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Modes, scales, tonoi, and thingimajiggs

I have a question for you all. Do you consider the modes to be a subset of scales? Or is there some distinction, other than historical development?Jbailhe 00:25, 11 July 2014 (UTC)

BTW -- I suggest the recent discussion which is primarily about the form of the article and not the question of Major theorists, be moved to the section on the proposed TOC. I'd do it, but I'm not sure I have appropriate authority.Jbailhe 00:36, 11 July 2014 (UTC) — Preceding unsigned comment added by Jbailhe (talk • contribs)

Yes.

Less cryptically (though also less succinctly), it depends on what you mean by "mode". If you examine the edit history of the article Mode (music), on which I have spent a fair amount of time, you will see that there has been an ongoing struggle over this issue there, and Harold S. Powers pretty much broke the bank on this subject at the New Grove with an article that threatened to require an entire volume to itself. If you use the word in the way jazz theorists do, then it is a way of describing different scales. The medieval church modes are something else again. Even if scales are embedded in the concept (and I insist on the "if", since there are dissenting opinions about this), there is certainly a great deal more to them than just scalar construction. Trying to apply the term to non-Western musics runs into all sorts of further difficulties, the first and biggest being the issue of whether or not we are emulating Procrustes by forcing an alien conception onto the native conception of tone/note relationships, adding in bits we cannot find and lopping off things that do not fit our preconceptions. This is just as true of trying to use the word with relation to ancient Greek theory, where the fluid relationship amongst concepts such as tonos, harmonia, octave species, and transposition type quickly lead to problems, and we must remind ourselves that there was probably a good reason the Greeks didn't speak Latin ("mode" being a Latin word, awkwardly imposed by various writers retrospectively on what was imagined to be what the Greeks were talking about).—Jerome Kohl (talk) 00:41, 11 July 2014 (UTC)

@ your "BTW" (which arrived while I was in the midst of writing the above—we call this an "edit conflict" on Wikipedia), you certainly have the "authority", though I should caution that these discussion pages can become badly snarled up when people start inserting replies into the middle of already established text. So long as a comment is relevant, it can be added to any pre-existing topic/section and, if done prudently, you may move your own remarks, just as long as you do not tamper with another editor's contribution, unless there is an obviously good reason. See the guideline Wikipedia:Refactoring talk pages.—Jerome Kohl (talk) 00:52, 11 July 2014 (UTC)

No.

Less cryptically, I do believe, and I trust Jerome Kohl agrees, that we could only say that modes are scales if we make clear that we are dealing with Western modes – even more, perhaps, with modern Western ones (e.g. jazz). Medieval church modes became scales in Medieval theory, but had not first been conceived as such, as becomes apparent if one reads the theory "between the lines", so to say. So far as I know (what I know comes from Gombosi), ancient Greece did not know modes in our modern sense. I do not agree with Harold Power's idea that mode "is not real". I think that our medieval church modes belong within a group of, say, Mediterranean modes (a group extending to the Near East) that were not scales; the fact that they became scales in Latin theory should not deceive us.

About your BTW, I would remain cautious about moving things on this page, as that would make it difficult to follow recent changes. I'd rather remove a subdivision (if that is possible; I see no reason why it wouldn't). I added comments to the "Major theorists" subdivision a minute ago, and I'm afraid they soon will be difficult to find.

Hucbald.SaintAmand (talk) 09:35, 11 July 2014 (UTC)

I agree wholeheartedly that we must make absolutely clear which type of "mode" we are talking about before we plunge ahead into a summary description. I disagree that the church modes ever came to be reduced to mere scales, however. They retain their particular set of scale-degree functions and many characteristic melodic patterns—certainly in the Gregorian repertoire, for all the damage it has suffered over the years, but even polyphonic modal literature differentiates certain modes by characteristic cadence types, for example, which are not an automatic consequence of the interval patterns in scales (I am thinking especially of the difference between modes 3 and 4, but the separate identities of other authentic/plagal pairs, as well as the distinct Lydian/Ionian/Mixolydian characters also depend on this sort of thing, because of the obvious problems created by polyphonic textures). This is of course a highly problematic area, and if it was in this context that Powers held modes not to be real, then he may have had a point. This hasn't stopped music theorists right down to the present day struggling to define them, though.—Jerome Kohl (talk) 16:14, 11 July 2014 (UTC)

100% agree with Jerome. When we say a piece is in the "major mode", that doesn't necessarily refer to the scale it's based on but on traditional melodic and harmonic patterns. It's perfectly possible to write music using the major scale which isn't in the major mode (e.g. pandiatonic music). The same applies to church modes and, as far as I know, to ragas. —Wahoofive (talk) 16:47, 11 July 2014 (UTC)

So interesting! But I remain uncertain (perhaps thick-headed?). If the definition of a scale, at its most basic level and as worded in the Wikipedia article on Scale, is "... any set of musical notes ordered by fundamental frequency or pitch," doesn't it follow that the modes are the same thing, albeit with a unique set of qualities that make them one of many subsets of scales? 5 tone, 7 tone, diatonic, non-diatonic, etc. As I'm sure you all realize, I'm asking about this because in the theory article I'm trying to be as accurate as possible without unnecessarily digressing--accidentally or intentionally--into complex theoretical issues best handled on specialized pages. Where there is no way around explaining a complexity, so be it, but for instance, would it be incorrect to say "a mode is a type of scale"? The Scale article seems to consider mode as a type of scale by saying, "Western music in the Medieval and Renaissance periods (1100–1600) tends to use the white-note diatonic scale C–D–E–F–G–A–B.--Jbailhe 17:49, 11 July 2014 (UTC)

OK, let me try to clarify this, with respect to medieval music theory, as practiced in northern France, on a wet Thursday afternoon in October. As I said before, scales are usually part of the definition of mode but, because there are other identifying features (range, tenor, mediant, characteristic melodic behaviours, etc.), scale and mode are not identical concepts. Furthermore (to elaborate that big "if" I mentioned previously), some theory treatises of the period resist the scale idea entirely, relying instead on tetrachords and pentachords. One further issue involves the "mutable" note B, which is many modes may be either "soft" or "hard" (what today we would call B♭ and B♮, respectively). This particularly affects modes 4, 5, and 6, but also modes 1 and 2. This is the basis for the resistance of theorists to the expansion of the eight-mode system to either twelve or fourteen modes, until they finally were worn down and threw in the towel when that radical troublemaker Glareanus arrived on the scene, waving fancy Greek words around and thumping people over the head with his book, the Dodecachordon. You see, any reasonable person would understand that having either hard or soft B available renders unnecessary modes with C and A as finals, since these are simply transpositions of modes 4/5 (Lydian/Hypolydian) and 1/2 (Dorian/Hypodorian), respectively, and of course B itself, as a mutable tone, lacks the stability to be a mode final itself. But Glareanus, being Swiss, was not a reasonable person at all, and managed to infect enough people with his insane ranting that he got into the history books by establishing four "new" modes (authentic/plagal pairs on C and A), though even he was not crazy enough to argue that B should also be included, even if he did commission one experimental piece to demonstrate his point. It was more or less at this moment in history that civilization crumbled into dust, and it became possible to believe that mode and scale might be one and the same thing. However, a few sane people did manage to survive the cataclysm to continue fighting a rear-guard running battle, and in the 19th century formed up into something called the Cecilian Movement, with the goal of reforming Church music and rooting out all those smelly, unsuitable compositions made by incompetent composers like Haydn and Mozart, who fell into the trap of using that decadent work of the Devil, tonality, and filled their allegedly religious compositions with revolting dissonances of every kind. The Cecilians were responsible for refining and extending modal theory, but evidently were corrupted by fifth columnists in their midst (probably Vikings from Iceland), and ended up with fourteen modes by forgetting that B could be soft as well as hard. This folly ensured their demise and no one today has ever heard of them, the monks of Solesmes having eradicated every trace. And here I must pause today, but shall resume this tale on a later occasion.—Jerome Kohl (talk) 18:32, 11 July 2014 (UTC)

"...all those smelly, unsuitable compositions...." You do have a flare!--19:56, 11 July 2014 (UTC)Jbailhe

I'm noticing a return to what I think is unnecessary complexity in the Music theory article. Examples of some recent edits marked by asterisks: “In some instances, tones of a chord not sounding simultaneously but successively, for example in an arpeggio **, in compound melody, or in the style brisé**, may still be considered to form a chord.” Isn't one example enough to explain the concept? And later, “Chords may be inverted by changing the vertical arrangement of tones, extended by adding tones **which in the common definition of consonance and dissonance necessarily are dissonant**, or [otherwise] altered **by modifying one or several of their tones usually by a chromatic semitone**. Are these details necessary to present the theoretical concept that chords may be variously configured? It's my opinion that over-explaining and digression make basic concepts difficult to understand. I have not removed those edits, but encourage reconsideration.--19:48, 11 July 2014 (UTC)Jbailhe

The difficulty with using arpeggio as the one and only example for non-simultaneity of a chord is that it involves immediate adjacency and an ordered presentation, unlike the style brisé or compound melody (the fact that the latter presently redirects to the Schenkerian concept of "unfolding" is unfortunate for my purposes, but not critical). Further considerations might include intervention of non-harmonic tones in all three of these textures but, as you say, things are getting too complicated for an introductory article. How can we best convey the idea that notes do not even need to be adjacent to be heard as members of a chord, without unnecessary complication? If you mean to include my somewhat fanciful account of the history of modal theory in this criticism, I couldn't agree with you more. All I was trying to do was to show you why (medieval) mode really cannot be equated with scale. The complexity serves a purpose on this talk page, but certainly does not belong in the article itself. Most if not all of this is already in the article "Mode (music)", in any case, albeit in more encyclopedic style.—Jerome Kohl (talk) 22:18, 11 July 2014 (UTC)

This goes a trifle too fast for me... I have to come back on several points of the above.

• Jerome Kohl writes: "I disagree that the church modes ever came to be reduced to mere scales". It is clear to us today that Church modes always have been formular as well as scalar. Medieval treatises, however, NEVER explicitly mention the formular aspect and describe modes exclusively as scales. If you believe otherwise, I'd be most interested in knowing what treatises you have in mind. The problem of describing modes as scales, in other words, is not a modern problem, but a medieval one.
• Jacques writes: "The Scale article seems to consider mode as a type of scale by saying, 'Western music in the Medieval and Renaissance periods (1100–1600) tends to use the white-note diatonic scale C–D–E–F–G–A–B'". The Scale article explicitly says that this is true of Western music, and one may safely deduce that things might be otherwise in other cultures. Otherwise, defining the diatonic scale as "C D E F G A B" (the major scale!) is odd; why not, say, D E F G A B C?
• Jerome writes: "some theory treatises of the period resist the scale idea entirely, relying instead on tetrachords and pentachords". But tetrachords and pentachords are (fragments of) scales! These descriptions, in the Reichenau treatises in particular, are some of the most strictly scalar ones in the Middle Ages!
• Jerome says that the movable B "particularly affects modes 4, 5, and 6, but also modes 1 and 2." To my knowledge, the problem NEVER affects mode 4 (hypophrygian); it does not really "affect" modes 5 and 6 which always have B flat, in the middle ages at least (the idea that the lydian and hypolydian modes may have a B natural is Glarean's idea).
• And further "any reasonable person would understand that having either hard or soft B available renders unnecessary modes with C and A as finals, since these are simply transpositions of modes 4/5 (Lydian/Hypolydian) and 1/2 (Dorian/Hypodorian), respectively". First, the lydian/hypolydian pair, unless I am mistaken, is modes 5/6. Then, while it is true modes 1/2 could be described as D or as A modes depending on the nature of the B, this is not true of modes 5/6 because their B, until Glarean, was always flat. The Lydian mode properly speaking is a creation of the 16th century and Lydian pieces began to be composed only because one wanted to propose cycles in all 8 modes.
• Jacques criticizes recent changes in "Chords may be inverted by changing the vertical arrangement of tones, extended by adding tones **which in the common definition of consonance and dissonance necessarily are dissonant**, or [otherwise] altered **by modifying one or several of their tones usually by a chromatic semitone**." I am responsible for these changes, which must be read comparing with the older version: "Chords may be inverted by changing the vertical arrangement of tones, extended by adding tones, or altered by adding dissonant tones." The older version said that one could either extend by adding tones, or "alter" by adding "dissonant" ones. I wanted to point that any tone added to a triad necessarily is dissonant (but to say so requires a definition of consonance/dissonance), and that so far as I know "altering" a chord means chromatically modifying one of its notes, usually without "adding" any note, dissonant or not. My way of expressing this probably can be improved, but the earlier version clearly was wrong.
• About "compound melody" and Schenkerian "Unfolding", see the article Melodic fission, especially its note 3, about the origin of the term. See also note 2 of the same article: comparing the two shows that "compound melody" is older than "melodic fission", even although the articles were written in the reverse order. Compound melody is of paramount importance in early Schenker (Harmonielehre and above all Kontrapunkt I) and we may no more realize today that he probably was among the very firsts to call attention to the phenomenon. I had considered moving a good deal of Melodic fission to Compound melody, but this is a somewhat heavy decision, and may cause the ire of cognitivits...

Hucbald.SaintAmand (talk) 07:02, 12 July 2014 (UTC)

A lot of very good and interesting things there, Hucbald. I do have one niggle, though: "But tetrachords and pentachords are (fragments of) scales!" To start with, we're talking about hexachords, not pentachords, right? Anyway, unless you mean merely that theoretical descriptions of these things always put the notes in order, no one at the time would have thought of them as fragments of an 8-note scale. It's like saying Newton's theory of gravity is a special case of the theory of relativity. True from a modern perspective, but would have been incomprehensible at the time. Saying a tetrachord is a "scale fragment" is a backwards projection in the same way.

But it really comes down to the meaning of "scale", something that's been battled about for years. To be a scale, the notes have to be in order by pitch. But if I'm presenting a set of notes available to be used in a composition, but happen to list them in order, does that make them a scale, or are they only scale when they're intended to be played in that order? The notes used in Bach's famous motif based on his name are A, B♭, B♮, C. Have I just written a scale, or a scale fragment? Or just listed the notes in order? —Wahoofive (talk) 17:47, 12 July 2014 (UTC)

Jermone--First, although I'd love to include your riotously funny history of modal theory, I anticipate we'd get the lash. RE: yours and others comments about the dizzying array of examples of how separated notes may be considered a chord, I urge that we take the view that all we're trying to do is give an example to make the concept understandable by the average reader. Introducing complex concepts that are unnecessary to that purpose simply cloud and confuse. --18:19, 12 July 2014 (UTC)Jbailhe

Hucbald's argument for clarifying altered chords is very good, and as he says, the trick will be to find a way to explain it concisely. The Oxford Companion to Music offers, "altered chord. A Chord which has one or more of its notes chromatically altered by accidentals foreign to the key." I have some vague memory about some other methods of "alteration," but this issue is frankly out-runnin' my learnin', so I leave it to the wiser to figure out how to word that small, but important detail in the chord section (e.g. by raising or lowering a chord member by a semitone.) Shorter would be better! The other way to handle this is to avoid all explanation of chord forms and simply name them with links to specialized articles, but I do think it'd be more helpful to readers to supply elementary explanations of those terms if we can without creating confusion. In the proposed TOC, dissonance and consonance will be explained before we get to chords which I hope will allow using those concepts to be used in following sections without further explanation. The order of the introduction of concepts is a problem throughout the existing article and the main reason I suggested re-writing from the ground up.

On the subject of modes v. scales, my reading agrees with Hucbald--although I wish my books had some of Jerome's panache. I imagine you all are familiar with the life-long argument between Zarlino and Galileo (sr.), as well as actual practices in singing organum and musica ficta. Also, the difference between Pythagorean and Ptolemaic theory. But more directly, as Hucbald asks, does anybody have an authoritative reference that modes are not a subset of scales? I can't find one in my books. I do, however find:

“Modes: The scales which dominated European music for 1,100 years….” Kennedy, Michael, The Oxford Dictionary of Music, Oxford University Press, 1985, ISBN 0-19-311333-3

“…meanings better known today … that of ‘scale’ or ‘melody type’….” Latham, Alison ed., The Oxford Companion to Music, Oxford University Press, New York, 2002 ISBN 0-19-8212-2

“Mode. Usually a *church mode, Dorian, Lydian, etc. In a wider sense, any of the scales used in a composition, e.g. in terms such as major mode, minor mode, pentatonic mode. Used in this broader sense, the difference between scale and mode is that scale is usually understood as being related to a given key, as in C-major scale, while “major (or Dorian) mode” denotes the general characteristic of all the major (or Dorian) scales, transposed to any key.” Apel, Willi, Daniel, Ralph T., The Harvard Brief Dictionary of Music, Heinemann, London, 1961

“…what we call a mode consists of the octave of a single sound within which all the sounds that can be used for melodies and chords are to be found.” Rameau, Jean-Philippe, trans. Gossett, Philip, Treatise on Harmony, Dover Publications, Inc. (1971). P.157. Orig. pub. Jean-Baptiste-Christoph Ballard, Paris (1722).

The scale section will, of course, briefly discuss cultural variations, etc.--18:28, 12 July 2014 (UTC)Jbailhe

Hucbald--you ask "Otherwise, defining the diatonic scale as "C D E F G A B" (the major scale!) is odd; why not, say, D E F G A B C?" I imagine you know it was defined beginning on D for a long period and, though I can't remember precisely when or by who (Glenarus?), it was eventually switched around to the current order starting with C.--18:54, 12 July 2014 (UTC)Jbailhe

My (Hucbald's) answers to some of these interesting comments:

@Wahoofive: "A lot of very good and interesting things there, Hucbald. I do have one niggle, though: "But tetrachords and pentachords are (fragments of) scales!" To start with, we're talking about hexachords, not pentachords, right? Anyway, unless you mean merely that theoretical descriptions of these things always put the notes in order, no one at the time would have thought of them as fragments of an 8-note scale. It's like saying Newton's theory of gravity is a special case of the theory of relativity."

We are speaking here of medieval theory. The first guy to have reintroduced tetrachords and, for that matter, scales at large (i.e., who "put the notes in order") in medieval theory is Hucbald, in the 9th century, a guy that I know particularly well. He made clear, from the very start, that notes put in order cover an octave and that notes an octave apart somehow are the same, as when a grown man and a child sing together. In any case, "putting the notes in order" does not necessarily entail covering a whole octave. But my statement was answering one by Jerome Kohl, about tetrachords and pentachords. I took this to refer more specifically to the 11th-century treatises from the St-Emmeran monastery, the first ones to have defined 'species' of fourths and fifths (or, if you want, of tetrachords an pentachords); all of these treatises add fourths and fifths (or in the reverse order) to form species of [diatonic] octaves. I agree that many medieval theorists had a conception of the system as formed of tetrachords (or hexachords, it boils down to the same) rather than of octaves. But not a single one of them was unaware of the special properties of the octave. And once again, if "scale" means "putting the notes in order", then a tetrachord can do the trick as easily as an octave: you merely have to put the notes in the order re mi fa sol, and repeat that as needed to form the whole diatonic system.

@Jbailhe: Of course, I am aware that the diatonic scale has been described starting on D (hence why I chose that presentation). Everybody should be aware, however, that the first "litteral" presentation obviously was that starting on A: A B C D E F G, first presented by the pseudo Odo of Cluny in the early 11th century. This merely replicated with letters, and with a better awareness of the special meaning of the octave, the order chosen before by the ancient Greeks, by Boethius, by Hucbald, etc. What I meant merely is that the choice to start on C is a very biased one. (I think Zarlino, rather tham Glarean, was first responsible for it.)

@??? [Jacques, if it is you, you really should learn how to sign your postings! It would help all of us!] "'…what we call a mode consists of the octave of a single sound within which all the sounds that can be used for melodies and chords are to be found.' Rameau, Jean-Philippe, trans. Gossett, Philip, Treatise on Harmony, Dover Publications, Inc. (1971). P.157. Orig. pub. Jean-Baptiste-Christoph Ballard, Paris (1722)"

Nobody today could really believe that what Rameau called a "mode" (or a "modulation") in any way represents what we understand by these terms. Mentioning this in our context merely raises questions about 18th-century French vocabulary which I'd gladly answer if needed (it may not be obvious that I am a native French speaker myself), but which I think are way too specialized for our purpose.

Some of your other quotations preceeding Rameau's are merely outdated: scholarly reflexion on modes tremendously progressed since the last thirty years or so. The one mentioning "'scale' or 'melody type'" actually opposes the two concepts, instead of considering them synonyms: modes can be either 'scales', or 'melody types' (or both, as a matter of fact).

Hucbald.SaintAmand (talk) 20:03, 12 July 2014 (UTC)

Hucbald - Appreciate the clarifications. First regarding signing comments, this is what I see at the end of my comments, copied and pasted here: "--18:54, 12 July 2014 (UTC)Jbailhe." Is there some other way I should be signing? RE: references to scale v. mode, 2002 and 1961 don't seem all that out of date and I would be genuinely happy to have an authoritative reference that disagrees. I've been looking. RE: Dear old Rameau, we have certainly progressed since 1722. I just thought it was interesting that even in his era, the overall concept is a group of tones, and as such mode and scale seemed to be part and parcel of the same concept.--20:41, 12 July 2014 (UTC)Jbailhe — Preceding unsigned comment added by Jbailhe (talk • contribs)

Jbailhe, whenever you fill in the window of your edit on a talk page, you'll see just below its bottom limit several mentions, among which this one: Sign your posts on talk pages:, followed by four blue tildes (i.e. four "~"). Leave your cursor where you want to sign, and click on these four tildes. That's all! – Hucbald.SaintAmand (talk) 21:10, 12 July 2014 (UTC)

I think his posts are signed [e.g. 20:41, 12 July 2014 (UTC)Jbailhe] -- he just has a custom signature which doesn't link to his user page. —Wahoofive (talk) 22:40, 12 July 2014 (UTC)

Made some changes to my user preferences. Hopefully, they'll clear up my signature problems.Jacques Bailhé (talk) 16:56, 13 July 2014 (UTC)

@Hucbald: My apologies about mis-numbering the Lydian and Hypolydian. Of course you are correct. (I am still struggling to get the hang of these new-fangled Arabic numerals ;-) You are partially correct that I had in mind the St Emmeran treatises, though I was also thinking of the peculiar juxstaposition of tetrachords in the Musica enchiriadis. As soon as a theorist starts putting tetrachords together, of course the result will begin to resemble an octave scale, but my point (perhaps not so clearly phrased) is that for some medieval theorists one does not start from an octave scale and break it down into tetrachords, but rather the reverse, and the theoretical description of a mode may rely almost exclusivey on the structure and juxtaposition of tetrachords. As for the exclusivity of B♭ in modes 5/6 ("because their B, until Glarean, was always flat"), surely you are overstating the case here. As you yourself wrote (though it was such a long time ago perhaps you have forgotten), "While examples of the tetrachord of the synemmenon are often encountered in all the modes, or tones, they can be seen especially in the authentic and plagal tritus [i.e., modes 5 and 6] so ubiquitously that in these scarcely any melody is found without a mixture of the tetrachords of the synemmenon and the diezeugmenon" (GS1:114a/10, in Warren Babb's translation, emphasis added). Indeed, your elegant exposition on the five tetrachords is another example I had in mind where the notion of "scale" as it is generally understood today is subservient to the conception of a tetrachordal constellation, for not only do the synemmenon (A₃ B♭₃ C₄ D₄) and diezeugmenon (B♮₃ C₄ D₄ E₄) substantially overlap, but the tetrachord of the hypaton always retains hard B, regardless of the fact that synemmenon may be in use an octave higher. (Of course I recognize that this is almost purely a theoretical condition, but we are speaking here of theory rather than of practice.)—Jerome Kohl (talk) 23:21, 12 July 2014 (UTC)

Yes, Jerome, you are right, I did write that, and your guy Babb made a good job of translating it. But you may realize that in these times we sang somewhat differently, and as soon as they decided to notate music, especially after this young Italian, Guido, I think, had imagined staff notation, one dropped many of these paramese notes, which are so to say never found in notation. Also, in Ecce iam venit, the paramese on iam really is a trembling of the voice (a neighbour note, my friend Heinrich would say); also in Paganorum, on multitudo fugiens, but that one is not sung so often nowadays. Anyway, you are right and I should reread myself from time to time.

On the other hand I fail to see why you guys today consider that an octave is a scale and a tetrachord is not. It is true that the same Guido wrote in Chapter VII of his Micrologus: Cum autem septem sint voces, quia aliae ut diximus, sunt eaedem, septenas sufficit explicare ("As there are only seven notes, because the others, as we said, are the same, it suffices to explain seven of them"); having said that, however, he explained only four, adding that the notes knew only four modes! (Let me ask, in passing how a mode of one note could be a scale?) He was right in this, but he could have said it more clearly!!! – Hucbald.SaintAmand (talk) 09:30, 13 July 2014 (UTC)

A mode of one note does rather evoke the famous "sound of one hand clapping", but on Wikipedia, anything is possible. I suppose that using such a scale would be insurance against any accidental occurrence of bitonality. On a related subject (and since I see that Jacques is moving on to a new question about terminological overlapping), I believe that the word most often used by medieval theorists for what we call a "mode" is actually "tone". Consequently, when Glareanus finally succeeded in adding four new modes to the traditional eight, didn't that make him the first twelve-tone theorist?—Jerome Kohl (talk) 19:03, 13 July 2014 (UTC)

Hucbald asks "... how a mode of one note could be a scale?" Hazarding a guess, if we can take scale to mean a ratio of the dimensions of members of a set, this allows a ratio of one to one, or a scale that is one pitch. Regarding the musical usefulness of such a concept, I think about a drum playing a rhythm. The only way I can think of to describe its scalar attribute would be that its scale has only one value, or the ratio of 1:1. You and Jerome would know better than I, but some examples might also be found in chant. Not familiar enough with minimalism, but perhaps there too.Jacques Bailhé (talk) 17:29, 15 July 2014 (UTC)

I believe that the modern conception of what a scale is (or at least, what it normally is) involves division of the octave. As a division of the octave into one step, the monotonic scale is therefore a single pitch class, but not necessarily a single note, since this scale (like any other) can be regarded as repeatable in higher or lower octave transpositions. Additionally, any "complete scale" normally includes both the upper and lower bounding pitches, an octave apart. The linked article may be of some use in understanding the actual use of this (dubious, in my opinion) theoretical construct, though it is a bit shy on substance.—Jerome Kohl (talk) 18:32, 15 July 2014 (UTC)

My (purely formal) question concerned the fact that Guido of Arezzo used the term "mode" to characterize individual notes, before discussing anything having to do with what we call a mode. (What is "the linked article"?) Guido's "modes of the notes" (modi vocum) actually concern the four notes of the tetrachord and are repeatable at tetrachordal distance (i.e. at distances of a 4th or a 5th). This probably is too technical for our purpose, but IMO it does stress the complexity of the concept of mode. And we did not even begin discussing the case of maqams (oriental modes), which hardly could be reduced to scales. – Hucbald.SaintAmand (talk) 08:32, 16 July 2014 (UTC)

I could not possibly agree with you more. This is exactly what I have been saying from the start: "mode" cannot be reduced to the equivalent of "scale", except in very particular circumstances where it is defined in this narrow sense (in jazz theory, for example). As for the linked article, it is the one titled monotonic scale, which I linked two sentences before mentioning it, and which I had linked previously under the rubric anything is possible. (I shall have to stop going to the trouble of making these links, as well as writing edit summaries and placing editorial messages in hidden text, since no one ever seems to take advantage of them.)—Jerome Kohl (talk) 17:13, 16 July 2014 (UTC)

Sorry, Jerome. I didn't see the link (the blue colour does not enough contrast with the black on my laptop screen). As to Edit summaries and Hidden text, I am to recent a user of WP, but ready to learn... – Hucbald.SaintAmand (talk) 18:43, 16 July 2014 (UTC)

They say a week is a long time in politics, and so also is it on Wikipedia. I reckoned you as a seasoned old-timer when I saw from your user page that you have been around since January 2013. My apologies for making unwarranted assumptions. For my own part, I have a hard time seeing redlinks, because I have a degree of red-green colorblindness. I did not mean to suggest that either hidden text or edit summaries were an issue here. This was on my mind from a separate exchange with another editor, and I let it spill out here. Sorry. However, if you are not familiar with these, you might like to follow the blue-links (if you can see them!) and read the articles to which they point. Edit summaries are an important part of working on Wikipedia; hidden text is a bit more arcane, but also worth knowing about.—Jerome Kohl (talk) 22:43, 16 July 2014 (UTC)

Conflict with article "Chord (music)"

The section "chord" here is contradicted in some respects by the article which it cites as the "Main" article. In particular, the main article stipulates (with two supporting reliable sources) that a chord must have at least three notes, and provides two references to support this claim. The present article says that two notes are sufficient, but does not offer any verifying source. Ordinarily, I would simply change this statement, but the situation is not this simple. The issue of course has to do with differing opinions amongst various sources, but this in turn involves the question of undue weight. How should this be resolved in the present case?—Jerome Kohl (talk) 17:57, 7 July 2014 (UTC)

One of those two references, Károlyi, supports the claim that "two or more" notes form a chord. This issue has come up before and it's been back and forth in the Chord (music) article, most recently becoming "three or more" last April. As a fiddler who uses double-stops to represent chords (sixths work well for suggesting the usual triads, as do thirds) I'm biased towards "two or more," but I will defer to actual music theorists on this one. I now have a paper copy of the Károlyi book, and can confirm that on p.63 he says ""Two or more notes sounding simultaneously are known as a chord." Just plain Bill (talk) 21:02, 7 July 2014 (UTC)

Thanks for the history—I haven't been watching that article very closely at all lately. This answer, however, leads me neatly into my second question: How much weight should be given to Károlyi, as opposed to Benward & Saker, and (let us say) a random sampling of two hundred other theory books, dictionaries, and encyclopedias? Now, to back up a moment, you describe your fiddling as using two-note sounds (double-stops) to represent chords. This suggests that what you are representing involves more than two notes, and this leads to another problem formerly found in the same paragraph, which I tagged just before putting the "conflict" banner up, and that is the issue of just how one pair of notes can imply a chord, while another pair cannot. I think I know the answer to this question, but I believe it would take me five or six paragraphs to explain it, and it would presuppose a fairly lengthy discussion of chord construction had already been presented. User:Jbailhe has already (I think wisely) deleted this, together with the claim of two notes being sufficient to constitute a chord, on grounds that this article is not the place to introduce such a degree of complication. I do not believe this is adequately addressed over on the "main" Chord (music) article, either (though I have not re-read it carefully to be sure). Should it be? (Can it be?) Knowing how this works is certainly one of the rudimentary skills required of any jazz improviser, not to mention for composers in all styles of harmonically based music. If we are going to fob off the reader here by saying that the more complicated aspects are explained elsewhere, hadn't we better make sure that those things actually are explained where we are sending them?—Jerome Kohl (talk) 22:43, 7 July 2014 (UTC)

As far as I'm concerned, G4 and B4 are a G major chord, as are B4 and G5, at least in most contexts where I play them like that. When I'm being lazy, I might play a power chord on the open G3 and D4 strings in the same contexts. Being strictly an amateur, I did not press the issue when some anonymous editor from an IP in the Netherlands changed it to "three" a few months ago. Have I thanked you lately for your tireless contributions? Thanks! I will have my eyes on this page, but I'm not sure how much cognizant help I can offer. Just plain Bill (talk) 23:24, 7 July 2014 (UTC)

I'm sure that your word must count as a reliable source ;-), but I might just suggest that, had you been in E minor, and played a downbeat E4 just before playing your G4/B4 double stop on beat two of the bar (or if an accompanying bass instrument was playing a sustained E), I would probably hear those two notes as the third and fifth of an E minor triad. Context is a very important element in such matters, and is one reason I would demand at least five paragraphs to attempt an explanation. The issue of the minimum number of notes to qualify as a chord is of course entirely a matter of definition, and the question of undue weight boils down to whether the two-note opinion is overwhelmingly opposed in the literature or not. I have not surveyed this literature, so I do not know what the situation actually is, and I would not be at all surprised to learn that there is one rogue source out there that refuses to recognize as a chord anything with less than four notes in it. You are very kind to describe my work on Wikipedia as "tireless" (others might use a different adjective). You are very welcome.—Jerome Kohl (talk) 23:54, 7 July 2014 (UTC)

I sometimes grab a couple of notes from an easy D major chord when a B minor triad doesn't suit my fingers, so point taken. (Bit of side chat regarding your edit comment: every thing I know of Yorkshire English I learned from Stanley Holloway's recorded readings of the poetry of Marriott Edgar. I once heard a familiar twang at a Boston Early Music gathering, and looked up at the rebec vendor's banner to see that his shop was from thereabouts.) Just plain Bill (talk) 00:30, 8 July 2014 (UTC)

Pardon me for interjecting here, but since you're discussing an edit I made, I thought I should. Checking my reference books, it seems that the widely mistaken idea that chords must contain at least three notes may derive from the entirely accurate observation that most Western music uses triads predominantly. Most any Bach chorale will illustrate, but will also show dyads at cadences as octaves and 5ths. Checking some etymology, OED tells me our word "chord" is an aphetized form of the Fr. "accord", or perhaps "concord." It became "cord" and later an "h" was inserted, I imagine to distinguish between "cord" as in a string, and "chord" meaning sonority. Either way, the concept is that no more than two parties are necessary to make an accord or concord, and so, it would seem to follow, that no more than two pitches are necessary to make a "chord." This is also corroborated by the Oxford Companion to Music which states, "chord (Fr.: accord, Ger. Akkord, Klang, It.: accordo) Two or more notes sounded together." I'll be pleased to revise if that is the consensus of opinion, but personally, I know of no more trusty sources than those I've cited and regrettably, find that many contemporary music books have muddled terms. I haven't looked at the Wiki entry for "chord," but if you wish, I would make the argument above on that page and address discrepant opinions. — Preceding unsigned comment added by Jbailhe (talk • contribs) 02:43, 8 July 2014 (UTC)

You must not apologise for commenting here. (Actually, you are forbidden to apologise, especially because we are discussing your edit ;-) Your argument is very interesting, but I'm afraid it is a little beside the point. Forgive me if I am telling you things you already know perfectly well about Wikipedia, but what matters here is not what is logical or correct in your or my opinion (in Wikispeak this is an assertion of "truth" based on "original research), and what supercedes this is "verification" based on reliable sources. As I alluded to further up in this discussion, there is actually a surfeit of reliable sources here, which means that there is an issue of striking some sort of balance. If the vast majority of current reference sources say just two notes are required, then there is no problem; if on the other hand an overwhelming majority insists at least three notes must be present, then equally there is no problem. But, if the sources actually show substantial disagreement, then this difference must be acknowledged and, if they are not equally divided, some position has to be taken about which view predominates.—Jerome Kohl (talk) 04:42, 8 July 2014 (UTC)

Reviewing the article titled "Chord," I find it also discusses the etymology of the word (See Definition and History), but draws no conclusion regarding two notes making a chord, as I do for the sake of argument. The article states, right off the bat, that it takes three notes to do the trick, but as discussed above, my most trusted references tell me otherwise. So does harmonic analysis. In four part harmony, would it be appropriate to identify two pitch sonorities as anything other than a chord with a specific harmonic function? My analysis teacher would say "no." I think most others would too. As authoritative example, Gauldin in Harmonic Practice in Tonal Harmony, example 8.2 on p.120 cadences on 3 F's and an A natural identified as a I chord. On p.122 example 8.3 a cadence lands on 3 C's and an E identified as a I chord. The Oxford Companion to Music shows other examples of two pitch cadences identified as chords (see Cadence). I agree whole-heartedly that if good references seem to split this argument down the middle, that should be acknowledged and presented, but in my own library, I find no disagreement that two pitches can make a chord.Jbailhe 05:42, 8 July 2014 (UTC) — Preceding unsigned comment added by Jbailhe (talk • contribs)

First of all let me stress, as a native French speaker, that the same problem arises for the French word accord: it is not clear whether two notes are enough to form an accord, or at least three are needed. (And note that Hugo Riemann's theory of "feigned consonance" probably means that many three-note chords implicitly stand for four-note ones.) When we were preparing the first edition of the New Grove, about forty years ago, one rule given by the editors was that we should not present as sure anything that remained open for discussion. I think the same applies here: rather than wondering whether there are more or better sources for two or for three notes, the safest solution would be to state that this question remains a matter of debate and to quote a choice of sources pro and/or again.

There are many other things that should be said about "chord", either here or in Chord (music), for instance that the largest number of notes (or, better, pitch classes) consonant with each other (in a common understanding of the word "consonance") is three, and that these specific chords of three notes are called "triads" (dissonant groupings of three notes usually are not called triads, if only because they often stand for more notes, e.g. F G B which is a dominant 7th); that there is a now widely adopted theory, dating from the early 17th century, that such triads are formed of a 3d and a 5th above a note called the "root" and describing other positions as "inversions"; that from this another widely adopted theory arose, that chords in root position are formed of a piling-up of thirds – and, as a result, that any empty 5th in a chord in root position (or its equivalent in inversion) is implicitly understood as containing a missing third; that the very notion of chord entails that the combined notes are understood as forming a unity, a construction block, and that music made up of such blocks is considered 'harmonic'; that the notion of 'chord' therefore does not exist before the 16th century of the 15th at the earlied (contrarily to what Chord (music) claims).

And this brings us back to the question of two or three notes: insofar as the notion of 'chord' implies more than a mere vertical interval, it might be argued that it requires at least three notes, even if one or even two of them are merely understood. As a matter of fact, the definition of 'chord' may not be dependent on how many notes, but rather of whether it is conceived as a unity, as a harmonic building block. — Hucbald.SaintAmand (talk) 08:17, 8 July 2014 (UTC)

Hucbald's comments are illuminating for me. Thank you. No doubt there will be other good arguments in both directions, but as I see it, Wikipedia needs a generally acceptable working definition of "chord" to be used in most articles and can, as Jerome mentioned above, discuss the theoretical quandaries in detail in the main article on chords. Pulling out a number of other references I haven't looked at for a while, I find a great many (but not all) insist a chord requires a minimum of “two intervals,” therefore three and not two pitches. Short of that we have an “incomplete” chord. Scouring through quite a number of music excerpts from Couperin to Tchaikovsky, I find that although there are examples of cadences landing on only two pitches, which would be correctly identified as having chordal function in harmonic analysis, those examples turn out to be comparatively rare. Scanning my Bach Reimenschneider 371 Harmonized Chorales for a few minutes, I was surprised to find not one example of a cadence on two pitches. A dyad fulfilling the function of a complete chord appears to be the exception to the rule. Gauldin, as mentioned, does identify dyads as chords in cadences by various composers, but I am increasingly convinced that is only theoretically correct because they imply a third tone. Furthermore, Rameau in his Treatise on Harmony makes persuasive arguments verbally and mathematically, that a chord must have a minimum of two intervals to be a complete chord. Piston, Perischetti, Schoenberg, and the Harvard Brief Dictionary of Music agree. Added to the references cited by others, the preponderance of theoretical and music sources appears to come down on the side of three tones as the generally accepted minimum.

So, despite other authoritative references and my formidable arguments to the contrary, I make an about-face and recommend Wikipedia states something like the following in the main article on chords:

Chords are generally considered to be built with a minimum of three pitches. Although two pitches can function harmonically as a chord in some instances, they typically do so by implying a third pitch. In such instances, they may more accurately be called “incomplete” chords. Not all theorists agree and the on-going debate is discussed more thoroughly below. But since the preponderance of music examples and theoretical writing indicates a complete chord must contain a minimum of three pitches, that will be used as the general explanation of the constitution of a chord.

Uses of the word “chord” in other articles can then link to the more thorough discussion in the main article titled “Chord.” Jacques Bailhé --Jbailhe 09:29, 8 July 2014 (UTC) — Preceding unsigned comment added by Jbailhe (talk • contribs)

Chords: 2 v 3 notes - solved? The Chord article does a thorough job discussing the question and it seems to me, is excellent the way it is (see Definition and History). I've taken cues from there and revised the opening remarks about chords in the Music theory article accordingly. It should now be consistent - at least in that regard. Jacque Bailhé 070814--Jbailhe 01:08, 9 July 2014 (UTC) — Preceding unsigned comment added by Jbailhe (talk • contribs)

I have added a few minor changes to the "Chord" section in the hope to make things even clearer without disturbing your work. Note that if you make further interventions in Wikipedia and considering that you have your own page (i.e. you are logged in), you should learn to use the automatic signature, either typing four tildes (~) or clicking on the tildes just below the "edit" window. – Hucbald.SaintAmand (talk) 06:47, 9 July 2014 (UTC)

This is getting better as it goes on, but I am still uneasy about one detail in the present wording. The direct succession of a "group of tones heard or conceived as sounding simultaneously" and "Arpeggios sound the tones of a chord in succession, but are still considered to form a chord" appears to suggest that arpeggios are the only way in which a group of tones not actually sounded together might be "conceived" as so sounding. This is of course a rather complex issue, and I think we are trying to keep this page as simple as possible, but on the other had we should't mislead the reader if we can avoid doing so.—Jerome Kohl (talk) 17:58, 9 July 2014 (UTC)

Although this is all a bit off-topic for this page, let me suggest that we re-consider the definition of "chord" outside the context of tonal harmony. Suppose you are listening to music by Hindemith or Webern or Luciano Berio. Without a context to tell you that D-F♯ is part of a pre-existing triadic structure, could it be considered a "chord"? There's a difference between saying "a chord need have only two notes" and saying "sometimes two notes are sufficient to imply a 3-note chord to the listener". I'm not advocating a particular answer to this question, but I propose that thinking about it might clarify some of the earlier discussion. —Wahoofive (talk) 16:33, 9 July 2014 (UTC)

Yes, this discussion probably belongs on the talk page for the Chord article, but this is a good point. Another issue has to do with chord voicing and octave doubling, since the basic assumption here (and on the Chord article) seems to be that chords are constructions not so much of pitches but of pitch classes. As soon as you turn to jazz chords or an article like the one on the Psalms chord, you discover it ain't necessarily so: you can't just re-stack an added-sixth chord and identify it as a seventh chord, and octave duplications may be essential ingredients in a chord's identity. Even the number of notes actually present in a chord may not be so straightforward, as in the case of the so-called "power chord". I know absolutely nothing about this except what I have read on the Wikipedia article about them, but that article seems to suggest that the two notes played are not actually the whole description of what is heard, since some vague thing called "distortion" (which sounds an awful lot like ring modulation to me) is a crucial part of the identity of these things, and it appears that an octave added to the bare fifth may not be entirely optional. This, by the way, is also an issue in the early music contexts cited above by Jacques Bailhé, where the "bare fifth" at cadences is never just that, but almost always involves an octave as an essential interval in the cadencing sonority. Thankfully, musicians (or at least, music theorists) did not think in terms of "chords" at that early date (even if the notion of accord in the sense of "agreement" was understood), so we do not need to concern ourselves with 14th- or 15th-century styles. But the question of how many notes are actually involved in a chord, as opposed to how many notes a theorist sees (we theorists are well known for relying solely on our eyes, and never actually listening to the music we analyse ;-) is very much an issue here.—Jerome Kohl (talk) 17:58, 9 July 2014 (UTC)

A couple notes: I revised wording to address issue of chord members not sounding simultaneously: “A chord is group of tones heard or conceived as sounding simultaneously. In some instances, tones of a chord not sounding simultaneously, but successively as in an Arpeggio, are still considered to form a chord.” RE: peculiar forms of “chord” in various styles and eras, I suggest that anomalies and complexities, important as they certainly are, can best be handled in more specialized pages. The purpose of the Music theory article, as I see it anyway, is to explain to readers the concepts and concerns of music theory – and importantly, give them the links to explore further. Where current sections get into complexities, I think they become off-topic and confusing because of course, it often takes paragraphs and audio-visual aids to explain some of these things clearly. This is why I think we need to re-think the article, as described below.--Jbailhe 22:13, 9 July 2014 (UTC)

Hucbald, thanks for your help. --Jbailhe 22:20, 9 July 2014 (UTC)

Jerome -- Got a notice about links “pointing to disambiguation pages… merely a list….” The links in question are to Chord, Dynamics, Range, Transposition, and Martelé. hes see ke helpful links to me, but should I link to other pages? Jbailhe 19:40, 10 July 2014 (UTC) — Preceding unsigned comment added by Jbailhe (talk • contribs)

This is nothing to be alarmed about. The helpful bot is simply calling your attention to the fact that you have linked terms that have multiple articles associated with them. As a result, your link goes to what is called a "disambiguation page", where there is a list of these articles, with separate links to each. The separate articles will have titles designed to distinguish them. In the case of "Chord", for example, "Chord (music)", "Chord (geometry)", "Chord (astronomy)", "Chord (graph theory)", and so on. You can go back to the article and substitute the correct link, using a "pipe" syntax to avoid displaying those disambiguating terms in parentheses, thus: [[Chord (music)|chord]], which will display: chord. However, if you simply ignore the message, some other editor is likely to make the correction for you, sooner or later. It is of course the courteous thing to make the change yourself. There is even a little "wizard" linked from the message sent to your talk page that can help finding the most appropriate article for your purpose. It is really cool when writing your edit summaries for these corrections to use the abbreviation "dab" for "disambiguation" or "disambiguated", as in "dab link", meaning "I have disambiguated a link". It is also easier to spell ;-)—Jerome Kohl (talk) 22:26, 10 July 2014 (UTC)

Thanks for the help, but what about links to List pages? Is that not appropriate? If it is, how do you link to such a page properly to avoid dab problems?Jbailhe 16:47, 11 July 2014 (UTC) — Preceding unsigned comment added by Jbailhe (talk • contribs)

Do you mean pages like List of music theorists? Sure, it is perfectly appropriate to link to those, and it is done in the usual manner, using double square brackets. There should be no problem with disambiguation in such a case. If on the other hand you are thinking of disambiguation pages when you say "List pages", then I think I have already explained how ambiguity is avoided: change any such links to the specific page you intend. Very rarely, this may not be possible. When the link to a disambiguation page must be kept, there may be a recommended way of marking it so that later editors will not try to "solve" a nonexistent problem, but I don't know what that is. The only example I can think of is in this list, where an explanatory note is added in the introductory paragraph.—Jerome Kohl (talk) 17:41, 11 July 2014 (UTC)

Returning for a moment to this topic, although I think we've found a way to discuss this in the article without getting overly complex or otherwise opening Pandora's box, I thought you all might be interested in:

Cook and Fujisawa's "The Psychophysics of Harmony Perception: Harmony is a Three-Tone Phenomenon," Empirical Musicology Review Vol 1, No. 2, 2006. The full article is downloadable at http://kb.osu.edu/dspace/handle/1811/24149

ABSTRACT: In line with musical “common sense” (but contrary to the century-old tradition of musical psychophysics), we show that harmony is an inherently three-tone phenomenon. Previous attempts at explaining the affective response to major/minor chords and resolved/unresolved chords on the basis of the summation of interval dissonance have been notably unsuccessful, but consideration of the relative size of the intervals contained in triads leads directly to solutions to these historical problems. At the heart of our model is Leonard Meyer’s idea from 1956 concerning “intervallic equidistance” – i.e., the perception of “tension” inherent to any three-tone combination that has two intervals of equivalent size (e.g., the augmented chord). By including the effects of the upper partials, a psychophysical explanation of the perceived sonority of the triads (major>minor>diminished>augmented) and the affective valence of major and minor chords is easily achieved. We conclude that the perceptual regularities of traditional diatonic harmony are neither due to the summation of interval effects nor simply arbitrary, learned cultural artifacts, but rather that harmony has a psychophysical basis dependent on three-tone combinations. Jacques Bailhé (talk) 20:45, 22 July 2014 (UTC)

Notation Systems

Came across an intriguing image of what is presented as a notation system from Egypt c. 400ce.

http://33.media.tumblr.com/tumblr_mcvdngf2K61r5yt7ko1_1280.jpg

It is described in Theresa Sauer's book, Notations 21, Mark Batty Publisher, USA, 2009 on pages 290-291, as: a Coptic score that demonstrates Ptolemy's theory of Harmonia Mudi; the colored circles represent chromatic tones; their circumference indicates duration and rhythm; at the top is an inscription in Greek that means "spiritual harmony, or more literally "spiritual chord." I can't find a way to verify any of this. I emailed Sauer and asked her if she could tell me where this artifact is kept, etc., but have yet to receive a response. Any help? Jacques Bailhé (talk) 04:29, 17 July 2014 (UTC)

I've found references that verify the authenticity of the above. Jacques Bailhé (talk) 20:03, 22 July 2014 (UTC)

The Notation section states, "Spoken language and hand signs are also used to symbolically represent music, primarily in teaching." Is this appropriate? Notation means exclusively that which is written, deriving of course, from the word "note" which is an exclusively written thing. Hand signs may be considered symbols, provided they are indeed symbols and not signs. In this context that distinction is probably not terribly significant, but "spoken language" seems completely distinct from notation, in any sense. I recognize the value of solfège, etc., but suggest those things, especially hands signs and spoken language, more accurately fall under pedagogy, not notation. Any thoughts?Jacques Bailhé (talk) 05:09, 22 July 2014 (UTC)

Jacques,

• Strictly speaking, spoken language cannot be used to "symbolically represent" music, it can only describe (or translate) it, which is not the same thing: the article certainly is wrong and you are right on this point.
• The case of hand signs is more complex. The hand signs of an orchestra conductor do not symbolize the music, but the medieval Guidonian hand did, and neumatic notation is sometimes said to reproduce chironomic signs (from the Greek cheiros, "hand"), which also did symbolize the music.
• The Latin nota (and the English "note") may derive from notus, "known", from noscere, "to know". That is to say that a note (and therefore perhaps a notation) needs not per se be written. You are right, though, that "note" and "notation" strongly suggest written symbols.
• Notation, in other words, is but one (important) case of music symbolization. I think that the article should say so, but other means of symbolizing may not be out of place. The point is that music is a symbolic language, a semiotic system, and its symbols, as is the case with any such system, can take on different appearances. Our languages are notated alphabetically, that is with letters representing phonemes (sounds, if you want: alphabetic writing is a case of phonetic notation); but a normally competent reader does not read letters, (s)he reads words, which are perceived as blocks: words become ideograms. And ideograms (as in Japanese, Chinese, etc.) by no means represent the sound of the language: they form a graphic language parallel to the spoken one. A competent music reader similarly does not need to read the notes one by one – and, I am convinced, does not even need to form a "hearing" of what (s)he reads: inner hearing is a complex and mysterious thing. But this isn't our concern just now.
• To sum up, I think that the section on notation may want to better explain why it mentions other types of symbols, but I find it excellent that it does.

Hucbald.SaintAmand (talk) 14:52, 22 July 2014 (UTC)

Hucbald--Excellent! Thanks. Jacques Bailhé (talk) 20:03, 22 July 2014 (UTC)

Under the section above about "Chord" (No. 21), I put up an abstract and downloadable link to an article that I thought might be of interest to you all. Cook and Fujisawa's "The Psychophysics of Harmony Perception: Harmony is a Three-Tone Phenomenon," Empirical Musicology Review Vol 1, No. 2, 2006. The full article is downloadable at http://kb.osu.edu/dspace/handle/1811/24149 Jacques Bailhé (talk) 20:51, 22 July 2014 (UTC)

Jacques, this link does not give access to Cook and Fujisawa's paper, only to its review by Richard Parncutt. Parncutt has the very novel idea that one reason of the prevalence of the diminished 5th over the augmented 5th is that it may serve as an incomplete dominant 7th. Formidable discovery! Fétis (and many others) had already said so about two centuries ago... – Hucbald.SaintAmand (talk) 06:53, 23 July 2014 (UTC)

Hucbald--I didn't notice your comment about the above link not functioning. Pardon me. If you're interested, you can click the below or paste it in your browser and it should take you directly to downloading the pdf.

https://kb.osu.edu/dspace/bitstream/1811/24080/1/EMR000008a-Cook-Fujisawa.pdf

Jacques Bailhé (talk) 00:08, 3 August 2014 (UTC)