Talk:Function (music)

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Difficult to read

Hyacinth, you know I'm one of your biggest fans, but I find this article to be extremely difficult to read. I think it needs quite a bit more explanation, and examples that are spelled out step-by-step. I'd jump in myself and do it, but I'm afraid I don't know enough about the subject. Perhaps, if you are willing, I could just pose questions to get you to make changes to improve the article. To start: Perhaps you can fix the following paragraph. I can't make heads or tails of it. --Samuel Wantman 06:01, 19 Oct 2004 (UTC)

Thus a pitch may or may not fulfill one or more functions. Functional tonality refers to tonality which uses diatonic functions, non-functional tonality being when the diatonic elements are present (for instance the major scale) but do not use or fulfill their possible function as in, for instance, pandiatonicism.

Here is what I think that meant:

Thus a pitch may or may not fulfill one or more functions since it may be a part of many chords. For example a G natural may be the root of, say, a G major chord, the fifth of, say, a C major chord, or the third of, say, an e minor chord. To say that a piece or composer uses "functional tonality" is to say that they use pitches and chords according to and in their "proper" function or functions. "Non-functional" tonality is thus when normally functionally tonal diatonic elements, such as the pitches of the major scale, are present, but are used without regards to their "function", as in, for instance, pandiatonicism.

Hyacinth 06:44, 19 Oct 2004 (UTC)

This is a big improvement, but the words that you have in quotes are road-blocks to understanding. I wonder if you put them in quotes because their meaning is stretched or un-clear. "Functional" and "Non-functional" seem to mean traditional and conventional or non-traditional and un-conventional. Pandiatonicism has a function. Perhaps if you elaborate on and define what makes something "proper" or "normally functionionally tonal diatonic elements". I understand more from reading about Harmonic Function, but I think the basic problem is that your writing about "Diatonic functionality" assumes some knowledge of "Harmonic Function". I think it is possible to explain "Diatonic functionality" in even simpler terms. I sometimes try to imagine that I am writing for an intelligent 12 year old who knows nothing about the subject. --Samuel Wantman 20:24, 25 Oct 2004 (UTC)

As far as I know: Diatonic function = harmonic function.

You seem to have understood the quotation marks very well. One problem is that the term is usually not explicitly defined, and as with a lot of musical terms, appears to be defined by what it is said not to be, or what it is said to describe, in any given discussion. For instance, as in the article, function is said to be the names given to pitches to describe their functions (and not in a figurative manner). The circularity is found outside of this article. The article dominant describes: dominant note (second most important) of a key is that which is a perfect fifth above the tonic." Thus, in this usage, neither "dominant" and "perfect fifth above the tonic" describe or explain each other, they are just different words for the same name.

One explination of function: "Regardless of what system is chosen to model tonal function, solmization training cannot be undertaken halfheartedly. Developing listerners must cast the syllables across the diatonic collection with constant repetition and learn to associate specific syllables with specific scale degress--particularly the tonic during early stages--so that a kind of brainwashing in musical functionality takes hold." Karpinski, Gary S. (2000). Aural Skills Acquisition: The Development of Listening, Reading, and Performing Skills in College-Level Musicians, p.87. Oxford University Press. ISBN 0195117859.

If the quote directly above is accurate, "function" is an intuitive knowledge of what the scale degrees (I, IV, etc) and functions (tonic, subdominant, etc) are supposed mean.

Food for thought. Hyacinth 21:08, 27 Oct 2004 (UTC)

From Tristan chord:

"Wagner actually provoked the sound or structure of musical harmony to become more predominant than its function, a notion which was soon after to be explored by Debussy and others."

Here's an attempt:

The function of the dominant, for example, is to preceed the tonic, providing, for instance the strongest (most final) and thus final (last) cadence. If this is done in a piece that piece uses functional harmony in that respect. If, however, a piece where to preceed the tonic with a chord other than the dominant in the last cadence it would be nonfunctional.

Hyacinth 07:35, 30 Dec 2004 (UTC)

what follows below is from Chord (music):

Harmonic Function

Tonal music relies upon a key to indicate the natural relationships between the major and minor chords that result from the natural diatonic relationships. For instance, in any major key, the quality of a chord built on the fifth note of the scale will be major. This is because of the constant relationship between the tonal intervals of major scale.

Chords are also said to have a function in their diatonic scale, which relates to the expected resolution of each chord within a key. The strongest form of motion has root movement by fifth, which is the characteristic sound used as finality in most music of the baroque and classical periods (common practice period), and is also exploited to modulate a piece of music into a different key. The chord function for a major scale is as follows:

The I, III and VI chord are said to have a Tonic Function, due to the fact that they have a stable sound and do not have a tendency to resolve. When a chord progression resolves to a III or VI chord, it is called a Tonic Substitution, because the stable III or VI chord is being used as a substitute for the expected I chord.

The VII and the V chord are said to have a Dominant Function, and they have a strong tendency to resolve to other chords. The five down a perfect fifth to the I chord and the VII chord up a minor second to the I chord, due to the expected resolution of the tritone, or the highly unstable diminished fifth which is present in a diatonic VII chord.

The II and IV chords have Subdominant Function, partially due to the fact that they are a fifth away from the Dominant chords of a key, and partially because in their own Tonic keys, their respective Dominant chords are built on the root notes of the stable Tonic function I and VI. They are also referred to as Dominant Preparation chords, and are used to approach a Dominant function chord. The progression IV-V-I, (subdominant, dominant, tonic) is by far the most common chord progression in all of music, and can be found in an astonishingly wide variety of styles, forms, and genres.

The spellings of the diatonic triads of the C major scale are given in the following table, along with their quality, name, and function"

I       -- C E G -- major -- C major -- tonic
ii      -- D F A -- minor -- D minor -- subdominant
iii     -- E G B -- minor -- E minor -- tonic
IV      -- F A C -- major -- F major -- subdominant
V       -- G B D -- major -- G major -- dominant
vi      -- A C E -- minor -- A minor -- tonic
vii°    -- B D F -- dim.  -- B dim   -- dominant

There is another type of chord function, Subdominant Minor, which is reserved for non-diatonic chords, or chords that do not occur naturally in the diatonic key, and will be dealt with separately under the heading Modal Interchange.

end paste

Removed: Meantone

I removed the following

Diatonic functionality cannot be defined in pure equal temperament terms, but it can, however, be defined in meantone terms. Diatonic functionality for music tuned to equal temperament can be thought of as deriving from equal temperament as a tuning of logical, or abstract, meantone. That is, it is basic to the diatonic scale and diatonic functionality that four fifths up and two octaves down gives a major third, and that the supertonic or ii chord is both in a relation of a fifth above the dominant, or V chord, and a minor third below the subdominant, or IV chord. This entails the presence of logical meantone, but diatonic functionality does not assume other characteristic structural features of equal temperament.

I don't think this is true or correct, but more importantly I think it is not relevant. Hyacinth 12:42, 4 December 2005 (UTC)[reply]

Unreadable

I find the introduction particularly repulsive, whereas it should be the most accessible section. "Excercise"? You mean "exercise"? And if so, what do you mean? Where does Wilson's quote start? I would do with a few wikilinks, because using Google for each word/expression and failing to find meaningful hits is a very frustrating way to attempt to read an article that I should have some familiarity with. Also I don't like the title ("Diatonic functionality"), because it suggests "feature". I propose "Diatonic functions" instead. Thanks. PizzaMargherita 02:12, 25 December 2005 (UTC)[reply]

We might debate the title change, but for everything else, wade right in and fix it. —Wahoofive (talk) 04:30, 25 December 2005 (UTC)[reply]

I can only fix what I understand, sorry. Your revised version of the intro (circa April 2005) read much better. PizzaMargherita 08:31, 25 December 2005 (UTC)[reply]

PM, please see Talk:Diatonic_function#Difficult_to_read as an example of how we can improve the article. To answer your questions so far:

There is no Wilson quote. I have simply summarized his information and sited the source.
I moved the article to "Diatonic function" per your request and on the principle that "diatonic function" is simpler and thus preferrable to "diatonic functionality". However, functionality is a "feature" and music which uses diatonic fucntions may also be described as using functional tonality (meaning the same thing).
Looking at Special:Search/Excercise this is quite the common misspelling. Exercise is what was meant, however, and was meant in the sense of use, performance, practice, or "the act of bringing into play or realizing in action" ([2]). I use the word after Wilson.

Wahoofive's version of the introduction is at[3] (I assume). Note that this information is still in the article as the first paragraph of the first section Diatonic_function#Diatonic_functions_of_notes. Hyacinth 13:40, 25 December 2005 (UTC)[reply]

Equivalency vs equivalence

Is it common practice in musical theory to use e.g. "transpositional equivalency" instead of "transpositional equivalence", or even better "equivalence under transposition" or similar? Otherwise it looks like we want to use pompous terms only because they look cool... PizzaMargherita 08:36, 25 December 2005 (UTC)[reply]

Please tone down your language. Calling the article introduction "repulsive" is amusingly over the top. Calling contributors pompous is inappropriate. Please see: Wikipedia:No personal attacks ("Comment on content, not on the contributor"). Hyacinth 13:45, 25 December 2005 (UTC)[reply]

"Repulsive" as in repelling readers who don't already know the subject. "Exoteric", if you prefer.

"Pompous" was also not referred to any contributor, but to content. PizzaMargherita 13:59, 25 December 2005 (UTC)[reply]

Ah, repulsive may make sense, though this puts this article in league with almost any on a technical or scientific subject. Hyacinth 14:43, 25 December 2005 (UTC)[reply]

I'm not sure what is "pompous" about adverbs or the suffix "-ly". Perhaps the grammar is incorrect, but this is hardly pompous. Lastly the purpose of phrasing it that way on this page is that Transpositional equivalency redirects to Transposition (music) while Transpositional equivalence didn't (until just now). Hyacinth 12:44, 26 December 2005 (UTC)[reply]

Removed

"Generally speaking, the most important notes are the members of the tonic triad: the tonic, the mediant and the dominant. All other notes are understood to have some relation to those notes. The leading tone, for example, the seventh scale degree, has a significance of being a half-step below the tonic and has a tendency to resolve there. The fourth scale degree, the subdominant, has a tendency to resolve to the third degree, the mediant."

I removed the above paragraph as I would argue the most important notes are the tonic, dominant, and subdominant and that, for example, the fourth scale degree relates more importantly and directly to the tonic as the subdominant than to the mediant as an upper leading tone. Hyacinth 12:32, 26 December 2005 (UTC)[reply]

Baffling

I find the last sentence of the passage quoted below quite baffling. What does it mean?

'Functions in the minor mode

In the US the minor mode or scale is considered a variant of the major, while in German theory it is often considered, per Riemann, the inversion of the major. In the late eighteenth-early nineteenth centuries a large amount of symmetrical chords and relations known as "dualistic" harmony. The root of a major chord is its bass note in first inversion or normal form at the bottom of a third and fifth, but, symmetrically, the root of a major chord is the US fifth of a first inversion minor chord, and the US root is the "fifth".' yoyo 11:14, 5 January 2006 (UTC)[reply]

In addition, the second sentence in the quote (starting "In the late eighteenth-early nineteenth centuries") has no main verb, which makes it less than perspicuous. Tom Duff 20:22, 5 January 2006 (UTC)[reply]

Obviously, "inversion" is used in two quite different ways in that paragraph. As for the first usage, calling a minor key (whether the relative minor or the other one, the one sharing the same keynote) an "inversion," that's news to me, but plausible.

In the next sentence, I wonder whether "symmetrical" means mirror-image, referring to the relationship, for example, between a C triad and an A-minor triad, which looks like a C triad on a piano keyboard when it's viewed through a mirror, the E being immediately adjacent to the group of two black keys, like the C in the normal view. Beats me.

But the third sentence makes sense when you call the "first" inversion the inversion which isn't inverted at all, that is, a plain triad. Then "normal form" makes sense, and (in a C triad) C could be considered "the bass note" or "the root," and indeed it is "at the bottom of" a "third" (the C-E third, or the third of the chord) and a "fifth" (the C-G fifth, or the fifth of the chord).

But the second half of the sentence has me stumped. Perhaps it means that C (the root of a C triad) also happens to be the fifth of the triad built on the E below it, which is, indeed, minor -- but why does he say it twice, shifting only the "US"? Unfree (talk) 21:21, 1 December 2008 (UTC)[reply]

The passage still remains baffling garbage two years after above comments. "The root of a major chord is its bass note in first inversion or normal form at the bottom of a third and fifth," No, the root of a major chord (or any chord for that matter) is its bass note in ROOT position, NOT in first inversion. If that is not what the author meant to say then it's author should please clarity. RichardJ Christie (talk) 10:38, 29 July 2010 (UTC)[reply]

If you want assistance or improvements perhaps you shouldn't throw around insults ("baffling garbage"). Hyacinth (talk) 02:53, 2 August 2010 (UTC)[reply]

German and US systems

For the love of God, separate the explanations of the German and US systems. They shouldn't be constantly compared as they're being explained. Explain each, and then compare. I already know about this stuff and I can't even follow some parts.

Please sign your posts on talk pages per Wikipedia:Sign your posts on talk pages. Thanks! Hyacinth 20:04, 27 April 2006 (UTC)[reply]

Yes, this is exactly what I was thinking. I don't know this stuff, and I can't follow anything trying to keep track of both systems at the same time. --24.59.119.198 22:58, 20 June 2006 (UTC)[reply]

Vincent D'Indy

Is there an English translation of the 1903 work of D'Indy here referenced, or is this the French? - User:Lself 23:36, 2 August 2006

Diatonic and chromatic

The article uses the term "diatonic" extensively, but without adequate explanation. This term, along with "chromatic", is the cause of serious uncertainties at several other Wikipedia articles, and in the broader literature. Some of us thought that both terms needed 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 22:24, 3 April 2007 (UTC)[reply]

Tonic Counter Parallel

Dear all, I tried to edit the section "Diatonic functions of notes and chords" but it was reverted.

Supertonic ii Subdominant parallel/Tonic counter parallel Sp/tKp

the ii chord (supertonic) is NOT a tonic counter parallel. From what I understand, a parallel or counterparallel must be a 3rd away from the reference chord, and the supertonic is not a 3rd away from the tonic. Please let me know if this is correct. —Preceding unsigned comment added by Microcosmmm (talk • contribs) 01:41, 28 May 2008 (UTC) Microcosmmm (talk) 01:45, 28 May 2008 (UTC)[reply]

Providing an Wikipedia:Edit summary in the future may help prevent your edits from being undone. If you check the counter parallel article it disagrees with you in regards to minor keys, though it lacks sources. Do you have a source you can cite? Hyacinth (talk) 03:15, 28 May 2008 (UTC)[reply]

ok, I read the counter parallel page very carefully. It does not explicitly state that the ii chord in either a major or minor key is a tonic counter parallel. I'm only seeing it as a subdominant parallel - which makes sense to me. I only have an internet source to site, http://cazoo.org/music/harmony.html it's probably not the most credible thing on earth, but it makes sense to me. Now, I have read in jazz theory, that a ii chord can substitute a I chord (particularly in the chord progression John Coltrane made famous, starting with a I in "Giant Steps" and a ii in the tune Countdown http://en.wikipedia.org/wiki/Coltrane_changes). Maybe that's what y'all mean? I'd love to see an example in standard western classical music. I find it to be more "modal" than "tonal" though. —Preceding unsigned comment added by Microcosmmm (talk • contribs) 05:17, 28 May 2008 (UTC) Microcosmmm (talk) 05:18, 28 May 2008 (UTC)[reply]

Major and minor are different. According to counter parallel, the counter parallel of the tonic in major is iii while the counter parallel differs in minor, being ii. Hyacinth (talk) 08:49, 28 May 2008 (UTC)[reply]

to quote the article: "In a minor key the intervals are reversed: the tonic parallel (e.g. Eb in Cm) is a minor third above, and the counter parallel (e.g. Ab in Cm) is a major third below. Both the parallel and the counter parallel have two notes in common with the tonic (Am and C share C & E; Em and C share E & G)."

I still don't see the ii chord being a tonic counter parallel. It doesn't share any notes with the tonic - and the article says that the bIV chord (the Ab in the key of Cm), not the ii chord, is the tonic counterparallel in minor. Please directly quote where the ii chord in major or minor is the tonic counterparallel.Microcosmmm (talk) 18:42, 28 May 2008 (UTC)[reply]

You're right, I confused sP and Sp. Thanks. Hyacinth (talk) 05:41, 29 May 2008 (UTC)[reply]

Functions in the minor mode

The paragraph under this heading should be placed in context. Unfree (talk) 20:18, 1 December 2008 (UTC)[reply]

What function?

I thought I was learning something new when reading this article. It appeared at first as though I was learning about the psychological effect certain things have on the ear of the listener, known by a new and unfamiliar term, "diatonic function." But now that I think it over, it occurs to me that this might be a rather elaborate article simply about the role a note plays in a chord, or the role a chord plays in the context of a diatonic key, called by a name ("Diatonic function") I hadn't heard before. I wonder, Which is it? Something profound or mundane? In a C triad, G is "the fifth." That's its function in the chord. Is that sort of thing all this article is about? Unfree (talk) 20:36, 1 December 2008 (UTC)[reply]

So, to answer your question, it really is just about notes in chords, and chords in scales. What makes it interesting is that built into a major scale is tendencies that are built-in to the notes in the scale for a note to "resolve" upward or downward. For instance, the note B in the C major scale has a stronger tendency to resolve upward to a C than fall downward to an A. Especially if this note is in a G major chord, which is the Dominant (V) chord in the key. The reason Dominant (G major) tends to go to Tonic (C major) is this built in "diatonic function." Another note in the C scale which tends to resolve a certain way is F, which commonly resolves downward to E. The 4th and 7th scale degrees (F and B in the key of C major) are the important "tendency tones."

Here's an excerpt from a book I'm writing, called Music Theory for Anyone:

"Functionality applies when one intends to use the chords functionally. A chord progression does not have to follow the rules of functionality. The blues form exhibits "regression" from V to IV and uses non-functional dominant seventh chords. Chords, when not used functionally, can be used motivically, in parallelism, or merely for "color." But, for one with the intention of modulating to another key, or establishing simple tonal stability, it is valuable to understand chord function.

The key to grasping functionality is understanding the process of moving from stability, increasing tension, and finally releasing this tension. Tonic, Pre-dominant, Dominant, Tonic (T-P-D-T) is the traditional music theory paradigm which mirrors the above process. Here's an analogy I like to use: "A tonic chord is enjoying the comfort of being in your own home. Moving to a pre-dominant chord is stepping outside of your house to somewhere relatively safe, but you are no longer in the comfort of your own home. The dominant chord is the crisis; something happens and we are at the height of tension. Fortunately, we solve the problem; were able to resolve back to the tonic and go home safe and sound." Microcosmmm (talk) 06:27, 2 March 2009 (UTC)[reply]

"Some may at first be put off by the overt theorizing apparent in German harmony...Yet this ongoing conflict between antithetical theories, with its attendant uncertainties and complexities, has special merits. In particular, whereas an English-speaking student may falsely believe that he or she is learning harmony 'as it really is,' the German student encounters what are obviously theoretical constructs and must deal with them accordingly." - Gjerdingen (1990). Hyacinth (talk) 12:05, 6 May 2010 (UTC)[reply]

I agree that this article is difficult to read. Forcing the pov of Rameau in Riemann doesnt make sense. The multiple functions names should be exposed, at least, in comparison in the first chart (minor and major together). Furthermore, Riemann doesnt know any supertonic or subtonic, mediant or submediant, etc. Have a look at my article in http://fr.wikipedia.org/wiki/Fonction_(musique) and feel free to inspire. I am not so good in english for a wiki-worth translation.

On the top, I see in the web that more and more often, practical harmony is named functional harmony, this is worth a point in the article. Pipecat (talk) 18:05, 3 April 2012 (UTC)[reply]

Merge

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Diatonic function, harmonic function, tonal function?

I wanted to make a few simplifications in the lead of this article (I fail to figure out what a statement like this: "A fourth feature is the ambiguity that arises from the use of the same terms to describe functions across all temporal spans of a hierarchical structure from the surface to the deepest level, and that the longer term or deeper functions act as a center for shorter higher level ones and that the functions of each tend to counteract each other" might possibly mean), but soon stumbled over another problem.

This article appears to be about what may better be called "harmonic" or "tonal" functions. I don't think that Riemann, who is correctly presented as the originator of the concept, ever spoke of diatonic functions. It is true that the tonality of which we are speaking is diatonic, but it seems to me that "diatonic functions" must be something quite different, that people today may perhaps call "diatonic qualia"...

At any rate, it seems that the article should be renamed either "Harmonic function" or "Tonal function". At present, Tonal function redirects here, but I think that it should be the other way around. Harmonic function (which deals with mathematical functions) refers to Diatonic functionality, which in turn also redirects here. Although I am myself convinced that diatonic functions properly speaking do exist (along the lines drawn by Jacques Handschin in Der Toncharakter, or the medieval descriptions of the qualitas or the mode of notes), I think that the time is not yet ripe for an article on these functions: the references would be missing.

Hucbald.SaintAmand (talk) 10:49, 12 October 2016 (UTC)[reply]

Thanks for bringing up this question. I have been wondering for a long time why the article bears this title, instead of "tonal" or "harmonic" function, which were the only terms I had come across before finding this on Wikipedia. Since "harmonic function" is already taken for the mathematical sense, it seems reasonable to rename this article "Tonal function", unless someone can come up with a strong argument for keeping the current title. As for that impenetrable sentence, it ought to be nominated for some sort of award for obfuscation.—Jerome Kohl (talk) 17:35, 13 October 2016 (UTC)[reply]

Requested move 13 October 2016

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. No further edits should be made to this section.

The result of the move request was: NOT MOVED.(non-admin closure) Iazyges Consermonor Opus meum 00:55, 7 November 2016 (UTC)[reply]

Diatonic function → Tonal function – The name "diatonic function" does not appear to be used anywhere else than on WP; in addition, it may be considered misleading. Harmonic functions (which might by another possible title for this article, but already taken for the mathematical usage) are found and make sense only in tonal music. Hucbald.SaintAmand (talk) 20:38, 13 October 2016 (UTC) --Relisting. GeoffreyT2000 (talk, contribs) 17:23, 24 October 2016 (UTC)[reply]

Oppose. The term is widely used, albeit in a specialised area. I get 2400 ghits excluding Wikipedia and our compliant mirrors. Andrewa (talk) 04:59, 24 October 2016 (UTC)[reply]
- Query: In what specialised area do you find this term? Does it have to do with what is called "functional harmony" in music, or something entirely unrelated?—Jerome Kohl (talk) 06:28, 24 October 2016 (UTC)[reply]
  - I only looked at the first two pages of the 2400 ghits, but they were all relevant (do your results vary?). The current title also seems to me to describe the topic far better than the proposed title, but that's probably because it was a standard term when I studied (and performed) experimental music back in the late 1960s... and of course I'm not a reliable source. Anyway, the claim that the term does not appear to be used anywhere else than on WP surprised me, and still does having now done a little research. Not you? Andrewa (talk) 17:15, 24 October 2016 (UTC)[reply]
    - I cannot see the list you generated, but when I try to replicate it, I get about 3700 hits (including Wikipedia and its mirrors), most of which have the two words separately rather than together, and most of which also include the expression "functional harmony", which was the only term I was familiar with when I studied and performed experimental music back in the middle 1960s through the late 1970s. Perhaps it is a national thing, since my studies were in the US rather than Australia?—Jerome Kohl (talk) 17:33, 24 October 2016 (UTC)[reply]
      - My (European) Google gives about 3750 ghits for "diatonic function" (with quotation marks, which excludes the separate words) and 6660 for "tonal function"; but many of these results point to web sites which could hardly be accepted as valid references. Scholar Google gives 74 hits for "diatonic function" and 1300 for "tonal function"; Google books gives 99 and 1380 respectively. One may conclude that "tonal function" is more than ten times more common in serious sources. Let me add that in 50 years of career as a professional music theorist, I had never seen the expression "diatonic function". But my career, it is true, was not in English. The keywords "Fonction diatonique" and "Fonction tonale" (in French) give respectively, on Google: 114/1540 hits; on Google Books: 0/155; on Scholar Google: 0/114. — Hucbald.SaintAmand (talk) 17:54, 24 October 2016 (UTC)[reply]
        My Google was a simple "diatonic function" -Wikipedia and now gives me About 2,450 results (0.39 seconds) and the first two pages gave 19 ghits, some web, some books, all looking relevant enough to seriously challenge your conclusion above that the term does not appear to be used anywhere else than on WP, in my opinion. I asked whether the contributor to whom I was replying agreed with that, and note that there has been no reply. Your research now seems to indicate that both terms are common, does it not? The question then becomes, which is the better article title? Andrewa (talk) 23:43, 24 October 2016 (UTC)[reply]
      - My teacher (or rather performance leader)... whose name I cannot remember!.. had worked in England with Cornelius Cardew, but we seem to have both sides of the Atlantic represented here so that can't be it. Andrewa (talk) 23:50, 24 October 2016 (UTC)[reply]
Oppose—A diatonic scale is a seven-note scale in which two semitones are maximally separated; this includes the pre-tonal church modes. "Tonal function" would refer to ... function (sounds vague) ... during the tonal period in which a central triad, not a central note, is the centripetal force (approx. 1600–1900, give or take a few decades). Tony (talk) 10:37, 24 October 2016 (UTC)[reply]
- Query: Tony, can you quote if only one single published reference to "diatonic functions in church modes"? You'd find in the specialized litterature some (scant) references to "hexachordal functions", but that is not what this paper is about. — Hucbald.SaintAmand (talk) 17:10, 24 October 2016 (UTC)[reply]
  Are you really suggesting that the church modes are not diatonic??? I suppose I could go to a kids' music textbook. I've never thought of having to justify something so fundamental. Tony (talk) 10:32, 25 October 2016 (UTC)[reply]

I never suggested such a thing, Tony. On the contrary, I would even agree that "Diatonic functions" exist in Church modes. I only mean that such an idea is not documented in the literature. I personally understand it quite differently from "tonal" or "harmonic" functions. To make things short (because this is not our present topic), I believe that in Church modes, there is a conflict between "diatonic functions" (more often described as "hexachordal functions", say, the function inherent in a mi, a fa, an ut, etc, which are properties of the diatonic system, whatever the mode) and what might be called "modal functions" (say, the function of being the final, or the reciting note, etc.). The conflict is that the modal function of, say, final, may fall on the diatonic function of mi, or fa, etc. I am presently engaged in scholarly discussions about this with specialists, but the only thing I could say here is that none of this is ripe for inclusion in WP. See also below. — Hucbald.SaintAmand (talk) 13:23, 25 October 2016 (UTC)[reply]

Hucbald, I understood some of the tech you described, but it goes a little beyond my knowledge. I'm a little concerned about what "function" actually means to readers. And is there a need (in the article lead?) to clarify harmonic vs melodic? Is the scenario different for monophony? Tony (talk) 02:34, 26 October 2016 (UTC)[reply]

This is a quite complex question, Tony. The idea that individual notes may have a function is not generally shared (not that I know, at least), and I think that the article maintains some confusion between the names given to the degrees of the tonal scale (tonic, supertonic, mediant, etc.) and the names of the functions – which belong to chords. The difference is clear in Riemann's theory, because there are only three functions for seven degrees: the function of dominant for instance can be exerted by the 5th degree (the dominant), the 7th (the leading tone) and in some cases the 3d (the mediant). It was not immediately obvious, in the 19th and early 20th century, that what is called the "theory of the degrees" (Stufentheorie, the Viennese theory) could also be considered a theory of functions. This may have been an American development. Walter Piston (1941), for instance, writes "Each scale degree has its part in the scheme of tonality, its tonal function" [tonal function!]. But the context shows that for Piston, "degree" here means "root", subsuming the chord that it supports. Shirlaw (1917) discusses "tonal functions" (tonal!) in relation with the tonic, subdominant and dominant as discussed by Rameau; he provides an extended discussion of Riemann's theory of the three functions; but he never speaks of seven (or six) different functions. In addition, whenever Shirlaw speaks of "tonal functions", he puts the expression within quotation marks.

Functions of degrees as such, when discussed, usually imply that these degrees are roots (of chords). I know only one modern book that does discuss functions of notes, and it does not qualify them as "functions". It is Jacques Handschin Der Toncharacter (1948), a strange and not very well considered book, but which I personally find most interesting. Handschin clearly speaks of what I'd call "diatonic" functions: he discusses the "character" of, say, the note C in the diatonic system, not in this or that tonal scale, and claims that C somehow retains that "character" in any key. So doing, he actually catches up with a medieval theory, expressed for instance by Guido of Arezzo as the "mode or quality of the notes" (modi, or qualitates vocum). This all could be discussed in a "Diatonic function" (or "Diatonic character") article, but which would be entirely different from the present one. And once again, it would be rather difficult to find secundary references to such ideas which, I repeat, are presently under discussion among (a few) specialists. — Hucbald.SaintAmand (talk) 08:59, 26 October 2016 (UTC)[reply]

A better name would be Harmonic function (music); the math article already has a hatnote. The word "tonal" isn't exclusively used to mean common-practice harmony. —Wahoofive (talk) 21:34, 24 October 2016 (UTC)[reply]

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Article is a mess

Goodness, having been brought here to comment on the suggestion to rename the article, I've just had a look at its content. Very confused. I think we need to discuss whether part of it can be saved and relocated in one of the other articles related to diatonic music/theory. Tony (talk) 10:36, 25 October 2016 (UTC)[reply]

Tony, as I had written in Talk:Diatonic function#Diatonic function, harmonic function, tonal function?, I thought that the first step towards rewriting this article was its renaming. I am sorry that this operation now is ill embarked, probably by my fault.

I keep thinking that the real topic of this article is tonal function; even the name "Harmonic function" presupposes tonal harmony.

The article states, among others, that the "position within a gamut (the available collection) of notes determines a note's function". One is made to believe that the collection in question is the diatonic scale itself, while obviously a position in the diatonic scale does not and cannot determine a function. It is the position in the tonal scale (possibly but not necessarily diatonic) that does. Functions exist in minor as well, even although the scale may not be diatonic. Besides, this statement is given as one of "Three general and inseparable essential features of harmonic function in tonal music".

Beginning the paragraph on "Functional harmony", the article refers to Riemann; the "Further reading" section quotes one of his books: Vereinfachte Harmonielehre, oder die Lehre von den tonalen Funktionen der Akkorde (1893), a book that was translated early in English (1896, I think) under the title Harmony Simplified, or the The Theory of the Tonal Functions of Chords.

After this, the article almost always refers to functions in terms of Roman numerals, which inherently presuppose a tonality. The only section in which it does not is that on "Functions in the minor mode", which is but an extremely poor account of mistaken ideas about Riemann's dualism and his theory of the three functions (and their substitutes).

You suggested that the expression "Diatonic function" could also cover the Church modes. You are perfectly right in this, but once again you could hardly find a published reference to such an idea. That the article is not about functions in Church modes is one of the reasons why I consider that it should not be named "Diatonic function". (Diatonic functions in Church modes are more often refered to in the specialized litterature as "Hexachordal functions".)

Some of the article could be saved, but it should begin stating that Functions are properties of tonal music (in a wide sense of the term). It should then explain that there exist today two theories of tonal functions:

the German one (Riemann, but also Daube, von Oettingen, etc.) which envisages three functions only, tonic, subdominant and dominant, which the seven degrees of the scale can take up in various ways, where the functions are notated with the three letters T, S and D, etc.
the Viennese one (Sechter, Schoenberg, Schenker, Piston, etc.) which envisages a separate function for each of the seven degrees of the scale (or, some say, for six of them), and which notates the function with Roman numerals.

It goes without saying that both systems, the letters T S D and the Roman numerals, are used in minor as well as in major. The German theory remains practiced in Eastern Europe (Germany included), the Viennese one in Western Europe and in the United States. Etc. Etc.

Perhaps the renaming of the article could still be saved? But that would require more explicit support... — Hucbald.SaintAmand (talk) 13:09, 25 October 2016 (UTC)[reply]

I am extremely disappointed that the request to move was rejected without explicit justification – and also that this section of the talk page for some reason apparently was included in the Please do not modify it advice, even although it was a separate section. I keep thinking that something should be done about this article, which indeed remains a mess. We are but very few to feel concerned wiht music theory articles: it is therefore of utter importance that anyone having even but a slight interest of the matter should give her/his opinion. It seems to me that the requested move is rejected merely because noone really concerned made the effort to answer. I cannot suggest the move anymore, but I hope that someone else will. — Hucbald.SaintAmand (talk) 21:33, 7 November 2016 (UTC)[reply]

I have fixed the source so that the discussion is closed properly, and this topic is not inside the closure. —Wahoofive (talk) 22:16, 7 November 2016 (UTC)[reply]

I think it's safe to say that the word "tonal" doesn't really have a fixed definition in music theory literature. In some cases it means "using common-practice harmony" based on dominant-tonic chord relationships, and in other cases it means "having a tonal center" (i.e. the antonym of "atonal"). Music in church modes, or by Bartok, might fit the second definition but not the first. We can't resolve this on WP. And we've had years of battle over the term "diatonic". I'd still advocate Harmonic function (music) as a compromise. —Wahoofive (talk) 22:36, 7 November 2016 (UTC)[reply]

Oh, and I agree that the German and Viennese systems should be detailed, although there are other possible systems of describing harmonic function for non-common-practice music (if by that you mean the relationship between various chords), such as the that of Hindemith. —Wahoofive (talk) 22:40, 7 November 2016 (UTC)[reply]

"Function" is a term used loosely to mean all sorts of things, in music and elsewhere: "the special purpose or activity for which a thing exists or is used". There is the very specific meaning of mathematics, of the kind y=f(x), covered in the article Function (mathematics). We could devote an article to the general meaning, dealing, say, with the function of the clarinet in the orchestra, or of the decrescendo in this or that work, etc. For this, I'd suggets that the article be named "Function (music)".

Then there is the very specific meaning devised by Hugo Riemann in the late 19th century, under the form Tonale Funktion ("Tonal function"), the meaning of which was later enlarged, especially in American theory, to describe the role of chords in tonal common practice. But "function" in this sense has again been loosely used, turning back to the general meaning.

In other words, there is a musical technical usage of the term, of German origin, under the form "Tonal function". Its meaning might be slightly enlarged as "Harmonic function", but I think that "harmony" (at large) always presuppose some form of tonality (at large). It is from such considerations that we should decide... — Hucbald.SaintAmand (talk) 06:28, 8 November 2016 (UTC)[reply]

PS. Hindemith's Craft of Musical Composition has a section with the title "Harmonic function", but the title is not in the German edition, which reads Harmonisches gefälle. — Hucbald.SaintAmand (talk) 06:33, 8 November 2016 (UTC)[reply]

Everything you say is true, but I would suggest that it's more important that the article title convey to the casual reader what the article is going to be about (harmony) rather than be based on technical usages (or translations) from the past, especially when the terms are used inconsistently in the literature. Harvard Dictionary calls this topic Harmonic analysis, which wouldn't be a bad title for us either (though this is also a math term); Functional harmony is a separate article about Riemann's work. "Tonal" is a term just as vague as "function". —Wahoofive (talk) 17:06, 8 November 2016 (UTC)[reply]

I'd be very (or, say, reasonably) happy with the article being titled "Harmonic function", possibly with a redirection from "Tonal function". My real problem is with "Diatonic function", which I consider meaningless and misleading. Let me add, however, that even if I agree that WP should aim at the casual reader, this IMO is no reason to lack accurateness and consistence – including historical ones. That the terms are used inconsistently does not authorize us to repeat the inconsistence. — Hucbald.SaintAmand (talk) 21:01, 8 November 2016 (UTC)[reply]

(A german musicologist here...) This article made me laugh from my deepest heart. It seems as if someone tried to explain everything like a systematic method of general analysis of music. There's no way to achieve this goal. If one has to write a harmonic/melodic analysis of any sort, he should know how to choose the very method that fits. These (meaning f.e. roman numeral... & diatonic function...) are not rivals in an arena of musicologists competing with each other, but tools for special kinds of compositions. Every epoche developed its methods to achieve an aptitude in doing this kind of work. Less is more. Get aquainted with the concepts of tonality itself, divide between the compositional branches and aeras and be brave enough to omit superfluous babbling (which is to be found and provided for by the hundreds over the last 200 years). It is a Wikipedia-Article and not the New Groove...--85.179.182.176 (talk) 22:51, 1 March 2017 (UTC)[reply]

Well, yes indeed. Tony (talk) 13:55, 4 March 2017 (UTC)[reply]

Rewriting begun

Considering that many of us agreed that the article is (was) a mess, I began rewriting it -- starting with the lede. As usual, I tried to save some of the former version, but in this case there was really very little to save. I invite everybody, especially the "experts" among us, to contribute.

I intend to do more, but it might take time.

Hucbald.SaintAmand (talk) 20:05, 5 March 2017 (UTC)[reply]

The lede is already so much better that I am sure there will be a chorus of voices objecting to it ;-) I will not be among them.—Jerome Kohl (talk) 01:01, 6 March 2017 (UTC)[reply]

Thanks for your support, Jerome. I added in the lede more details about the German and Viennese theories, which probably also should form two of the main sections of the article. I find it somewhat difficult, especially at this point, to sort out what may be said in the lede and what should better be retained to the following sections; this probably will become more evident as the rewriting progresses. I certainly need help from all those who agreed on the messy state of this article. My problem often is that I am more familiar with primary sources than with secundary ones, and I will need help if only to add the needed secundary references. Also, I find that the musical examples may not be properly positioned as they are, or may not be useful at all; but I remain reluctant to remove them (I probably will move them at a later stage): opinions about this will be welcome. I also have major doubts about the expressions "tonic parallel", etc. (see also Parallel and counter parallel, equally doubtful IMO) which seem literally translated (sometimes improperly) from the German and which, so far as I know, are not common in music theory in English – at least, the term means something completely different in American neo-Riemannian theory. Not being a native English speaker, I need help on such points. — Hucbald.SaintAmand (talk) 17:36, 7 March 2017 (UTC)[reply]

Huge improvement. Keep up the good work. I think there needs to be a clarification between the function of a note vis-a-vis a chord. The lede starts out by identifying the names of the notes of the diatonic scale, but the rest of the article is about chords. Do the notes of the scale have functions independent of their membership in chords? (Kodaly certainly thought so.) If not, then there needs to be some additional explanation that the names of the chords are extended from their roots. —Wahoofive (talk) 02:37, 8 March 2017 (UTC)[reply]

You are perfectly right about this, Wahoofive. The idea that notes may have functions is implyed in the quotation "Each degree of the seven-tone diatonic scale has a name that relates to its function", from Benward & Saker (2003) which I consider an often somewhat naive source. And there also is the first musical example, which I think should appear only later (for the same reason). The text continues with "The concept of harmonic function rests on the recognition of essential hierarchies between the degrees of the tonal scale", which does not clearly say that the degrees of the scale have funtions (nor that the degrees are notes), but at least that the concept originates in the hierarchies between them. This is a statement that I added and it certainly needs qualification.

The fact is that the concept did originate in the qualities of the degrees, IMO, even if this is something that I cannot really prove. And this has to do with the name of the article, "diatonic function", which I dislike. The idea of the "qualities of the degrees" (or "modes of the notes") arose in Guido of Arezzo's Dialogus and before (there is a paper on this point, "Modi vocum. Réflexions sur la théorie modale médiévale", Con-Scientia Musica. Contrappunti per Rossana Dalmonte e Mario Baroni, 2010, p. 21-34. See http://nicolas.meeus.free.fr/NMTheorie/Modi%20vocum.pdf.): such "qualities" could be described as "diatonic functions". They have been described as "characters of the notes" (Toncharakter) by Handschin in his book of the same name.

The present article, however, is not about these but about "harmonic" (or "tonal") functions. And whether these could concern individual notes seems to me quite doubtful. The fact is, however, that some (naive) theorists do think so, and that therefore we have to take them in account. I'll think of it. But this confirms me in the idea that we cannot properly solve the problems of this article without renaming it – as "Harmonic function", probably. The case of medieval diatonic functions is too speculative for Wikipedia, I am afraid, and should not retain us here. It would be easy to say that the idea of harmonic function at times is extended to concern individual notes, even if in essence it concerns harmonies...

Wuddyathink? — Hucbald.SaintAmand (talk) 08:12, 8 March 2017 (UTC)[reply]

Hucbald, why not define "diatonic" first? And there still seems to be confusion about tone vs triad. Tony (talk) 10:46, 8 March 2017 (UTC)[reply]

Well, Tony1, because that would be extremely difficult. You will gain some idea of the difficulty in Diatonic and chromatic#Modern meanings. I for one advocate the usage described there as "exclusive", which excludes the minor scales – and, therefore, also excludes the title "diatonic function" for the article under discussion here.

As to the confusion about tone and triad, I don't find it, in the lede at least (where the word triad does not appear and the word tone only once, in the expression "seven-note diatonic scale", in a quotation that I think must disappear). In German function theory, triads often are described as "faked consonances", i.e. as dissonant chords (7th chords) apparently made consonant (triads) by concealing one of their notes. The concept of "faked consonances" is essential to Riemann's idea that different chords could share the same function: this will have to be explained in one way or another. As to notes, it will have to be explained somewhere that they can be considered to have a harmonic function only by assuming that they implicitly support a full harmony.

Keep in mind that the rewriting is only in a beginning stage, and don't hesitate to rewrite yourself what you think needs it. — Hucbald.SaintAmand (talk) 17:53, 8 March 2017 (UTC)[reply]

I think we should aim to maximise simplicity for the readers. At the moment it seems full of (unnecessary) complexity. ... overintellectualised. Tony (talk) 06:24, 9 March 2017 (UTC)[reply]

The concept of harmonic function is inherently complex. Vulgarizing it involves explaning this complexity in simple terms, but it would be idle to make believe that it is simple. I agree that any unnecessary complexity should be removed, but I am afraid that much of it will remain necessary. WP is for ordinary people, but there is no reason to assume that ordinary people are unintelligent. Hucbald.SaintAmand (talk) 16:48, 9 March 2017 (UTC)[reply]

I made a first attempt at reorganizing and rewriting the first section of the article, now under the heading "History of the concept". My attempt mainly concerned the first subsection, "Origins of the concept", and the two following ones are but remnants of the earlier version. I am quite confident in my idea that functional theory originated with theories of just intonation, but I must confess that I lack secundary references to support it. The article Just intonation#Diatonic scale provides some, but others must exist.

It goes without saying that this reorganization will involve modifications of the following subsections, on German and Viennese theories. May I insist that everyone feel free to participate in this work? — Hucbald.SaintAmand (talk) 21:14, 11 March 2017 (UTC)[reply]

German functional theory

Awaiting comments and objections, I continued my rewriting of this subsection. Riemann's theory is frighteningly complex, especially in its fully dualist version, and I am not sure that my summary really will make sense to the reader. I may have to reread it myself several times... This section seems unescapable, however, because it really is in Riemann's theory that the name "function" originated. I trust that (with some help) Riemann's theory can be explained to the layman.

I linked with the article Parallel and counter parallel which I think also needs revision because what is described there is named "relative" and "counter relative" in English, as I already stressed above. This other article should better be renamed accordingly; it could possibly mention the fact that "relative" at times is termed "parallel" in translations from the German, but that "parallel" in English (and particularly in neo-Riemannian theory) means a change of mode on the same fundamental.

I find your explanation so far clear, but then I'm a music professional. I know little about Riemann's theory, but isn't the point of Riemann's categorization that chord "progressions" are those which move from Subdominant-Dominant-Tonic functions, in that order, and those which move backwards in this sequence are "retrogressions," which serve to increase tension? That seems worth mentioning. Also, isn't the I-6/4 chord considered a dominant chord (with appoggiaturas) in Riemann's theory? Furthermore, Riemann must have had thoughts about chords from the various minor scales, including such altered chords as the Neapolitan sixth.

Also, as a minor point, I wonder if this theory needs to be wrapped under "history of the concept." It's not like we've grown past the Riemann and Viennese theories and come to some modern synthesis. —Wahoofive (talk) 21:51, 17 March 2017 (UTC)[reply]

Thanks, Wahoofive. The points you raise are interesting. Here are my answers:

No, so far as I know, the idea of "progressions" (S D T) vs "retrogressions" (T D S) is not Riemann's. On the contrary, this idea may be characteristic of the Viennese school, among others of Schoenberg (who, in Harmonielehre at least, had explanations for this opposition based on a consideration of the "natural harmonics"), of Sadaï (who I think dubbed T S D T the "functional cycle"), and others. For Riemann on the contrary, the opposition is between "dominant" moves, I–V and V–I alike, and "subdominant" ones, I–IV and IV–I. It is very characteristic that Riemann is not interested in the direction of these moves, only whether they concern D or S.
Similarly, I don't think that Riemann ever considered I 6/4 as a dominant chord. I am quite sure that at one point, he considered on the contrary the I–IV–I 6/4–V–I cadence as T–S–T–D–T, with a T in the middle (the I 6/4 chord), a cadence that I think to remember he dubbed the große Kadenz. This was because he considered that the movement from S to D necessarily had to pass through T, as S and D are on opposite sides of T. It was August Halm, I think, who said that an "abyss" separated S from D. But Riemann might have changed his mind on this point: I'll have to check. (I must confess I don't enjoy reading Riemann that much; my knowledge comes mainly from having had teachers who themselves had been taught in the German tradition – quite a long time ago.)
Your question about the Neapolitan sixth is a good one. First of all, it must be realized that for Riemann dissonant chords are derived from triads by the addition of either a 7th or a 6th. The Neapolitan sixth must have been for him a s (a minor subdominant chord) with added 6th, resulting in an inverted sL chord (with ♭6 being the inverted leading tone to 5). The chord on II, on the other hand, would involve borrowing the major subdominant and taking its relative (Sr), or adding the 7th below the S chord (Rameau would have done that too). But there is no simple explanation of all this, because the whole thing must be considered upside down, in a way that always makes me dizzy. And I don't know how Riemann would have considered the chord that we would label ii°. I'll try to check that.
Your point about whether Riemann's theory must appear under "History of the concept" is excellent. I started writing what I wrote in the idea that one should be short about this theory and merely describe it as the one where the term "Function" first appeared. While writing, though, I realized that it could not be described shortly and that it might therefore better be dealt with in a separate section, where all the points that you raise above would be discussed (and a few others, such as his idea of "feigned consonances").

My feeling at this point is that the article should have a strong first section on "History", probably subdivided in "Origins of the concept" (with more details about Zarlino, Rameau, perhaps Adam Serre, Daube, Marpurg, etc. etc.), "German functional theory" (with more about Hauptmann, von Oettingen, and Riemann's followers), and "Viennese theory of the degrees" (Sechter, Bruckner, Schenker, Schoenberg, Sadaï, Meeùs, etc.). A second section may describe what all this became in modern Western theory – roughly what is now included in the "Diatonic function of notes and chords", but fully rewritten and corrected. I'll rename the first section immediately, for the rest keeping it for the time being as it is.

Hucbald.SaintAmand (talk) 09:39, 18 March 2017 (UTC)[reply]

My examples of the Neapolitan sixth and I-6/4 chords are from the Harvard Dictionary article.

I'm not sure it's necessary to have any section about "history," since the concepts are still essentially active. But a background on concepts such as Rameau might be helpful. —Wahoofive (talk) 23:30, 19 March 2017 (UTC)[reply]

Yes, Wahoofive, I already see that in my very old version of the Harvard Dictionary (6th edition by Willy Apel, 1950, art. "Functional harmony"). One reads there: "Among [the subdominant's subsitutes] is the Neapolitan sixth which, in functional harmony, is simply a (doubly altered) S, while in the orthodox system it is the 'first inversion of the lowered submediant.'" Now this hardly makes sense: the first inversion of the submediant is a 6th chord on the tonic, and if the submediant is "lowered", then it is a ♭6 on the (minor) tonic – this has nothing to do with the Neapolitan sixth. The Neapolitan 6th, in "the orthodox system", is the first inversion of the lowered supertonic – which says nothing of its function. Apel is right, on the other hand, that the Neapolitan sixth is some kind of subdominant; everybody agrees about that, even if the best of us consider it to belong to that particular brand of subdominant that is now named "predominant".

Apel continues: "Another example of functional interpretation is the six-four chord of the first degree (I 6/4) which functionally is nearly always a plain dominant (V) involving a double appoggiatura." What is not clear at this point is whether the article is speaking of functional harmony at large, or of Riemann. I am positive, however, that Riemann did not consider the I 6/4 as a dominant, especially in the I – IV – I 6/4 – V – I progression. I'll find references (in Riemann himself, I am afraid, I am not good at secundary references) for my claim. — Hucbald.SaintAmand (talk) 13:38, 20 March 2017 (UTC)[reply]

Yeah, that's pretty much the same thing I read. I'll trust you on that point.

There must have been somebody by Riemann's time who realized that some chord sequences flowed more naturally than others, since composers wrote music on that principle pretty consistently since at least 1700. I realize that the theory of chords was slow to catch on, and conservatories continued to teach Renaissance counterpoint and church modes, but that seems like an awfully long time.
When did the idea of music being "in a key" come about? Mozart certainly didn't describe his pieces as being "in E-flat major" or whatever, but did Beethoven? Chopin? When did that vocabulary become common? That seems like an essential prerequisite to discussions of harmonic function. —Wahoofive (talk) 16:03, 20 March 2017 (UTC)[reply]

Wahoofive, as long as you ask me such interesting questions, you turn me away me from working on the article and seeking appropriate references ;–)).

For sure, the Viennese theory (of Simon Sechter, basically, but it had antecedents) was much interested in chord sequences. What Riemann did was to search for an abstract justification not only for sequences, but also for the fact that they pointed to a goal, the tonic. His answer was sort of philosophical, describing tonality as a kind of dialectic movement away from and back to the tonic. Rameau, for instance, probably had a more processual view, in which each (dissonant) chord was a kind of dominant to that which followed, until the next-to-last one, the dominante-tonique, which resolved on the tonic itself which remained free of any attraction. Rameau's sequence was limited in its end, but not in its beginning. To this, Riemann wanted to oppose something more like a circle, beginning in the tonic and returning to it after an essentially short circuit. Note that Schenker, although he hated Riemann, shows some understanding for this "functional harmony" in what is known today as his "swan slur", which always denotes a kind of sinusoïdal movement, from the tonic down to the subdominant, up to the dominant, and back to the tonic (see Schenkerian_analysis#Articulation_of_the_span_from_I_to_V_in_the_bass_arpeggiation, especially the discussion of "I–IV–V or I–II–V").

Note also that the theory of chords was very much alive in the earliest years of the Paris Conservatoire, e.g. in Catel's Traité d'harmonie, which introduced the very characteristic distinction between "natural" chords, those that could be found in the harmonic series (perfect major, dominant 7th, half diminished and diminished 7th, etc.) and the "artificial" ones (all the others) that could only result from suspensions.

I very much believe that the idea of music being "in a key" originates (or, at least, is first described) in Christopher Simpson's The Principles of Practical Musick, 1667, who wrote that the degrees on which a 6th was to be built in fundamental bass accompaniment were "1. The Half-Note, or lesser 2d under the Key of the Composition. 2. The greater 3d above the Key. [etc.]." This is a rather isolated case, but it is striking. In the 18th century, Rameau (and others) had a very strong notion of the "three principal chords of the mode" (i.e. of the key), I, IV and V – a notion which, as I indicate in the article, has its origin in theories of just intonation.

All this makes fascinating reading, and I am too easily loquacious on the subject. — Hucbald.SaintAmand (talk) 22:13, 20 March 2017 (UTC)[reply]

The lead is appalling

It's not that big-picture assertions in the lead need to be referenced with a fine comb if they're referenced in the sections beneath; though if there's anything contentious or exotic in the lead, a ref should be provided. Here, some of the assertions are ... weird. Most authoritative sources, for example, classify the so-called church modes (all seven of them, not just the two that evolved as the basis of western European tonality, of the canon variety). So the second word in the lead is a problem, I think. Actually, most of the current lead needs to be put in the furnace. Tony (talk) 07:10, 7 May 2018 (UTC)[reply]

Tony, the article is not about diatonicity, but about (Diatonic) function. I cannot imagine how a function could exist outside some kind of tonality. So, what is weird may not be the second word in the lead, but the title of the article itself. I must say that on reflexion, I don't see why tonal functions (which is what I think the article is about) should be diatonic – they often are, but it is not one of their inherent characteristics. And I don't think anyone ever described functions in church modes (not that it would be impossible, but that I don't think it has been done, at least in the sense of "function" in this article).

What is also weird is that the lead not only considers "harmonic function", "tonal function" and "diatonic function" to be synonyms, but adds "or also chord area". On the one hand, an area is not a function, but on the other hand this makes it clear that functions can be associated with chords – an additional reason to exclude modes.

In short, what I think really is needed is an agreement about what an article on Diatonic function wants to describe. — Hucbald.SaintAmand (talk) 08:21, 7 May 2018 (UTC)[reply]

Or syphon off anything that's worthy and delete the article? As you suggest, we can't even get the name right. And so many terms are used that are unexplained here, or ambiguous or contested in the sources. I'm at a loss to understand what it's all about—and I'm a music theorist. Tony (talk) 11:15, 7 May 2018 (UTC)[reply]

At present, Tonal function redirects to Diatonic function; it obviously should be the other way around. Otherwise, I think that much of what you consider "unworthy" arises from this mistaken conception of "diatonic" – and also, perhaps, from a tendency to describe Stufentheorie (Roman numerals) as sort of universal, while at the same time trying to give an idea of Riemann's Funktionstheorie. You are a music theorist. I am a historian of music theory. I think that, with the help of some others, we should be able to make sense of all this. — Hucbald.SaintAmand (talk) 14:01, 7 May 2018 (UTC)[reply]

(Another music theorist chimes in.) What recently caught my eye—and caused me to tag two things in the opening paragraph—was finding the second reference, in an article ostensibly on diatonic function, being an article on chromatic function. For sure, "diatonic" should not be in the article's title. "Tonal function" would be a far better choice. I am far from being a specialist in chant theory, so please correct me if I am wrong, but I believe that some 19th-century theorists (particulary those associated with Mechelen and Regensburg) did attempt to develop a more elaborate form of church-mode theory, assigning different functions to various scale degrees. And, of course, these theories were meant to address twelve (or even fourteen) modes, not seven. This might have some bearing on whether "harmonic function" or "tonal function" is the better title for this article.—Jerome Kohl (talk) 15:50, 7 May 2018 (UTC)[reply]

PS: I should have thought to do so sooner, but I have just taken a look at the very first version of this article, from February 2004, and it is plain that the creator, User:Hyacinth, had something quite different—even unrelated—in mind from what has evolved subsequently.—Jerome Kohl (talk) 15:58, 7 May 2018 (UTC)[reply]

I myself spoke of "modal function" in several recent papers (not in English, though). I can only say here that the notion is controversial (even if I believe in it), and rather different from the functions described in the article. It certainly does not justify a WP article on diatonic functions, and probably should not be mentioned in any WP article because it could not easily be referenced. (Handschin's book Der Toncharackter of 1948 is about something of the kind.)

As to the 2004 version of the article, I think that it would be extremely difficult to support such an idea by references. That enharmonic notes cannot (or can) be considered equivalent hardly could be considered ther "function" (or their "functionality"). The idea is not without interest, but I don't think it was given the right name. Hucbald.SaintAmand (talk) 18:15, 7 May 2018 (UTC)[reply]

It would be much more convenient for other editors if, rather making them look at when a comment was posted and then finding the version from that time in the article history and then reading what the second word is, you stated what the word you have a problem with is. It's hard to complain about quotes that aren't quoted. Hyacinth (talk) 22:39, 7 May 2018 (UTC)[reply]

It's hard to imagine a single word making an article lead "appalling". It seems that a single misused word is something that can be corrected, not armageddon. Hyacinth (talk) 22:45, 7 May 2018 (UTC)[reply]

Hyacinth, forgive my bluntness, but in my view the article was misconceived when started, and has grown like topsy-turvy hospital architecture, often in an attempt to address the initial lack of delination and the unsatisfactory use of sources. Above all, it is very confusing to readers in its current form. Yes, I agree with Hucbald and Jerome that the redirect should be reversed. Do we need this as a stand-alone article? Tony (talk) 07:22, 10 May 2018 (UTC)[reply]

I don't think articles or deletions are justified by quality. See: WP:N. Hyacinth (talk) 11:13, 10 May 2018 (UTC)[reply]

Independently of judgements about the quality of articles, It seems clear to me that WP needs an article about (tonal) functions. The real question is whether these (and the article itself) sould be termed "tonal," "harmonic," "diatonic," or whatever.

I don't think that the term "function" has been used as a more or less technical term in music before Riemann, who described his theory in a book entitled Vereinfachte Harmonielehre oder die Lehre von den tonalen Funktionen der Akkorde, published in London in 1893. The book was translated in English in 1896, under the title Harmony Simplified or the Theory of the Tonal Functions of Chords. Roman numerals had been used before, really starting with Gottfried Weber in 1817-1821 (there had been an earlier but occasional usage by Georg Joseph Vogler, 1776); however, it is only in the 20th century that the underlying theory, known as Stufentheorie ("Theory of the Degrees") began to be considered an alternative function theory (I mean, alternative to Riemann's). It is therefore beyond doubt for me that this first article should be named "Tonal function".

Whether other articles should deal with "modal function" and/or "diatonic function" may be an open question. I have used both terms in discussions of medieval and Renaissance modality, and also of non-European (Arabic) modality. I doubt however that one could find enough secondary sources about such concepts. But what is clear to me is that in any case they are quite different from that of "tonal function" and that these other articles (if ever created) may link to, but should be distinct from, each other and even more from "tonal function".

Hucbald.SaintAmand (talk) 15:36, 10 May 2018 (UTC)[reply]

Riemann? Maler!

It seems that people here want to explain what Riemann said. This is of no real benefit - Riemann invented functional analysis, but he stumbled into a new area and created something that needed much overhaul. Functional theory, as it is understood now, is essentially what Wilhelm Maler (and, to some extent, his teacher Hermann Grabner) streamlined from Riemann in the 1920s - this (and later additions to it, e.g. the historical viewpoint of de la Motte) is what should be explained to the contemporary reader who wants to understand what functions are in music. Riemann was the big inventor, yes, but what he wrote is only interesting for historical reasons. It should be dropped from an explanation in the same way that nobody explains Newtonian physics the way Newton did it (read his great "Principia mathematica" - you'll see that his explanations have been out of vogue, and out of use for at least 150 years).

Maler, for the good of all of us, removed Riemann's speculative and, in hindsight, unnecessary "dualism" (that minor is in some sort the "inverse" of major) - and since then, musical functions have been an understandable and well-founded tool for musical analysis.

And why isn't there an entry for Wilhelm Maler in the enWP? (to be fair, also the German WP mentions his eminent contributions to music theory almost in passing - even though it references his "Beitrag zur durmolltonalen Harmonielehre (München und Leipzig, 1931; vielfach neuaufgelegt)", i.e. "reprinted many times". --User:Haraldmmueller 20:05, 2 June 2018 (UTC)[reply]

@User:Haraldmmueller, the reason why the German WP mentions the "eminent contributions" of Maler only in passing may be that there are doubts about how eminent this contribution has been. Wilhelm Maler was a national-socialist. He actively contributed to the eradication of all jewish voices (i.e. among others Schenker, Schoenberg and Kurth) in German music theory and to questionable changes in the theory itself. As Ludwig Holtmaier wrote (ZGMTH 2003),

"The German "pragmatic" post-war theory of music arose under the influence of the avowed national-socialist anti-intellectualism, through the influence of the youth movement, supported by the spirit of the Wandervogels (a movement through which almost all German music theorists since August Halm were culturally and socialy "socialized"), and eventually through the soon complete expulsion of jewish theorists (mainly Kurth and Schenker). It was essentially performed by personalities who had a responsibility in the decline of the discipline in the third Reich (Herman Grabner, Wilhelm Maler and Fritz Reuter) and retained an hostility to theory that can still be felt today."
(Unter dem Einfluß des erklärten nationalsozialistischen Anti-Intellektualismus, durch Einflüsse der Jugendbewegung, getragen vom Geist des Wandervogels (einer Bewegung, durch die fast alle deutschen Musiktheoretiker seit August Halm kulturell und gesellschaftlich sozialisiert wurden) und schließlich durch die fast vollständige Verdrängung jüdischer Theoretiker (vor allem Kurth und Schenker) entstand die deutsche ›pragmatische‹ Nachkriegs-Musiktheorie. Sie wurde im wesentlichen von den Persönlichkeiten mitgeprägt, die den Niedergang des Faches im Dritten Reich mitzuverantworten hatten (Hermann Grabner, Wilhelm Maler und Fritz Reuter), und bewahrte sich eine bis auf den heutigen Tag spürbare Theoriefeindlichkeit.)

The article mentions Grabner and Diether de la Motte, who both wrote about Riemann in less suspect times than Maler (the first before, the second after Nazism). The intention, in any case, is not of converting an English readership to function theory; and to stress the role of Maler above that of Riemann would seem to unduly distort history. On the other hand, it may prove useful to simplify the description of the substitutions. In particular, denotations such as "tL", etc., may be too much influenced by neo-Riemannian theory; they seem unnecessary in de la Motte's version of Riemann's theory. — Hucbald.SaintAmand (talk) 08:34, 3 June 2018 (UTC)[reply]

Please, leave the Naziness of them out of the discussion. It bears nothing on the merits of music theory (but ...: Grabner was, in contrast to Maler, really and, it seems, staunch Nazi; also according to the music he wrote for them).

You write "to stress the role of Maler above that of Riemann would seem to unduly distort history": This is the point where I disagree with you: If you write an article under the title "History of musical diatonic functional harmonic theory" or something like that, of course Riemann would be the center of it (as Newton is to the - too, or at least quite, short - History of classical mechanics). But if the article is "Diatonic function (music)", the topic is of course to explain the current scientific view, which has evolved so much form Riemann that one should mention him in a short introduction, but not too much more (go to Classical mechanics to see how it deals with Newton: He is mentioned in the introduction, and then there is a "history" section at the very end). Mixing historical development and current stance is a detriment for every explanation. But if you hold a different view, you are entitled to it ...

"an hostility to theory that can still be felt today" - mhm. Schenker's wide encompassing theories had nothing (or only very indirectly) to do with harmonic questions; his Ur-Melodie came from a completely different problem space and view on musical analysis. In this area, there seems - as far as I can see it, i.e. by personal observation - to be a consensus in German-language publications that Schenker analysis overdoes it (neo-Schenkerian analysis, to be fair, has also shed many of Schenker's obscure ideas - this seems to be a recurrent pattern: The romantic theorizers had to be stripped of their vague, psychological and sometimes psycho-bubble ideas to make their ideas useful for our rationalistic times). On the other hand, in the area of harmonic problems and analysis, it seems clear that the US scene by following Schönberg with his "Viennese" degree description was much more hostile - or at least neglient - of theory than the functionalists.

In a modern sense, some claim that all of these theories aren't any, as e.g. Ulrich Kaiser demonstrates (I have to look up where ...): All of that are ways of describing events, but not finding any "rules" that would guide how music works. Whether this is (again) specific German "Theoriefeindlichkeit" or, as I would see it, the general inclination towards "scientific" theories also in the humanities - with the tendency to request that a "real" theory has to have "rules" -, is certainly debatable - I am convinced of the latter. But if this is the modern stance, it should be reflected in a WP article, and not the historical viewpoints and devlopements (except, as mentioned, in articles named "History of ...").

Re Holtmeier: This is (of course?) a very valid description of what happened between - say - 1910 and 1980. But that's now 40 years past - Holtmeier doesn't even mention de la Motte (you claim the oppositce: "The article mentions ... Diether de la Motte", but my search for "Motte" did not hit anything), let alone his pupils (yes, de la Motte is already a gone generation). The reason is, of course, that his topic is the time mentioned; but this cannot be any reason to ignore what has happened afterwards (and even Holtmeier's article is more than 15 years old). Moreover, Holtmeier - in my view - uncritically refers to the amount written: There is an underlying argument in his text that "the older wrote much thicker books". That unfamous reducton to the "Volkslied" is certainly reason for it, but another one is that in modern times, the creation of holistic, all-encompassing theories (like Riemann's, Schenker's, maybe also Maler's 3-volume one - I have never read it) is no longer fashionable or even usable or even acceptable: "We" want, it seems, to solve smaller problems precisely, instead of painting with a big brush over all of it. One of the reasons is that people like de la Motte (and also, from the practical side, Harnoncourt!) have taught us to view many things historically - so there is no longer a chance to write "the musical theory": It has now to go into separate articles or chapters "the ... during the renaissance", "... in early classics", "... in late romantics". So Holtmeier's "accusation" of "Theoriefeindlichkeit" can actually be read as the rise of the concept that one has to do music theory - and all humanities - in a much more piecemeal fashion, in order to do jsuticeto reality - and then, it's no longer hostility to theory, but on the contrary, creating better theories about what happened during the history of musical composition.

--User:Haraldmmueller 08:49, 3 June 2018 (UTC)[reply]

When I wrote that "the article mentions de la Motte", I was thinking of our WP article, not of Holtmeier. I think in addition that the description of Riemannian theory should come closer to de la Motte (certainly more "current" than Maler), and abandon that mix of neo-Riemann that merely is incorrect. Unless you can quote more recent sources; but so far as I am informed, de la Motte is still used as a reference book in 2018 in the Mendelssohn Hochschule für Musik, Leipzig (I have no recent information about other institutions). I leave you the responsibility of your comments on Schenker, but to say that you perhaps should do better to read Schenker himself and not rely on secondary or tertiary sources - especially if you seriously think that Schenker's theories "had nothing (or only very indirectly) to do with harmonic questions". — Hucbald.SaintAmand (talk) 10:00, 3 June 2018 (UTC)[reply]

Re de la Motte - as of textbooks, I believe his is really the latest. His pupils only wrote articles.

Re Schenker - my sister (who was a musicologist, not a hobby musician like me) had even harsher words for me. So yes, I have, at some time, to read Schenker from a not-church-organist-limited-harmonic non-secondary-tertiary point of view. Or, in other words, I don't understand this! But that's not something I (would, can, should) criticize the WP article for - I just got carried away.

And, finally, you are right: My headline should have been "Riemann? de la Motte!" to make the point. I'm happy that you seem to agree with this - nothing more that I wanted to bring up.

--User:Haraldmmueller 10:43, 3 June 2018 (UTC)[reply]

I tried a new version of the section on German functional theory. Tell me whether you agree and feel free to modify. (I am afraid I did not quote Diether de la Motte from a secundary source, as WP normally expects: I merely browsed through his Harmonielehre, which I happened to have in my book shelves.) — Hucbald.SaintAmand (talk) 15:28, 3 June 2018 (UTC)[reply]

Yes, thank you - that's, in my eyes, a good compact description! I just changed a few minor details.

What I would like to see is that de la Motte, or some term to say that others have modified/adapted/improved/... it (the Grabners/Malers/de la Mottes), is shortly introduced also in the introduction - right now the impression the text leaves is that Riemann's original theory/concept is still taught and used and en vogue more or less unchanged. And is Schönberg's 1954 treatise actually the last word on Stufentheorie?; also, would it be correct to cite the word "degree" in the explanation of the Stufentheorie? --User:Haraldmmueller 17:28, 3 June 2018 (UTC)[reply]

1) I am aware of how (revised) Riemannian theory is used in several East-European countries: in some cases, the revisions do not really match the Grabner/Maler/de la Motte line. (In Romania, for instance, I have seen a combination of functional notations with Roman numerals – say T^vi for Tp.) But this goes way beyond what can be expected of an English (or, better said, American) WP article.

2) Let's say, similarly, that Schoenberg 1954 is the last word about Stufentheorie that can reasonably be documented in this WP article. The article Root (chord)#Root progressions in music, which is more specialized in this topic, mentions more recent theories by Sadaï and Meeùs which may or may not be considered developments of Stufentheorie (I think they are).

3) I don't quite understand your question about the word "degree" in the explanation of Stufentheorie. "Theory of the degrees" seems to be the standard translation of Stufentheorie, and I don't see how it could be translated otherwise.

Hucbald.SaintAmand (talk) 19:22, 3 June 2018 (UTC)[reply]

Requested move 23 August 2018

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. No further edits should be made to this section.

The result of the move request was: consensus to move. QEDK (後 ☕ 桜) 13:53, 30 August 2018 (UTC)[reply]

The request to rename this article to Function (music) has been carried out.

Diatonic function → Function (music) – It seems odd that this article has been listed as a level-5 vital article, while we still do not agree as to its exact object, as can be read in the comments above. Renaming it "Function" would allow explaining the possible differences between Diatonic function (Chromatic function?), Harmonic function, Tonal function (Modal function?), etc. Hucbald.SaintAmand (talk) 13:08, 23 August 2018 (UTC)[reply]

Oppose—sorry, Hucbald; I think that still suffers from vagueness, not to mention the difficulty of finding agreement among published scholars on what music "function" is. Tony (talk) 13:25, 23 August 2018 (UTC)[reply]

But, Tony, that is precisely our problem: there is no consensus on what a musical function is, neither on WP nor in the literature. This disagreement would be better served by a documented discussion than by an article which chooses one definition for its title and remains unable to justify this choice in its content... So far as I can tell, there is not a single reference in the WP article justifying the name "Diatonic function". The New Grove Online solves the problem by naming its article merely "Function". — Hucbald.SaintAmand (talk) 21:08, 23 August 2018 (UTC)[reply]

Concur—sorry, Tony1; I think Hucbald has got an open-and-shut case here. There is no justification for including the word "diatonic" in the article title, since this is contrary to use.—Jerome Kohl (talk) 22:31, 23 August 2018 (UTC)[reply]
Support (without much enthusiasm, but a more general name would surely be an improvement). The article is utterly obscure. What is it talking about? It says "concept", but I think it is fairly clear this should be "term": various people have used the term "function" to mean a whole range of things, most of them ill-defined. The table listing "diatonic functions" in America and Germany (??!) has columns "Function" and "English", giving different ways of describing the same thing: if "English" means the English name for the function, in what language is the "Function" written? Imaginatorium (talk) 04:12, 24 August 2018 (UTC)[reply]

Imaginatorium, the table that you mention indeed mistakes terms for concepts. The column "Function" actually gives the names (not the functions) of (diatonic) degrees, and the columns "English" and "German" gives names of some of the functions that these degrees may take. It gives one function per degree, while several degrees could exert different functions, and it wrongly translates the German parallel as "parallel" in English, while the correct translation would be "relative".

One additional question that may be raised in this context is whether the various forms of the minor scale are all diatonic, which is another reason to consider that the term "diatonic function" is inappropriate. The article Degree (music) seems to imply that only "natural" (Aeolian) minor is diatonic. On the other hand, at times it appears to equate the names of the degrees with their "diatonic function"...

The New Grove article, which in the 2d edition is almost identical to its 1st edition, really is a disambiguation article. It carefully avoids all qualification ("harmonic", "tonal", etc.) and refers to the articles "Harmony"; "Tonality"; and "Analysis". For the WP article, it may be better to discuss the various meanings of the term (and the concepts that it may denote) in separate subsections. — Hucbald.SaintAmand (talk) 07:17, 24 August 2018 (UTC)[reply]

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Functions in music

However we may name this article, I think that we will have to consider what the following quotations from the Cambridge History of Western Music Theory may suggest – some of them indicate types of musical function of which we may not have been enough aware:

Mattheson’s systems of relationships may be conceived as specifying four musical functions, and hence four discrete domains of study: (1) the "natural" – the domain of acoustics (the phenomenal basis of sound); (2) the "moral" – the domain of affect and style (the particular psychology of music); (3) the "rhetorical" – the domain wherein are studied the performative and grammatical aspects of musical composition (as in the musica poetica tradition or in the later treatises on performance itself ); and (4) the "mathematical" – the traditional theorization of musical material. [Leslie Blasius, p. 38.]
The final distinction of scales as modulating or non-modulating pertains to the number of "functional" mesai. According to Aristoxenus, "function" (Dynamis) is a matter of context; Cleonides, the Aristotelian Problems, and especially Ptolemy (Harmonics ii) elaborate on the term, making it clear that the "function" of notes involved their relationship in a specific sequence of intervals typical of any one of the genera. The mese, in particular, played an important role because of its strategic position at a point from which a scale could proceed either by conjunction or by disjunction. [Thomas J. Mathiesen, p. 125.]
The names of the notes and tetrachords obviously had some functional correspondence in their origins, yet in the Latin theoretical tradition of the early Middle Ages no musical function or character is ascribed to any note; the construct exists as an abstract entity determined by arithmetic principles. [Calvin M. Bower, p. 147.]
The tetrachords are given names according to their function in chant: low pitches (graves), final pitches (finales), high pitches (superiores), upper pitches (excellentes). [Calvin M. Bower, p. 154.]
In Hauptmann’s dualistic model, there are three "functions" assigned to pitches that constitute major and minor triads (or as we will call them, following Hauptmann, "klangs"): unity (Einheit); duality or opposition (Zweiheit); union (Verbindung). The functions or "Moments" (as Hauptmann prefers to call them) are respectively associated with the octave, the perfect fifth, and the major third, whose primacy he derives from string division. [Henry Klumpenhouwer, p. 460.]
Riemann – Properly speaking, "functionality" in tonal music concerns the behavior of chords in relation to the tonic. A function theory differs from a theory of chordal scale degrees (Stufentheorie) in that the former goes beyond the description of chords according to their position within the scale and constitutes a systematic ratiocination of chordal relationships around a tonal center. [David W. Bernstein, p. 796.]

We should also consider the following books and articles, which all include the word "function" in their title:

Wallace BERRY. Structural Functions in Music. Englewood Cliffs, Prentice Hall, 1976.
William CAPLIN. Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. New York, Oxford University Press, 1998.
Daniel HARRISON. Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents, University of Chicago Press, 1994.
David LEWIN. "A Formal Theory of Generalized Tonal Functions". Journal of Music Theory 26 (1982), pp. 23–60.
Hugo RIEMANN. Vereinfachte Harmonielehre; oder, Die Lehre von den Tonalen Funktionen der Akkorde. 1893. Harmony Simplified; or, the Theory of the Tonal Functions of Chords, trad. H. Bewerung, London, Augener, 1896.
Arnold SCHOENBERG. Structural Functions of Harmony. New York, Norton, 1954.

Hucbald.SaintAmand (talk) 16:42, 25 August 2018 (UTC)[reply]

I think your extensive list above illustrates the real problem: there is no coherent concept of a "function" in music theory. "Function" is just a function word (ha!), just like "relationship", or "purpose", so it may appear in all sorts of different ways in the writings of different authors, of varying degrees of coherence, but a WP article hooked to this word will inevitably end up as a non sequitur patchwork. I can never avoid a feeling of "mathematics envy" in almost all articles on "music theory" (so-called "musical set theory" is surely the worst); in mathematics, by contrast to music, "function" has a very clear and specific definition. Add in general confusion between English words, translations of German words, and anglicised German words, and you get a mass of ambiguous parsings, as in the titles you have mentioned above. (For example, what does Caplin mean by a "formal function"?) Imaginatorium (talk) 03:32, 27 August 2018 (UTC)[reply]

I don't think it's that problematic. The article, with its (current) lemma "diatonic function", obviously does not want to cover all things called "function" - rather, "that what Riemann introduced and what was developed from it". And in that "mathematical envy", one should not overlook that mathematics has the same problem at many places - for example, there are multiple concepts of Polyhedron (that article contains a quote saying "... at each stage ... the writers failed to define what are the polyhedra"; there's also Lakatos's book Proofs and Refutations about this problem) or Almost all. And an encyclopedia is also about selection, even if some people think this constitutes original research - yes, it may sometimes overlap with it, just because more clarity is needed; but it is necessary.

More concretely: I do not know the English books cited above. In German, the important "definitional works" are Hermann Grabner's Handbuch der funktionellen Harmonielehre, Diether de la Motte's Harmonielehre and maybe (but I do not know it) Wilhelm Maler's Beitrag zur durmolltonalen Harmonielehre. Riemann is certainly "only" of historical interest, as some of his central concepts (e.g. that the minor chord is an inverted major one ... if I remember correctly) have been wholeheartedly discarded. I have heard - but maybe someone contradicts this - that functional theory, and thereby "diatonic functions" are still more of a "German" thing, whereas in the English-speaking world, it is more on a sideline (and more descriptive concepts like Roman numeral analysis are predominant); this would mean that one might concentrate on publications and concepts therein that are aligned with the three works I have just mentioned. --User:Haraldmmueller 06:51, 27 August 2018 (UTC)[reply]

Imaginatorium, music theory obviously is not an exact science. Its language is not a formal language like that of mathematics. I can see what you mean by "mathematics envy", which may be typically American. What must we do? Renounce discussing it in this Encyclopedia, or on the contrary explain why and how music theoretic concepts leave space for discussion?

But you are right, there are cases in my quotations where the word "function" is used merely as a function word. I deliberately avoided commenting the citations when I first quoted them, but they should of course not all be taken at the same level (they are quoted in the order of page numbers in the Cambridge History). Some describe the function of music more than functions in music. Music may be festive or funeral, it may accompany danse or work, etc,: these are the functions of music and the term "function" is used here in a sense that does not deserve an entry in WP.

What I call functions in music, on the other hand, is a partial answer to the question posed by Ian Bent defining music analysis in the New Grove: "how does it work?" What is the function of this or that note or chord in the working of a piece of music? The idea that notes or chords "function" is due to Hugo Riemann, as implied by User:Haraldmmueller. The concept had been prepared by Hauptmann (and Rameau, and others) and survives in Grabner and Diether de la Motte, as in the teaching, even today, of many Eastern European countries up to Russia.

The origin of the expression "diatonic function" (which I now see can be found on Internet; I had never encountered it in 50 years of activity in music theory and I did not find it in any important music theory book) is somehow explained in the quotation by David Bernstein and in comments above. It is the idea that, as much as Riemann describes three tonal functions, the Stufentheorie may be taken to describe six or seven functions in the scale. This is documented in books, among others (in German) by Martin Vogel (and perhaps Renate Imig), I think – and I'll find references about that. Because the scale is sometimes thought as diatonic (even although it may not be), the expression is found in texts without much theoretical background.

Mathiesen translates dynamis in Aristoxenus as "function". And Bower (p. 147) alludes to something similar in the Middle Ages, obviously thinking of terms such as qualitas or modus in Guido of Arezzo; he is mistaken when he adds that "in the Latin theoretical tradition of the early Middle Ages no musical function or character is ascribed to any note", I have documentation to the contrary (depending on what is called the early Middle Ages, though). These translations should not be dismissed: they refer to something that explains the role of notes in the working of music. On the other hand, Matheson's "domains of study", or the functions of tetrachords in chant, seem more of the order of the function of music and need not retain us. As to Caplin's Formal Functions, I am afraid I should reread the book.

But I think that all this provides important material for a WP article, however we decide to name it ... — Hucbald.SaintAmand (talk) 13:11, 29 August 2018 (UTC)[reply]

Hucbald.SaintAmand, I believe everything what you say - either because it makes sense, or because I cannot disprove it, but - what are you (or we) trying to do here? I propose that the root term we should be talking about is whatever corresponds to the German word "Funktionstheorie" - this is what is commonly ascribed to Riemann, with improvements/developments be Grabner and others; and sort of precursors back to Rameau. I looked up functional theory, but this redirects to a linguistic concept. I am very much of the opinion that the lemma should be "functional theory (music)" if the term "functional theory" is used e.g. in translations of modern German authors of Funktionstheorie texts. This selection of a lemma - aligned with the main term (again: if I am right) and its history - would then, more or less forcefully, lead to a limited horizon of the contents, to be derived from texts on Funktionstheorie only. Everything else which might be or have been called "function" in music would be relegated to a "Other uses of the term function" section. I very much believe that this would be much more helpful to readers, than to try to write something which encompasses many or even "all" uses of the term "function" in music, or even in harmonics contexts. I even suspect that the all-encompassing view on "function" indicated above by Hucbald.SaintAmand borders on, or is, "original research", as I cannot believe that such a encompassing view is proposed in any single source. This last is, of course, speculation - but I'd like to be shown a text that tries to collect that many meanings of "function" in music at a single place before accepting that this should be mirrored in a WP article. --User:Haraldmmueller 19:32, 29 August 2018 (UTC)[reply]

User:Haraldmmueller, you may note (see Talk:Diatonic_function#Requested_move_13_October_2016) that a suggestion to rename the article as Tonal function (which is the term used by Riemann himself) was refused with the main argument that this would restrict the article to functions in tonal music. The same could be said of "Harmonic function". Funktionstheorie, so far as I can tell, is a term never used by Riemann himself (I checked the Handbuch der Harmonielehre, Vereinfachte Harmonielehre, Musilalische Syntaxis and Die Natur der Harmonik, with OCR). Its translation as "functional theory" would not at all be as restrictive as the German term, if only because Funktionstheorie is not much known in (American) English. The fact is that Stufentheorie, which is much practiced in Western Europe and the US, often is considered a theory of (six or seven) musical functions (this probably being the cause for the erroneous conception of "diatonic function"). I didn't have the possibility today to access my paper library, but I think to have German sources about this (mentioned above: Martin Vogel and Renate Imig); and this is a matter we cannot dispense to address. A WP article in English about "functional theory (music)" hardly could be restricted to the German Funktionstheorie. In addition, I think that it may be important to say some words about functional theories before polyphony, those that I mentioned: Aristoxenus (Dynamis) or Guido (modus or qualitas). There are enough modern references about these.

To make things short, I'd think that restricting the article to Funktionstheorie would lead to similar problems as those of a "diatonic function" article. But we certainly need other opinions about this. — Hucbald.SaintAmand (talk) 06:13, 30 August 2018 (UTC)[reply]

Ok - I see all your points: Most important, there is no "narrow" equivalent for the German Funktionstheorie in English, so an English article cannot be reasonably limited to "it" - this almost fully lays to rest my previous remarks. Re Riemann himself not using the (German) term, I see this as a purely historic artefact (almost all scientific, mathematical, arts terms were not coined by their inventors, but later-on). Re "some words about ... others", this would of course be necessary, but (I think) should be kept brief. Nevertheless, not having any overview over the English literature (be it translated or genuine), I see that I must refrain from having too much of an opinion ... --User:Haraldmmueller 06:46, 30 August 2018 (UTC)[reply]

It's a good thing there are not multiple ways to be related to someone, or the family article would have been as difficult to write as this article supposedly is. Hyacinth (talk) 22:35, 8 September 2018 (UTC)[reply]

Chaotic already at the opening

I see a recent edit that has produced this:

Function, in music, is the term used "to denote the relationship of a chord to tonal centre."^[1] Strictly speaking, the term refers mainly to Hugo Riemann's theory of "tonal functions", according to which there are only three possible functions (tonic, dominant, subdominant), but its meaning has been extended, especially in (American) English, to cover a more general conception according to which each scale degree has its own specific function.

So which is it? Chord (as announced at the start) or both chord and tone? Tony (talk) 09:43, 9 September 2018 (UTC)[reply]

Just curious - where does it say "tone"? If you interpret "scale degree" as "a tone in the scale", I'd risk assuming that the (primary and/or WP) author of "each scale degree has its own specific function" means the chords associated with the scale's degrees: Many texts (no ref here ... I'd have to dig ...) start quite early with placing a triad over each scale degree and then more or less explicitly identify the chords with the degrees. Even WP's article Degree (music) does this: The introductory text there says "scale degree refers to the position of a particular note[!] on a scale[3] relative to the tonic" - but the first image near it shows, without further ado or explanation, a scale of triads, with its caption ignoring the chord aspect: "Scale degree roman numerals". So the confusion, or ambiguity, or overlapping meaning, seems to be the state of the art? --User:Haraldmmueller 10:11, 9 September 2018 (UTC)[reply]

Let me add that both statements (the first mentioning "a chord" and the second dealing with "scale degree") are referenced. The New Grove speaks of chords, Walter Piston of scale degrees. Piston never clearly defines what he means by "scale degree", but it may reasonably be argued that he means "the degrees of the scale", i. e. notes. He writes for instance (p. 12) "Roman numerals identify not only the scale degree but also the chord constructed upon that scale degree as root". But he also writes (p. 17): "Chord succession can be reduced to root succession (or root progression), which in turn can be translated into Roman numerals representing a succession of scale-degrees". Then, (p. 29): "Tonality is the organized relationship of tones in music." And eventually, (p. 31): "Tonality, then, is not merely a matter of using just the tones of a particular scale. It is more a process of setting forth the organized relationship of these tones to one among them which is the tonal center. Each scale degree has its part in the scheme of tonality, its tonal function." Etc.

The fact is that the New Grove associates functions with chords and Piston with scale degrees (notes) as roots of chords. It seems to me that the lead of our article in its present form correctly gives account of this relative imprecision. To answer Tony's question "Which is it?", I do think that it is both and that this first paragraph of the article not only says so, but also indicates that the matter is not without some confusion – which is the reason of the present discussion. I consider nothing of this "chaotic", it merely presents a complex matter as complex, and does so with references. The intelligent reader (and I presume that all our readers are intelligent) will know what to do of this, especially if the rest of the article provides further information (but that remains in need of improvement).

Hucbald.SaintAmand (talk) 13:55, 9 September 2018 (UTC)[reply]

What you've posted is clear in the opening paragraph. But you've worded the first proposition as exclusive. That was my problem. Tony (talk) 01:32, 10 September 2018 (UTC)[reply]

I see what you mean. Would you have another suggestion? It seems difficult to keep neutral. This initial statement was but a quotation ... What would you think of something like this:

Function, in music, is the term used to denote the relationship of a chord or a scale degree to a tonal centre.

without the quotation marks, adding "a" before "tonal centre" (missing in the NG), and perhaps nevertheless keeping the footnote refering to the NG, which remains the origin of this statement? — Hucbald.SaintAmand (talk) 07:27, 10 September 2018 (UTC)[reply]

Better, perhaps with a ref-tag after chord and after scale degree? I'd hyphenate the latter, and unlink music. Tony (talk) 07:34, 10 September 2018 (UTC)[reply]

I wont hyphenate "scale degree" because that is how Piston writes it (and also because it is my own usage ;–)). — Hucbald.SaintAmand (talk) 09:48, 10 September 2018 (UTC)[reply]

The article remains incomprehensible. It is a disservice to readers. Tony (talk) 11:56, 12 September 2018 (UTC)[reply]

Can we agree that it's, right now, "work in progress"? ;-) ... let Hucbald.SaintAmand tackle the large sins (deleting whole bunches, suggest topics), then in a next step find an agreeable text. Alternative: You write - in your user space? - a complete alternative suggestion (I did that for a large part of the GDPR article in the German WP, so you don't think that I don't know what that means ... much work, at least; and certainly also discussions afterwards ...). --User:Haraldmmueller 12:10, 12 September 2018 (UTC)[reply]

References

^ "Function", unsigned article, Grove Music Online, [1].

Square brackets in "German functional theory"

The table has entries like "Dp or [Tg]"; the square brackets are explained a few sentences later, but they made me wonder whether I missed an additional notation. Could this be rewritten as "Dp (or Tg)" - again with an explanation like "the less likely one is shown in parentheses in the table". But parentheses in situations like this have, I think, a common (vague) meaning "not the typical case", so that also a casual reader would gather roughly the correct meaning. --User:Haraldmmueller 10:13, 10 September 2018 (UTC)[reply]

Tkp?

In the second table in the article,

I do not understand what the "thing" under "English" (and also "German") would be: Being German-speaking I'd say these are the "functions" - but what is then what is indicated below "Function"? Could we have two category names for these classifications?
the "counter parallel" is not given under "German" - that would be "Gegenklang".
yet, an abbreviation for it is given under "German abbreviation" - but "Tkp" is, as far as I know, wrong: It should be Tg.
the slashes for iii are "uninformative"; the word "or" would indicate more clearly that the mediant can be assigned two different ... whatevers.

Am I correct for 2...4.? then I'd change it; re 1., if anyone has a term to write near "English", I'd be happy to hear it. Instead of German, I'd put in the header German "Funktion" if that's ok. --User:Haraldmmueller 10:23, 10 September 2018 (UTC)[reply]

Minor is inversion of major in German(y)?

"Functions in the minor mode" starts with

"In the US the minor mode or scale is considered a variant of the major, while in German theory it is often considered, per Riemann, the inversion of the major."

Historically, this is certainly true for "German theory"; but I doubt that "often" is true today. Is there a(ny) source for this claim? --User:Haraldmmueller 10:26, 10 September 2018 (UTC)[reply]

Unclear double plagal cadence

Under "Tonicization", it says (for a possibly explanation of the blues turnaround):

"doubled plagal cadence, IV/V–V–IV–I (IV/V–I/V, IV/I–I/I)".

I would understand this easily if it simply said:

"doubled plagal cadence IV/V–I/V-IV/I–I/I."

or maybe better

"two subsequent plagal cadences IV/V–I/V and IV/I–I/I."

(to reduce "symbol confusion"). What is the explanatory value of the "IV/V–V–IV–I" in the current version? --User:Haraldmmueller 10:35, 10 September 2018 (UTC)[reply]

Parallel or relative?

My revision of the article supressed several links to articles that puzzle me: tonic parallel, dominant parallel, subdominant parallel. Each of these redirects to another artile, parallel and counter parallel, which states that

In music, a parallel chord (relative chord, German: Parallelklang) is an auxiliary chord derived from one of the primary triads and sharing its function: subdominant parallel, dominant parallel, and tonic parallel.

and refers to Frank Haunschild, The New Harmony Book, 2000. Gjerdingen, however, in his Guide to the terminology of German harmony, states that "the [German] names for the so-called secondary degrees may strike the English reader as foreign in both sound and concept." And indeed I had never encountered the English word "parallel" as a synonym for "relative". "Parallel", on the contrary, usually denotes something different: the chord of the same root but of opposed mode – C major an C minor, for instance, are "parallel chords", e.g. in neo-Riemannian theory, or as clearly described in the article parallel key.

Oddly, the article parallel and counter parallel does not make use of the German abbreviations (P and G for Parallele and Gegenparallele, but uses the neo-Riemannian abbreviation, L, for Leittonwechsel. It also proposes Cp for "counter parallel" and a fancyful German version, Kp, which does not seem to exist in German.

I don't know what to do of this... — Hucbald.SaintAmand (talk) 10:47, 11 September 2018 (UTC)[reply]

Parallel and counter parallel appears to refer only to Haunschild's "The New Harmony Book", which is published by a German publisher and which is not even able to give the contents on that web page in English. I suspect very much that either a German person translated the work (maybe with some last editing by a native English speaker, who might not know enough about music to boldly change "parallel" to "relative"), or by an "average" English translator who also might believe - or have been made to believe - that "parallel" is fine. If someone has access to that book, it would be interesting to find out (by researching the translator/s and by judging the quality of the English text) whether my suspicions do have some basis in fact ... I, personally, suspect very much that this is a book in bad (musical) English, and so the WP article Parallel and counter parallel is simply based on a wrong lemma. --User:Haraldmmueller 09:12, 12 September 2018 (UTC)[reply]

Deletion of the section on the "Circle of fifths"

I decided to delete the section on the "Circle of fifths". Here are my reasons.

Nattiez writes that "most American musicologists" analyzing the Tristan chord choose a solution "in which functional succession is explained by the circle of fifths (in which, therefore, scale degree II is closer to the dominant than scale degree IV)." He never says that this is "another theory regarding harmonic functionality" and, indeed, it is not. At best, it is a particular reading of Simon Sechter's theory of the degrees. Goldman's statement that "the IV chord is actually [...] at the greatest distance from I" (etc.) is a rereading of Sechter's explanation of the circle of fifths, I-IV-VII-III-VI-II-V-I, in his Die richtige Folge der Grundharmonien ("The right succession of the fundamental harmonies"), vol. I, 1853, p. 19 ss., in wich indeed II is closer to V than IV. The circle of fifths is mentioned by Nattiez in the very special context of the analysis of the Tristan chord, and it is not particularly concerned with the question of tonal functions in music. (It might be added that none of this can be found in the French version of Nattiez' book, Musicologie générale et sémiologie, despite what footnotes mentioning the original French may have led to think.)

The use of the I-V-IV-I turnaround as explanation of how functions may be notated (in Roman numerals) in the case of tonicization or modulation is not referenced. It proposes a notation that I have never seen and that I hope never to see again, IV/V-I/V-IV/I-I/I. The deleted text also said that this succession is "considered tonally inadmissible", while the V–IV–I turnaround article more reasonably says that it "is considered nontraditional from the standpoint of Western harmony". "Nontraditional" does not mean "inadmissible". All this had already been questioned above by User:Haraldmmueller.

(Let me add that I understand nothing of the following section, "Functional behaviours". It might be replaced, I think, with a section on the "new" American function, "predominant", as alternative to the subdominant. This, by the way, is not without relation with the above. There certainly exist references about the concept of predominant, which remains much discussed. But I have to first make some searches. Any help will be welcome.)

Hucbald.SaintAmand (talk) 08:55, 12 September 2018 (UTC)[reply]

+1.

As a "harmonic hearing person with a modest historical interest", I do believe that there is some merit in having the Circle of Fifths as a "functional abstraction"; in the same way that also the Rule of the octave is certainly some sort of "functional concept", in that they both have helped, for centuries, explain composition teachers to their pupils how one could, and should not, connect chords in acceptable, interesting, boring, ... ways. However, they (a) certainly fall short of a more encompassing theory of harmonic progressions; and, more importantly, (b) there is, it seems, no somewhat spread-out literature that would put forward these two (O of 5s, and rule of 8) as theories. So they should go (ok, the rule of 8 wasn't there anyway).

(Ad hoc addition: The German WP article on the regola dell'ottava cites an article "Ludwig Holtmeier: Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave. In: Journal of Music Theory. Bd. 51, Nr. 1, 2007, S. 5–49, doi:10.1215/00222909-2008-022." that seems to connect functional theory and the rule of the octave ... might be interesting to read).

--User:Haraldmmueller 09:25, 12 September 2018 (UTC)[reply]

User:Haraldmmueller, I believe that the theory of the scale degrees (Stufentheorie) is a theory mainly based on the circle of fifths. Clearly, the section Function (music)#Viennese theory of the degrees should be more developed and should mention this. But all that cannot be done at once. Certainly, what the former section on the circle of fifths said (mainly that II is closer to V than IV) was far from sufficient, and even possibly not true. I'll check Simon Sechter about that.

As to the rule of the octave, I don't think that it can be considered to concern functions; as a matter of fact, whether it is a theory (I mean, more than a mere rule) might also be questioned. In its 18th-century versions at least, it does not explain how to connect chords – on the contrary, the connections that it appears to describe at times are problematic. I'll check Ludwig Holtmeier's article as soon as possible, and see whether something should be mentioned here.

You mention "theories of harmonic progressions" and, indeed, one may wonder whether these could be considered functional theories. One might therefore consider that the theories mentioned in Root (chord)#Root progressions in music should be described here, probably with more details than there. I am not sure of that, but your opinion (and that of others) would be welcome.

Hucbald.SaintAmand (talk) 13:21, 12 September 2018 (UTC)[reply]

I browsed through Holtmeier's article and did not find anything worth mentioning. He actually does not seem to be speaking of the kind of functions considered here. The article is far from easy and I did not quite understand what its point was. Holtmeier most often speaks of "functionality" and almost never of "function", and he appears to understand it in the ordinary sense of the term, e.g. showing how things function in their context. — Hucbald.SaintAmand (talk) 17:19, 12 September 2018 (UTC)[reply]

Delete "Functional behaviours"?

... as hinted at by Hucbald.SaintAmand above, I'd say: Delete it. It is, at best, partially based on a single book "The Music of Béla Bartók" - so it is questionable whether this is a theory on its own, or just one for Bartok's music; and even if it is a general theory, just having it supported by a single, specialized work should not be enough to include it in a general article on Function (although WP has this tendency to hunt for and gather everything that might even be remotely linked to a lemma ...). --User:Haraldmmueller 09:32, 12 September 2018 (UTC)[reply]

I replaced this section with a new one, "Functions in American Music Theory", based mainly on Caplin. Unfortunately, Caplin does not clarify the difference between the function of predominant (as preparation of the dominant; this should be said more clearly in the section) and that of subdominant properly speaking (as in a plagal cadence). I did not (yet) find a reference that makes this difference clear (or that clearly makes it). — Hucbald.SaintAmand (talk) 11:50, 22 September 2018 (UTC)[reply]

Opening quote

Just dropping by to see how bad it is at the very opening. An indented quote is a big deal, so I'd normally expect the author to be named. In any case, is an indented quote appropriate in the lead?

Let's look at the wording of the quote:

Harmonic function essentially results from the judgment that certain chords and tonal combinations sound and behave alike, even though these individuals might not be analyzed into equivalent harmonic classes [...]. Harmonic function is more about similarity than equivalence.
- Whose judgment? The listener's, the analyst's, the composer's? Or is it just the author's judgment?
- Sound and behave: these concepts are not defined. How will even musicians know how they are different from each other? What is a harmonic class? I don't know what it means, and I'm a music theorist.
- Individuals: pluralised, this almost always refers to people. Tony (talk) 01:59, 23 September 2018 (UTC)[reply]

@Tony You are perfectly right. This quotation had been there since quite some time and, as it seemed harmless and as I did not want to interfere in the work of others, I did not question it. But your comments let me return to the original text, Harmonic Function in Chromatic Music, by Daniel Harrison. This is what he writes:

Dominant, Tonic and Subdominant are harmonic labels denoting perceptual impressions that I will refer to as harmonic functions. The reader may wonder why the previous sentence was so carefully phrased since harmonic function is neither a new nor a revolutionary idea. While neither of these things, it is elusive and equivocal and has been from its origins. The inventor of the term, Hugo Riemann, was never quite clear himself about what a harmonic function is, and his confusion inspired many subsequent authors to attempt clarifications and refinements that unfortunately, in too many cases, trapped the idea further in a sticky web of ambiguity.

Nothing too bad until there. The quotation reproduced in the article is inserted here, but things soon go astray in what follows:

Harmonic function goes beyond chord roots and fundamental basses in order to hear the harmonic "attitude" of a given chord with respect to a key. This idea of "attitude", improbably borrowed from aeronautics, nonetheless illuminates harmonic function in a pertinent and insightful way by offering the image of function as a kind of axis used to plot a specific tonal event. Just as the attitude of an aircraft, no matter how unusual or unsafe, can be expressed by degrees of inclination with respect to three axes, so too, I submit, can the attitude of a tonal structure in the musical flow be expressed with respect to the three functions.

Etc. This all makes no sense at all. The comparison with aeronautics is laughable, it certainly fails to bring the attempted "clarifications and refinements" and remains as trapped as any other "in a sticky web of ambiguity". What Harrison proposes cannot be considered "one explanation", as the article claimed. In short, I removed the quotation. Thanks for having called this to attention. — Hucbald.SaintAmand (talk) 15:38, 23 September 2018 (UTC)[reply]

More criticism

Sorry to be mean, Hucbald et al. I feel like I'm aiming for you, but I'm not—it's certainly nothing personal. Let's look at the section "Origins of the concept", which buzzed on my watchlist because a self-announced "beginner" edited it in frustration at the fuzziness. As you know, my opinion is that this is a poorly scoped legacy topic, rooted in the musings of a few 19th-century German-speaking theorists, and likely to confuse musicians. Perhaps it was imported from de.WP without thinking about the context of our readers.

"It was realized that three perfect major triads, distant from each other by a perfect fifth, produced the seven degrees of the major scale in one of the possible forms of just intonation: for instance, the triads F–A–C, C–E–G and G–B–D (sub-dominant, tonic, and dominant respectively) produce the seven notes of the major scale. These three triads were soon considered the most important chords of the major tonality, with the tonic in the center, the dominant above and the subdominant under.

This symmetric construction may have been one of the reasons why the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under [the tonic]". It also is one of the origins of the dualist theories which described not only the scale in just intonation as a symmetric construction, but also the minor tonality as an inversion of the major one. Dualist theories are documented from the 16th century onwards."

Not a single reference. How on Earth did this make it into a supposedly professional-standard article?

Let's pull it apart (a bit).

"three perfect major triads"—what is a perfect major triad? A triad is either major, minor, diminished, augmented (perhaps other exotic types exist, but they shouldn't concern us in this context).
"produced the seven degrees of the major scale in one of the possible forms of just intonation"—"produced" isn't a good word here (consider using present tense, too). To be fussy, "major mode" would be technically more precise than "major scale", but I can live with "scale". Nowhere is it clear why the crux of this is just intonation. There's no reference—and please not a modern UK Associated Board–type dumbed-down textbook, but the original(s) please, since an significant historical point is being claimed. There's no anchoring in historical time.
Why does the coverage of every degree of the major mode not apply in non-just intonations? Just intonation is proposed as the lynchpin of the realisation. Why? Even I am confused—not to mention suspicious of the assertion.
Chord IV is elevated to equal status with V and I (against many modern sources, minus the Associated Board and their ilk). If this is merely because IV covers the fourth and sixth degrees (which I and V do not), why is ii not a more-important part of the picture? Many authorities see only V and I as the core, with V approached more naturally by ii (root-movement successively by falling fifths / rising fourths)—typically ii6. Chord ii covers the fourth and sixth degrees, too. Where is the logic presented, from whatever sources are being used, that symmetry of root-distance from the tonic is more important than the circle of falling fifths?
Horse before cart: "This symmetric construction may have been one of the reasons why the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under [the tonic]".—well yes, no one doubts this, so "may be" is an inappropriate level of certainty. But it's still not a reason to worship IV in this way.
What does "soon" mean?
"the minor tonality as an inversion of the major one"—unfortunate use of "inversion", which has a well-established technical meaning in harmony. What does it mean here?

Excuses based on "not everything can be said at once" won't wash. I believe our obligation is not to confuse at the start. Thanks. Tony (talk) 03:13, 3 February 2019 (UTC)[reply]

@Tony, I accept your criticism all the more easily that I think it justified. I think to be responsible for the section "Origins of the concept", or certainly for most of it. Please keep in mind that English is not my mother language, which may explain some of the points you criticize. For sure the section needs references, and I should have provided some. I must have planned to add these, and probably forgot. But they should easily be found. My problem is that I am more familiar with primary sources than with secondary ones. Let me answer your points in turn:

"three perfect major triads". This must be understood in relation with the phrase that precedes: "The concept of harmonic function originates in theories about just intonation." By "perfect major triads", I meant major triads perfectly in tune, i.e. just intonation triads, with a 5th of ratio 3:2 and a major 3d of ratio 5:4.
major scale and major mode. No, it is the major scale (or better perhaps, the diatonic scale) that is "produced" (or any other term that you could suggest), but certainly not the major mode which is something quite different. Just intonation may not be the "crux" of this, but for the fact that this reflexion, beginning with Zarlino, originally was about just intonation, at a time of intense reflexions on temperament and tuning. This was a reflexion on the naturalness of music, on its being based on "natural" (physical) rules, e.g. harmonic partials. This reflexion continued among others with Sauveur, Rameau and several other French theorists of the 18th century, who considered that harmony had to be built on the accords principaux du mode ("mode" in the sense of "scale", in this case). The theory of the double fundamental bass of Jean-Adam Serre (1753) is a concrete application of this idea.
Once again, it is not that "the coverage of every degree of the major mode does not apply in non-just intonations", but that the whole question was first thought (by the authors mentioned above, to which you may add Mattheson, Euler, Helmholtz, and many others) in terms of just intonation. I agree that this could be made clearer.
"Chord IV is elevated to equal status with V and I". I am not sure of the "equal status", but certainly IV was considered the main chord after I and V, and more important than II (which is the puzzling aspect of this history). The reason is that the construction followed the cycle of fifths and that the main chords appeared to be those a fifth above and a fifth below I.
"Many authorities see only V and I as the core". Can you quote if only one such authority? You may be thinking of Schenker, but even Schenker considered that the chord preparing V was of utmost importance. See Schenkerian_analysis#I–IV–V or I–II–V. Of course, V is better approached by II, but if the early theorists had realized that, the theory of harmonic functions would never have existed.
Subdominant as the dominant under the tonic. Well, you may have no doubt about this, but the term did not appear in English before the last years of the 18th century, and its true meaning (in French, where it originated) had been the subject of heated discussions throughout the 18th century. Today, French (and probably Italian) speaking musicians usually think that the reason why the subdominant is so named is because it is the degree under the dominant.
Minor as inversion of the major. See Riemannian_theory#Dualism, and the figure illustrating this article.

I don't think this to be a case of "not everything can be said at once". Rather, the whole matter is more complex than it seems. But I fully agree that a lot remains to be done about this article. Consider what has been done since a year. — Hucbald.SaintAmand (talk) 16:16, 3 February 2019 (UTC)[reply]

I further examined this, Tony, and verified that I had written this section on the origins of the concept in March 2017, when we began the thorough revision of the article that I consider still in progress. I realize now that it requires more detailed explanations and I will think of it. Allow me some time (I am busy with other things just now) – and go on criticizing: as you see, it is useful, and I don't mind. — Hucbald.SaintAmand (talk) 08:01, 4 February 2019 (UTC)[reply]

Not to worry, Hucbald. I'll return to comment on your points in a while. Thank you. Tony (talk) 09:30, 4 February 2019 (UTC)[reply]

Just a word. Rereading the section "Origins of the concept", I do realize that what it includes for now are but the first two paragraphs of something that probably was supposed to become quite longer. For sure, these paragraphs should not be kept in the end. The concept of [tonal] functions certainly began with Rameau (Nouvau systeme, p. 62: Nous ne connoissons que la Dominante & la Sous-dominante pour Sons fondamentaux, dans la Modulation d’un Son principal donné, "We know only the dominant and subdominant as fundamental degrees in the tonality of a given principal degree") and other 18th-century French theorists (d'Alembert, Jean-Adam Serre, Pierre-Joseph Roussier, etc.), soon followed by German ones (Daube, etc.). It remains that all of them were influenced by Zarlino's system, just intonation, as can easily be deduced from this figure reproduced in the Just intonation article. But just intonation should be mentioned after these theorists, not before.

I will be too busy during the next weeks to be able to do much about this, especially with respect to secondary sources, with which I am less familiar than with primary ones. But if anyone feels like it ... — Hucbald.SaintAmand (talk) 19:09, 11 February 2019 (UTC)[reply]

"Functions in American music theory"

Why are they specifically American? Tony (talk) 12:54, 25 August 2019 (UTC)[reply]

Because Americans tend to believe that there is no theory outside of North America. Caplin, quoted in this section, says that

Most North American textbooks identify individual harmonies in terms of the scale degrees of their roots.

This is Simon Scheter's Stufentheorie, from his Die richtige Folge der Grundharmonien, oder von Fundamentalbass und dessen Umkehrungen und Stellvertretern, Leizig, 3 vols, 1853-1854. (i.e. "The correct succession of fundamental harmonies, or of fundamental bass, its inversions and its substitutions".)

Caplin continues:

Many theorists understand, however, that the Roman numerals do not necessarily define seven fully distinct harmonies, and they instead propose a classification of harmonies into three main groups of harmonic functions: tonic, dominant, and pre-dominant.

Which means: many (American) theorists realize that they are wrong to believe that theories based on Roman numerals (as in Sechter's theory, but also in those by Kirnberger or Vogler or Gottfried Weber) and propose instead a theory of three functions that in essence is that of Hugo Riemann.

The only really original contribution of American theorists is the concept of "pre-dominant" function. Caplin is not entirely clear in the description above, for many American theorists conceive of a "subdominant" fuction as well as a "pre-dominant" one. The pre-dominant function is when a chord that Riemann's theory would describe as having a subdominant function serves as a preparation of a dominant function. So doing, these theorists distinguish the function of IV or II in progressions I–IV–I or I–II–I from that in progressions I–IV–V or I–II–V. This indeed in an important distinction. August Halm wrote in Riemann's time that there is an "abyss" between the subdominant and the dominant. Riemann indeed conceived the subdominant as the Unterdominante, the dominant under the tonic, and the dominant as the Oberdominante, the dominant above. He even thought for a while that passing from the subdominant to the dominant necessarily involved passing through the tonic (as in I–IV–V^6–5
_4–3–I).

Hucbald.SaintAmand (talk) 16:34, 25 August 2019 (UTC)[reply]

Oops! Rereading some of the comments above, I realize that I might be quite responsible for the section "Functions in American music theory" in its present form. I should check the history of the section, but I have little time to do so just now. I suppose that my quotation of Caplin as representing an American conception of functions results from a reusing of anterior versions. I should have made it clearer that the true contribution of Americal theory is the matter of the "pre-dominant" function (which, by the way, is very much contested by tenants of a more orthodox Riemannian theory, e.g. in Russia today). — Hucbald.SaintAmand (talk) 21:12, 25 August 2019 (UTC)[reply]

It happens that most anglophone music theory (perhaps most music theory in any language) is done by and published by Americans—including some excellent "textbooks". That doesn't mean someone like Caplin is claiming that there's something distinctively "North American" or "American" about their work. The article is misleading in this respect. Could you point to discrepancies between UK and US/Canadian music theory? I think you'd be getting into difficult territory—hard to find explicit justification in the sources. Tony (talk) 02:56, 26 August 2019 (UTC)[reply]

Tony, what do you mean when you write that "most music theory in any language is done and published by Americans"? Would you be one of those who "believe that there is no theory outside of North America"? The fact is that American theorists have "colonized" the discipline, as Jonathan Cross once wrote. American publishers would hardly publish a single line in any other language than English and are extremely reluctant to accept texts proposed from outside North-America (or England). Yet, Europeans have organized in 1989 in Colmar, France, their first European Conference on music analysis and they are planning the tenth one in Moscow in 2020.

I'll stress only two recent occasions. 1. The Conservatoire in Brussels, Belgium, recently called the European Seminar on Harmony and Analysis, calling teachers from Conservatoires that participate in the European Erasmus program (transnational exchange of teachers and students). This proved a success, with close to a hundred participants from about twenty-five European countries (and some Americans). 2. The Europeans announced at their ninth European Conference (EuroMAC 9) in Strasbourg in 2017 that they would form a "network" of European societies for theory and analysis. This network, EuroT&AM is in the process of development and may become in the future a force in the discipline.

The situation in Europe is more difficult than in North America for at least two reasons: first, that geographic Europe counts fifty different countries, and second, that it counts thirty-five official languages, not to mention the hundreds non official ones. Even so, I can assure you that music theory here is alive and well. — Hucbald.SaintAmand (talk) 07:22, 26 August 2019 (UTC)[reply]

It happens that most anglophone music theory ... I think no-one is talking here and anywhere about "anglophone music theory". (perhaps most music theory in any language) is done by and published by Americans ... that's a wild claim and most probably wrong, if one looks at German publications (all foundations of modern music theory were developed in Austria and Germany, and much comments on them are still published in Germany and by German researchers), French, Italian and Russian. What the section claims is actually that there is a difference between "American" (which might be more like "Anglo-American") music theory and "continental" music theory, nothing else; but and of course, this should be supported by sources - and the "American" or "Anglo-American" might be "orginal research" and hence might better be replaced with names of concrete authors that present such views, like Caplin. I think Hucbald.SaintAmand indicates above that he wants to check that out ... --User:Haraldmmueller 07:26, 26 August 2019 (UTC)[reply]

There seems to be major confusion here, and lots of wasted key-taps. I was objecting to the idea that Americans construct music theory produced/published by Americans as somehow part of a distinct "school" of music theory. That's all. The responses seem to take umbrage at a perceived slight against European music theory? Not from what I said, I hope. Again, why is there even a section on "American" music theory, this imponderable classification? Tony (talk) 11:42, 26 August 2019 (UTC)[reply]

...lots of wasted key-taps [or words]... :-). So it goes in discussions - not a real problem, tho, I'd reckon. ... why is there even a section on "American" music theory, this imponderable classification? - yes, that's the right question, and it's why I said "American" or "Anglo-American" might be "orginal research" and hence might better be replaced with names of concrete authors that present such views, like Caplin above .... --User:Haraldmmueller 12:03, 26 August 2019 (UTC)[reply]

I fully agree with User:Haraldmmueller. Would one of you be so kind and change the article? By the way, I begin to wonder after how long a discussion page like this becomes a valid source for Wikipedia ;–)) — Hucbald.SaintAmand (talk) 17:36, 26 August 2019 (UTC)[reply]

I do, too. Hucbald, sorry if I seem to be continually critical. Tony (talk) 12:09, 27 August 2019 (UTC)[reply]

As a first "quick fix", I just removed the section heading "Functions in American music theory"; I think Caplin's text is fine as a part of the "Comparison ..." section, and the "American music theory" is then gone from the WP text - well, there is still "Reviewing the American usage of harmonic theory", but this is clearly from Caplin's own text "Most North American textbooks ...", so might be fine(r ;-) ). But maybe there are better solutions? --User:Haraldmmueller 15:35, 27 August 2019 (UTC)[reply]

It certainly is much better, thank you. I remain somewhat puzzled that the table comparing English and German terminologies mixes names of degrees with names of functions. This is particularly obvious when "leading tone" is translated as verkürzter Dominantseptakkord, which is not at all the same thing. The phrase "In English, the names of the scale degrees are also the names of their function" appears to indicate that functions are properties of scale degrees. We already had extensive discussions about this above. The case is particularly bothersome for the leading tone, once again: many consider that the Stufentheorie counts six functions only and that VII (or vii°) is not an independent function. I don't know what to do ... — Hucbald.SaintAmand (talk) 16:52, 27 August 2019 (UTC)[reply]

German Chord Functions Nearly Unreadable

I understand functional harmony but am still struggling with the chord function table. Instead of cryptic 2-letter symbols, why not just use English words in the table, e.g. dominant parallel? Put the German abbreviations in paragraph text.

I fail to see the problem with this table – unless you cannot read and you only look at the images. The German abbreviations are explained two paragraphs before the table (in the paragraph beginning "In Diether de la Motte's version of the theory"). If there is a problem with these explanations, then that is what must be corrected. The table then shows the meaning of the abbreviations. You suggest to use English words such as "dominant parallel"; but what does this mean? The German parallel means "relative", and the English "parallel" means "of the opposite mode". What do you suggest?

In addition, there is another table in the section "Comparison of the terminologies" that tries to explain all that. It does not use "parallel" in English, because that is not the name of a function. This table, as indicated, is valid only for the major mode. In minor, the German parallel and gegenparallel would be inversed. The submediant in minor, for instance, would be Tonikagegenparallel (tG) instead of Tonikaparallel (Tp). Perhaps another table should be given for the minor mode.

There is no point in pretending that something complex is simple. Our aim can only be to make it understandable. I trust that if you read the text (and possibly reread it), you could understand it. — Hucbald.SaintAmand (talk) 06:38, 5 August 2021 (UTC)[reply]

[NG_Function-1] "Function", unsigned article, Grove Music Online, [1].

[1]