[Heath Watts]

The augmented scale has the half step/minor third or minor third/half step structure; there are only four possible augmented scales. There is also a whole tone scale that is built on whole steps, and there are only two of these.

All the other scales you list can be reduced to:
Major
Melodic Minor
Harmonic Minor
Harmonic Major (i.e. C D E F G Ab B C)
The modes of these four scales allow the construction of all the other scales you list. For example, the C major scale contains the D dorian, E phrygian, F lydian, G mixolydian, A aeolean, and B locrian modes (scales). The bebop scales are built by adding a chromatic tone to these heptatonic (seven tone) scales.

There is also the:
Blues Scale
Pentatonic scales (C major pentatonic is the same as the A minor pentatonic)

There are several great books available about scale theory. One I like is the Jazz Theory book by Mark Levine. Another is the Lydian Chromatic Concept by George Russell (expensive, but worth it).

I don't really think about key signatures, because most songs modulate into several keys; if you stick with the key signature to construct your solos, you might hit some harmonically dissonant notes, which can sound great too. For example, if the key signature is G (one sharp) and it modulates to an Eb (three flats), the G major scale won't work very well over the Eb major chord.

Also, the idea of G major and E minor being equivalent is great for classical music, but in jazz the A minor (dorian mode) of the G major scale is more appropriate.

Good luck,
Heath

i've been playing for around a year right now and over this time i have realised how important key signatures are, i have already learnt the concept of chord changes and inversions, but what used to get me was how to improvise say if the key was in G major/E minor

then i started to realise the possibilitys from this key, so i've set myself a project, which (like the title) is pretty much arming myself for improvisation

For all Major keys i will learn these scales

Major
Major pentatonic
Lydian
Bebop scale
Harmonic Major
Lydian augmented
Augmented
6th mode of Harmonic minor
Diminished
Blues scale

And for all Minor keys

Minor(dorian)
Minor Pentatonic
Bebop Scale
Melodonic minor
Bebop Minor
Harmonic Minor
Diminished
Phrygian
Natural minor/Aeolian

I plan to spend a Day on each key to ensure i really do learn this stuff, if there are any scales can u tell me the Formula of them

thanks alot