Given all the time I spend practicing arpeggios, I've often pondered their origins. I'm familiar with 3 methods of deriving them: stacked thirds, scales, and altering notes. I'll stick with 7th arpeggios.

#### Stacked Thirds

Limited to major or minor thirds, you get the following arpeggios:
(M3 M3 M3 = 1 3 #5 8 = aug triad)
M3 M3 m3 = 1 3 #5 7 = aug7
M3 m3 M3 = 1 3 5 7 = maj7
M3 m3 m3 = 1 3 5 b7 = 7
m3 M3 M3 = 1 b3 5 7 = m/maj7
m3 M3 m3 = 1 b3 5 b7 = m7
m3 m3 M3 = 1 b3 b5 b7 = m7b5
m3 m3 m3 = 1 b3 b5 bb7 = dim7

That gives you 7 viable arpeggios based on stacked major and minor thirds.

#### Scales

You need 7-note scales to get the 1st, 3rd, 5th, and 7th scale degrees. The most common are the major scale, melodic minor, harmonic minor, and their modes. Constructing a 7th arpeggio on each scale degree yields the following:

##### Major

1: 1 3 5 7 = maj7
2: 1 b3 5 b7 = m7
3: 1 b3 5 b7 = m7
4: 1 3 5 7 = maj7
5: 1 3 5 b7 = 7
6: 1 b3 5 b7 = m7
7: 1 b3 b5 b7 = m7b5

These are the 4 essential arpeggios I practice most. Still missing aug7, m/maj7, and dim7 from the list above.

##### Melodic Minor

1: 1 b3 5 7 = m/maj7
2: 1 b3 5 b7 = m7
b3: 1 3 #5 7 = aug7
4: 1 3 5 b7 = 7
5: 1 3 5 b7 = 7
6: 1 b3 b5 b7 = m7b5
7: 1 b3 b5 b7 = m7b5

This one introduces m/maj7 and aug7. Notice there's no maj7.

##### Harmonic Minor

1: 1 b3 5 7 = m/maj7
2: 1 b3 b5 b7 = m7b5
b3: 1 3 #5 7 = aug7
4: 1 b3 5 b7 = m7
5: 1 3 5 b7 = 7
b6: 1 3 5 7 = maj7
7: 1 b3 b5 bb7 = dim7

This scale delivers. With no repeats, the list is identical to that of the stacked thirds.

#### Altering Notes

In the above arpeggios, we've seen a few alterations for each note. If you're willing to step outside major and minor thirds, there others lurking. I excluded bb7 (reserved for dim7). Some are useful. Some don't make sense.

1 3 5 7 = maj7
1 3 5 b7 = 7
1 3 b5 7 = maj7b5
1 3 b5 b7 = 7b5
1 3 #5 7 = aug7
1 3 #5 b7 = 7#5
1 b3 5 7 = m/maj7
1 b3 5 b7 = m7
1 b3 b5 7 = m/maj7b5?
1 b3 b5 b7 = m7b5
1 b3 #5 7 = m/maj7#5?
1 b3 #5 b7 = m7#5?

Of note are maj7b5, 7b5, and 7#5. I practice these sometimes, but I'd rather master the basic ones above before I start using these. Applications are more visible if they're thought of as b5 = #11 and #5 = b13.