Chords

[motet]

In the classical world's common practice era harmony, a 9th is an extension of the 7th (3, 5, 7, 9) no matter how the chord is voiced and which note is above or below which. I don't think one speaks of an "added 2nd chord." It's a matter of harmonic functionality. Aside from which note is in the bass, all permutations are considered functionally equivalent. They do sound different, of course.

[zuill]

What I explained is how you spell the chord. If you are a composer and want a certain chord and sound that is what you would write. Your example of the two chords would not sound the same.

In classical harmony, the way I learned it, as well as with pop chords, inversions are very common. If a 9th always has to be on top, then that would be true of a 7th as well. I don't agree that the 7th is always on top. If that were the case, then things would get pretty boring pretty fast. Chord inversions are needed for good voicing.

Zuill

[ebiggs1]

If a 9th always has to be on top, then that would be true of a 7th as well.

You are confusing how players play (voice) a certain chord and how a chord is technically spelled. An A add9 is always going to be A, C#, E and B in that order. And, A9 is A, C#, E, G, B. This is simple, basic Tertian Music theory.

I don't agree that the 7th s always on top.

Quite right, it doesn't always have to be played that way. And in practice it is not but in basic music theory an A add9 has to be A, C#, E and B on top. This is the answer to the OP's original question. If we need to go back to basic music theory OK. Music theory tertian chords (chords built from thirds) or triads with added notes, 7th, 9th, 11th and/or 13th are extended chords. The 13th being the farthest extension diatonically possible because all seven tonal degrees have been played. Since the 15th is the same note as the root note. Now if you choose to not follow this as you are playing a tune that is fine, you are just not playing an A add9 (A9) chord. You could be playing an inversion but that isn't correct either if you still play the A in the root position. If you do play the A (root position) you now played an A add2 chord. I realize it is common for a piano player to omit the root A letting the base player play it and he play C#, E, G and B. It is also more common to omit the 5th or the 7th. However, the correct spelling of that chord has also changed, A9 (omit 5), etc. This is just the way it is guys.

Let's examine the A add4 and/or the A add11. Both chords contain the same notes. However the added note is in different octaves. The 11th and the 4th are the same notes in the A scale. The spelling specifically tells the musician that the chord is to be played A, C# E and D in the case of A add 11 (A11). And our A add4 (A4) chord is played A, C# D and E. The same thing applies to our A add9 compared to A add2.

[Anders Hedelin]

It seems that we have different definitions.

'Spelling' of a chord usually refers to how the chord symbol or the figures of the figured bass are spelt, and tells just of the contents of the chord.

In what order, and with what distance, you arrange the played notes in a chord is called 'voicing'.

The spelling is not influenced by the voicing.

EDIT: I came a little too late with this post obviously. Or, possibly ebiggs1 had time to correct his posts before I noticed.

An A add9 or A9 is always going to be A, C#, E, G and B in that order. This is simple, basic Tertian Music theory.

I think you have misunderstood the meaning of 'add'. A9 usually includes 7 - Aadd9/Aadd2 doesn't.

[ebiggs1]

I think you have misunderstood the meaning of 'add'. A9 usually includes 7 - Aadd9/Aadd2 doesn't.

Yes you are correct. Too many fingers on the keyboard at a time! The concept is correct, though. However, omit 5 in a 7 chord is common as is omit 7 in a 9 chord.

The spelling is not influenced by the voicing.

Only in jazz!
It becomes impossible to play some chords on certain instruments so "creative voicing" is used. A guitar only has 6 strings and most piano players only have 5 fingers on each hand. Besides the reach of most people isn't sufficient to play all the extended chords. The spread is out to far.

[ebiggs1]

To be totally clear, A9 is A, C#, E, G and B. Plus it is always in that order or it isn't that specific chord. It is something else. Perhaps an Asus2, perhaps an inversion, whatever.

A add9 is A, C#, E and B always in that order and this is the answer to the OP's query. How you play these chords has no effect on how they are spelled or their meaning. When you alter the way these chords are played vs the way they are spelled you change their sound.

[Anders Hedelin]

To be totally clear, A9 is A, C#, E, G and B. Plus it is always in that order or it isn't that specific chord. It is something else. Perhaps an Asus2
A add9 is A, C#, E and B always in that order..

Why so adamant that the chord symbol expresses the order of the notes? When, in what genre of music, is that true? I'm just curious.

[ebiggs1]

Yes, it is called basic music theory.

[Anders Hedelin]

It might be a good idea reading up on music theory before lecturing old music theory teachers.
"Basic music theory", Jeez.

[ebiggs1]

If strict guides are not followed and anybody can play anything any way they want why have a spelled out chord at all. Just a suggestion?
Grammar besides music has a set of rules. Although the rules are laid out clearly people talk any way they want and sometimes slaughter the language.

It might be a good idea reading up on music theory before lecturing old music theory teachers.

Perhaps, just perhaps you and some others need that refresher course, also. I am not perfect and I may have made some typing errors or edits but the basic concept I put forth is correct.

[Anders Hedelin]

I'm sorry but I think further instruction would be fruitless. End of discussion for my part.

[ebiggs1]

'Sounds' good to me!

[mrjnace]

The correct answers are all provided throughout this discussion, but are buried under a lot of nonsense from those who claim to know and admonish others for their poor grounding in music theory, while themselves demonstrating once again that a little knowledge is a dangerous thing.

To establish my bona fides to set the record straight, I have a PhD in music theory. Specifically, I am an expert in Classical theory (what has been characterized in this thread as "basic music theory") and historical theory; I am also extremely competent in theory and performance of popular music (loosely speaking, the term Classical theorists use to describe anything that isn't Classical, jazz, or ethnic --so, including rock and roll, blues, country, gospel, R&B, pop, etc.), and while I am only an intermediate jazz performer, I am very well read in jazz theory.

First things first: a couple of disclaimers disclaimer. Theory follows practice. It is rare for a composer to invent music theory before applying it. Far more commonly, a composer tries something new, it catches on, and then theorists follow afterwards and describe and name what the new performance practice. Thus, when the performance practice changes, so does the theory (this will be important when we need to consider suspended chords). Additionally, it is important to remember that chord symbols have never been entirely standardized (this could actually be said of much more of music theory than most people would believe), and people use them in unexpected ways. Just as with language, what is correct in not truly determined by what is in the textbooks or dictionarirs but what will be understood; if a chord symbol is likely to be understood, then it is correct.

Now, the original question: A+9 vs. A(add9). These two chords are completely unrelated. In standard usage, a + sign indicates a pitch raised by one semitone compared to what is expected. Its use goes back to at least the Figured Bass tradition of the Baroque period (ca. 1600-1750); note that the concept of chord inversion only began to spread very late in that era, and so in general, a + sign before a number meant to raise that pitch relative to the bass note, not the chord root, and also relative to the key signature, rather than the chord quality. For example, the vii⁰ chord in Classical theory is usually assumed to be in first inversion (for instance, in the key of A minor, a G#⁰ chord usually puts the B in the lowest voice by default (that is, G#⁰/B). The G# is the root of the chord, but it does not belong to the key signature (it is the characteristic feature of the harmonic minor scale form). In figured bass, this chord could be indicated with the symbol +6 (also #6 or a 6 with a slash through it). Both # and + before a number mean the same thing. However, when the number is omitted and only the symbol remains, the usage has diverged, especially when paired with a Roman numeral to indicate the chord's root relative to the key. As a rule, any chord followed by just a # sign without a number in Classical usage is understood to mean that the third has been raised (and almost always means that the chord would have been expected to have a minor third but has been altered to have a major third). The most common example is V# in minor keys, where the v chord would naturally be minor according to the key signature but is usually major in practice (again, the characteristic feature of the harmonic minor scale). By contrast, the + sign on its own, without a number after it, is understood to apply to the fifth of the chord, generally altering a major chord into an augmented chord.

As an instructive digression, augmented seventh chords (and thus, ninth chords, such as the one posed in the original question) pose an interesting problem. Should the seventh be major or minor if it is not specified? It is frequently said that the augmented chord arises in the harmonic minor scale on the III chord (this is equivalent to the I chord in the relative major key), and so the expected seventh above this root in the key is the major seventh. However, III+ is almost never used as a III in Classical music. An augmented chord is fully symmetrical. Ignoring chord spelling (which we cannot hear), each of the three notes of the chord could be understood as the root of the chord. One of those notes is the fifth note of the scale, and in practice, this is the true root of the augmented chord, however it might be spelled. Despite some of the comments made by previous posts above, Classical composers frequently spelled the chords in the manner that would be easiest to read, rather than the form that we would now consider to be theoretically correct. Thus, an apparent III+ chord is really a V+ chord in which the augmented fifth has been respelled as a minor sixth because it happens to fit into the key signature that way; that this is the superior interpretation of the chord is usually confirmed by the more expected chord progression (V - I rather than III - I) and voice leading (the augmented fifth, occurring on the second scale degree, becomes the third scale degree, as in a V+ chord). Thus, the usual interpretation of an augmented chord with a seventh (i.e., A+7) is as a dominant seventh with a raised fifth, not a major seventh with a raised fifth. The same would be true of A+9.

Within the realm of jazz chords, it is important to be aware of the important difference between A+9 and A7+9. Because most jazz chords are understood to be seventh chords by default, the 7 is part of the standard chord symbol. As a result, a + sign that occurs before the 7 is part of the fundamental quality of the chord, and thus, automatically applied to the fifth of the chord. There is, in any case, no such standard symbol as +7 to imply a raised seventh in jazz chords; it may be seen occasionally in Classical analyses (but in this case, both the + and the 7 will usually appear in superscript). However, a + sign after the 7 usually applies to whichever number follows, of which 9 is a common example. In practice, though, the symbol A7+9 is more commonly given as A7#9 -- and it is generally held to be best practice to put the altered note in parentheses to eliminate confusion, as in A7(#9). As has already been observed in this thread, this is the common approach for the half-diminished seventh chord, which is labelled Aø⁷ in classical theory but Am7(♭5) in jazz.

The A(add9) chord is an entirely different kettle of fish. As the symbol implies, this is an A chord to which the ninth above the root has been added -- but importantly, without having already added the seventh. It is generally understood that extended chords are created by adding subsequent, odd-numbered chord tones to a chord that already contains the all of the previous odd-numbered chord tones. Thus, a triad (the usual type of root) contains 1 3 5, a seventh chord contains 1 3 5 7, a ninth chord contains 1 3 5 7 9, and a thirteenth chord contains 1 3 5 7 9 11 13. (Eleventh chords are controversial in classical theory because their behaviour differs somewhat from the other extended chords and they are usually best described in some other way). Thus, the A9 chord contains A C♯ E G B, while the A(add9) chord contains only A C# E B, without the seventh (G). It is therefore quite different from the A+9 chord A C# E♯ G B, which contains the G and raises the E to E♯ (quite possibly respelled as F in the sheet music, particularly if we are in the key of D minor -- in which A+9 would be the V+9 chord -- since the F belongs to the key signature and would therefore be easier to read).

Here's where the conversation gets... interesting. There has been much discussion about add2 vs add9. I need to make an important disclaimer here: these chords largely do not exist in Classical theory. Classical theorists acknowledge the concept of adding additional notes to a chord but seldom use this concept to describe music older than the late Romantic period (i.e., the late nineteenth century) or even until the early twentieth century, and in general, the note is generally thought of as colouristic effect, rather than as a standardized chord type. However, the terminology by which pop and jazz musicians describe these chords is built upon the edifice of classical theory.

The underlying concept is intervals - the standard way of measuring the distance between notes in pitch space, roughly by counting all the letter names between two pitches, including the names of those two pitches themselves. Thus, the interval between C and G is C₁ D₂ E₃ F₄ G₅ = a fifth. Each interval has two typical forms: a simple form (2 - 8 ) and a compound form (9 - 15). The compound form simply means the simple form plus an octave. Thus, from C up one tone to D is a second, whereas from C up an octave plus one tone is a ninth. One might suppose, then, than A(add9) is A C♯ E _ B (note the lack of a G), while A(add2) is A B C♯ E. This is, however, a distinction without a difference. Despite what has been said in posts above, the definition of a chord does not require that the actual pitches of a chord occur in any particular order, nor in any particular octave relative to the root, nor does is specifically mandate any particular number of instances of each chord tone. A C major triad contains the notes C E G. In principal, E E G C E E E G E, which each E being one octave higher than the last, is still a C chord.

This is not just a question of voicing, inversion, or performance practice, as has been discussed above; it is intrinsic to the concept of a chord itself. This has been true since the concept of chord inversion was popularized by Jean Philippe Rameau's Traité sur l'harmonie in the eighteenth century. This is not to say that no great theorists or composers would ever have disagreed; J.S. Bach, who died nearly thirty years after the publication of the traité rejected Rameau's ideas, as described in the correspondence of Bach's son, Carl Phillipe Emmanuel Bach, who was also a notable composer. However, the principal of chord inversion is now at the very heart of standard chord analysis. Even chords that are inversions of one another are usually (with a few exceptions) understood to be conceptually the same chord, not merely convenient alternatives of some true form. Chords most certainly are not the snowmen that they often appear to be when drawn on a staff the first time we teach them to beginners. Chords have an abstract existence in the background of a piece of music even while they are not being directly manifested in the musical surface. In monophonic melody, which can only play one note at a time, there are still harmonies that are understood by the listener -- not merely implied, but inferred or intuited by the listener in the same way that we can sometimes leave out words in language; notice that I could have left out the word "that" the last two times that I used it (and now, the last three) without any fear that the reader would have failed to supply it; it could have been omitted and yet still meaningfully present as far as the grammatical conditions of the sentence are concerned. In the same way, when the chords are not played, they are still present. Also in the same way, if a chord is missing its fifth above the root, it is still effectively present. Is the octave above the root a default member of the chord? If not, and it is present in the chord, must we acknowledge it by calling it an add8 chord. Or, if it is part of the default for the chord and is not present, must we acknowledge it as an omit8 chord? To my knowledge, no one has every suggested either case. It is understood that the octave in which the tone is present is largely irrelevant. Suppose that a chord added the seventh in the second octave above the root, rather than the first; should it then be called a fourteenth chord? Or an (add14) chord, since the intervening notes would not be present? Of course not. It is still a seventh chord. A question was also raised about whether the seventh must be the highest tone. The answer is no. It may occur anywhere, including as the lowest tone (e.g.,C/B♭). This would be considered the third inversion of the seventh chord, but still a seventh chord. If it were not, what else would it be? In Rameau's time, prior to the wide-spread adoption of the notion of chord inversion, what we would call a first-inversion seventh chord was called a chord of the large sixth (because of the 6/5/3 figured bass signature); a second-inversion seventh was called a chord of the small sixth (because of the 6/4/3 figured bass signature); and the third-inversion seventh chord was called a chord of the second (because the signature 6/4/2 is the only standard chord signature to contain a 2); we will need to return to this last point shortly. That we no longer use these terms is a strong argument against the idea that order in which the notes are added to a chord changes the chord's identity.

As far as I can tell, the same thing is effectively true for add2/add9 chords. Although one can easily find arguments over this issue throughout the internet, this argument seems to have arisen from a fundamental misunderstanding of the classical theory upon which all of this is built. Although classical theory has a mechanism to distinguish between simple and compound intervals (e.g., seconds vs ninths), in practice, this distinction is rarely strictly employed. Even in Figured Bass -- the first version of chord symbols -- the number 2 is seldom used for anything other than third-inversion seventh chords. In fact, Rameau says so explicitly. He dedicates two separate chapters of his traité to the proposition that ninths and elevenths are the only two compound intervals that are meaningfully different from their simple counterparts, the second and the fourth, but for Rameau, the difference is not the difference between octaves or the difference between extended chords and add-note chords, but rather the difference between an extended chord and an inversion. Simply put, for Rameau, the numbers 2 and 4 should only occur in a chord symbol if they arise as a result of chord inversion.

However, this issue is also tied up with the concept of suspensions and suspended chords, and a quick examination of these should prove enlightening. In popular and jazz usage, we speak of suspended chords, but there is no such thing as a suspended chord in Classical theory. The phenomenon exists, but it is understood entirely differently, as a note that is not a true member of the chord. In Classical theory, a suspension (not a suspended chord!) is a melodic device by which a note belonging to the previous chord but not the current chord is held over into the current chord for part of its duration, and then resolved downward by step to a note that is a member of the chord. For a relatively simple example, when a C chord (C E G) changes to a G chord (G B D), the C is held over into the G chord, delaying the arrival of the B note of the G chord, giving G C D for a short time, until the C finally resolves down to the B that we are expecting. Since the C note is a fourth above the bass note G and resolves down to the B, the third above the bass note, this melodic pattern is called a 4-3 suspension, and in combined Roman numer/Figured Bass notation, this chord would be notated as V⁴-³. As harmony developed over time, it gradually became more common for these suspensions to not resolve until the change into the subsequent chord, or eventually not at all, or to not be held over from the previous chord. In Classical conventions, these are usually not labelled on the chord symbol, but rather directly on the sheet music, with the symbol IN (which stands for "incomplete neighbour tone", a generic term that encompasses several related concepts, including appoggiaturas). In jazz and pop, these became the sus4 chord. In pop, it is generally said that the fourth replaces the third, and therefore, there should be no third. This is sometimes also said in jazz, but jazz authorities also sometimes say that this is only true of the third in the same octave as the fourth; thus, a third could still be present in a different octave. Since this is jazz (and slightly outside my area of expertise), I will include a citation from Mark Levine's very highly regarded The Jazz Theory Book:

A persistent myth is that 'the fourth takes the place of the 3rd in a sus chord.' This was true at one time, but in the 1960s, a growing acceptance of dissonance led pianists and guitarists to play sus voicings with both the 3rd and the 4th. [...] Note that the 3rd is always above the 4th. Mark Levine (1995), The Jazz Theory Book, Sher Music Company, p. 46

Another notable difference between jazz and pop for these chords is that a chord simply marked sus (and not sus4) implies sus4 in pop music, but may imply more than just sus4 in jazz, sometimes implying the second, fourth, and sixth all in a single chord (that is, Gsus may imply Fmaj7/G = G(sus2,sus4,sus6). This practice is closely related to the standard Classical interpretation of eleventh chords, which are usually interpreted as a triad over a non-chord tone a step above the triad's root (i.e., G11 = F/G) -- and since the chord's third is usually omitted in an eleventh chord (the third clashes with the eleventh, to which it is related by semitone or the compound equivalent), this is effectively equivalent to a suspended chord.

Most relevant here is the sus2 chord. In pop theory, it is generally felt that the 2 replaces the third, implying (to a classical musician, anyway, an upward resolution of the 2 up to the 3 part way through the chord). For a Classical theorist, this is an aberration, because the expected resolution of a suspension is downwards. There is, in fact, a 2-3 suspension in classical theory, but in that suspension, it is, in fact, the bass note that is suspended, creating a second against the true third of the chord, and thus the expansion of 2-3 actually results when the suspended bass note moves downward to its correct place, producing the third. The Classical equivalent of a sus2 chord is a 9-8 suspension, which resolves downwards, not upwards. In such a chord, it is rare for the suspension to occur in the lowest octave (thus creating a true second against the bass note) because it must then resolve down to double the root (an not at an octave, but at a unison); thus, the label 2-1 is not typical in Classical theory. It is also worth remembering that in Classical theory, suspensions are labelled against the bass note of the chord, including inverted chords. Thus, the 7-6 suspension might also be a sus2 chord if the chord is in first inversion.

There has also been some discussion of omit-note chords above. From a Classical perspective (so-called "basic music theory"), omit-note chords are rarely labelled as such unless there is a particular point to be made. If a chord is missing its third (other than a suspended chord, where such is expected), this would be considered unusual and it would be labelled as omit3 (this would include modern "power chords", which in pop music are often labelled as 5 chords; thus, C(omit3) = C5 ). If the root is omitted, this would certainly be noted (this is sometimes considered to be the case for vii⁰ chords, which are often interpreted as V⁷ chords without the root). But when the fifth note of the chord is omitted, this is rarely acknowledged. It is simply accepted that triads and root-position dominant seventh chords may be missing their fifths. Contrastingly, inverted seventh chords and non-dominant seventh chords (with the occasional exception of ii⁷) are usually assumed to be complete, and so the absence of the fifth might be noted. In principle, an (add9) chord could be labelled as 9(omit7), but I have never seen this. We also need to be aware that Classical theorists routinely think in terms of four notes in a chord, regardless of the theoretical degree of chord extension, without needing to note omitted chord tones. Certainly, no Classical theorist (again, so-called "basic music theory") would expect to label a ninth chord as 9(omit5), as has been done above; the missing fifth is the expected voicing of a dominant ninth chord in the standard four-voice texture. Similarly, a thirteenth chord is expected to be missing the fifth, the ninth, and the eleventh, carrying only the root, third, seventh, and thirteenth, all without comment about the omitted notes.

A few other quick points to make in response to previous comments. First, extended chords larger than seventh are rarely inverted because they tend to lose their identities (indeed, Rameau says they cannot be inverted, but there are instances in the repertoire where ninths are occasionally inverted); the same may be said to apply to sus chord, since a sus2 chord has the same notes as another sus4 chord (for instance Csus2 is C D G, and Gsus4 is G C D; same notes in a different order; thus, in this special case, inverting may change the interpretation of the chord). Second, not all chords are equal with respect to inversion. The iii and vi chords are rarely inverted in Classical theory because the bass note of a first-inversion vi or iii chord (the scale degrees 1 and 5, respectively) are too strong and tend to over-rule the identities of these chords. This is comparable to the notion of a 6 chord in pop and jazz. Note that C6 = C E G A has the same notes as Am7/C = C E G A, and many would assume that the Am7/C label fits better with standard theory. But in certain positions in the scale (for instance, the I and IV chords in jazz), the sixth above the root of the chord is treated as a replacement for the seventh chord tone without confusing the chord's function within, for instance, a ii-V-I progression. Note that the use of 6 in this instance instead of 13 has nothing whatsoever to do with the octave in which the 6 occurs, as it may well occur in the second octave. The number 6 is used instead of 13 in order to distinguish between this kind of chord, where the 6 replaces the 7, and a true thirteenth chord, in which the seventh, at least, is assumed to still be present, and also the ninth and eleventh if there are enough voices to allow it.

With regard to whether sevenths (or any other extension -- or any other chord note) need to be "on top": in general, the order of the appearance of chord tones does not matter. As most musicians know, there is terminology to describe which note is lowest (inversions); most musicians today do not know that there is also a set of terminology for identifying the highest note (positions), which was once in widespread use in keyboard pedagogy (and is sometimes still used in that context today, but is rarely used anywhere else). But they always remain the same chord. To be fair, inversions are not always used completely interchangeably with root position chords (there are times where one or the other is clearly called for) -- and Schenkerian analysis deals with chords entirely differently, but is a rather specialized subdiscipline.

However, within mainstream Classical theory, it is generally held that when upper extensions (9ths and beyond) are used, the furthest chord extension is usually found in the melody, which is usually the highest part. Additionally, in Classical theory, the upper extensions must all be prepared and resolved down, similar to the way that suspensions are prepared and resolved; the ninths resolve down by step, but the thirteenths frequently resolve down by third to the tonic. Thus, in a manner of speaking, it is reasonable to expect the ninth or thirteenth to be on top, while the same expectation does not apply to seventh chords; neither is it to be expected for suspensions. Ninths and thirteenths also tend to occur the vast majority of the time on V chords.

In jazz, on the other hand, higher extensions are much more common and their use is less restricted. However, it is also worth keeping in mind that in jazz, upper extensions need not be specified; they can be played even when they are not called for in the sheet music, and conversely, they need not be played every time they are indicated. In fact, in some jazz lead sheets, some chord suffixes are not even intended to be played, but rather are included for the benefit of the soloist, to indicate the appropriate scale to use for improvisation, in a manner of speaking encoding the same information as Roman numerals through the use of suffixes unique to a particular chord within a key, though this practice is far from universal. Thus, pedantic insistence on highly restrictive definitions of a ninth chord have very little basis in any sensitive application of music theory.

A final observation regarding a key point from earlier: the chords sus2 and sus4 are common, and generally lack a third (though the third may occur in a higher octave); the add9 chord is common and the add11 slightly less so (but a bit more common on minor chords). The chords add2 and add4 are relatively uncommon. They seem to exist primarily because some musicians misunderstood the difference between seconds and ninths and believed that the octave in which the note appears makes the difference. To return to one of my disclaimers from the very beginning of this discussion, since some people use it this way, if others correctly understand their intentions in using it that way, it is essentially correct. But it is not a standard distinction that I am aware of in any genre of music theory, and it is certainly far from universal. The very fact of the argument present in this thread implies that the distinction between add2 and add9 is not widely known, understood, or accepted, which tends to detract from the merit of the distinction being correct because it is understood. I have only encountered the chord add2 a couple of times in real music and have never encountered an add4 in real music; the only place I occasionally encounter either of these is in internet arguments similar to these or sights purporting to teach some cool new thing. Additionally, despite the Classical practice of labelling 9-8 suspensions, I have never encountered a sus9 chord (except the sus♭9 chord in jazz, which is not a suspended chord at all, but a shorthand for a iii chord), nor have I ever encountered a sus11 chord in any genre. As a rule, the common practice among pop musicians has seemed to be that we use simple intervals (2 and 4) for suspensions and compound intervals (9 and 11) for added-note chords.

Okay, at this point, almost any reader will have long since lost the connection to the original question. To summarize the most important points:

A+9 is an A9 chord (which must include the seventh) in which the fifth has been raised by a semitone, thus making it an augmented chord. A(add9) is an added-note chord in which the seventh is not present.

To summarize other points made throughout this thread: a quite small minority of musicians distinguish between add2 and add9 by the octave in which the added note appears; for the vast majority of musicians, however, the two chords are synonymous, and in any case, the add9 label is many, many times more common than the add2 label. In general, the numbers 2 and 4 are used for suspensions, while the numbers 9 and 11 are used for added-note chords; in the same way, 6 is used for a chord in which the 6 is a replacement for the 7 (in a manner similar to suspensions), while 13 is used for a full thirteenth chord, with all the lower extension that implies. Neither the order nor the octave in which chord tones are added generally change the identity of a chord. Atypical chord tones (tones other than 1 3 5 7) have a strong tendency to appear in the melody, but depending on the genre, are not required to do so, and chords with such atypical tones are less likely to be inverted than more typical chords. And while extended chords (ninths, elevenths, thirteenths) conceptually include all the lower extensions, even in classical theory, certain pitches (notably the fifth) are routinely omitted without comment; omit-tone chords are indicated only for unusual and unexpected omissions.

Apologies for the length -- and also for any spelling/grammar errors, etc. As you can imagine, with the length of this post, I have not taking the time to proofread. I hope that someone has benefited for this.

[miker]

Eek! Kinda makes me glad I never had to take any music theory classes...

Nevertheless, thank you.