Maj7#5

Update: I linked some parts to my previous posts on Augmented Scale ideas.

Over at the All About Jazz forum, someone asked for suggestions about how to approach Maj7#5 chords. As this is a sound I'm fond of and have spent considerable time exploring, I posted a rather lengthy response.
I'm reprinting part of my response here, since I think it may be of general interest. It's somewhat off the cuff, so the information is probably not optimally organized, so apologies in advance.

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Maj7#5 can take some different sounds, depending on context. Lydian Augmented (third mode of melodic minor) is one of the scales most commonly recommended as being compatible with a Maj7#5 chord. It's not the only one, though, and others might work much better, depending on the context.

Here are some other possibilities:

Harmonic Minor, 3rd mode (A harm.minor = CMaj7#5)

Harmonic Major (C harm. major = CMaj7#5)

Harmonic Major, 6th mode (E harm. major = Cmaj7#5)

Lydian #5 #2 (C D# E F# G# A B --this is Melodic Minor #4, 3rd mode, i.e., A Melodic Minor #4 for Cmaj7#5)

Symmetrical Augmented scale (C D# E G Ab B)

Harmonic Major (6th mode) is the same as Melodic Minor #4 (3rd mode) AKA Lydian #2 #5. Just two ways of thinking about it.

What notes will work best over the chord will depend greatly on the harmonic context, e.g. the preceding and following chords, etc.

Try finding some tunes that have the sound in it, substituting it in standards, or writing your own, to experiment with different contexts.

The symmetrical augmented scale is a great sound and can be considered as two augmented triads a 1/2 step apart (contrast with the whole tone scale: two augmented triads a whole step apart). Since augmented chords are symmetrical, any note can be considered the root.

Cmaj7#5: C+/B+ or E+/D#+, or Ab+/G+

You can also extend each triad into a maj7 arpeggio:
Cmaj7, Emaj7, Abmaj7

see: More Augmented Scale

or maj7#9:
Cmaj7#9, Emaj7#9, Abmaj7#9

Or you could construct arpeggios by combining the triad pairs into polychords:

B+|C+
=
C E G# B D# G

Eb+|E+
=
E G# C Eb G B

G+|Ab+
=
Ab C E G B D#


You can also reconsider the scale as a major and minor triad a m6 apart:

C/Abm or E/Cm or Ab/Em

There are a million ways to practice these.

Triads in the Augmented Scale

One observation:

Of all the different scale choices over Maj7#5, two particular areas tend to stand out for me:

The choice of whether to incorporate a P4 vs. an A4
The choice of whether or the M6 is included (the alternative is generally the P5)

Since these involve half-steps above the determining color tones of the chord, care must be taken with the melodic resolution tendencies.

The choice of A2 vs. M2 (i.e., #9 vs. 9) is a useful color, but rarely obscures the harmony.

1. Lydian Augmented: has #4 and M6. The #4 implies a Lydian sound and can be a sustained tension, but the dissonance of the M6 obscures the harmony and must be used carefully

2. Harmonic Minor, 3rd mode (Ionian #5): Has P4 and M6, both of which can obscure the harmony and require careful use.

3. Harmonic Major (Ionian b6): Has P4, but no M6.

4. Harmonic Major, 6th mode (Lydian Augmented #2): Has #4 and M6, like Lydian Augmented.

5. Symmetrical Augmented: has neither P4, A4, or M6.

Since #5 omits the problematic tones, it may be an easier scale to start with: it is less likely to lead to obvious clams.

One could create another 6-note scale that leaves out both P4, A4 and M6:
C D E G Ab B. Such a scale might be useful. It could be viewed as a C+/G triad pair or (perhaps less usefully) as a C/Abdim triad pair.

There are a couple of hexatonic subsets that leave out P4 and M6, but include the A4:
C D E F# G# B: this is C+/Bm, a subset of Lydian Augmented
C D# E F# G# B: This is C+/B, a subset of Lydian Augmented #2

The following pentatonics can work as well:
E F# G# B D (these notes form an E9 chord)
Ab B C E F# (these notes form an Ab7+5+9 chord)
C D E F# G# (this is a subset of the whole tone scale, omitting the b7, or the Lydian Augmented, omitting the 6 and 7)
E F# G# B C# (E6 chord or E Maj pentatonic)

The last one includes a b9 on the chord, but this can be a great sound on a modern tune, especially if the chord lasts for a measure or more. It usually works better in the upper register, where it sounds like an extension.
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So there end up being four primary 7-note scale and one 6-note scale possibilities, and a number of pentatonic and hexatonic choices. Here again are the five primary types:

1. Lydian Augmented (AKA Melodic Minor, 3rd mode):
R M2 M3 A4 A5 M6 M7

2. Harmonic Minor, 3rd mode (AKA Major #5):
R M2 M3 P4 A5 M6 M7

3. Harmonic Major:
R M2 M3 P4 P5 m6 M7

4. Harmonic Major, 6th mode (AKA Melodic Minor #4, 3rd mode AKA Lydian Augmented #2):
R A2 M3 A4 A5 M6 M7

5. Symmetrical Augmented:
R A2 M3 P5 m6 M7

Not all choices work equally well in all situations.
No warranty is expressed or implied; indiscriminate scale usage may result in clams, tomatoes, or acts of violence. I do not take responsibility for the careless use of the above information.

happy improvising!