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The Hendrix chord contains both a major third and a sharp 9th (or flat 10th if you prefer), which are a half step (plus an octave) apart. From a classical harmony standpoint, those two notes in the same chord should clash, but the chord as a whole works somehow.
Why is that? It feels like somehow the 7th is the the glue that holds it together, since the 7th and #9th are a perfect fourth apart, enharmonically speaking.
There are a lot of chords that have notes that clash that we use all the time. The 7th of a Major 7th chord is a half step away from the root of the chord.
Notes in chords clashing and dissonance in general doesn't mean a chord sounds bad or that it shouldn't be used and in fact the dissonance/clashing nature of the dominant 7th chord with the tritone which in classical music theory is a very dissonant interval and needed to be approached and resolved correctly is very big driving force in a lot of today's music.
Voicing also plays a very big role in general in how chords sound. There are always good voicings and bad voicings of chords. The typical voicing of a 7#9 chord on a guitar is very effective with two distinct groupings of notes being utilize in the voicing. The lower grouping consists of the root and the 3rd and the upper grouping consists of the 7th and the #9. These two distinct groupings are separated by tritone both stand out individually meld and create interesting resulting sound. How good or bad it sounds is in the ears of the beholder.
To add to Dom's great answer - there are other chords, the notes of which should clash. b9 is one, where the root and b9 are also a semitone apart. 11th is another, where 4th and maj3rd are a semitone apart. Playing them an octave apart blends their sound. Yes, I also think the 7th acts as a sort of catalyst. There's also the blues conundrum to consider - often a m3 is played over a major/dom7 chord. This gives exactly the same effect as the Hendrix/7#9 sound. Something Classical and Baroque music frowned upon. Centuries later, having heard the effect many, many times, it's become acceptable to modern ears - in the Western world at least.
I can't add anything to the basic question of why the chord sounds "good" as that is above my paygrade! (LOL) In other words, why does any chord sound "good" or "bad"? This is a question of tradition, context, and personal aesthetics, so I try not to use these two words to describe any chord or tone cluster.
The part where I do want to add my two cents actually has to do with a couple of other things:
I know that ever since Jimi Hendrix wrote and performed "Purple Haze" and "Foxy Lady," people have called the 7th/#9th chord the "Hendrix chord." It's a nice tribute, but in truth, the chord has a long history in jazz and blues before Hendrix. Eric Clapton used it when he played with John Mayall's Bluesbreakers, and I can pretty much guarantee he didn't hear it from Jimi! :-)
It may be a lost point on some heads, but we need to be careful about treating the #9th (augmented ninth) in this chord as if it were a b3 (flat third or minor third). Here's why: When you first learn how to build chords on a chordal instrument, you usually learn first where to put your fingers, then either the names of the notes or their intervals. If we look at the 7th/#9 chord (in music theory context, I prefer the term Dominant Augmented 9th) in "Purple Haze," the song is mostly in a blues E tonality, and the famous chord has an E root. So, the intervals in the chord (ignoring voicing) are: Root, Major Third, Perfect Fifth, Minor Seventh, and Augmented Ninth. This resolves to the note names: E, G#, B, D, and Fx (F double sharp).
"F DOUBLE SHARP? Are you sh**ting me?" Wouldn't it be simpler to just call that last note a G natural, since that's what you see when you play it on a guitar or keyboard? Nope. Here's why: Any ninth above a root is going to have the same generic note name as a second. If Jimi had played a "regular" 9th chord instead of this more interesting version, we wouldn't have an issue, right? Root (E), Major Third (G#), Perfect Fifth (B), Minor Seventh (D), and Major Ninth (F#). Guitar players can play that one all day, barred at the fifth fret, yes? But what if you want to play an E7/b9 (Dominant Diminished 9th), as in John Lennon's song on the Beatles' Abbey Road album, "She's So Heavy"? That would be E, G#, B, D, F. Again, no problem, and this is another chord even more familiar in the jazz harmonic lexicon, but it sure sounded weird to our rock ears when that album came out, especially with those percussive rhythms!
The point is, all of these versions of a 9th stacked up on an E Dominant 7th chord have some flavor of F, because any 9th interval above a root of E has to be some form of F: NEVER a G! Please let me know if this doesn't make sense.
Elf Raad
P.S. I recognize that, especially for more modern composers from the Impressionists onward, who often write linearly, and don't care so much about the names of whatever chord temporarily falls out of the woodwork, there might not be a problem with having a G# and a G natural occurring at the same time over an E root! That's a totally different topic for another day, but think of it this way: In a piece with an A minor tonality, adhering to the rules for the A minor melodic scale in a contrapuntal piece might find you using G# in one instrument playing the ascending version of A minor melodic (A, B, C, D, E, F#, G#, A) while another instrument simultaneously plays a passage using the descending version of A minor melodic (A, B, C, D, E, F, G, A, or more likely going down: A, G, F, E, D, C, B, A). The collision between G# on the way up and G on the way down will make some people cringe like it was a wrong note, and other people sigh, thinking: Ohh, sounds like Hendrix! Isn't music just the most wonderful, mind-blowing thing sometimes?
In the words of Joe Pike: Stay Groovy!
