Talk:Leading-tone

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Diatonic and chromatic[edit]

The article uses the term "diatonic" without adequate explanation. This term, along with chromatic, is the cause of serious uncertainties at several Wikipedia articles, and in the broader literature. Specifically in this case, the leading note in the harmonic minor is not under discussion at all, if we assume that scale not to be diatonic. Some of us have thought that both diatonic and chromatic need special coverage, so we started up a new article: Diatonic and chromatic. Why not have a look, and join the discussion? Be ready to have comfortable assumptions challenged! – Noetica♬♩Talk 05:40, 6 April 2007 (UTC)[reply]

Reqaudio[edit]

I added one audio example to the article. Hyacinth (talk) 22:34, 22 July 2008 (UTC)[reply]

Cleanup[edit]

Unclear citation style[edit]

Why, what, where, and how does this article have an unclear citation style and what should be done about it? Hyacinth (talk) 12:13, 16 August 2011 (UTC)[reply]

Tag removed. Hyacinth (talk) 00:19, 19 March 2012 (UTC)[reply]

Tone[edit]

Why, what, where, and how does this article's tone and voice need to be made more consistent with the rest of Wikipedia? Hyacinth (talk) 12:13, 16 August 2011 (UTC)[reply]

Tag removed. Hyacinth (talk) 00:19, 19 March 2012 (UTC)[reply]

Proposal to unify the layout of scale-degree pages[edit]

WikiProject Music Theory is spearheading a proposal to unify the layout of the scale-degree pages. The discussion can be found here. Since these pages not only include discussion of the scale-degrees, but also occasionally discuss triads and seventh chords built on these scale-degrees, it is important to systemize these pages. This will also curtail the creation of pages for each individual triad and seventh chord, some which may not necessarily contain enough content to be expanded beyond a stub. I invite you to comment on the proposal with thoughts, criticisms, or suggestions. Thanks! Devin.chaloux (chat) 19:07, 18 March 2012 (UTC)[reply]

B and C as example[edit]

It is not the best example. G# and A is a better example. Qwertyxp2000 (talk) 06:17, 8 August 2014 (UTC)[reply]

Why?—Jerome Kohl (talk) 16:03, 8 August 2014 (UTC)[reply]
I assume it's because of the accidental. Hyacinth (talk) 09:17, 3 August 2017 (UTC)[reply]

Hyphen[edit]

Does anyone know why the title is hyphenated? I've only seen it as two words with no hyphen. Squandermania (talk) 21:02, 4 November 2018 (UTC)[reply]

Upper leading tone[edit]

The article, in its section on the upper leading tone, describes the resolution of the dominant seventh (scale degree 4scale degree 3) as an upper leading tone. It seems to refer to Bernward and Saker on this point, but they certainly do not describe the example quoted (Scott Joplin) as a case of upper leading tone. They specifically say that the leading tone leads to the tonic, but never mention the upper leading tone (in the 2008 edition, at least). The article also later seems to refer to Kotska (which I don't have), associating his mention of "tendency tones" with the "upper leading tone scale degree 4", but I strongly doubt that Kotska associates the two.

I never encountered the expression "upper leading tone" applied to the resolution of a dominant seventh, nor to any degree other than scale degree 2 (usually scale degree 2, but not always). The case is all the more annoying that a reference to this section has been added in the Voice leading article, about the resolution scale degree 4scale degree 3. Has anyone ever encountered this expression applied to scale degree 4? — Hucbald.SaintAmand (talk) 09:26, 5 November 2018 (UTC)[reply]

I cannot recall ever seeing it applied to scale degree 4, but I have seen it applied to scale degree 6. At the moment, I cannot think of a reliable source, but I am sure that one can be found.—Jerome Kohl (talk) 18:56, 5 November 2018 (UTC)[reply]
In Kotska, he refers to it as a "tendency tone". I've never heard of a scale degree 4 referred to as an upper leading tone either – it struck me as strange, too. I don't have Benward and Saker, but unless you it's not actually in Benward and Saker or there are sources that dispute it, I can't see a reason to remove/change it. Squandermania (talk) 20:28, 5 November 2018 (UTC)[reply]
The expression "upper leading tone" is not found at all in Benward and Saker (if I can trust my OCR). About the Scott Joplin and other examples, they write "Note that although the chord sevenths resolve downward, the leading tones resolve upward".
I have no problem accepting that the 7th in a dominant seventh is a tendency tone – but certainly scale degree 4 is not a tendency tone in all cases. And a tendency tone is not the same as a leading tone. The example from the Waldstein in the article shows what has been termed a "secundary leading tone", and this in turn might justify scale degree 6 as a "secundary upper leading tone". But to assume that scale degree 4 may be an upper leading tone, one would have to accept scale degree 2 as a lower leading tone to scale degree 3 (as the article in its present version seems to imply, when it says "The lower and upper leading-tones, scale degree scale degree 7 and scale degree scale degree 4, [...] have a tendency to move to [...] scale degree scale degree 1 and scale degree scale degree 3, respectively") – and to assume that the 7th in a 7th chord is an upper leading tone would lead to consider that any degree can become an upper leading tone. This seems to me utterly farfetched.
It might be more interesting to mention that, in German – and particularly in Schenker –, even scale degree 2 (not scale degree 2!) is considered an upper leading tone. In a Schenkerian Urlinie, scale degree 2 is for Schenker an upper leading tone; but it is not a tendency tone.
You made this problem apparent when you added a link to upper leading tone in Voice leading, because you added this link at a point concerning the resolution of 7ths. There is an additional problem in the present article, in that the example showing the tritone substitution has a C above D, instead of B, which at first reading appeared to me an example of parallel 7th, while it really is an example of augmented 6th. Something must be done about all this, in my opinion, and I'll do so as soon as we aggreed. I very strongly doubt that any serious source could be found describing scale degree 4 as an upper leading tone. — Hucbald.SaintAmand (talk) 21:35, 5 November 2018 (UTC)[reply]
If they don't mention upper leading tone in Benward and Saker, then it should definitely be deleted. Does it have the "Maple Leaf Rag" example on p. 203? This was added in 2010 (https://en.wikipedia.org/w/index.php?title=Leading-tone&diff=363386993&oldid=363386689&diffmode=source) and was clearly referring to the 7th of a dom7 resolving as an example of an upper leading tone. If it's not in the citation and seems wrong, you should definitely delete that.
I'm not as sure about the tritone resolution example because jazz theorists sometimes use words differently than Classical theorist. You could certainly call it an augmented 6th but a jazz theorist would definitely call it a tritone substitution. It doesn't have a citation, so I would normally just stick a [citation needed] on it and wait a few months before deleting it. I have Mark Levine's Jazz Theory Book and I couldn't find "upper leading tone" in it.
You could also add to the upper leading tone section by adding some Schenkerian ideas to it as well. It would be good to have some verified information on the topic. :) Squandermania (talk) 18:46, 7 November 2018 (UTC)[reply]
I have a later edition of Bernward and Saker. They definitely give the Maple Leaf Rag example, but the page number is different (I should check). And it is about that example that they say what I mentioned above, "Note that although the chord sevenths resolve downward, the leading tones resolve upward". The example will have to be removed, anyway, so that the page number does not matter.
The Schenkerian informations that I give are always verified: I am a compulsive reader of Schenker ;–)). But I think that the expression "upper leading tone" applied to scale degree 2 is common in German, not specifically Schenkerian. I have to check that.
While working on an analysis of Debussy's La fille aux cheveux de lin, I discovered that this WP article mentions "plagal leading tones" and links about these to our Leading-tone, where the term is nowhere mentioned. It also refers to an article by J. Day-O'Connell, which I read. Day-O'Connell probably coined the expression, which is worth quoting in our article.
I'll do all that, but I am somewat too busy with other things just now. — Hucbald.SaintAmand (talk) 21:23, 7 November 2018 (UTC)[reply]
I deleted the sentences about the seventh of a seventh chord resolving down. Squandermania (talk) 22:26, 7 November 2018 (UTC)[reply]

Given Escribano Lamentation example score with trill [as at 13 June 2021][edit]

Cadence featuring an upper leading tone from a well known 16th-century lamentation, the debate over which was documented in Rome c.1540.

Hi everyone, It seems to me that the score example has a trill from C# to D#. While enharmonically the D# is the same as E flat, it doesn't seem to me to be an example of an upper leading tone, which would have the main melodic line going from E flat to D. I suggest perhaps a different example might be better.Fh1 (talk) 15:06, 12 June 2021 (UTC)[reply]

Which sound file are you referring to? File:Escribano - Lamentation, upper leading-tone cadence diatonic.mid or File:Escribano - Lamentation, upper leading-tone cadence.mid, or both? In any case, we should ping User:Hyacinth who created those. -- Michael Bednarek (talk) 02:08, 13 June 2021 (UTC)[reply]
Hi Michael Sorry I meant the one that links to: https://upload.wikimedia.org/score/o/6/o6edxpqjxyxmltdfxqmnpfjrk6jmmqs/o6edxpqj.png
i.e. the one with four staves in D minor.
By the way User:Hyacinth if you're reading this, I've enjoyed seeing all your examples in music theory articles! :) Fh1 (talk) 11:17, 13 June 2021 (UTC)[reply]
That score was entered by User:Squandermania on 5 November 2018 as a LilyPond transcription of File:Escribano - Lamentation, upper leading-tone cadence.png which was originally uploaded by Hyacinth. I agree that it doesn't seem to show a downward leading-tone. -- Michael Bednarek (talk) 13:30, 13 June 2021 (UTC)[reply]
What might be considered a downward leading-tone in this example is the progression E–D in the tenor. Schenker certainly called this an abwärtssteigende Leitton (see Kontrapunkt I and II, passim, or Der freie Satz, § 10, 1935 p. 34, 1954 p. 43), a "descending leading tone," especially in a contrapuntal context. In Free Composition, § 10, p. 13, John Rothgeb felt compelled to add a footnote: "In German theoretical writings the second step of the scale is sometimes rererred to as der abwärtssteigende Leitton, litterally 'the descending leading tone'" – from which one may deduce that he considered the expression unusual in (American) English. A Google search for "descending leading tone" gives about 999 results, however. So, the example does show a downward leading tone, but it should at least say where. In addition, any perfect cadence also has a downward leading tone, there is nothing special about this particular example. I will leave it to others to decide wether the example should be removed, or kept with more detailed explanation. — Hucbald.SaintAmand (talk) 08:50, 14 June 2021 (UTC)[reply]

It seems that the distinction needs to be made or clarified between the motion of a leading tone and the position of the leading tone in relation to the tone it leads to. A leading tone which moves upwards may be called "an upper leading tone", as may a leading tone which is above the tone it leads to, even those are opposites, and the terminology used in the literature and scholarship regarding leading tones. Hyacinth (talk) 09:08, 14 June 2021 (UTC)[reply]

I agree with Hyacinth that the expression "upper leading tone" is unclear. I think that "descending leading tone" is clearer. And I note that Michael Bednarek added a mention of where the descending leading tone is to be found in the example. There are aspects that remain unclear to me, though:
  • Why does the caption not say that this example if from Juan Escribano's Lamentations du prophète Jérémie?
  • Why does it say that "the debate over which was documented in Rome c.1540," while the debate in question did not concern what is shown in the example? (The debate was about whether the B in the bass should be sung earlier, where it is not formally written. There are indeed two B's in the bass in the measures preceding those represented here, and a debate arose c.1540 about whether these should be made flat by musica ficta – which would have resulted in unsolvable conflicts with the upper voices. See [1] for a detailed discussion.) I have been unable to check the reference given to Berger 1987, but I presume that it concerns this debate, and in no way the presence of a descending leading tone in the cadence.
  • Why is it this particular example that is given here, while many examples of a V–I cadence similarly would show a descending leading tone? There is such a leading tone, G–F, in the top part of the example in the Function subsection, for instance. There are two (both F–E) in the examble illustrating the Voice-leading subsection. (No, I wrote too fast, the descending F–E are scale degree 4scale degree 3, which should not be considered cases of descending leading tone). And there are two less visible ones (both D–C) in the example from Beethoven's Piano sonata n. 5 in the Leading-tone seventh chord section.
Hucbald.SaintAmand (talk) 11:14, 14 June 2021 (UTC)[reply]
  • @Hucbald.SaintAmand: Thanks for sending that link about the papal choir debate: interesting reading! From looking at the link:
  • it seems the descending leading tone then, is not E natural to D in the tenor, but B flat to A in the bass. And it's quite a nice example of a descending leading tone (Thanks Hyacinth and Squandermania!)
  • The sharp above the stave is not referring to the upper note of a trill as I (and probably others) previously imagined, it's a musica ficta sharp, and it's not a trill at all.
  • So what we probably need then is for a single audio examples with no trill (and no D#) in the top stave, and perhaps the example to be put in modern notation (i.e. the sharp in front of the C, perhaps in square brackets to show it's editorial)? Fh1 (talk) 17:02, 20 June 2021 (UTC)[reply]
@Fh1: This example is not particularly known as an example of descending leading tone, and I remain puzzled that it was chosen as illustration here. Everyone is free, of course, to call "leading tone" what they want, but I at least would link the idea of leading tone to that of cadence. With this in mind, B–A could not be a leading tone, because there is no cadence on A (which obviously is a dominant). It seems to me, therefore, that even if some might consider B–A an example of descending leading tone, it would form a very bad example for this WP article, as the whole remains highly questionable.
I had not listened to the sound examples (I feel the score itself so much better than Midi sound), but the two c of course are sharpened by musica ficta and the idea that the denote d is of course incorrect. I think that the best solution would be to remove this example completely. — Hucbald.SaintAmand (talk) 17:36, 20 June 2021 (UTC)[reply]
Hello @Hucbald.SaintAmand:, I think we should definitely remove or replace the two sound examples, as they include a trill, which is wrong in both of them (as it isn't a trill). The one with a trill from C# to D# is doubly incorrect, as D# was never intended by the composer (as the sharp refers to the C)! I may create a correct version if I ever get time!
I think the criteria for a descending leading tone doesn't really depend on whether there's a cadence (compare: the seventh scale degree in major is still the leading note even when it's not near a cadence).--Fh1 (talk) 00:06, 1 September 2021 (UTC)[reply]
@Fh1: Well, this is a complex case. The article claims that scale degree 6scale degree 5 could be a leading tone, but this rightly is marked as needing a citation: I for one am not familiar with that usage. As I already wrote above, there is a descending leading tone (in Schenker's sense) in the last two measures of the example, E–D, scale degree 2scale degree 1 in the tenor , but the same could be found in any perfect cadence. To quote this particular case of scale degree 6scale degree 5 as an example of descending leading tone seems to me rather misleading, especially in view of the discussion c1540 whether B needed a flat or not. What we need is an example of a clear Phrygian cadence; this particular example is not clear in this respect — Hucbald.SaintAmand (talk) 08:38, 1 September 2021 (UTC)[reply]

Leading tone triad[edit]

In the section about the leading-tone triad, one reads the following statement followed by an example:

In C major and C minor, it is a B diminished triad (though it is usually written in first inversion, as described below)

I don't know to what "as described below" refers, but certainly not to the example which shows triads in root position. The example should be redone, with triads in first inversion, because as it is it shows something that even a first-year student would not write. Triads in root position cannot follow each other, even when the first is a diminished triad. In first inversion, parallel chords are fully acceptable. — Hucbald.SaintAmand (talk) 13:39, 8 November 2018 (UTC)[reply]

@Hucbald.SaintAmand: What example needs, or needed, to be redone? I assume an image no longer present. Hyacinth (talk) 09:23, 14 June 2021 (UTC)[reply]
@Hyacinth: Indeed, the example does not seem to be there anymore (it must have been an example with chords in root position and parallel voice leading, resulting in parallel fifths – never mind). As to the mention of "written in first inversion, as described below", the description is in the "Voice-leading" subsection. It might be better to link to it, but I don't immediately see how to do it. — Hucbald.SaintAmand (talk) 10:23, 14 June 2021 (UTC)[reply]

What is a leading tone?[edit]

The usual represented interpretations of leading tones are not compatible with the laws of nature. Perceptions of striving forces in tones are impossible and not even imaginable. However, there are leading tones. Here I insert two links to articles that provide a realistic understanding of leading tones:
Academia: What is a leading tone?
Prezi: What is a leading tone? — Preceding unsigned comment added by 2A02:8071:3E81:9900:659D:6D32:B2B6:6A46 (talk) 07:42, 1 April 2020 (UTC) --2A02:8071:3E81:9900:659D:6D32:B2B6:6A46 (talk) 07:45, 1 April 2020 (UTC)[reply]

Two links, but to the same article, it appears. As a self-published blog, this does not seem to qualify as a reliable source. Can you offer something better?—Jerome Kohl (talk) 08:15, 1 April 2020 (UTC)[reply]

Here some links about the “Theory of Musical Equilibration” which provides a realistic understanding of leading tones:

Ukulele.Space

Operalively

Cycle Defrost

Prezi Ganguly

Prezi Ali

Music on Stage, P. 202ff

Music and Emotion in Cinema

A story through notes

Anita Sayar

An essay about happy memory songs

Music. The Vision of Humanities and Sciences --Willimek (talk) 12:41, 1 April 2020 (UTC)[reply]

Willimek, but a simple search shows that so to say none of the texts linked above contains the words "leading tone"! The only one that does is Music on Stage, but some of the statements that can be read there question the meaning that you give to "leading tone". For instance:

As a dominant minor ninth chord without a root, [the diminished seventh] contains the third, the minor seventh and the minor ninth as leading tones.

You seem here to consider that the 7th and the 9th above the root (the dissonances) are "leading tones", but that is not at all the definition given in our article. Do you consider that any note with an obligatory voice leading is a "leading tone"? This is a specific meaning of the German term Leitton. Even Riemann is quite clear about this, when he writes:

Leitton means a note that leads to another and creates the expectation of this other, particularly the note a semitone under the tonic (subsemitonium modi, French note sensible, English Leading tone), f. i. b in C major, f in G major, etc. The Leitton of this type always is the third of the [upper] dominant. (Musik-Lexikon, 1st edition, 1882, p. 516, my translation.)

Riemann makes it very clear in this that the French note sensible and the English Leading tone specifically refer to the 3d of the dominant, even if in German (or at least in his view), any note with an obligatory leading could be considered a Leitton. Our article makes a concession to the German usage when it speaks of the upper leading tone (Gegenleitton), but even that is not very common in English, I think – nor in French, for sure. And the case of 4 and 6 as dissonant 7th and 9th in the dominant minor ninth (with or without root) is a case of obligatory resolution of the dissonances, which is utterly different. — Hucbald.SaintAmand (talk) 13:56, 1 April 2020 (UTC)[reply]


266/5000 It is true that the articles often do not contain the term "Leading Tone" literally. But they contain the term "Theory of Musical Equilibration". And the "Theory of Musical Equilibration" is nothing more than a new meaningful definition of the leading-tone-effect.--Willimek (talk) 08:41, 2 April 2020 (UTC)[reply]

Is it not rather a theory of the Leitton effect? Are you sure that your understanding of that German concept is the same as our understanding of the American (or the French) one? Riemann, at least, indicates that the concept of Leitton is broader than that of "leading tone" or note sensible. I am afraid that such fine distinctions (you mention yourself "a new meaningful definition") belong to other discussions than what is possible on Wikipedia. — Hucbald.SaintAmand (talk) 16:08, 2 April 2020 (UTC)[reply]

The definitions of the terms "Leitton", "Leading tone" and "Note sensble" actually differ. The term “Leading tone” is broader than the term “Leading tone”. But I think the phenomenon it's about is the same thing, because Germans don't feel differently than Americans. The "Theory of Musical Equilibration" is also valid for the American understanding of "leading tone", that is, for the perception of the sound quality of the dominant third. In the English Wikipedia "Leading tone" there are also music theorists like Ernst Kurth mentioned who describe the sense of the leading tone as perception of a "force". Wolfgang Böhler, one of the best-known Swiss music psychologists, writes about the Theory of Musical Equilibration: "...It cannot be ruled out that the Theory of Musical Equilibration could make interesting contributions to explaining the expressiveness of music.[...]" Wolfgang Böhler --Willimek (talk) 09:23, 3 April 2020 (UTC)[reply]

Wolfgang Böhler: "Refering to Schopenhauer and Nietzsche, the authors create a theory that is intuitively difficult to understand and rather unsystematically infused with metaphor. [...] They do not say a word about historically influential Gestalt theoretical approaches, which would explain the directional energies of notes much more plausibly and naturally than their own approach. [...] It cannot be ruled out that the Theory of Musical Equilibration could make interesting contributions to explaining the expressiveness of music. To achieve this, however, it would have to be made much clearer and more systematic – docked onto already existing theoretical concepts and results of music psychology, with methodologically solid interfaces for experimental testing." (Einmal mehr: Musik und Emotionen, in Schweitzer Musikzeitung.)
Don't misundersand me, Bernd Willimek. I have known about your theory for years now, and I am aware that it could bring a complement to existing theories – including some that are also not mentioned in our article, and that apparently you don't know. See for instance Thomas Noll, Facts and Counterfacts (2005), Nicole Biamonte, Modal Function in Rock and Heavy Metal Music (2012) or Thomas Hedges, Advances in Multiple Viewpoint Systems and Applications in Modelling Higher Order Musical Structure (2017), etc., which all discuss harmonic progressions with leading tones, about which they provide new insights. Obviously, you are not the only one to have reflected on such progressions.
But I think that neither these theories nor yours should figure in a vulgarizing encyclopaedia such as Wikipedia. — Hucbald.SaintAmand (talk) 15:30, 3 April 2020 (UTC)[reply]
As a supplement to the leading tone discussion, I would like to refer to our paper recently published in the journal “Auditory, Perception & Cognition” (Taylor & Francis):
https://www.tandfonline.com/doi/abs/10.1080/25742442.2023.2185064
Here, a completely novel conception of the leading tone experience is defined, which also creates the possibility of understanding the emotional impact of musical harmonies. Perhaps this aspect should be taken up in the article. 2A02:8071:3483:6D80:6545:EE90:DE10:DE2E (talk) 07:54, 18 May 2023 (UTC)[reply]

The new representation of the leading tone phenomenon can also be found here: https://psyarxiv.com/g29xy/--2A02:8071:3483:6D80:CC5B:4BA1:CEBA:AAE6 (talk) 12:31, 26 May 2023 (UTC)[reply]

Notation? Reference needed![edit]

I am unfamiliar with the notation used throughout this article, e.g.,

A leading-tone triad is a triad built on the seventh scale degree in a major key (viio), while a leading-tone seventh chord is a seventh chord built on the seventh scale degree (viiø7). Walter Piston considers and notates viio as V0
7
, an incomplete dominant seventh chord (Goldman 1965, 17).

I read Template:Music, and while I mostly understand the use of the template to generate the notation, I blank on much of what its symbols refer to. There's no name or explicit reference to the symbol system — the article assumes that the reader is familiar with it: Not reliably true. Is this a standard notation, and is it described anywhere, either on WP or elsewhere? If so, it needs an explicit reference, preferably early in the text rather than buried in one of the many references.

I considered adding Template:No footnotes, but refrained because there are many inline Harvard-style references.

--Thnidu (talk) 19:10, 12 February 2021 (UTC)[reply]

This notation apparently is common in music theory teaching in the US (insofar as one still teaches tonal theory in the US). It is an adaptation of Gottfried Weber's usage, as illustrated here, and the presence of these signs in Template:Music confirms that people consider them common enough. I think that any music theorist reading English would be aware of them. The question that you implicitly raise is whether en.Wikipedia must be considered mainly American ... — Hucbald.SaintAmand (talk) 17:11, 14 February 2021 (UTC)[reply]
@Hucbald.SaintAmand: Thank you for that information. But it isn't (just) the geography of the readership that concerns me, but the type of readers. Your own words reveal the difference: "...people consider them common enough. I think that any music theorist reading English would be aware of them." Wikipedia is an encyclopedia, not a work on music theory, and as such the article should include, at the bare minimum, references to allow the general reader to learn about the notation.--Thnidu (talk) 15:03, 15 February 2021 (UTC)[reply]
@Thnidu: When I wrote that "people" consider them common enough, I was thinking of the guys who create templates for Wikipedia. I don't suppose that they are all music theorists. Would you think that anyone without any idea of music (and of some elementary music theory) be interested in what a "Leading-tone" is? Note also that the fragment of the lede that you quote always mentions in full the chord concerned, and adds the notation only in parentheses. You say that this notation is used "throughout the article", but it actually is used only rarely. Anyway, I added a link to Roman numeral analysis: I don't see what else one could do. — Hucbald.SaintAmand (talk) 18:28, 15 February 2021 (UTC)[reply]
@Thnidu: Sometimes music is like math in that if one does not know the name of a symbol or the name of the system of symbols it is a part of then one may have great difficulty attempting to look it up. However, Wikipedia is not a classroom, per WP:NOTHOWTO. I think what your section heading should say is that explanation would help understanding of the article, not that it needs a reference, because most readers who couldn't understand this article would most likely have more difficulty with references to technical/instructional manuals in a specialized field. Hyacinth (talk) 10:08, 14 June 2021 (UTC)[reply]
@Hyacinth: Thank you for these observations. I think that when I get home later I will review this discussion on a larger screen (laptop vs smartphone), so I can see most of it without scrolling (and more than 12 words of my response!), and maybe take your suggestion. Thnidu (talk) 23:55, 14 June 2021 (UTC)[reply]
@Thnidu: Hi great to have you here! I know this reply is a bit late, but I think the info you want about the notation is at Roman numeral notation. Fh1 (talk) 15:32, 20 June 2021 (UTC)[reply]