Assuming 'common practice era' harmony.
If you want an easy, general "rule" to follow, using the harmonic minor scale to build chords in a minor key works well. But, let's take a look why that is so with a chart.
Cm: vim7 iiø7 V7 i
G C F Eb
Eb Ab D C
C F B G
Ab D G C
Notice that all the As and Bs are either A♭ or B natural. For those four chords the harmonic minor scale will provide the tones.
Of course the next question is, what about the other chord roots iv VII III? For those we can say two things.
- As the sequence of fifths harmony gets further back from the tonic chord and primary chords, and into the secondary chords region, the modal region, there is a tendency for harmony to use sequential progressions, and
- those progressions in minor tend to be plain diatonic.
So, if you put the two together, and do a complete descending fifths sequence, it would be: diatonic ivm7 VIIIM7 IIIM7 then continue with harmonic minor VIM7 iiø7 V7 i.
I don't really like mixing up the artificial notion of three kinds of minor scales with harmony. There is just one minor mode key and the treatment of the ^6 and ^7 scale degrees works through a combination of melodic direction of voice movement along with whether the harmony is dominant harmony. If ^6 goes down to ^5 then ^6 is lowered, if ^7 goes up to ^1 then ^7 is raised, if the passages involves long, step wise movements like ^1 ^7 ^6 ^5, ^5 ^6 ^7 ^1, ^7 ^6 ^5, or ^6 ^7 ^1, and the harmony is dominant, usually ^7 and ^6 are both raised.
Anyway, the full descending fifths sequence above is a good rule of thumb.
Add to it:
- if
F is in the bass, the chord is often inverted iiø6/5 as apposed to ivm7
- root position
viio7 to i is very normal
- if
N6, the neapolitan chord on ♭II, is a seventh chord, then it will be a major seventh chord
- the German and French augmented sixth chords should be added to the list of seventh chords. Despite the fact that they feature a augmented sixth above the bass, they involve four pitch factors and can be viewed as altered seventh chords. Those chords resolve to a plain dominant triad, not a
V7, usually with a half cadence feel.
- the augmented triad, ex.
E♭ G B♮ in Cm, is usually the result of voice leading, with the B♮ basically coming from some kind of dominant harmony, and the E♭ being the minor third of the mode. The linear motions will be some kind of D E♭ or B♮ C movements where the directions and order can vary. It's like a transitional chord between tonic and dominant harmonies.
What seventh chords belong to the minor mode in actual practice after allowing the conventional alterations?
When the convention is the 'common practice era' convention, the real insight is to understand that harmony in that era was really a counterpoint practice where voice leading is very important. The chart of all permutations of raised/lowered ^6 and ^7 in the bass and harmonizing voices, in my opinion, doesn't help much to illuminate that historical practice.
There is an actual historic teaching rule you might be interested in called the rule of the octave. You can read about it here: https://partimenti.org/partimenti/about_parti/index.html. Essentially, there is one ascending and one descending rule, and in minor the Roman numeral analysis would be like this: i V4/3 i6 iiø6/5 V IV6 V6/5 i & i v(min)6 V43/V V V4/2 i6 V4/3 i.
Important points to notice, in comparison with the Sessions chart, chord roots do not include all scale degrees, the chord roots are mostly tonic and dominant, and seventh chords are not used for all chords, only for the dominant or the ii subdominant. That is way, way different that the Sessions, but it will go a long way toward playing characteristic common practice era harmony. Also, the melodic direction of the bass is hugely important in the rule of the octave, notice the difference in harmonizing ^3 and ^4 depending on whether the bass ascends or descends.
That aspect of the bass movement strikes a major contrast between the "modern" type of harmony textbook, like Sessions, and the historic teaching of the rule of the octave/partimenti/thoroughbass practice. Modern texts suggest an array of possible chords built over basses, for example ^3 and ^4. The rule of the octave is totally different and provides an exemplar rule dependent on the melodic/voice leading context. Modern text would suggestion ^3 could be harmonized by a root position mediant triad, but by the rule of the octave that would be an uncharacteristic choice. The historic teaching was less about what is possible versus what was good taste.
I don't think of this as a failing or limitation of the historic practice. It was just a manifestation of the style. You could flip it around and look for a book on jazz harmony and whether it teaches harmonization using on simple triads. Not likely, because that isn't the harmonic style.
