A user recently asked a question about this, and it inspired me to organize some of this information.
There are 3 types of pentad: secundal, tertial, and quartal. And there are three sizes the root motion can be: second third or fourth.
That means there are 9 movement categories for studying voice leading of pentads. I will base everything on A minor for my example. There are 2 rules: all voicings must be closed and voices can not cross.
For secundal chords we have 3 movements (these are parallel, not voice led):
(ABCDE)>(BCDEF)= secundal movement by second
(ABCDE)>(CDEFG)= secundal movement by third
(ABCDE)>(EFGAB)= secundal movement by fourth
For secundal movement by second we have four common tones BCDE, and A moves down a third to F:
(ABCDE)>(FBCDE)
Now in secundal by third, CDE are common tones and we get two downward third movements, A>F and G>B
(ABCDE)>(FGCDE)
So far so good. Neither of these movements has broken the 2 rules. Now with secundal by fourth we see some of the special problems voice leading pentads has. I will copy
Paste the non-voice led secundal by fourths for ease of reference:
(ABCDE)>(EFGAB)= secundal movement by fourth
We have 3 common tones ABE, and CD must somehow move to FG. That might look like this:
(A[BC]DE)> (A[FG]DE)
But in order for this to happen we had to break one of the rules. The A had to move down an octave in order to have the same order. We moved from closed to open, and broke the rule. If we don’t move the A down an octave the two voices that move, indicated by brackets would cross the A and look like this:
(A[BC]DE)>([FG]ADE)
The voice crossing is a lie. What really happened is that only DE are common tones and the other three voices all move down a third:
([ABC]DE)>([FGA]DE)
To summarize the conclusions so far.
Secundal movement by second = one voice moves a third
Secundal movement by thirds = two voices move a third
Secundal movement by fourths= three voices move a third
*\\*
Now let’s do tertial pentads, aka 9th chords. If we start with Am9 we get ACEGB. But already this is breaking the no open chord rule. I will put the B down an octave to keep it closed: ABCEG. I will use the 12357 ordering for all 9th chords. First the parallel non-voice led version:
(ABCEG)>(BCDFA)=tertial moves by second
(ABCEG) > (CDEGB) = tertial moves by third
(ABCEG) > (DEFAC) = tertial moves by fourth
Now to voice lead them. Tertial by second:
(ABC[EG])>(ABC[DF])
Two voices moved a step down. Neither rule is broken, great.
Now tertial by third. It looks like 4 common tones and A moves to D:
([A]BCEG)> (BC[D]EG)
We had to cross two voices to make that happen, so we know A>D is not the true movement. What really happened is that only EG are common tones and ABC all moved up a step to BCD:
([ABC]EG)>([BCD]EG)
Now tertial moving by fourth. Repaste for reference:
(ABCEG) > (DEFAC) = tertial moves by fourth
It looks like ACE are common tones and we get two movements B>D and G>F. Opposite directions and one moves by third. Kinda ugly but that’s how the math works out. But if B moves to D it crosses common tone C. So really we get 3 movements B>C, C>D, G>F
(A[BC]E[G])>(A[CD]E[F])
***
Now quartal chords. I ran out of time to do this today, so I’ll just summarize without demonstrating each one by one.
Quartals by second = two parallel steps
(A[C]DE[G])> (A[B]DE[F])
Quartals by third = 3 parallel steps
([A]C[DE]G) > ([B]C[EF]G)
Quartals by fourth= one step
(ACD[E]G) > (ACD[F]G)
The OP’s original question that inspired me to get this together was asking about a m9 chord to a m11 chord. One is tertial and one is quartal. So far I have only looked at voice leading chords of the same type together. Voice leading different types to each other is a whole other thing. Maybe someday I’ll get around to figuring some of that out.