Your guitar tuner should show you that Eb and D# are the same identical note, with the same number of cycles per second.

The use of the sharp or flat is only a matter of human perception in order to use our present day notation system and have it make sense. It is a good system.

When dealing with some of the chords that have extensions outside the octave, it is necessary to know the full rule set involving those chords.

Spelling such chords in closed position is a good starting point towards understanding, but in actual use, other factors are observed.

Spelling of a C7#9 chord in the closed position yields, C,E,G,Bb,D#.

That is a rather "dense" sound and contains the 5 of the chord, which when played along with the root, generates another root that is one octave lower than the actual root played, at half amplitude. Rock guitarists take advantage of that effect, known for centuries to organists and composers as the "Resultant". Jazz players typically avoid the Resultant with good reason, use of such will "muddy" things too much and result in more of a clash than something harmonious.

So, again in closed spelling, we drop the Dominant (5) note: C,E,Bb,D#.

Try playing both on a keyboard and listening to the difference. Without the 5 in there, the chord takes on an "airiness" that is harmonically desirable.

Now let's look at two of the popular guitar voicings for the 7#9 chord:

Switching to key of E, for the "Jimi" example, a first position E7#9 chord spells out as: E,B,D,G#,D,E the way Jimi often fingered it, or 1,5,7,3,7,#9. But he may have fingered the chord with the 5 in it, but watch some videos to see how he PLUCKS it -- often hitting the low E and then skipping the B, but playing from that 3 up for the echo or top of the chord.

Another good E7#9 on the guitar is found at the 7th fret, an "inside" chord, meaning that it takes place on the four strings that are inside the two E strings, is:

(Frets 7,6,7,8) -- which is E,G#,D,G or 1,3,7,#9. This one is often used by Jazz players, as well as R&B and Soul guitarists.

On the piano or organ, one of my favorite grabs for a 7#9 is even sparser. The RH plays, 3,b7,#9. If I'm playing by myself, then the LH plays the root. I like the "clean" sound this voicing provides with the use of only the one hand for most of the notes. If I'm wanting it to be open, then I might play the tritone with LH, say, 3 and b7 (or b7 and 3) and play the #9 with RH -- and now that we are safely an octave or more above the root, I might add the 5 in the RH, above the #9, or reverse those two such that the chord is even more open and the #9 is on top with the 5 below it.

When notating for others to read, I often use the Eb as the Sharp Nine on a chart that is in the key of C. This is not harmonically correct, of course, but it makes for a faster read by not confusing musicians by having both sharps and flats as accidentals in the same piece or passage. If there are already flats involved, I use the flat. No, it likely won't get you a good grade in school to do that, but I'm always about making for the easiest read possible out in the real world.

Errol Garner's "Misty" is originally written such that the first three notes, "Look at me..." are a Bb, G, and D in his original key of Eb, all played over an Ebmaj7 chord. Try playing it the second time around like this: Ebmaj7, E7#9, Ebmaj7. That's a great example of how Bill Evans would use the Sharp Nine as a transition chord. The E7#9 here combines the Tritone Sub for a Bb7 chord (the turnaround chord for Eb), which is the 7 and 3 of Bb - but also the 3 and 7 of E, with the G note of the melody. Way cool.

--Mac