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I have a question about "slash" chords.

Look at the chord E/G:

E  G♯  B  G
1  3   5  ?

G is the minor 3rd interval (♭3) in the key of E.

However, I would have thought by definition chords cannot contain both minor and major thirds, so when looking at just the E major chord, can you really say the G is a ♭3?

The way I think about it, the G doesn't have a relationship to the rest of the notes in the E major chord. In the E/G chord, G is a tone that is played "over" the top of the underlying E major chord.

I wouldn't have thought the G necessarily has to be represented by an interval. I mean, the chord is called E/G not E/♭3.

To that point, my observation is that in all other chord names - the altered notes, or any other special notes - are represented by an interval. E.g. G♯ m(maj7)♯5

Slash chords are the only chord names (that I'm aware of) which extend the chord name with an additional note, not an interval. I was assuming that this was because there is not actually an interval associated with the slash note (in context of the underlying chord).

So... what is the correct way to think about the relationship of the G in E/G ?

Is it correct to say that G is a ♭3 interval in this chord, or do you say it doesn't have an interval in this context?

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by definition chords cannot contain both minor and major thirds -- by definition, chords are two or more notes. That's it. –  Matthew Read Jan 6 '13 at 4:22
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Looking at a single chord in isolation is not going to tell you anything useful. You need to examine the entire chord progression to see how the bass note fits in to the composition. Perhaps it is a passing tone rather than a chord tone in this particular example. –  Wheat Williams Jan 6 '13 at 16:39
    
@MatthewRead True. I think what I meant to say is the chord spellings I have seen don't contain both minor and major thirds. (where the intervals really are written as 3 and ♭3, not 3 and #9). As Owen S. says, I am probably incorrect in that understanding though. –  asgeo1 Jan 6 '13 at 23:30
    
In the key of C this could be considered a simplification of G13♭9, a pretty common chord in jazz standards. It often appears after a Dm7, which takes a whole F triad and slides it down a semitone. A neat trick. –  Steve Clay Dec 10 '13 at 4:54

4 Answers 4

Sure, chords can contain major and minor thirds at the same time! We see 'em all the time in jazz. I call it a major-minor chord (which however is quite different from a major-minor seventh chord). It's also called a mixed-third chord. In jazz chords you will also sometimes see it notated as a ♯9 instead of as a ♭3, though that implies a slightly different use for the added note – that is, as part of the harmonic "juice" – i.e. a triadic extension to the chord – instead of as the bass.

In theory, every note in a tonal system can be represented by an interval relative to a given root. For slash chords, you use the root of the chord above as your root. In this case, ♯2 (♯9) and ♭3 are usually considered enharmonic, and therefore either could be used to describe G, so you have to resolve the ambiguity. You use the note name as your guide. If your root is some sort of E (e.g. E♭, E, or E♯), and the note is some sort of G, its interval is some sort of 3 (think of G as two "note names" away from E). If the note is some sort of F, its interval is some sort of 2. So in this case, G is considered a ♭3. (A ♯2 in this case should be notated F double-sharp).

In practice, however, there's not a single correct answer to "how to think about the G". In fact, when a slash chord gives a bass note that isn't related to the chord, I think it's often more illuminating to simply think of the bass note as a note or part that is independent of the chord above it, rather than trying to think up a warped chord description that includes it. I suspect that might be the case here.

It may be that the music is polytonal; i.e. one part plays in one key while another part plays in another. In that case, trying to mash the two into a single functional harmonic structure and understand the piece that way is likely going to result in chaos and tears.

It may also be that the bass note is not a functional part of the harmony, but rather a line that moves linearly and logically through a progression, but in harmonic conflict with the harmony above it. In this case, trying to figure out the note's position in the harmony might bury its true significance as part of a horizontal line. This kind of horizontal thinking is especially important to develop as a bass player, and I think is the key reason slash chords are written the way they are, instead of via intervals: so that the progression of the bass line is crystal-clear regardless of what comes above it.

The language of chords and harmony has developed not just to tell you what notes to play, but why. It's a powerful tool for communicating a lot of musical information quickly, but it's not the only tool at your disposal.

P.S. Interestingly, in 20th century theory, when wrangling with atonal music, musicologists have given up on the traditional interval system and switched over to using a purely numeric interval system based on half-steps. In that system, let E=0. Then G=3 (it is 3 half-steps away from E), G♯=4, and B=7, so you might call the chord [0347]. I've only seen that done in atonal music, though.

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+1 "trying to figure out the note's position in the harmony might bury its true significance as part of a horizontal line". Yes, yes, yes! It took me 10 years to start learning this. –  luser droog Jan 5 '13 at 6:19
    
I'd like to know more of these mixed-third chords you speak of ;) Will have to do some reading. –  asgeo1 Jan 7 '13 at 9:57
    
This was a good answer, thanks. The reason I asked this question, was because I was writing a program that given a chord name, it would tell you what the associated intervals / spelling was. I was debating what was the best way to handle slash chords, and thought perhaps it didn't need to show the interval of the slash note for the reasons I mentioned. Being a fellow software guy, is that the approach you would take? –  asgeo1 Jan 7 '13 at 10:03
    
Depends on what you plan to use the intervals/spelling for; it's not really a software problem since software is happy to do it whichever way you want! If you were to give an interval name, #2 (aka #9) and b3 are usually considered enharmonic, and you use the note name as your guide. If your root is E, and the note name is some sort of G, and you should call it some sort of 3. If the note name is based on F, you would call it some sort of 2 or 9. 9 is traditional when describing chords with triadic extensions, but for a slash bass I think I might just stick with the 2. –  Owen S. Jan 7 '13 at 16:39
    
Updated answer to include some of this explanation. –  Owen S. Jan 7 '13 at 16:56

The notation can often give a hint on how to play things. If you were to play the notes E G# B G the most appropriate notation would be E#9 (or more likely E7#9 which replaces the B with a D). This indicates that the "odd" note (G) should be played on top.

The slash notation puts the G bass note on the bottom, i.e. it would be played as G E G# B or maybe G B E G#. In a band situation the bass player would pick the G and the chord instruments would probably just play an E chord. It's a convenient way to write out bass line and chords in one go. For example you could write some rock &roll riff like this

|E        |  E/G  E/G#  | A     | A/G   A   |
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"Slash notation" is also known as Macro-analysis, which is an analytical tool sometimes used in analyzing compositions. Most of your confusion lies in the fact that the chord in question is actually mislabeled. Before I answer your question, I will briefly explain Macro-analysis.

Macro-analysis is derived from the practice of Figured Bass, which was a shorthand notation system for realizing harmonic accompaniment (along with continuo lines) as part of performance practice during the Baroque period. Over time, the use of Figured Bass became less and less frequent with analysts favoring macro-analysis as composers became more specific with their notation. Macro-analysis is particularly useful when labeling non-functional chord progressions.

The first letter of the chord "E/G" signifies what chord is being played. The second letter of this chord signifies which note of this chord is played in lowest voice; thus giving the inversion of the chord. This label would be more correct if it were written "Em/G" or "e/G" where the "m" signifies "minor"; the same as if a lowercase letter would as well. The "G" itself indicates that the chord is in first inversion such that the notes in the chord from lowest to highest in closed position would be "G,B,E".

To answer your question directly, you are correct in saying that "G" is a b3 (minor third) with respect to E major. However, in chord labeling the note merely identifies the inversion of the chord.

Hope that helps.

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Yes, this would be a simple first-inversion triad if the note were G♯, and it is common in practice for the slash notation to indicate first or second inversions of a triad to be played by the bass. But G natural is not part of the E major triad, so I'd say that calling it a first inversion in this case is misleading. –  Owen S. Jan 9 '13 at 16:31
    
Regardless of the quality of the chord, it still indicates a first inversion triad. This is merely semantics of minor or major; of which I believe I addressed the correct chord labeling in the third paragraph of my answer. –  jjmusicnotes Jan 10 '13 at 8:16
    
It's not semantics, because it's not a minor triad either. The chord E - G - G# - B is simply not a triad. Unless the asker read it wrong and the chord was really Em/G or e/G, but that would have been a different question. –  Owen S. Jan 11 '13 at 1:35
    
This confusion was precisely my point; that the chord was improperly and incorrectly labeled. In my original answer, I said that the chord label should be re-written to be either "Em" or "e". Simply put the chord labeling put forth by the original poster does not imply or show a chord with a split third. If you were trying to indicate a split third then you would have to notate a diminished 4th in your labeling for it to be appropriate. The quality of the chord IS semantics because your reply implied that it wasn't first inversion; which it is without a doubt. –  jjmusicnotes Jan 11 '13 at 20:35
    
I generally wouldn't write it with a diminished 4th, nor have I seen that in practice. Context will usually make it obvious if the chord is incorrectly notated, but in the absence of context I don't think you can conclude the chord is incorrectly named. –  Owen S. Jan 12 '13 at 16:45

In a piece of music, if the melody instrument was the only thing playing an F# while accompanying instruments were playing a G chord, one might figure that the instruments together form a Gmaj7 chord, but it may be more meaningful to recognize that the accompanying instruments are playing a G chord and the melody instrument is playing something that isn't in the chord, for the purpose of creating a certain level of dissonance.

An E/G "chord" would be conceptually the same thing: an E chord, and a bass line which is playing a G which is not part of the chord. Although a bass line would usually play notes that were part of the chords, sometimes it is useful for a bass line to "do its own thing", and it is more helpful to recognize it as doing something outside the chordal harmonic progression of the piece than to interpret the harmonic progression as including it.

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