a modern 12 note equal temperament the semitone is exactly half a tone logarithmically.
If the semitone is allowed to be more than half a tone, one can get a better approximation to just intonation.
If the semitone is a rational fraction of a tone logarithmically, one gets a finite number of notes in an octave.
 Semitone/Tone  Notes
      1/2        12
      4/7        43
      3/5        31
      5/8        50
      2/3        19  
One can make some intervals perfectly tuned.
In Pythagorean tuning, 1:2 (the Octave) and 2:3 (the Fifth) are perfect and 9:10 is approximated by 8:9. This gives a semitone of 243:256, a tone of 8:9, and a major Third of 64:81 (1.265625).
Quarter comma meantone tunes 1:2 and 4:5 (the major Third) perfectly, giving a tone ratio 2:sqrt(5), a semitone ratio 5^(5/4):8, and a Fifth of 5^(1/4) (1.495349).
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: The preceding comment and removal of material was made by User:Camembert at some unspecified date.  I've taken the liberty of adding a section heading so this shows up in the Contents list for the talk page.  yoyo (talk) 19:42, 21 March 2018 (UTC)
thread_title:  Early material replaced 

message: The page as it stands has a nonstandard notation for accidentals (black notes). The usual is to notate all accidentals on the flatward side of the wolf as sharps, and vice versa. That is, if the wolf is between G# and Eb, you use F#, C#, G#, Eb, Bb. This is also easier to understand because A# is an unfamiliar note whereas Bb is very common. Then the flats and sharps form a mnemonic for which intervals are 'bad': the fifth G#-Eb is bad as are all thirds where the root is a sharp or where the third is a flat. 
--Tdent 21:53, 14 Apr 2005 (UTC)
thread_title:  Notation and the wolf 

message: The definition of meantone should not imply that the major 3rd is 'just', since in 1/5 comma, 1/6 comma, etc. etc. (all of which were historically referred to as mean-tone) it is not. The correct definition is that each perfect fifth is an equal interval apart from the wolf, with a corollary that the fifths are narrower than equal-tempered. (Otherwise Pythagorean tuning and equal temperament would also qualify.)
It would be useful to indicate the historical uses of (the various types of) mean-tone, which was widespread in the Renaissance, Baroque and early Classical eras. Even though keyboards began to be tuned to other types of temperament in the 18th century, vocal and wind/string instrument intonation was still taught according to a 1/6-comma meantone scheme in the time of Mozart. It appears likely that keyboard instruments were tuned to a slightly altered form of meantone through the 19th century, for example temperaments based on 1/8 comma meantone.
--Tdent 22:24, 14 Apr 2005 (UTC)
thread_title:  Definition and history 

message: Dear friends,
The Unequal Temperaments book of 1978 was described-in writing-as the definitive reference on the matter by authorities such as John Barnes, Hubert Bédard, Kenneth Gilbert, Igor Kipnis, Rudolf Rasch and others. In the 1990's I also developed the first professional-grade temperament spreadsheets.
Eventually I setup the "Unequal Temperaments" website, where I uploaded the spreadsheets which, kept permanently updated, are available for FREE. I also uploaded years ago a provisional "Update" to the book of 1978. The website lately gives information on the recently released new version of Unequal Temperaments 2008, which includes a detailed treatment of MEANTONE TEMPERAMENT.
(Please note: the website does NOT sell the book)
I would find it useful to Wikipedia readers if my website was included among External Links:
* Unequal Temperaments website, with Preview of the new 2008 book by Claudio Di Veroli
Kind regards
Claudio
Dr. Claudio Di Veroli
Bray, Ireland 
 86.42.128.58 (talk) 17:19, 26 February 2009 (UTC)
thread_title:  Unequal Temperaments book and website 

message: What the hell does the shape of the keyboard have to do with anything?  —Preceding unsigned comment added by 184.189.220.19 (talk) 00:28, 21 May 2011 (UTC)
thread_title:  Clarification 

message: 1>  It seems that the .jpg of the "Thummer" keyboard is missing.
2a> As a physicist / singer / early music listener I find this article excellent, but have trouble following the para with Easley Lockwood's "R" and its relation to various mean tones.  
Accepting that the stated relationship is exact:
                 log2 [interval of fifth] = (3R+1)/(5R+2)
then it seems to me that R cannot be the ratio of (frequencies) for wholetone to semitone, but rather its logarithm (log2).  Am I missing something?
: It's not even the logarithm of the ratio, but the ratio of the logarithms. —Tamfang (talk) 00:11, 23 October 2011 (UTC)
thread_title:  Difficulties following argument; missing thummer.jpg 

message: I came to this article because I read of an organ being a mean-tone organ, and I wanted to find out what that meant. I read the introduction and attempted the rest of the article, and I still don't know what it means. Is there anyone who could rewrite the introduction so that it's understandable by non-experts? Thanks.
G (talk) 09:19, 14 July 2012 (UTC)
replies: text: Do you understand what musical temperament is for? (That's the first link in the intro.) —Tamfang (talk) 15:05, 14 July 2012 (UTC)
thread_title:  But what is it? 

message: Early in the article, one can find the following utterly puzzling (IMO) statement:
:[Meantone temperament] by choosing an appropriate size for major and minor thirds, tempers the syntonic comma to unison.
This not only is not true, but it also is meaningless. I vainly tried, since quite a long time, in many discussions either on WP or elsewhere, to eradicate this strange idea. I won't correct the article because I know that well-intentioned contributors would soon revert my correction, but let me at least explain here why such an idea is incorrect and silly.
All temperaments ever documented result from a tempering of the fifths. Meantone temperaments temper the fifths to less than pure (i.e. less than the 3:2 ratio of Pythagorean tuning) or, if one wants to exclude equal temperament from the set of meantone temperaments (I can see no reason to do this, but ...), they temper the fifth to less than the ET-tempered fifth.
Doing so has the explicit purpose of producing better major or minor thirds, or both. The syntonic comma is, by definition, the difference between the pure major third and the Pythagorean one, or the pure minor third and the Pythagorean one – the syntonic comma corresponds to 81:80 in both cases. Meantone temperaments always result in lessening this difference. None, however, achieves this by tempering the syntonic comma itself, once again only the fiths are tempered.
1/4-comma meantone is that which makes the major third pure (ratio 5:4): the syntonic comma that separates the major third from the Pythagorean one vanishes in this case. The minor third of 1/4 comma-meantone, on the other hand, is only 3/4 of a syntonic comma larger than in Pythagorean tuning. In other words, the 1/4-comma meantone makes the syntonic comma vanish for the major third, but retains 1/4 of the one of the minor third. 1/3-comma meantone, similarly, makes the syntonic comma of the minor third vanish but, as a result, produces a major third 1/4-comma lower than pure: obviously, the syntonic comma of the major third does not vanish.
Other meantone temperaments produce various results for the intervals between the major and minor thirds and their Pythagorean equivalent. None of them, however, is able to make any of these two intervals vanish – it would be utterly impossible to make both vanish in any regular temperament. (Irregular temperaments might make the interval vanish for some major thirds and some minor ones, but never for all of them.)
Tempering an interval means reducing (or widening) it to obtain a desired effect. Once again, all meantone temperaments reduce (temper) the fifths in order to obtain better thirds: pure fifths (3:2 ratios) are lessened to an interval which cannot be expressed in the form of a ratio. The syntonic comma, by definition, corresponds to the ratio 81:80. Diminishing this ratio transforms it in another interval that can no more be said a syntonic comma (no more than a tempered fifth can be said to be a pure one). Therefore, to claim that "the syntonic comma is tempered" is meaningless: first of all, which syntonic comma? and, in addition, if the interval is tempered, it is no more a syntonic comma...
What the statement quoted above means is this:
::[Meantone temperament] by choosing an appropriate size for major and minor thirds, creates an interval between them and their Pythagorean equivalent; 1/4-comma meantone produces major thirds a syntonic comma away from their Pythagorean equivalent, 1/3-comma does the same for the minor thirds. 
Meantone temperaments, in brief, create an interval between their thirds and the Pythagorean ones, an interval which is some cases may reach a full syntonic comma (or more) — is that "tempering to unison"? Am I making all this more or less clear? — Hucbald.SaintAmand (talk) 21:20, 8 August 2016 (UTC)
replies: text: 816-792 = 24 cents! The difference between the Pythagorean A♭ and the Pythagorean G♯ by definition is the Pythagorean comma. Values in the image are rounded up to integral figures; because of the rounding up of the values 816 and 792, the Pythagorean comma (23.4600) appears here as 24 cents, while the syntonic comma (21.5062) is rounderd up as 22 cents (316-294 or 408-386). There is no doubt that the comma that is labelled "Pythagorean" in the image is the Pythagorean comma. Hucbald.SaintAmand (talk) 13:47, 31 May 2017 (UTC)
replies: text: I couldn't stand it any longer and I removed the "tempering of the comma to unison". The reason why should be clear from the comments above. We'll see how long the change lasts before it is once again modified... — Hucbald.SaintAmand (talk) 14:03, 31 May 2017 (UTC)
replies: text: Well done!  It hasn't come back yet, thank goodness. :-)  yoyo (talk) 19:54, 21 March 2018 (UTC)
replies: text:  "I would also suggest that the comment about wolf intervals being an artifact of keyboard design be removed too..." I second this, as I believe it's just plain wrong.  The Wolf also doesn't depend on the number of notes in the scale.  Any finite scale will have tempering issues in reconciling P5s and P8s.Unhandyandy (talk) 15:52, 5 September 2018 (UTC)
replies: text:  As the person who added the section of the article that discusses the "wolf being an artifact of keyboard design" (in 2009) I vote against removing it. Having fewer note-controlling elements per octave makes the wolf more salient; having more, makes the wolf less salient. The number of notes per octave is a design choice. Hence, the wolf is an artifact of keyboard design.  --JimPlamondon (talk) 10:04, 7 May 2020 (UTC)
thread_title:  Tempering the syntonic comma to unison??? 

message: The article writes:
:"On the other hand, the piano keyboard has only twelve physical note-controlling devices per octave, making it poorly suited to any tunings other than 12-ET."
The keyboard in question was invented centuries before the piano and therefore hardly can be described as the "piano keyboard".
Meantone temperaments were devised for keyboard instruments. I cannot figure how keyboards were "poorly suited" to meantone temperaments, but these (the temperaments) obviously were suited to them (the keyboard instruments).
As a historian of music theory, I find quite irritating the way in which some today rewrite the history. Hucbald.SaintAmand (talk) 08:01, 5 December 2016 (UTC)
replies: text: "Temperament is especially important for keyboard instruments"
Hucbald.SaintAmand (talk) 08:16, 5 December 2016 (UTC)
thread_title:  Keyboard poorly suited to meantone??? 

message: Having recently completed a major revision to Wikipedia's Dynamic Tonality article -- which I encourage the followers of this page to review -- I have recently started updating other articles to refer to it and/or incorporate some of its content (e.g., its explanatory videos). The meantone article is an early beneficiary/victim of this process. I look forward to the inevitable debate over its beneficiary/victim-hood. Such debates are inevitable whenever a new paradigm arises, and serve to improve the content, explanation, and rate of adoption of the new paradigm. 😊 JimPlamondon (talk) 07:02, 8 June 2020 (UTC)
thread_title: Dynamic Tonality paradigm

message: To add to this article: mention of sixth-comma meantone. Why isn't it already included here? 173.88.246.138 (talk) 14:09, 24 January 2021 (UTC)
replies: text: Should the article mention all sorts of meantone temperament? There are many, among which 1/6-comma is not so notable. Sorge mentioned it in 1748 as one of Silbermann's temperaments, and it has been described in France in 1758 as an approximation of the division of the octave in 55 intervals. That's all, so far as I know, and the practical purpose of this temperament remains unclear. — Hucbald.SaintAmand (talk) 17:55, 25 January 2021 (UTC)

text: 1/6-comma meantone is mentioned in the table in the  Meantone temperaments subsection. What do you mean when you say that it "compromises" between the minor 3d and the 5th? The 5th in 1/6-comma meantone by definition is narrowed by 1/6 of a comma, i.e. about 4 cents, and the minor 3d is widened by 3/6 = 1/2 of a comma, about 12 cents. In what sense does that "compromise"? And how do you tune it? It would involve tuning the tritone a comma narrower than the Pythagorean one, but how does one do that? — Hucbald.SaintAmand (talk) 10:30, 1 January 2022 (UTC)
thread_title: To add to article

message: With its uniform sequence of half-steps, an equal-tempered instrument can start anywhere in the instrument’s range, and make, starting from there, any scale that uses its half-steps.
Likewise with a scale gotten from the Pythagorean sequence of 5ths (product of factors of 3/2) and frequencies gotten by multiplying or dividing those by two.   …except that somewhere there must be a discontinuity because the 3/2 factor of those 5ths doesn’t multiply to something evenly divisible by two. But, other than, aside from, that one discontinuity,  a Pythagorean instrument, like an equal-tempered instrument, can start anywhere in the instrument’s range and make the same Pythagorean scale.
Like an equal-tempered instrument, a Pythagorean-tuned instrument doesn’t achieve the Just scale’s harmonious intervals. Equal Temperament & Meantone Temperament improve the Pythagorean’s 3rds, by compromising the 5ths.
Meantone temperament merely differs by adjusting the 5th’s 3/2 by a factor that fixes or improves the 3rds.
The ¼ comma is the 4th root of the factor by which the Pythagorean major 3rd differs from the true (Just) major 3rd.
The 1/3 comma is the 3rd root of the factor by which the Pythagorean major 6th differs from the true (Just) major 6th.
The 1/6 comma is the square-root of the 1/3 coma.
In the sequence of 5ths,  adjusting each 5th’s 3/2 (in the appropriate direction) by one of the above factors will make the following improvements in the 3rds:
¼ comma:  Will make the major 3rds true.  (because the major 3rd is gotten from a product of four factors of 3/2)
1/3 comma: Will make the major 6ths (& therefore the minor 3rds) true.  (because the major 6th is gotten by a product of 3 factors of 3/2)
1/6 comma: Will compromise between the minor 3rd & the 5th.
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I'll comment inline on what you say below:
:The above has shortly been added on top of the article itself. This addition was removed by Jonesey95, and rightly so, I think. The above appears to attempt a description of what a "regular" temperament is, i.e. a temperament with all fifths equal, unless for the wolf fifth (if any).
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It was more than attempt. It was a description of the generation of Meantone Temperament...three of them in particular. Of course I didn't mention the much less familiar term "regular temperaments", and there was no need to.
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:But the wolf fifth does more than merely add a mere "discontinuity". It results in that any music played, because it should not involve the wolf fifth, should not exceed the range of (usually) 12 notes, say from E to G, in the order of the cycle of fifths. A regular temperament allows pieces to "start anywhere in the instrument's range" only if they do not exceed that range. But that means that pieces transposable by one fifth must not exceed 11 notes of the cycle, pieces transposable by two fifths must not exceed 10 notes, etc. This is a very strong restriction. It applies in all regular temperaments, including meantone temperaments; ET is the only one to escape it. 
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Yes, I intended to tell only a brief motivation & procedure for generating Meantone Temperaments. I didn't want to lengthen the section by talking about the problems. But yes, you're right--I shouldn't say that a scale can be started anywhere in the instrument's range. I should have qualified that by mentioning that the choice of where a scale or piece can be played is limited by the need to not use the wolf-note resulting from the discontinuity.   ...and by the need for more accidental-keys than might be feasible on the keyboard. So yes it isn't literally true that a piece can be played starting anywhere in the instrument's range, and something about that should probably be said in that brief introductory description (which the article needs).
But Meantone Temperament does achieve something in that direction, by making a variety of keys available, and sounding a lot better than Equal Temperament in some keys.
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Discussing all this may find its place in the Regular temperament article better than here.
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No. It belongs in the Meantone Temperament article. Meantone Temperament is the term that people look-up.  ...and it belongs at the top of the article.
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:As to comparing meantone temperaments in terms of "factors," I am not sure to understand what that means. 
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A factor is one of at least two numbers to be multiplied together. That's what that word means in mathematics.
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To say, for instance, that "The ¼ coma is the 4th root of the factor by which the Pythagorean major 3rd differs from the true (Just) major 3rd" seems to me unduly complex. 
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But without saying that, it's quite impossible to say what Meantone Temperament is.
It isn't possible to avoid some mathematics when explaining how Meantone Temperament is generated. But anyone who wants to find out what Meantone is, and how it was made, will expect to, & be willing to, read a little mathematics.  ...because it's unavoidably a mathematical matter.
You want unduly complex???  :D  Just look at the current article's pretentious, over- technical, pseudoscientific language, full of undefined terms & symbols.
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The syntonic comma (with two m's!) 
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The section was deleted after I fixed the spelling.
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You said:
The syntonic comma is the interval between a pure third and the third obtained by four pure fifths (or fourths). Therefore, diminishing each of these fifths by ¼ comma will yield a diminution by a full comma after four fifths, so reaching a pure third. In this, "¼ comma" merely means the 4th part (¼) of a comma, and I don't see that "the 4th root of the factor [etc.]" in any way simplifies this description
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You're speaking in terms of logarithmic measure. But when we're talking about ratios (like 3/2), it's simpler to not bring in logarithms. A sequence of four 5ths means that four 3/2 factors are multiplied together. 
Meantone Temperament is about ratios, and, instead of obscuring that by logarithmic-measures, the subject is clearly & simply explained by ratios & factors of 3/2.  Don't lose the clarity by muddying it with logarithmic-measures.  — Preceding unsigned comment added by 97.82.109.213 (talk) 01:03, 15 June 2021 (UTC)
replies: text: It might be that the description above is more rigourous (it really depends in what terms the comma is defined, in frequency ratio, 81:80, or in logarithms, ~22 cents), but it seems to me certainly less understandable. 
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So you think logarithms are more understandable to most people? Of course it's universal & unavoidable to speak of logarithmic measures like cents, and ET half & full steps. But to tell the mechanics, it's clearer, simpler & better to speak of a 5th as a factor equal to 3/2, to tell what's really going on.
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The fact is that ¼ comma meantone was described under this name at a time when neither the idea of "4th root" on the one hand, nor that of logarithms on the other hand, already were in existence. That it was described in terms of "¼" merely evidences an intuition of what logarithms would be – the same intuition makes this description more understandable today for people who really figure out neither "4th roots", nor "logarithms."
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But if you speak 1/4 of the syntonic coma, without clarifying that you're talking about logarithmic-measure, then you're deceiving the reader. You're not doing her/him any favor. And if you bring up logarithmic-measure, you're complicating the explanation.
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 And, once again, this discussion should better appear in the Regular temperament article 
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When people want to find out where Meantone Temperament comes from, they look up Meantone Temperament, not Regular Temperament.
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(which I also find hardly understandable, but that's another problem). — Hucbald.SaintAmand (talk) 19:36, 14 June 2021 (UTC)
replies: text: I removed the text because it was malformatted, unsourced, and in the wrong place in the article, not for any content-related reasons. – Jonesey95 (talk) 21:34, 14 June 2021 (UTC)
thread_title:  Proposed, very brief, improvement & replacement for the article 

message: Maybe about 40% of this article seems to correspond to a fringe theory by user JimPlamondon. This is against wikipedia's philosophy, as you can see here. In the fringe theories page. This has nothing to do with whether I agree or disagree with this theory, it is an objective fact that this is not broadly supported and as such should be deleted. Wikipedia is not a place for promoting your own theories, it should reflect what is broadly acceped in a field, there are many other websites that can be used to promote or support this research.
In a nutshell, as my reference states: To maintain a neutral point of view, an idea that is not broadly supported by scholarship in its field must not be given undue weight. I don't think this deserves extra discussion, and JimPlamondon's own comments on the matter make this very clear. I will procede to delete everything associated with Dynamic Tonality IgnacioPickering (talk) 23:52, 17 July 2021 (UTC)
replies: text: Let me stress, in addition, that there exists a Dynamic tonality article that says all what WP readers might want to know (and even more). A link to that article might prevent further discussions. There also is a Quarter comma meantone article, with which this one at times is redundant. I wonder whether the present article could not be renamed "Meantone temperaments" (plural), leaving details about specific meantones to specific articles. — Hucbald.SaintAmand (talk) 09:17, 18 July 2021 (UTC)
thread_title: Remove everything related to Syntonic Temperament and Dynamic tonality

message: It has become customary to refer to any regular temperament with better thirds than equal temperament as meantone. However, as far as I can tell, this is modern terminology. Contrary to what is often claimed (without clear citations from sources), I am not aware of any historical sources that use this term other than for the 1/4 (syntonic) comma tuning. The historical concept seems to be clearly based on the fact that the whole tone (logarithmically) is the average of the major and minor whole tone from a pure tuning. To base the definition on the fact that a whole tone is half of a major third seems rather pointless to me for two reasons.
First, this terminology does not imply a delineation between temperaments with better thirds than equal temperament (as is meant in common usage). What then is this limitation based on, and why would just this term have come into being for this subset of regular temperaments? Especially as a delineation from the traditional pythagorean tuning, this definition of "meantone" is inadequate!
And second, what does "mean" mean if we don't assume well-defined different whole tones with simple string length ratios? However, these exist only in simple mathematical systems, such as pure tunings (which does not exclude that such intervals can also occur in some temperaments, but there they do not constitute a theoretical basis for the definition of a certain kind of whole tone). Therefore, also linguistically, the term "meantone" does not seem to be the most obvious designation for the notion of a "semi-(major)third".
Since I don't pretend to have read all possibly relevant historical sources, my first question to the other participants in this talk page is therefore: can you provide me with historical sources for the use of the term "meantone" in the currently common sense of a general third-oriented regular temperament?
And if not, shouldn't we make it clear in this article that the definition that in fact includes a whole range of regular temperaments is a modern definition that differs from historical usage?
I have no fundamental problem with unhistorical definitions if they describe a meaningful modern concept. However, we must be aware that the use of a historical term that does not (or worse, only partially) correspond to the historically associated concept has the serious disadvantage of causing confusion. Therefore it should then be clearly communicated. There are enough shaky theories circulating in the early music world that have more to do with the interpretation of some performers than with the sources. If these lead to a good musical result in practice, I have no problem with that. However, we should not ascribe to them a historical authority that they cannot pretend to have.
Koos van de Linde  — Preceding unsigned comment added by Niehoff54 (talk • contribs) 11:29, 26 January 2022 (UTC)
replies: text: Meantone temperaments other than the quarter-comma meantone have been documented since the 16th century, even if they may not have been called "meantone". Zarlino mentioned tempering the fifths by 2/7 comma in his Istitutioni harmoniche (1558), chapter 42, pp. 126-127. Salinas describes three methods of obtaining equal tones (vt Toni æquales fiant), namely 1/3 comma, 1/4 comma and 2/7 comma, in De musica, Book III, chapter XV (pp. 143-145). Both call the major third ditonus, which stresses its being made of two [equal] tones. (Ditonus comes from the Greek ditonos, of course, and Pythagoreans in Greek antiquity already were aware that the Pythagorean third also was a ditone.) Several other divisions of the syntonic comma were discussed in the 17th and 18th centuries: 1/5, 2/9, 3/10, 5/18, 1/6, 1/7, 1/8, 1/9 and 1/10, always coming closer to 1/11 (i.e. 1/12 Pythagorean comma) that would produce equal temperament. The authors of these descriptions were aware that these divisions produced major thirds formed of two equal tones. These temperaments may not have been described as "meantone" – determining this would involve a lot of checking. Ellis makes an abundant use of the term in his translation of Helmholtz' Tonempfindungen, but Helmholtz himself never names that temperament. I am not even sure that 1/4 comma meantone ever was so called before the 19th century. What other name would you suggest?  — Hucbald.SaintAmand (talk) 14:25, 26 January 2022 (UTC)
replies: text: @Koos van de Linde, on second reading of your message above, I realize that you worte that you are "not aware of any historical sources that use this term [meantone] other than for the 1/4 (syntonic) comma tuning." If you are aware of historical sources that do use it for 1/4 comma temperament, I'd be genuinely interested. I think to have read that Sauveur did, but was unable to find in Sauveur nor it in his writings (I suppose that the French term would have been ton moyen, nor in any of the French treatises that I have). In German, Mittelton has been used in discussions of enharmonies, or also to denote the third (Mediante) as dividing the fifth in a triad, etc., but not, that I am aware of, for temperaments – neither Helmholtz, nor Riemann, nor Brokhaus, use it in that meaning. — Hucbald.SaintAmand (talk) 15:04, 26 January 2022 (UTC)
thread_title:  The definition of ‘Meantone’ 

message: The caption on the diagram comparing the various temperaments is way too long. If the diagram can't be explained in a few sentences, it's probably not of any value to our readers. Half of the caption is just pointing out various spots on the diagram, which, if they are notable, should be expressed in the diagram itself. I'm going to boldly chop off a huge chunk of the caption and see how that works. Orange Suede Sofa (talk) 00:10, 18 August 2023 (UTC)
thread_title:  Diagram caption 

message: The term "major tone" is wikilinked to major second, which does NOT explain what a (just) major tone is: 9/8.  In the given context, which explains the term "meantone" as a mean between a major tone and a minor tone (i.e. 10/9), we had better not confuse the readers with the major and minor seconds of scale construction.  If there's a Wikipedia entry that explains "major tone" accurately, let's wikilink to that instead. yoyo (talk) 22:01, 15 October 2023 (UTC)
thread_title:  Major tone and minor tone