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I noticed while noodling on my acoustic guitar that playing Cm using the Am shape barred on 3rd fret, that opening the high E string gives a pleasingly discordant sound. I realised the E comes from the major C chord.
So for C we have the notes C, E, G from C-major and C, Eb, G from C-minor, giving us C, Eb, E, G in my chord.
Does this chord have a particular name - is it in any way special - or depending on the key would you just call it Cm(add E)or something?
I'd call it a Cadd#9 and there's a few reasons why.
First of all if you think about the chord in terms of extensions a #9 is rather common and if you added a Bb to the chord you described people would hands down call that a C7#9 which is a common altered dominant chord.
Second in general when naming chords we typically like to compare the notes to the naturally occurring in the major scale (with the exception of the 7th which we typically preferred lowered). Combine this with the fact that we build and name chords in stacks of thirds makes the major third much more preferable to include in a chord then a minor third.
For example including all extensions, a C13 would include the notes:
C E G Bb D F A
As you can see this includes all naturally named notes of a scale excluding B which has been modified to Bb. Let's take the notes you've given and see how they line up.
C Eb G E
We quickly see the root is there, but we are left with two thirds. Since the natural major 3rd is typically preferred, we will convert the minor third into it's enharmonic equivalent D# and since there is no seventh it becomes an added tone. This is why you see #9 sometimes, but you'll never see a b11 as the major 3rd is the default in chord construction.
There is an alternative way to view the chord that I talk about in this question, but it's a lot less neat. Pretty much If you view the E as the root, you could view the Eb as a D# which is a major 7th and the C as a B# which is an augmented 5h so you could call it a E#mM7#5/C.
While most pop and jazz musicians would call this chord a ♯9 chord of some sort, classical people may say that the chord has split thirds, and a theory professor would say that the chord is the pitch class set [0,3,4,7]. There are a lot of ways to rationalize this chord, and any of these would be acceptable depending on who you speak to. If you're just talking about a C major triad with an E♭ on top, then I would write C(add♯9). If you are talking about a C minor triad with E natural on top, then I would write (and I know I will get flak for this) Cm(maj10). Other people have stated that you might not want to have a Cm triad with a major 10 above it; this is because an interval of a minor ninth is created by the E♭/E combination, which is particularity jarring (though, again, not musically illegal) and obscures the sense of major versus minor. (The minor 7th created by E/E♭ is less jarring and creates more of a bluesy/funky kind of sound).
[However, if they are right next to each other without the octave distance between them, I would probably still write C(add♯9).]
Putting in the b7 as well makes it what is affectionately known as the Hendrix chord - 7#9. He didn't invent it - just loved using it. It sounds like the major and minor third are played within the same chord, but technically it's written as a #9. Usually 9ths will incorporate a 7th as well.In this case, a flat 7th. Without the 7th, it'll be, as already stated, add#9, as it's just a triad plus a sharpened 9 note.
When you swap the G for the E, you get rid of a perfect 5th and get a major 3rd. That 5th is being played anyway on fret 5, D string. You end up with:
If you want to see it strictly as a minor C chord, the E is a major 10th tension. This tension is not diatonic to any minor mode from the major scale, so it is an "outside" tension.
It all depends on the harmonic context, but you can also see this chord as a Dominant #9 chord with the 7th ommited. The minor 3rd can be seen as an augmented 9th (#9). That would be a C7#9. Since your chord doesn't have the minor 7th, maybe Cadd#9 would be more appropriate. You could also play the Bb in fret 3 of string G, although a more common fingering would be X3234X, the "hendrix" chord, which ommits the 5th. You should try this one out. Pretty common in jazz as well.
Dominant chords are built on the 5th degree of the major scale. They are formed by a major triad plus a minor 7th chord tone. A C7 belongs to the key of F major, with the notes C, E, G and Bb. That #9 is a D#, an altered tension that doesn't belong to the F major scale, but it's widely used to add dissonance to the dominant chord, even though it's not diatonic to the major scale.
C7#9:
If this didn't help at all, I suggest that you take a look into basic harmony, especially the diatonic 7th chord sequence of the major scale. Once you understand it, study altered harmony.
The Eb more typically comes at the top. I hear it much more as a flattened third than a sharpened 9th, so I prefer to label it C7(b10). People who want every chord to be built out of a pile of thirds may strongly disagree :-)
