Hi Scott, thanks for the question. This is a long reply 🙂 I would check out the Understanding Harmony course on minor harmony and understanding the melodic minor modes. Also the Bebop study course goes deep into the altered chord.
Dominant 7 chords in general contain natural tension due to the tri-tone interval. In the Major Modes we have the Mixolydian mode which gives us a chord scale for the V7 dominant chord. The contains tension 9 and 13. The 4th degree (tension 11) is considered a passing tone. We can use this scale as melodic content for most dominant chords like, II V I’s etc.
Due to the natural tension in the dominant chord we can pile on more tension. The Altered being the heaviest in tension as all the non chord tones are Altered. There is no natural 5th degree in the mode so we only consider the Root 3rd and b7th degrees. These are the main characteristics of a dominant sound. The tensions are b9, #9, #11 and b13.
If you want to think compositionally we could think of the b13 as a #5 and have the chord tones R, 3, #5, b7 with tensions b9, #9, #11.
We could think of the #11 as a b5 and have the chord tones R, 3, b5, b7 with tensions b9, #9, b13.
There are many mays to think about this mode, it’s just a very dark sounding scale to play over V7 chords. Herbie Hancock uses it a lot.
I personally like to use dominant chord scales depending on where the chord is going next. a II V I for example, I’m thinking of the 3rd degree on the Imaj7 chord. In the key of C major (Cmaj7) that note is (E), If we were thinking about G mixolydian for the V7, tension 13 is the note (E). This common tone really helps the listeners ears through the resolution. Common chord scale choices are, Mixolydian, Lydian b7, Symmetrical Diminished (half-whole) as they all contain tension 13. Altered is hip but very out.
II V I’s in a minor key tend to look like this, II-7(b5) V7(b9) I- The I- has a b3rd degree, so we want to look for dominant chord scales that contain a b9 and b13. If we were thinking C minor key (C-) The b3rd is (Eb). Tension b13 over a G7 chord is also (Eb). Again, the common tone really helps the melodic nature of your phrasing. The commonly used chord scales for a minot II V I are Spanish Phrygian (aka Phrygian Dominant), which is the 5th mode of the Harmonic Minor Modes.This mode gives us tension b9 and b13.
Another choice is the Altered mode which also contains tension b9, #9, #11 and b13.
Hope this helps.