Just checking into this thread...
Actually, you CAN have Enharmonic notes in Augmented Tuning. If you half-valve it, every draw note will bend a semitone, slide-in and slide-out. I call these Bend-Enharmonics. They can make a lot of difference, by giving you alternate choices on half the notes on the chromatic! They can be used to add soul to a note by giving you a nicer tone and vibrato, or make phrasing a lot easier than choosing the built-in note. Here are the Bend-Enharmonics available:
1. Every slide-in blow note can be substituted with a slide-out draw bend.
2. Every slide-out draw note can be substituted with a slide-in draw bend.
That's 6 notes per octave, 18 notes in a 3 octave range. It's a lot of extra options to have, and can help reduce the 'choppy' nature of Augmented Tuning (which has been mentioned) by giving you the same scale or phrase with fewer slide moves. That can help smooth out (and speed up) your phrasing a lot, if used cleverly.
BEND-ENHARMONICS IN DIMINISHED TUNING
A similar thing can be done with Diminished tuning, with even more beneficial effect. If the chromatic is half-valved and you use draw-bends instead of slide pushes to get your scales, you can reduce the three patterns necessary to play in all 12 keys to just two, by using Bend-Enharmonics instead of slide moves. For example, using the 12 major scales as an example
1. A pattern using draw bends starting on a slide-out blow note. It covers 4 keys: C, Eb, F#, A
1a. A pattern using draw bends exactly the same as pattern 1, but with the slide in. It covers the keys of C#, E, G, Bb
2. A pattern using draw bends starting on a slide-out draw note (D). It covers the keys of D, F, G#, B
You also have the option of playing pattern 2 with the slider in (call it 2a), which will give you an alternative version of the scales in pattern 1: C, Eb, F#, A.
For those of you wanting to half-valve your Diminished chrom and try playing in all 12 keys with Bend-Enharmonics replacing slider moves, see the attached pics showing Phrase Maps of how to play the 12 major scales without slide pushes. On a diatonic harmonica you still need three patterns. On a slider version of Diminished, you can reduce the patterns needed to play in all 12 keys to two if you wish... That's pretty amazing, in my opinion.