What is the full list of possible chord names? Are there chords that don't have a name in chord theory?

Question

My chord book covers 35 different chord types. When I look on the web or in other tools, all the same types of chords come up.

But I don't think this is the "full" set of possible chords. I'm not talking about different fingerings or positions of the chords. I'm talking about the number of possible chord formulas according to how the rules of chord naming works. (if that makes sense)

Surely that list of chords (for guitar anyway) is finite.

For instance, I was mucking around on guitar and came up with this (awful sounding) chord:

    x4x212

    D♭ A C G♭

Which I decided must be a D♭ Maj11♯5 chord - based on the 1, ♯5, 7, 11 intervals.

Now of course, my chord book has no such chord as a Maj11♯5, nor does any website I've ever seen - but does that mean it is not a real chord?

I think it must be, because I haven't broken any of the "rules" of naming chords that I'm aware.

Anyway, this chord is just an example. What I want to know is - are chords such as these real chords that exist in music theory:

1, ♭3, ♭5, ♭7, ♭9, 11        m11♭5♭9

1,  3,  5,  7, ♭9, 11        maj11♭9

1, ♭3,  5,  7,  9, 11        m11(maj7)

1, ♭3, ♯5,  7, ♭9, 11, 13    m13(maj7)♯5♭9

Perhaps these chords have little purpose in a practical music sense, but I'm more coming from a theory perspective.

And if you're interested, the real purpose of my question, is that for a programming exercise I wanted to write a program that could work out the name of any chord, based on what notes you gave it. Most chord programs that I've seen would not have picked the D♭ Maj11♯5 name above - does that mean they are too simplified, or (going back to my question) does that chord name not really exist?

Answer 1

Well, a musical chord is by definition a collection of two or more notes sounding simultaneously. So, mathematically, in the usually used 12-tone pitch system of Western/pop/jazz music, there are 2^11 - 1 = 2047 different possible combinations of pitch classes modulo transposition (2^11 is the number of ways additional tones can be added once you fix a root note; subtracting one because a note by itself does not a chord make). Of course, most of them are not usually used in music, as smacking every key down on a piano generally sound quite unmusical, and so I doubt if anyone has bothered to give a name to the, say, CM7 #9 b9 11 #11 b13 #13 chord. (In other words, there definitely a chords that exists in principle but not 'named' just because noone uses them.) But a list of 35 is very short of complete. Any two-note interval is by (some) definition a chord, so there's 11 right there. Between the commonly used tritones, 7th, 11th, and 13th chords, Wikipedia lists, if I count correctly, 41, which only includes 11th and 13th chords based on usual diatonic scales. If you include alterations you will get a lot more.

Now, for some of your examples:

• The notes Db A C Gb, or Maj11 #5 is the augmented-major 11th chord, sometimes written Db+(M11), it is based on the augmented-major seventh chord. The chord notes, as you notice, actually fit into the Bb harmonic minor scale: Bb C Db Eb F Gb A Bb, so is the chord associated to the third (Ionian augmented) mode of that scale (though some people call the mode a harmonic major, a term most people associate with the major scale with a flattened 6th). This is the natural 11th chord associated to it. The modes of the harmonic minor scale tend to sound somewhat weird due to the presence of the augmented step between the 6th (Gb) and the 7th (A) notes (though judicious use of it can create very nice tension), and is used, in my experience, less common than its close cousin the melodic minor scale. The chord Db F A C G would spell part of the 11th chord associated to the Lydian augmented scale, the third mode of the melodic minor.
• Your m11 b5 b9 is usually the half-diminished 11th chord, written Ø11
• What you call m11(maj7) is the minor-major 11th chord, which are denoted by several different symbols.
• Your b3 #5 b9 chord is a well, a bit strange. Without the flat 9 it would fit perfectly over the diminished scale. Off the top of my head I cannot see how to use it.

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Now, in regards of your programming exercise: the same set of notes can often be mapped into voicings of many different chords. For example, if a guitar were to play the Db A C Gb, and the bass a Db or an A, one would tend to think of it as the augmented-major 11th over Db. But if the bass were to play a Bb or an F, then the chord should be interpreted as Bb Db F A C Eb Gb which would be the Bb minor-major 11 with a flat 13. In the context of a small combo, I should imagine that this would makes more sense for the voicing, as it picks out the 3rd, 7th, 9th, and 13th of the chord, adding basically pure colour.

You may also be interested in the chord-scale system.

Answer 2

Other, better music theory people than me should give their opinion on this, but here's my thought:

In certain cases, the proper name of a chord can depend on its function in the chord progression where you find it. In other words, a certain group of notes in a certain voicing in one key and chord progression would properly be named differently if found in a different chord progression in a different key. This is especially common if you are talking about a chord that is in inversion (not in root position) and has a suspension in it (a 4th that needs to resolve down to a 3rd, for instance).

So you could devise an algorithm to identify a chord, but there may be more than one correct name for that chord if you put that chord in the context of a progression.

Furthermore, you are restricted in the kinds of chords you can write if you only consider guitar chords. Chord voicings on the guitar are constrained by the particular layout of the fingers on the fingerboard, and by the peculiarity of the major-third interval between the G and B strings.

If you examine chords on a piano keyboard, or if you compose chords for an ensemble of monophonic instruments such as a choir or a wind ensemble, you can of course write chords that have none of the fingering limitations that the guitar imposes. There is an entire universe of chord voicings that cannot be played on the guitar at all.

Addendum:

In the brief time that I studied jazz guitar, my instructor told me that he does not approve of using any kind of "guitar chord book" as an approach to learning to play jazz guitar. His point is that a chord has no purpose in isolation; chords only function in a chord progression. Therefore, he said, start with lead sheets or fake book charts of classic jazz standards and analyze their chord progressions, and figure out how to voice those chords in sequence on the guitar using your knowledge of theory.

(Pianists and composers, when they figure out chord voicings, take into account voice leading, which is the melodic motion of the notes inside the chords as you move from one chord to the next. Voice leading is a concept that is very difficult to apply to the guitar, which is why guitarists tend to think of a chord as a certain static voicing in a certain "shape" of the fingers on the fretboard. Orchestral composers never think in those terms.)

My instructor would say, "Do not try to memorize individual forms and shapes on the fingerboard in isolation and say, "I know 3,476 different chords". Instead, learn the classic repertoire of jazz standards and figure out the chords from that.

Note: when a group of notes sounded simultaneously does not obviously fit into the context of functional harmony, the technical name for this is a "tone cluster", which is another way of saying, "A music theory expert looked at this and couldn't identify a chord name for it, so he labeled it a tone cluster." ;-)

Answer 3

I think you've made a good start (and the other answers here are very good, too). But I think the heart of the issue is in a different place.

For chords naming, the interval between each note and the "root" is of primary importance; but for chord building you must also consider how each note relates to all the others. So relative intervals become very useful.

So a major triad consists of a major third and a minor third.

A minor triad consists of a minor third and a major third.

[Let's switch to a tabular format to save me some typing.]

    Interval Reference
    C played with ... is a(n) ...
    C Db D  Eb E  F Gb G Ab A  Bb B  C
    1 m2 M2 m3 M3 4 b5 5 m6 M6 m7 M7 8
    | |  |  |  |  | |  | |  |  |  |  Octave
    | |  |  |  |  | |  | |  |  |  Major Seventh
    | |  |  |  |  | |  | |  |  Minor Seventh
    | |  |  |  |  | |  | |  Major Sixth
    | |  |  |  |  | |  | Minor Sixth
    | |  |  |  |  | |  Perfect Fifth
    | |  |  |  |  | Flatted Fifth (Or Augmented Fourth)
    | |  |  |  |  Perfect Fourth
    | |  |  |  Major Third
    | |  |  Minor Third
    | |  Major Second
    | Minor Second
    Unison

         Major triad  M3\m3
         Minor triad  m3\M3
    Diminished triad  m3\m3
     Augmented triad  M3\M3

           Major Seven  M3\m3\M3
        Dominant Seven  M3\m3\m3
           Minor Seven  m3\M3\m3
    Minor (Major Seven) m3\M3\M3 (This is the "sting" chord from Man from U.N.C.L.E)

For "Jazz" chords, just repeat ad absurdam: keep stacking thirds on top. But different configurations of the "flavors" of the thirds will produce different musical effects.

Inversions of the chords are produced by raising the lower tones by octaves until they sit higher in the interval stack (for small chords, one octave will suffice).

But all this applies only to Western Music with the Equal-Temperament tuning system. Other musics build chords differently. Sitar music relies upon resonance relations which are between the cracks in the Western system. There is a fascinating chart in the liner notes to Mark Deutsch, Fool... which enumerates "66 Harmonically Resonant Divisions of the Octave"!

To answer your "'frinstance", Db-A-C-Gb would not be "major", but neither would it be "minor": it simply has not character at all. Db-A is a flatted fifth, so you'd probably start by calling it Db-b5-Maj7-(add 11). But what is this chord for? What does it do? For that you need to examine all the relations:

Db-A augmented fifth
Db-C major seventh
Db-Gb octave + perfect fourth
A-C minor third
A-Gb diminished seventh (or major sixth)
C-Gb flat fifth

So I'd call it Adim/Db. Even though it has no Eb (diminished fifth from A), there are enough flatted fifths among the other relations to give it a diminished "feel".

So you'd probably only use it as a special effect (ie. as a "chord that sounds bad") or when harmonizing a passing tone.

Answer 4

Supplemental note to the other answers:

Chords are "vertical" but sometimes music is "horizontal".

For example, play this and hold for 4 beats:

C F A C F

Now play this

C E G C F

Hold for two beats and then move the high F to E.

That is a "suspension". The first chord you played was an F major chord (IV, the subdominant of C).

The second chord you played was a C major chord (I) with a suspension from F to E. Thinking vertically you might think it's an 11th chord, but really it's a plain old major chord with one voice taking too long to get off the old chord and onto the new chord.

Answer 5

This is not a DbMaj11#5. Without a third, it must be a suspended chord, 11th or not. If the third was constituted in another voice, it is an "add" chord. (ex. Db F G A C = Db+maj7(add4)).

I'd call this a Db+maj7(sus4). Even with the 4 on top, it still functions as 4 and not 11.

Any upper tension (with the exception of dominant tensions), should avoid a b9 between any of the voices, so the implied F and the upper Gb wouldn't strictly be a "legal" tension anyway (if you were calling it an 11). Dominant tension is obviously expected, due to the already two half-step resolution from dominant to tonic, where the additional tension of a b9 serves to resolve that tension further.

Answer 6

There are only 351 possible different chords (strictly chord classes). This is considerably less than the 2047 suggested above because some chords are inversions of others. Fore example C6 has the same notes as Am7.

So if you want to know how many different chords there are (counting all As for example as the same note) there are 19 with 3 notes 43 with 4 notes, 66 with 5 notes, and 80 with 6 notes.

Answer 7

If you play a chord that sounds cool or good, even though the notation looks more like a mathimatical equation, it is still a valid chord.

Øystein Sunde, a norwegian singer/guitarist/song writer, sits by his guitar when he writes songs, and finds good sounding chords that suits his songs, and then afterwords tries to figure out what chord it is. Then the result can be quite unusual, like:

D^9-5 (D⁹ where the 5 is lowered)
http://www.updike.org/harmony/frets.cgi?5,5,4,5,5,4

G#⁷⁺⁵ (G#⁷ where the 5 is raised)
http://www.updike.org/harmony/frets.cgi?4,x,4,5,4,x

E⁹₆ (E⁹ where the 7 is replaced with 6)
http://www.updike.org/harmony/frets.cgi?4,x,4,5,4,x

F#¹³
http://www.updike.org/harmony/frets.cgi?2,x,2,3,4,4

You can in some cases get away with a quite simple notation if only the low base note is out of "standard chord":

F#⁷/C (F#⁷ using C as the low base)
http://www.updike.org/harmony/frets.cgi?8,8,x,9,0,0

Answer 8

From a PURELY musical standpoint, 3,881,803,044 different "chords" can be formed, if we use the definition that a chord must consist of at least 2 notes (which may, or may not, be in unison), but no more than 6 (number of strings on a standard guitar). This covers the range from a Ib-I 2-tone chord to a 1b-14# 6-note chord. Some of the weirder chords would be a 1b-7-8b-14 (2 octaves on the half-tone below the root), 1-7#-8-14# (2 octaves on the root), and the enharmonics, like 1-3-4#-5b-6-7bb (diminished) chords.

Answer 9

JP Doherty has correctly identified the chord. A more mainstreamed naming convention of his answer, however, is DbM7sus4+ ≡ 1-4-#5-7 = Db-Gb-A-C.

From my "Understanding Guitar Chords":

"Distinguishing between chord quality & interval quality. A symbol specifying chord quality, when necessary, appears directly after the chord name; otherwise the symbol refers to interval quality. E.g., in VmM7 the chord quality is “minor” while the interval quality is “major.”

I am 45-year guitar player & former part-time music theory teacher. Because there is no formal standardization of guitar-chord naming that's used in lead-sheet music, I put together my own notes based on (1) some informal agreements among UK studio musicians from the late 1960s & early 1970s (e.g., a chord's root shall be readily apparent & appear either as the first note or immediately following a bass note), & (2) academic understanding derived from modern-day technological advances (e.g., both digitized audio & alternative music genres permit tones well outside the paradigm of those used in Jimmy Page's day, so trying to identify octaves with "add 4," etc., is no longer done; one simply writes V4 or V11 as appropriate).